// SPDX-License-Identifier: MIT
pragma solidity 0.8.23;
import {IAccount} from "account-abstraction/interfaces/IAccount.sol";
import {UserOperation, UserOperationLib} from "account-abstraction/interfaces/UserOperation.sol";
import {Receiver} from "solady/accounts/Receiver.sol";
import {SignatureCheckerLib} from "solady/utils/SignatureCheckerLib.sol";
import {UUPSUpgradeable} from "solady/utils/UUPSUpgradeable.sol";
import {WebAuthn} from "webauthn-sol/WebAuthn.sol";
import {ERC1271} from "./ERC1271.sol";
import {MultiOwnable} from "./MultiOwnable.sol";
/// @title Coinbase Smart Wallet
///
/// @notice ERC-4337-compatible smart account, based on Solady's ERC4337 account implementation
///         with inspiration from Alchemy's LightAccount and Daimo's DaimoAccount. Verified by z0r0z.eth from (⌘) NANI.eth
///
/// @author Coinbase (https://github.com/coinbase/smart-wallet)
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/accounts/ERC4337.sol)
contract CoinbaseSmartWallet is ERC1271, IAccount, MultiOwnable, UUPSUpgradeable, Receiver {
    /// @notice A wrapper struct used for signature validation so that callers
    ///         can identify the owner that signed.
    struct SignatureWrapper {
        /// @dev The index of the owner that signed, see `MultiOwnable.ownerAtIndex`
        uint256 ownerIndex;
        /// @dev If `MultiOwnable.ownerAtIndex` is an Ethereum address, this should be `abi.encodePacked(r, s, v)`
        ///      If `MultiOwnable.ownerAtIndex` is a public key, this should be `abi.encode(WebAuthnAuth)`.
        bytes signatureData;
    }
    /// @notice Represents a call to make.
    struct Call {
        /// @dev The address to call.
        address target;
        /// @dev The value to send when making the call.
        uint256 value;
        /// @dev The data of the call.
        bytes data;
    }
    /// @notice Reserved nonce key (upper 192 bits of `UserOperation.nonce`) for cross-chain replayable
    ///         transactions.
    ///
    /// @dev MUST BE the `UserOperation.nonce` key when `UserOperation.calldata` is calling
    ///      `executeWithoutChainIdValidation`and MUST NOT BE `UserOperation.nonce` key when `UserOperation.calldata` is
    ///      NOT calling `executeWithoutChainIdValidation`.
    ///
    /// @dev Helps enforce sequential sequencing of replayable transactions.
    uint256 public constant REPLAYABLE_NONCE_KEY = 8453;
    /// @notice Thrown when `initialize` is called but the account already has had at least one owner.
    error Initialized();
    /// @notice Thrown when a call is passed to `executeWithoutChainIdValidation` that is not allowed by
    ///         `canSkipChainIdValidation`
    ///
    /// @param selector The selector of the call.
    error SelectorNotAllowed(bytes4 selector);
    /// @notice Thrown in validateUserOp if the key of `UserOperation.nonce` does not match the calldata.
    ///
    /// @dev Calls to `this.executeWithoutChainIdValidation` MUST use `REPLAYABLE_NONCE_KEY` and
    ///      calls NOT to `this.executeWithoutChainIdValidation` MUST NOT use `REPLAYABLE_NONCE_KEY`.
    ///
    /// @param key The invalid `UserOperation.nonce` key.
    error InvalidNonceKey(uint256 key);
    /// @notice Reverts if the caller is not the EntryPoint.
    modifier onlyEntryPoint() virtual {
        if (msg.sender != entryPoint()) {
            revert Unauthorized();
        }
        _;
    }
    /// @notice Reverts if the caller is neither the EntryPoint, the owner, nor the account itself.
    modifier onlyEntryPointOrOwner() virtual {
        if (msg.sender != entryPoint()) {
            _checkOwner();
        }
        _;
    }
    /// @notice Sends to the EntryPoint (i.e. `msg.sender`) the missing funds for this transaction.
    ///
    /// @dev Subclass MAY override this modifier for better funds management (e.g. send to the
    ///      EntryPoint more than the minimum required, so that in future transactions it will not
    ///      be required to send again).
    ///
    /// @param missingAccountFunds The minimum value this modifier should send the EntryPoint which
    ///                            MAY be zero, in case there is enough deposit, or the userOp has a
    ///                            paymaster.
    modifier payPrefund(uint256 missingAccountFunds) virtual {
        _;
        assembly ("memory-safe") {
            if missingAccountFunds {
                // Ignore failure (it's EntryPoint's job to verify, not the account's).
                pop(call(gas(), caller(), missingAccountFunds, codesize(), 0x00, codesize(), 0x00))
            }
        }
    }
    constructor() {
        // Implementation should not be initializable (does not affect proxies which use their own storage).
        bytes[] memory owners = new bytes[](1);
        owners[0] = abi.encode(address(0));
        _initializeOwners(owners);
    }
    /// @notice Initializes the account with the `owners`.
    ///
    /// @dev Reverts if the account has had at least one owner, i.e. has been initialized.
    ///
    /// @param owners Array of initial owners for this account. Each item should be
    ///               an ABI encoded Ethereum address, i.e. 32 bytes with 12 leading 0 bytes,
    ///               or a 64 byte public key.
    function initialize(bytes[] calldata owners) external payable virtual {
        if (nextOwnerIndex() != 0) {
            revert Initialized();
        }
        _initializeOwners(owners);
    }
    /// @inheritdoc IAccount
    ///
    /// @notice ERC-4337 `validateUserOp` method. The EntryPoint will
    ///         call `UserOperation.sender.call(UserOperation.callData)` only if this validation call returns
    ///         successfully.
    ///
    /// @dev Signature failure should be reported by returning 1 (see: `this._isValidSignature`). This
    ///      allows making a "simulation call" without a valid signature. Other failures (e.g. invalid signature format)
    ///      should still revert to signal failure.
    /// @dev Reverts if the `UserOperation.nonce` key is invalid for `UserOperation.calldata`.
    /// @dev Reverts if the signature format is incorrect or invalid for owner type.
    ///
    /// @param userOp              The `UserOperation` to validate.
    /// @param userOpHash          The `UserOperation` hash, as computed by `EntryPoint.getUserOpHash(UserOperation)`.
    /// @param missingAccountFunds The missing account funds that must be deposited on the Entrypoint.
    ///
    /// @return validationData The encoded `ValidationData` structure:
    ///                        `(uint256(validAfter) << (160 + 48)) | (uint256(validUntil) << 160) | (success ? 0 : 1)`
    ///                        where `validUntil` is 0 (indefinite) and `validAfter` is 0.
    function validateUserOp(UserOperation calldata userOp, bytes32 userOpHash, uint256 missingAccountFunds)
        external
        virtual
        onlyEntryPoint
        payPrefund(missingAccountFunds)
        returns (uint256 validationData)
    {
        uint256 key = userOp.nonce >> 64;
        if (bytes4(userOp.callData) == this.executeWithoutChainIdValidation.selector) {
            userOpHash = getUserOpHashWithoutChainId(userOp);
            if (key != REPLAYABLE_NONCE_KEY) {
                revert InvalidNonceKey(key);
            }
        } else {
            if (key == REPLAYABLE_NONCE_KEY) {
                revert InvalidNonceKey(key);
            }
        }
        // Return 0 if the recovered address matches the owner.
        if (_isValidSignature(userOpHash, userOp.signature)) {
            return 0;
        }
        // Else return 1
        return 1;
    }
    /// @notice Executes `calls` on this account (i.e. self call).
    ///
    /// @dev Can only be called by the Entrypoint.
    /// @dev Reverts if the given call is not authorized to skip the chain ID validtion.
    /// @dev `validateUserOp()` will recompute the `userOpHash` without the chain ID before validating
    ///      it if the `UserOperation.calldata` is calling this function. This allows certain UserOperations
    ///      to be replayed for all accounts sharing the same address across chains. E.g. This may be
    ///      useful for syncing owner changes.
    ///
    /// @param calls An array of calldata to use for separate self calls.
    function executeWithoutChainIdValidation(bytes[] calldata calls) external payable virtual onlyEntryPoint {
        for (uint256 i; i < calls.length; i++) {
            bytes calldata call = calls[i];
            bytes4 selector = bytes4(call);
            if (!canSkipChainIdValidation(selector)) {
                revert SelectorNotAllowed(selector);
            }
            _call(address(this), 0, call);
        }
    }
    /// @notice Executes the given call from this account.
    ///
    /// @dev Can only be called by the Entrypoint or an owner of this account (including itself).
    ///
    /// @param target The address to call.
    /// @param value  The value to send with the call.
    /// @param data   The data of the call.
    function execute(address target, uint256 value, bytes calldata data)
        external
        payable
        virtual
        onlyEntryPointOrOwner
    {
        _call(target, value, data);
    }
    /// @notice Executes batch of `Call`s.
    ///
    /// @dev Can only be called by the Entrypoint or an owner of this account (including itself).
    ///
    /// @param calls The list of `Call`s to execute.
    function executeBatch(Call[] calldata calls) external payable virtual onlyEntryPointOrOwner {
        for (uint256 i; i < calls.length; i++) {
            _call(calls[i].target, calls[i].value, calls[i].data);
        }
    }
    /// @notice Returns the address of the EntryPoint v0.6.
    ///
    /// @return The address of the EntryPoint v0.6
    function entryPoint() public view virtual returns (address) {
        return 0x5FF137D4b0FDCD49DcA30c7CF57E578a026d2789;
    }
    /// @notice Computes the hash of the `UserOperation` in the same way as EntryPoint v0.6, but
    ///         leaves out the chain ID.
    ///
    /// @dev This allows accounts to sign a hash that can be used on many chains.
    ///
    /// @param userOp The `UserOperation` to compute the hash for.
    ///
    /// @return The `UserOperation` hash, which does not depend on chain ID.
    function getUserOpHashWithoutChainId(UserOperation calldata userOp) public view virtual returns (bytes32) {
        return keccak256(abi.encode(UserOperationLib.hash(userOp), entryPoint()));
    }
    /// @notice Returns the implementation of the ERC1967 proxy.
    ///
    /// @return $ The address of implementation contract.
    function implementation() public view returns (address $) {
        assembly {
            $ := sload(_ERC1967_IMPLEMENTATION_SLOT)
        }
    }
    /// @notice Returns whether `functionSelector` can be called in `executeWithoutChainIdValidation`.
    ///
    /// @param functionSelector The function selector to check.
    ////
    /// @return `true` is the function selector is allowed to skip the chain ID validation, else `false`.
    function canSkipChainIdValidation(bytes4 functionSelector) public pure returns (bool) {
        if (
            functionSelector == MultiOwnable.addOwnerPublicKey.selector
                || functionSelector == MultiOwnable.addOwnerAddress.selector
                || functionSelector == MultiOwnable.removeOwnerAtIndex.selector
                || functionSelector == MultiOwnable.removeLastOwner.selector
                || functionSelector == UUPSUpgradeable.upgradeToAndCall.selector
        ) {
            return true;
        }
        return false;
    }
    /// @notice Executes the given call from this account.
    ///
    /// @dev Reverts if the call reverted.
    /// @dev Implementation taken from
    /// https://github.com/alchemyplatform/light-account/blob/43f625afdda544d5e5af9c370c9f4be0943e4e90/src/common/BaseLightAccount.sol#L125
    ///
    /// @param target The target call address.
    /// @param value  The call value to user.
    /// @param data   The raw call data.
    function _call(address target, uint256 value, bytes memory data) internal {
        (bool success, bytes memory result) = target.call{value: value}(data);
        if (!success) {
            assembly ("memory-safe") {
                revert(add(result, 32), mload(result))
            }
        }
    }
    /// @inheritdoc ERC1271
    ///
    /// @dev Used by both `ERC1271.isValidSignature` AND `IAccount.validateUserOp` signature validation.
    /// @dev Reverts if owner at `ownerIndex` is not compatible with `signature` format.
    ///
    /// @param signature ABI encoded `SignatureWrapper`.
    function _isValidSignature(bytes32 hash, bytes calldata signature) internal view virtual override returns (bool) {
        SignatureWrapper memory sigWrapper = abi.decode(signature, (SignatureWrapper));
        bytes memory ownerBytes = ownerAtIndex(sigWrapper.ownerIndex);
        if (ownerBytes.length == 32) {
            if (uint256(bytes32(ownerBytes)) > type(uint160).max) {
                // technically should be impossible given owners can only be added with
                // addOwnerAddress and addOwnerPublicKey, but we leave incase of future changes.
                revert InvalidEthereumAddressOwner(ownerBytes);
            }
            address owner;
            assembly ("memory-safe") {
                owner := mload(add(ownerBytes, 32))
            }
            return SignatureCheckerLib.isValidSignatureNow(owner, hash, sigWrapper.signatureData);
        }
        if (ownerBytes.length == 64) {
            (uint256 x, uint256 y) = abi.decode(ownerBytes, (uint256, uint256));
            WebAuthn.WebAuthnAuth memory auth = abi.decode(sigWrapper.signatureData, (WebAuthn.WebAuthnAuth));
            return WebAuthn.verify({challenge: abi.encode(hash), requireUV: false, webAuthnAuth: auth, x: x, y: y});
        }
        revert InvalidOwnerBytesLength(ownerBytes);
    }
    /// @inheritdoc UUPSUpgradeable
    ///
    /// @dev Authorization logic is only based on the `msg.sender` being an owner of this account,
    ///      or `address(this)`.
    function _authorizeUpgrade(address) internal view virtual override(UUPSUpgradeable) onlyOwner {}
    /// @inheritdoc ERC1271
    function _domainNameAndVersion() internal pure override(ERC1271) returns (string memory, string memory) {
        return ("Coinbase Smart Wallet", "1");
    }
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
import "./UserOperation.sol";
interface IAccount {
    /**
     * Validate user's signature and nonce
     * the entryPoint will make the call to the recipient only if this validation call returns successfully.
     * signature failure should be reported by returning SIG_VALIDATION_FAILED (1).
     * This allows making a "simulation call" without a valid signature
     * Other failures (e.g. nonce mismatch, or invalid signature format) should still revert to signal failure.
     *
     * @dev Must validate caller is the entryPoint.
     *      Must validate the signature and nonce
     * @param userOp the operation that is about to be executed.
     * @param userOpHash hash of the user's request data. can be used as the basis for signature.
     * @param missingAccountFunds missing funds on the account's deposit in the entrypoint.
     *      This is the minimum amount to transfer to the sender(entryPoint) to be able to make the call.
     *      The excess is left as a deposit in the entrypoint, for future calls.
     *      can be withdrawn anytime using "entryPoint.withdrawTo()"
     *      In case there is a paymaster in the request (or the current deposit is high enough), this value will be zero.
     * @return validationData packaged ValidationData structure. use `_packValidationData` and `_unpackValidationData` to encode and decode
     *      <20-byte> sigAuthorizer - 0 for valid signature, 1 to mark signature failure,
     *         otherwise, an address of an "authorizer" contract.
     *      <6-byte> validUntil - last timestamp this operation is valid. 0 for "indefinite"
     *      <6-byte> validAfter - first timestamp this operation is valid
     *      If an account doesn't use time-range, it is enough to return SIG_VALIDATION_FAILED value (1) for signature failure.
     *      Note that the validation code cannot use block.timestamp (or block.number) directly.
     */
    function validateUserOp(UserOperation calldata userOp, bytes32 userOpHash, uint256 missingAccountFunds)
    external returns (uint256 validationData);
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
/* solhint-disable no-inline-assembly */
import {calldataKeccak} from "../core/Helpers.sol";
/**
 * User Operation struct
 * @param sender the sender account of this request.
     * @param nonce unique value the sender uses to verify it is not a replay.
     * @param initCode if set, the account contract will be created by this constructor/
     * @param callData the method call to execute on this account.
     * @param callGasLimit the gas limit passed to the callData method call.
     * @param verificationGasLimit gas used for validateUserOp and validatePaymasterUserOp.
     * @param preVerificationGas gas not calculated by the handleOps method, but added to the gas paid. Covers batch overhead.
     * @param maxFeePerGas same as EIP-1559 gas parameter.
     * @param maxPriorityFeePerGas same as EIP-1559 gas parameter.
     * @param paymasterAndData if set, this field holds the paymaster address and paymaster-specific data. the paymaster will pay for the transaction instead of the sender.
     * @param signature sender-verified signature over the entire request, the EntryPoint address and the chain ID.
     */
    struct UserOperation {
        address sender;
        uint256 nonce;
        bytes initCode;
        bytes callData;
        uint256 callGasLimit;
        uint256 verificationGasLimit;
        uint256 preVerificationGas;
        uint256 maxFeePerGas;
        uint256 maxPriorityFeePerGas;
        bytes paymasterAndData;
        bytes signature;
    }
/**
 * Utility functions helpful when working with UserOperation structs.
 */
library UserOperationLib {
    function getSender(UserOperation calldata userOp) internal pure returns (address) {
        address data;
        //read sender from userOp, which is first userOp member (saves 800 gas...)
        assembly {data := calldataload(userOp)}
        return address(uint160(data));
    }
    //relayer/block builder might submit the TX with higher priorityFee, but the user should not
    // pay above what he signed for.
    function gasPrice(UserOperation calldata userOp) internal view returns (uint256) {
    unchecked {
        uint256 maxFeePerGas = userOp.maxFeePerGas;
        uint256 maxPriorityFeePerGas = userOp.maxPriorityFeePerGas;
        if (maxFeePerGas == maxPriorityFeePerGas) {
            //legacy mode (for networks that don't support basefee opcode)
            return maxFeePerGas;
        }
        return min(maxFeePerGas, maxPriorityFeePerGas + block.basefee);
    }
    }
    function pack(UserOperation calldata userOp) internal pure returns (bytes memory ret) {
        address sender = getSender(userOp);
        uint256 nonce = userOp.nonce;
        bytes32 hashInitCode = calldataKeccak(userOp.initCode);
        bytes32 hashCallData = calldataKeccak(userOp.callData);
        uint256 callGasLimit = userOp.callGasLimit;
        uint256 verificationGasLimit = userOp.verificationGasLimit;
        uint256 preVerificationGas = userOp.preVerificationGas;
        uint256 maxFeePerGas = userOp.maxFeePerGas;
        uint256 maxPriorityFeePerGas = userOp.maxPriorityFeePerGas;
        bytes32 hashPaymasterAndData = calldataKeccak(userOp.paymasterAndData);
        return abi.encode(
            sender, nonce,
            hashInitCode, hashCallData,
            callGasLimit, verificationGasLimit, preVerificationGas,
            maxFeePerGas, maxPriorityFeePerGas,
            hashPaymasterAndData
        );
    }
    function hash(UserOperation calldata userOp) internal pure returns (bytes32) {
        return keccak256(pack(userOp));
    }
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Receiver mixin for ETH and safe-transferred ERC721 and ERC1155 tokens.
/// @author Solady (https://github.com/Vectorized/solady/blob/main/src/accounts/Receiver.sol)
///
/// @dev Note:
/// - Handles all ERC721 and ERC1155 token safety callbacks.
/// - Collapses function table gas overhead and code size.
/// - Utilizes fallback so unknown calldata will pass on.
abstract contract Receiver {
    /// @dev For receiving ETH.
    receive() external payable virtual {}
    /// @dev Fallback function with the `receiverFallback` modifier.
    fallback() external payable virtual receiverFallback {}
    /// @dev Modifier for the fallback function to handle token callbacks.
    modifier receiverFallback() virtual {
        /// @solidity memory-safe-assembly
        assembly {
            let s := shr(224, calldataload(0))
            // 0x150b7a02: `onERC721Received(address,address,uint256,bytes)`.
            // 0xf23a6e61: `onERC1155Received(address,address,uint256,uint256,bytes)`.
            // 0xbc197c81: `onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)`.
            if or(eq(s, 0x150b7a02), or(eq(s, 0xf23a6e61), eq(s, 0xbc197c81))) {
                mstore(0x20, s) // Store `msg.sig`.
                return(0x3c, 0x20) // Return `msg.sig`.
            }
        }
        _;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Signature verification helper that supports both ECDSA signatures from EOAs
/// and ERC1271 signatures from smart contract wallets like Argent and Gnosis safe.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/SignatureCheckerLib.sol)
/// @author Modified from OpenZeppelin (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/utils/cryptography/SignatureChecker.sol)
///
/// @dev Note:
/// - The signature checking functions use the ecrecover precompile (0x1).
/// - The `bytes memory signature` variants use the identity precompile (0x4)
///   to copy memory internally.
/// - Unlike ECDSA signatures, contract signatures are revocable.
/// - As of Solady version 0.0.134, all `bytes signature` variants accept both
///   regular 65-byte `(r, s, v)` and EIP-2098 `(r, vs)` short form signatures.
///   See: https://eips.ethereum.org/EIPS/eip-2098
///   This is for calldata efficiency on smart accounts prevalent on L2s.
///
/// WARNING! Do NOT use signatures as unique identifiers:
/// - Use a nonce in the digest to prevent replay attacks on the same contract.
/// - Use EIP-712 for the digest to prevent replay attacks across different chains and contracts.
///   EIP-712 also enables readable signing of typed data for better user safety.
/// This implementation does NOT check if a signature is non-malleable.
library SignatureCheckerLib {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*               SIGNATURE CHECKING OPERATIONS                */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns whether `signature` is valid for `signer` and `hash`.
    /// If `signer` is a smart contract, the signature is validated with ERC1271.
    /// Otherwise, the signature is validated with `ECDSA.recover`.
    function isValidSignatureNow(address signer, bytes32 hash, bytes memory signature)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits of `signer` in case they are dirty.
            for { signer := shr(96, shl(96, signer)) } signer {} {
                let m := mload(0x40)
                mstore(0x00, hash)
                mstore(0x40, mload(add(signature, 0x20))) // `r`.
                if eq(mload(signature), 64) {
                    let vs := mload(add(signature, 0x40))
                    mstore(0x20, add(shr(255, vs), 27)) // `v`.
                    mstore(0x60, shr(1, shl(1, vs))) // `s`.
                    let t :=
                        staticcall(
                            gas(), // Amount of gas left for the transaction.
                            1, // Address of `ecrecover`.
                            0x00, // Start of input.
                            0x80, // Size of input.
                            0x01, // Start of output.
                            0x20 // Size of output.
                        )
                    // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                    if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                        isValid := 1
                        mstore(0x60, 0) // Restore the zero slot.
                        mstore(0x40, m) // Restore the free memory pointer.
                        break
                    }
                }
                if eq(mload(signature), 65) {
                    mstore(0x20, byte(0, mload(add(signature, 0x60)))) // `v`.
                    mstore(0x60, mload(add(signature, 0x40))) // `s`.
                    let t :=
                        staticcall(
                            gas(), // Amount of gas left for the transaction.
                            1, // Address of `ecrecover`.
                            0x00, // Start of input.
                            0x80, // Size of input.
                            0x01, // Start of output.
                            0x20 // Size of output.
                        )
                    // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                    if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                        isValid := 1
                        mstore(0x60, 0) // Restore the zero slot.
                        mstore(0x40, m) // Restore the free memory pointer.
                        break
                    }
                }
                mstore(0x60, 0) // Restore the zero slot.
                mstore(0x40, m) // Restore the free memory pointer.
                let f := shl(224, 0x1626ba7e)
                mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
                mstore(add(m, 0x04), hash)
                let d := add(m, 0x24)
                mstore(d, 0x40) // The offset of the `signature` in the calldata.
                // Copy the `signature` over.
                let n := add(0x20, mload(signature))
                pop(staticcall(gas(), 4, signature, n, add(m, 0x44), n))
                // forgefmt: disable-next-item
                isValid := and(
                    // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                    eq(mload(d), f),
                    // Whether the staticcall does not revert.
                    // This must be placed at the end of the `and` clause,
                    // as the arguments are evaluated from right to left.
                    staticcall(
                        gas(), // Remaining gas.
                        signer, // The `signer` address.
                        m, // Offset of calldata in memory.
                        add(returndatasize(), 0x44), // Length of calldata in memory.
                        d, // Offset of returndata.
                        0x20 // Length of returndata to write.
                    )
                )
                break
            }
        }
    }
    /// @dev Returns whether `signature` is valid for `signer` and `hash`.
    /// If `signer` is a smart contract, the signature is validated with ERC1271.
    /// Otherwise, the signature is validated with `ECDSA.recover`.
    function isValidSignatureNowCalldata(address signer, bytes32 hash, bytes calldata signature)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits of `signer` in case they are dirty.
            for { signer := shr(96, shl(96, signer)) } signer {} {
                let m := mload(0x40)
                mstore(0x00, hash)
                if eq(signature.length, 64) {
                    let vs := calldataload(add(signature.offset, 0x20))
                    mstore(0x20, add(shr(255, vs), 27)) // `v`.
                    mstore(0x40, calldataload(signature.offset)) // `r`.
                    mstore(0x60, shr(1, shl(1, vs))) // `s`.
                    let t :=
                        staticcall(
                            gas(), // Amount of gas left for the transaction.
                            1, // Address of `ecrecover`.
                            0x00, // Start of input.
                            0x80, // Size of input.
                            0x01, // Start of output.
                            0x20 // Size of output.
                        )
                    // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                    if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                        isValid := 1
                        mstore(0x60, 0) // Restore the zero slot.
                        mstore(0x40, m) // Restore the free memory pointer.
                        break
                    }
                }
                if eq(signature.length, 65) {
                    mstore(0x20, byte(0, calldataload(add(signature.offset, 0x40)))) // `v`.
                    calldatacopy(0x40, signature.offset, 0x40) // `r`, `s`.
                    let t :=
                        staticcall(
                            gas(), // Amount of gas left for the transaction.
                            1, // Address of `ecrecover`.
                            0x00, // Start of input.
                            0x80, // Size of input.
                            0x01, // Start of output.
                            0x20 // Size of output.
                        )
                    // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                    if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                        isValid := 1
                        mstore(0x60, 0) // Restore the zero slot.
                        mstore(0x40, m) // Restore the free memory pointer.
                        break
                    }
                }
                mstore(0x60, 0) // Restore the zero slot.
                mstore(0x40, m) // Restore the free memory pointer.
                let f := shl(224, 0x1626ba7e)
                mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
                mstore(add(m, 0x04), hash)
                let d := add(m, 0x24)
                mstore(d, 0x40) // The offset of the `signature` in the calldata.
                mstore(add(m, 0x44), signature.length)
                // Copy the `signature` over.
                calldatacopy(add(m, 0x64), signature.offset, signature.length)
                // forgefmt: disable-next-item
                isValid := and(
                    // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                    eq(mload(d), f),
                    // Whether the staticcall does not revert.
                    // This must be placed at the end of the `and` clause,
                    // as the arguments are evaluated from right to left.
                    staticcall(
                        gas(), // Remaining gas.
                        signer, // The `signer` address.
                        m, // Offset of calldata in memory.
                        add(signature.length, 0x64), // Length of calldata in memory.
                        d, // Offset of returndata.
                        0x20 // Length of returndata to write.
                    )
                )
                break
            }
        }
    }
    /// @dev Returns whether the signature (`r`, `vs`) is valid for `signer` and `hash`.
    /// If `signer` is a smart contract, the signature is validated with ERC1271.
    /// Otherwise, the signature is validated with `ECDSA.recover`.
    function isValidSignatureNow(address signer, bytes32 hash, bytes32 r, bytes32 vs)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits of `signer` in case they are dirty.
            for { signer := shr(96, shl(96, signer)) } signer {} {
                let m := mload(0x40)
                mstore(0x00, hash)
                mstore(0x20, add(shr(255, vs), 27)) // `v`.
                mstore(0x40, r) // `r`.
                mstore(0x60, shr(1, shl(1, vs))) // `s`.
                let t :=
                    staticcall(
                        gas(), // Amount of gas left for the transaction.
                        1, // Address of `ecrecover`.
                        0x00, // Start of input.
                        0x80, // Size of input.
                        0x01, // Start of output.
                        0x20 // Size of output.
                    )
                // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                    isValid := 1
                    mstore(0x60, 0) // Restore the zero slot.
                    mstore(0x40, m) // Restore the free memory pointer.
                    break
                }
                let f := shl(224, 0x1626ba7e)
                mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
                mstore(add(m, 0x04), hash)
                let d := add(m, 0x24)
                mstore(d, 0x40) // The offset of the `signature` in the calldata.
                mstore(add(m, 0x44), 65) // Length of the signature.
                mstore(add(m, 0x64), r) // `r`.
                mstore(add(m, 0x84), mload(0x60)) // `s`.
                mstore8(add(m, 0xa4), mload(0x20)) // `v`.
                // forgefmt: disable-next-item
                isValid := and(
                    // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                    eq(mload(d), f),
                    // Whether the staticcall does not revert.
                    // This must be placed at the end of the `and` clause,
                    // as the arguments are evaluated from right to left.
                    staticcall(
                        gas(), // Remaining gas.
                        signer, // The `signer` address.
                        m, // Offset of calldata in memory.
                        0xa5, // Length of calldata in memory.
                        d, // Offset of returndata.
                        0x20 // Length of returndata to write.
                    )
                )
                mstore(0x60, 0) // Restore the zero slot.
                mstore(0x40, m) // Restore the free memory pointer.
                break
            }
        }
    }
    /// @dev Returns whether the signature (`v`, `r`, `s`) is valid for `signer` and `hash`.
    /// If `signer` is a smart contract, the signature is validated with ERC1271.
    /// Otherwise, the signature is validated with `ECDSA.recover`.
    function isValidSignatureNow(address signer, bytes32 hash, uint8 v, bytes32 r, bytes32 s)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits of `signer` in case they are dirty.
            for { signer := shr(96, shl(96, signer)) } signer {} {
                let m := mload(0x40)
                mstore(0x00, hash)
                mstore(0x20, and(v, 0xff)) // `v`.
                mstore(0x40, r) // `r`.
                mstore(0x60, s) // `s`.
                let t :=
                    staticcall(
                        gas(), // Amount of gas left for the transaction.
                        1, // Address of `ecrecover`.
                        0x00, // Start of input.
                        0x80, // Size of input.
                        0x01, // Start of output.
                        0x20 // Size of output.
                    )
                // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                    isValid := 1
                    mstore(0x60, 0) // Restore the zero slot.
                    mstore(0x40, m) // Restore the free memory pointer.
                    break
                }
                let f := shl(224, 0x1626ba7e)
                mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
                mstore(add(m, 0x04), hash)
                let d := add(m, 0x24)
                mstore(d, 0x40) // The offset of the `signature` in the calldata.
                mstore(add(m, 0x44), 65) // Length of the signature.
                mstore(add(m, 0x64), r) // `r`.
                mstore(add(m, 0x84), s) // `s`.
                mstore8(add(m, 0xa4), v) // `v`.
                // forgefmt: disable-next-item
                isValid := and(
                    // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                    eq(mload(d), f),
                    // Whether the staticcall does not revert.
                    // This must be placed at the end of the `and` clause,
                    // as the arguments are evaluated from right to left.
                    staticcall(
                        gas(), // Remaining gas.
                        signer, // The `signer` address.
                        m, // Offset of calldata in memory.
                        0xa5, // Length of calldata in memory.
                        d, // Offset of returndata.
                        0x20 // Length of returndata to write.
                    )
                )
                mstore(0x60, 0) // Restore the zero slot.
                mstore(0x40, m) // Restore the free memory pointer.
                break
            }
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     ERC1271 OPERATIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns whether `signature` is valid for `hash` for an ERC1271 `signer` contract.
    function isValidERC1271SignatureNow(address signer, bytes32 hash, bytes memory signature)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40)
            let f := shl(224, 0x1626ba7e)
            mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
            mstore(add(m, 0x04), hash)
            let d := add(m, 0x24)
            mstore(d, 0x40) // The offset of the `signature` in the calldata.
            // Copy the `signature` over.
            let n := add(0x20, mload(signature))
            pop(staticcall(gas(), 4, signature, n, add(m, 0x44), n))
            // forgefmt: disable-next-item
            isValid := and(
                // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                eq(mload(d), f),
                // Whether the staticcall does not revert.
                // This must be placed at the end of the `and` clause,
                // as the arguments are evaluated from right to left.
                staticcall(
                    gas(), // Remaining gas.
                    signer, // The `signer` address.
                    m, // Offset of calldata in memory.
                    add(returndatasize(), 0x44), // Length of calldata in memory.
                    d, // Offset of returndata.
                    0x20 // Length of returndata to write.
                )
            )
        }
    }
    /// @dev Returns whether `signature` is valid for `hash` for an ERC1271 `signer` contract.
    function isValidERC1271SignatureNowCalldata(
        address signer,
        bytes32 hash,
        bytes calldata signature
    ) internal view returns (bool isValid) {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40)
            let f := shl(224, 0x1626ba7e)
            mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
            mstore(add(m, 0x04), hash)
            let d := add(m, 0x24)
            mstore(d, 0x40) // The offset of the `signature` in the calldata.
            mstore(add(m, 0x44), signature.length)
            // Copy the `signature` over.
            calldatacopy(add(m, 0x64), signature.offset, signature.length)
            // forgefmt: disable-next-item
            isValid := and(
                // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                eq(mload(d), f),
                // Whether the staticcall does not revert.
                // This must be placed at the end of the `and` clause,
                // as the arguments are evaluated from right to left.
                staticcall(
                    gas(), // Remaining gas.
                    signer, // The `signer` address.
                    m, // Offset of calldata in memory.
                    add(signature.length, 0x64), // Length of calldata in memory.
                    d, // Offset of returndata.
                    0x20 // Length of returndata to write.
                )
            )
        }
    }
    /// @dev Returns whether the signature (`r`, `vs`) is valid for `hash`
    /// for an ERC1271 `signer` contract.
    function isValidERC1271SignatureNow(address signer, bytes32 hash, bytes32 r, bytes32 vs)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40)
            let f := shl(224, 0x1626ba7e)
            mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
            mstore(add(m, 0x04), hash)
            let d := add(m, 0x24)
            mstore(d, 0x40) // The offset of the `signature` in the calldata.
            mstore(add(m, 0x44), 65) // Length of the signature.
            mstore(add(m, 0x64), r) // `r`.
            mstore(add(m, 0x84), shr(1, shl(1, vs))) // `s`.
            mstore8(add(m, 0xa4), add(shr(255, vs), 27)) // `v`.
            // forgefmt: disable-next-item
            isValid := and(
                // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                eq(mload(d), f),
                // Whether the staticcall does not revert.
                // This must be placed at the end of the `and` clause,
                // as the arguments are evaluated from right to left.
                staticcall(
                    gas(), // Remaining gas.
                    signer, // The `signer` address.
                    m, // Offset of calldata in memory.
                    0xa5, // Length of calldata in memory.
                    d, // Offset of returndata.
                    0x20 // Length of returndata to write.
                )
            )
        }
    }
    /// @dev Returns whether the signature (`v`, `r`, `s`) is valid for `hash`
    /// for an ERC1271 `signer` contract.
    function isValidERC1271SignatureNow(address signer, bytes32 hash, uint8 v, bytes32 r, bytes32 s)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40)
            let f := shl(224, 0x1626ba7e)
            mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
            mstore(add(m, 0x04), hash)
            let d := add(m, 0x24)
            mstore(d, 0x40) // The offset of the `signature` in the calldata.
            mstore(add(m, 0x44), 65) // Length of the signature.
            mstore(add(m, 0x64), r) // `r`.
            mstore(add(m, 0x84), s) // `s`.
            mstore8(add(m, 0xa4), v) // `v`.
            // forgefmt: disable-next-item
            isValid := and(
                // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                eq(mload(d), f),
                // Whether the staticcall does not revert.
                // This must be placed at the end of the `and` clause,
                // as the arguments are evaluated from right to left.
                staticcall(
                    gas(), // Remaining gas.
                    signer, // The `signer` address.
                    m, // Offset of calldata in memory.
                    0xa5, // Length of calldata in memory.
                    d, // Offset of returndata.
                    0x20 // Length of returndata to write.
                )
            )
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     HASHING OPERATIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns an Ethereum Signed Message, created from a `hash`.
    /// This produces a hash corresponding to the one signed with the
    /// [`eth_sign`](https://eth.wiki/json-rpc/API#eth_sign)
    /// JSON-RPC method as part of EIP-191.
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x20, hash) // Store into scratch space for keccak256.
            mstore(0x00, "\\x00\\x00\\x00\\x00\\x19Ethereum Signed Message:\
32") // 28 bytes.
            result := keccak256(0x04, 0x3c) // `32 * 2 - (32 - 28) = 60 = 0x3c`.
        }
    }
    /// @dev Returns an Ethereum Signed Message, created from `s`.
    /// This produces a hash corresponding to the one signed with the
    /// [`eth_sign`](https://eth.wiki/json-rpc/API#eth_sign)
    /// JSON-RPC method as part of EIP-191.
    /// Note: Supports lengths of `s` up to 999999 bytes.
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            let sLength := mload(s)
            let o := 0x20
            mstore(o, "\\x19Ethereum Signed Message:\
") // 26 bytes, zero-right-padded.
            mstore(0x00, 0x00)
            // Convert the `s.length` to ASCII decimal representation: `base10(s.length)`.
            for { let temp := sLength } 1 {} {
                o := sub(o, 1)
                mstore8(o, add(48, mod(temp, 10)))
                temp := div(temp, 10)
                if iszero(temp) { break }
            }
            let n := sub(0x3a, o) // Header length: `26 + 32 - o`.
            // Throw an out-of-offset error (consumes all gas) if the header exceeds 32 bytes.
            returndatacopy(returndatasize(), returndatasize(), gt(n, 0x20))
            mstore(s, or(mload(0x00), mload(n))) // Temporarily store the header.
            result := keccak256(add(s, sub(0x20, n)), add(n, sLength))
            mstore(s, sLength) // Restore the length.
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   EMPTY CALLDATA HELPERS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns an empty calldata bytes.
    function emptySignature() internal pure returns (bytes calldata signature) {
        /// @solidity memory-safe-assembly
        assembly {
            signature.length := 0
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice UUPS proxy mixin.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/UUPSUpgradeable.sol)
/// @author Modified from OpenZeppelin
/// (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/proxy/utils/UUPSUpgradeable.sol)
///
/// Note:
/// - This implementation is intended to be used with ERC1967 proxies.
/// See: `LibClone.deployERC1967` and related functions.
/// - This implementation is NOT compatible with legacy OpenZeppelin proxies
/// which do not store the implementation at `_ERC1967_IMPLEMENTATION_SLOT`.
abstract contract UUPSUpgradeable {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev The upgrade failed.
    error UpgradeFailed();
    /// @dev The call is from an unauthorized call context.
    error UnauthorizedCallContext();
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         IMMUTABLES                         */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev For checking if the context is a delegate call.
    uint256 private immutable __self = uint256(uint160(address(this)));
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                           EVENTS                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Emitted when the proxy's implementation is upgraded.
    event Upgraded(address indexed implementation);
    /// @dev `keccak256(bytes("Upgraded(address)"))`.
    uint256 private constant _UPGRADED_EVENT_SIGNATURE =
        0xbc7cd75a20ee27fd9adebab32041f755214dbc6bffa90cc0225b39da2e5c2d3b;
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                          STORAGE                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev The ERC-1967 storage slot for the implementation in the proxy.
    /// `uint256(keccak256("eip1967.proxy.implementation")) - 1`.
    bytes32 internal constant _ERC1967_IMPLEMENTATION_SLOT =
        0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                      UUPS OPERATIONS                       */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Please override this function to check if `msg.sender` is authorized
    /// to upgrade the proxy to `newImplementation`, reverting if not.
    /// ```
    ///     function _authorizeUpgrade(address) internal override onlyOwner {}
    /// ```
    function _authorizeUpgrade(address newImplementation) internal virtual;
    /// @dev Returns the storage slot used by the implementation,
    /// as specified in [ERC1822](https://eips.ethereum.org/EIPS/eip-1822).
    ///
    /// Note: The `notDelegated` modifier prevents accidental upgrades to
    /// an implementation that is a proxy contract.
    function proxiableUUID() public view virtual notDelegated returns (bytes32) {
        // This function must always return `_ERC1967_IMPLEMENTATION_SLOT` to comply with ERC1967.
        return _ERC1967_IMPLEMENTATION_SLOT;
    }
    /// @dev Upgrades the proxy's implementation to `newImplementation`.
    /// Emits a {Upgraded} event.
    ///
    /// Note: Passing in empty `data` skips the delegatecall to `newImplementation`.
    function upgradeToAndCall(address newImplementation, bytes calldata data)
        public
        payable
        virtual
        onlyProxy
    {
        _authorizeUpgrade(newImplementation);
        /// @solidity memory-safe-assembly
        assembly {
            newImplementation := shr(96, shl(96, newImplementation)) // Clears upper 96 bits.
            mstore(0x01, 0x52d1902d) // `proxiableUUID()`.
            let s := _ERC1967_IMPLEMENTATION_SLOT
            // Check if `newImplementation` implements `proxiableUUID` correctly.
            if iszero(eq(mload(staticcall(gas(), newImplementation, 0x1d, 0x04, 0x01, 0x20)), s)) {
                mstore(0x01, 0x55299b49) // `UpgradeFailed()`.
                revert(0x1d, 0x04)
            }
            // Emit the {Upgraded} event.
            log2(codesize(), 0x00, _UPGRADED_EVENT_SIGNATURE, newImplementation)
            sstore(s, newImplementation) // Updates the implementation.
            // Perform a delegatecall to `newImplementation` if `data` is non-empty.
            if data.length {
                // Forwards the `data` to `newImplementation` via delegatecall.
                let m := mload(0x40)
                calldatacopy(m, data.offset, data.length)
                if iszero(delegatecall(gas(), newImplementation, m, data.length, codesize(), 0x00))
                {
                    // Bubble up the revert if the call reverts.
                    returndatacopy(m, 0x00, returndatasize())
                    revert(m, returndatasize())
                }
            }
        }
    }
    /// @dev Requires that the execution is performed through a proxy.
    modifier onlyProxy() {
        uint256 s = __self;
        /// @solidity memory-safe-assembly
        assembly {
            // To enable use cases with an immutable default implementation in the bytecode,
            // (see: ERC6551Proxy), we don't require that the proxy address must match the
            // value stored in the implementation slot, which may not be initialized.
            if eq(s, address()) {
                mstore(0x00, 0x9f03a026) // `UnauthorizedCallContext()`.
                revert(0x1c, 0x04)
            }
        }
        _;
    }
    /// @dev Requires that the execution is NOT performed via delegatecall.
    /// This is the opposite of `onlyProxy`.
    modifier notDelegated() {
        uint256 s = __self;
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(eq(s, address())) {
                mstore(0x00, 0x9f03a026) // `UnauthorizedCallContext()`.
                revert(0x1c, 0x04)
            }
        }
        _;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import {FCL_ecdsa} from "FreshCryptoLib/FCL_ecdsa.sol";
import {FCL_Elliptic_ZZ} from "FreshCryptoLib/FCL_elliptic.sol";
import {Base64} from "openzeppelin-contracts/contracts/utils/Base64.sol";
import {LibString} from "solady/utils/LibString.sol";
/// @title WebAuthn
///
/// @notice A library for verifying WebAuthn Authentication Assertions, built off the work
///         of Daimo.
///
/// @dev Attempts to use the RIP-7212 precompile for signature verification.
///      If precompile verification fails, it falls back to FreshCryptoLib.
///
/// @author Coinbase (https://github.com/base-org/webauthn-sol)
/// @author Daimo (https://github.com/daimo-eth/p256-verifier/blob/master/src/WebAuthn.sol)
library WebAuthn {
    using LibString for string;
    struct WebAuthnAuth {
        /// @dev The WebAuthn authenticator data.
        ///      See https://www.w3.org/TR/webauthn-2/#dom-authenticatorassertionresponse-authenticatordata.
        bytes authenticatorData;
        /// @dev The WebAuthn client data JSON.
        ///      See https://www.w3.org/TR/webauthn-2/#dom-authenticatorresponse-clientdatajson.
        string clientDataJSON;
        /// @dev The index at which "challenge":"..." occurs in `clientDataJSON`.
        uint256 challengeIndex;
        /// @dev The index at which "type":"..." occurs in `clientDataJSON`.
        uint256 typeIndex;
        /// @dev The r value of secp256r1 signature
        uint256 r;
        /// @dev The s value of secp256r1 signature
        uint256 s;
    }
    /// @dev Bit 0 of the authenticator data struct, corresponding to the "User Present" bit.
    ///      See https://www.w3.org/TR/webauthn-2/#flags.
    bytes1 private constant _AUTH_DATA_FLAGS_UP = 0x01;
    /// @dev Bit 2 of the authenticator data struct, corresponding to the "User Verified" bit.
    ///      See https://www.w3.org/TR/webauthn-2/#flags.
    bytes1 private constant _AUTH_DATA_FLAGS_UV = 0x04;
    /// @dev Secp256r1 curve order / 2 used as guard to prevent signature malleability issue.
    uint256 private constant _P256_N_DIV_2 = FCL_Elliptic_ZZ.n / 2;
    /// @dev The precompiled contract address to use for signature verification in the “secp256r1” elliptic curve.
    ///      See https://github.com/ethereum/RIPs/blob/master/RIPS/rip-7212.md.
    address private constant _VERIFIER = address(0x100);
    /// @dev The expected type (hash) in the client data JSON when verifying assertion signatures.
    ///      See https://www.w3.org/TR/webauthn-2/#dom-collectedclientdata-type
    bytes32 private constant _EXPECTED_TYPE_HASH = keccak256('"type":"webauthn.get"');
    ///
    /// @notice Verifies a Webauthn Authentication Assertion as described
    /// in https://www.w3.org/TR/webauthn-2/#sctn-verifying-assertion.
    ///
    /// @dev We do not verify all the steps as described in the specification, only ones relevant to our context.
    ///      Please carefully read through this list before usage.
    ///
    ///      Specifically, we do verify the following:
    ///         - Verify that authenticatorData (which comes from the authenticator, such as iCloud Keychain) indicates
    ///           a well-formed assertion with the user present bit set. If `requireUV` is set, checks that the authenticator
    ///           enforced user verification. User verification should be required if, and only if, options.userVerification
    ///           is set to required in the request.
    ///         - Verifies that the client JSON is of type "webauthn.get", i.e. the client was responding to a request to
    ///           assert authentication.
    ///         - Verifies that the client JSON contains the requested challenge.
    ///         - Verifies that (r, s) constitute a valid signature over both the authenicatorData and client JSON, for public
    ///            key (x, y).
    ///
    ///      We make some assumptions about the particular use case of this verifier, so we do NOT verify the following:
    ///         - Does NOT verify that the origin in the `clientDataJSON` matches the Relying Party's origin: tt is considered
    ///           the authenticator's responsibility to ensure that the user is interacting with the correct RP. This is
    ///           enforced by most high quality authenticators properly, particularly the iCloud Keychain and Google Password
    ///           Manager were tested.
    ///         - Does NOT verify That `topOrigin` in `clientDataJSON` is well-formed: We assume it would never be present, i.e.
    ///           the credentials are never used in a cross-origin/iframe context. The website/app set up should disallow
    ///           cross-origin usage of the credentials. This is the default behaviour for created credentials in common settings.
    ///         - Does NOT verify that the `rpIdHash` in `authenticatorData` is the SHA-256 hash of the RP ID expected by the Relying
    ///           Party: this means that we rely on the authenticator to properly enforce credentials to be used only by the correct RP.
    ///           This is generally enforced with features like Apple App Site Association and Google Asset Links. To protect from
    ///           edge cases in which a previously-linked RP ID is removed from the authorised RP IDs, we recommend that messages
    ///           signed by the authenticator include some expiry mechanism.
    ///         - Does NOT verify the credential backup state: this assumes the credential backup state is NOT used as part of Relying
    ///           Party business logic or policy.
    ///         - Does NOT verify the values of the client extension outputs: this assumes that the Relying Party does not use client
    ///           extension outputs.
    ///         - Does NOT verify the signature counter: signature counters are intended to enable risk scoring for the Relying Party.
    ///           This assumes risk scoring is not used as part of Relying Party business logic or policy.
    ///         - Does NOT verify the attestation object: this assumes that response.attestationObject is NOT present in the response,
    ///           i.e. the RP does not intend to verify an attestation.
    ///
    /// @param challenge    The challenge that was provided by the relying party.
    /// @param requireUV    A boolean indicating whether user verification is required.
    /// @param webAuthnAuth The `WebAuthnAuth` struct.
    /// @param x            The x coordinate of the public key.
    /// @param y            The y coordinate of the public key.
    ///
    /// @return `true` if the authentication assertion passed validation, else `false`.
    function verify(bytes memory challenge, bool requireUV, WebAuthnAuth memory webAuthnAuth, uint256 x, uint256 y)
        internal
        view
        returns (bool)
    {
        if (webAuthnAuth.s > _P256_N_DIV_2) {
            // guard against signature malleability
            return false;
        }
        // 11. Verify that the value of C.type is the string webauthn.get.
        //     bytes("type":"webauthn.get").length = 21
        string memory _type = webAuthnAuth.clientDataJSON.slice(webAuthnAuth.typeIndex, webAuthnAuth.typeIndex + 21);
        if (keccak256(bytes(_type)) != _EXPECTED_TYPE_HASH) {
            return false;
        }
        // 12. Verify that the value of C.challenge equals the base64url encoding of options.challenge.
        bytes memory expectedChallenge = bytes(string.concat('"challenge":"', Base64.encodeURL(challenge), '"'));
        string memory actualChallenge =
            webAuthnAuth.clientDataJSON.slice(webAuthnAuth.challengeIndex, webAuthnAuth.challengeIndex + expectedChallenge.length);
        if (keccak256(bytes(actualChallenge)) != keccak256(expectedChallenge)) {
            return false;
        }
        // Skip 13., 14., 15.
        // 16. Verify that the UP bit of the flags in authData is set.
        if (webAuthnAuth.authenticatorData[32] & _AUTH_DATA_FLAGS_UP != _AUTH_DATA_FLAGS_UP) {
            return false;
        }
        // 17. If user verification is required for this assertion, verify that the User Verified bit of the flags in
        //     authData is set.
        if (requireUV && (webAuthnAuth.authenticatorData[32] & _AUTH_DATA_FLAGS_UV) != _AUTH_DATA_FLAGS_UV) {
            return false;
        }
        // skip 18.
        // 19. Let hash be the result of computing a hash over the cData using SHA-256.
        bytes32 clientDataJSONHash = sha256(bytes(webAuthnAuth.clientDataJSON));
        // 20. Using credentialPublicKey, verify that sig is a valid signature over the binary concatenation of authData
        //     and hash.
        bytes32 messageHash = sha256(abi.encodePacked(webAuthnAuth.authenticatorData, clientDataJSONHash));
        bytes memory args = abi.encode(messageHash, webAuthnAuth.r, webAuthnAuth.s, x, y);
        // try the RIP-7212 precompile address
        (bool success, bytes memory ret) = _VERIFIER.staticcall(args);
        // staticcall will not revert if address has no code
        // check return length
        // note that even if precompile exists, ret.length is 0 when verification returns false
        // so an invalid signature will be checked twice: once by the precompile and once by FCL.
        // Ideally this signature failure is simulated offchain and no one actually pay this gas.
        bool valid = ret.length > 0;
        if (success && valid) return abi.decode(ret, (uint256)) == 1;
        return FCL_ecdsa.ecdsa_verify(messageHash, webAuthnAuth.r, webAuthnAuth.s, x, y);
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @title ERC-1271
///
/// @notice Abstract ERC-1271 implementation (based on Solady's) with guards to handle the same
///         signer being used on multiple accounts.
///
/// @dev To prevent the same signature from being validated on different accounts owned by the samer signer,
///      we introduce an anti cross-account-replay layer: the original hash is input into a new EIP-712 compliant
///      hash. The domain separator of this outer hash contains the chain id and address of this contract, so that
///      it cannot be used on two accounts (see `replaySafeHash()` for the implementation details).
///
/// @author Coinbase (https://github.com/coinbase/smart-wallet)
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/accounts/ERC1271.sol)
abstract contract ERC1271 {
    /// @dev Precomputed `typeHash` used to produce EIP-712 compliant hash when applying the anti
    ///      cross-account-replay layer.
    ///
    ///      The original hash must either be:
    ///         - An EIP-191 hash: keccak256("\\x19Ethereum Signed Message:\
" || len(someMessage) || someMessage)
    ///         - An EIP-712 hash: keccak256("\\x19\\x01" || someDomainSeparator || hashStruct(someStruct))
    bytes32 private constant _MESSAGE_TYPEHASH = keccak256("CoinbaseSmartWalletMessage(bytes32 hash)");
    /// @notice Returns information about the `EIP712Domain` used to create EIP-712 compliant hashes.
    ///
    /// @dev Follows ERC-5267 (see https://eips.ethereum.org/EIPS/eip-5267).
    ///
    /// @return fields The bitmap of used fields.
    /// @return name The value of the `EIP712Domain.name` field.
    /// @return version The value of the `EIP712Domain.version` field.
    /// @return chainId The value of the `EIP712Domain.chainId` field.
    /// @return verifyingContract The value of the `EIP712Domain.verifyingContract` field.
    /// @return salt The value of the `EIP712Domain.salt` field.
    /// @return extensions The list of EIP numbers, that extends EIP-712 with new domain fields.
    function eip712Domain()
        external
        view
        virtual
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        )
    {
        fields = hex"0f"; // `0b1111`.
        (name, version) = _domainNameAndVersion();
        chainId = block.chainid;
        verifyingContract = address(this);
        salt = salt; // `bytes32(0)`.
        extensions = extensions; // `new uint256[](0)`.
    }
    /// @notice Validates the `signature` against the given `hash`.
    ///
    /// @dev This implementation follows ERC-1271. See https://eips.ethereum.org/EIPS/eip-1271.
    /// @dev IMPORTANT: Signature verification is performed on the hash produced AFTER applying the anti
    ///      cross-account-replay layer on the given `hash` (i.e., verification is run on the replay-safe
    ///      hash version).
    ///
    /// @param hash      The original hash.
    /// @param signature The signature of the replay-safe hash to validate.
    ///
    /// @return result `0x1626ba7e` if validation succeeded, else `0xffffffff`.
    function isValidSignature(bytes32 hash, bytes calldata signature) public view virtual returns (bytes4 result) {
        if (_isValidSignature({hash: replaySafeHash(hash), signature: signature})) {
            // bytes4(keccak256("isValidSignature(bytes32,bytes)"))
            return 0x1626ba7e;
        }
        return 0xffffffff;
    }
    /// @notice Wrapper around `_eip712Hash()` to produce a replay-safe hash fron the given `hash`.
    ///
    /// @dev The returned EIP-712 compliant replay-safe hash is the result of:
    ///      keccak256(
    ///         \\x19\\x01 ||
    ///         this.domainSeparator ||
    ///         hashStruct(CoinbaseSmartWalletMessage({ hash: `hash`}))
    ///      )
    ///
    /// @param hash The original hash.
    ///
    /// @return The corresponding replay-safe hash.
    function replaySafeHash(bytes32 hash) public view virtual returns (bytes32) {
        return _eip712Hash(hash);
    }
    /// @notice Returns the `domainSeparator` used to create EIP-712 compliant hashes.
    ///
    /// @dev Implements domainSeparator = hashStruct(eip712Domain).
    ///      See https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator.
    ///
    /// @return The 32 bytes domain separator result.
    function domainSeparator() public view returns (bytes32) {
        (string memory name, string memory version) = _domainNameAndVersion();
        return keccak256(
            abi.encode(
                keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"),
                keccak256(bytes(name)),
                keccak256(bytes(version)),
                block.chainid,
                address(this)
            )
        );
    }
    /// @notice Returns the EIP-712 typed hash of the `CoinbaseSmartWalletMessage(bytes32 hash)` data structure.
    ///
    /// @dev Implements encode(domainSeparator : ?²⁵⁶, message : ?) = "\\x19\\x01" || domainSeparator ||
    ///      hashStruct(message).
    /// @dev See https://eips.ethereum.org/EIPS/eip-712#specification.
    ///
    /// @param hash The `CoinbaseSmartWalletMessage.hash` field to hash.
    ////
    /// @return The resulting EIP-712 hash.
    function _eip712Hash(bytes32 hash) internal view virtual returns (bytes32) {
        return keccak256(abi.encodePacked("\\x19\\x01", domainSeparator(), _hashStruct(hash)));
    }
    /// @notice Returns the EIP-712 `hashStruct` result of the `CoinbaseSmartWalletMessage(bytes32 hash)` data
    ///         structure.
    ///
    /// @dev Implements hashStruct(s : ?) = keccak256(typeHash || encodeData(s)).
    /// @dev See https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct.
    ///
    /// @param hash The `CoinbaseSmartWalletMessage.hash` field.
    ///
    /// @return The EIP-712 `hashStruct` result.
    function _hashStruct(bytes32 hash) internal view virtual returns (bytes32) {
        return keccak256(abi.encode(_MESSAGE_TYPEHASH, hash));
    }
    /// @notice Returns the domain name and version to use when creating EIP-712 signatures.
    ///
    /// @dev MUST be defined by the implementation.
    ///
    /// @return name    The user readable name of signing domain.
    /// @return version The current major version of the signing domain.
    function _domainNameAndVersion() internal view virtual returns (string memory name, string memory version);
    /// @notice Validates the `signature` against the given `hash`.
    ///
    /// @dev MUST be defined by the implementation.
    ///
    /// @param hash      The hash whose signature has been performed on.
    /// @param signature The signature associated with `hash`.
    ///
    /// @return `true` is the signature is valid, else `false`.
    function _isValidSignature(bytes32 hash, bytes calldata signature) internal view virtual returns (bool);
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.18;
/// @notice Storage layout used by this contract.
///
/// @custom:storage-location erc7201:coinbase.storage.MultiOwnable
struct MultiOwnableStorage {
    /// @dev Tracks the index of the next owner to add.
    uint256 nextOwnerIndex;
    /// @dev Tracks number of owners that have been removed.
    uint256 removedOwnersCount;
    /// @dev Maps index to owner bytes, used to idenfitied owners via a uint256 index.
    ///
    ///      Some uses—-such as signature validation for secp256r1 public key owners—-
    ///      requires the caller to assert the public key of the caller. To economize calldata,
    ///      we allow an index to identify an owner, so that the full owner bytes do
    ///      not need to be passed.
    ///
    ///      The `owner` bytes should either be
    ///         - An ABI encoded Ethereum address
    ///         - An ABI encoded public key
    mapping(uint256 index => bytes owner) ownerAtIndex;
    /// @dev Mapping of bytes to booleans indicating whether or not
    ///      bytes_ is an owner of this contract.
    mapping(bytes bytes_ => bool isOwner_) isOwner;
}
/// @title Multi Ownable
///
/// @notice Auth contract allowing multiple owners, each identified as bytes.
///
/// @author Coinbase (https://github.com/coinbase/smart-wallet)
contract MultiOwnable {
    /// @dev Slot for the `MultiOwnableStorage` struct in storage.
    ///      Computed from
    ///      keccak256(abi.encode(uint256(keccak256("coinbase.storage.MultiOwnable")) - 1)) & ~bytes32(uint256(0xff))
    ///      Follows ERC-7201 (see https://eips.ethereum.org/EIPS/eip-7201).
    bytes32 private constant MUTLI_OWNABLE_STORAGE_LOCATION =
        0x97e2c6aad4ce5d562ebfaa00db6b9e0fb66ea5d8162ed5b243f51a2e03086f00;
    /// @notice Thrown when the `msg.sender` is not an owner and is trying to call a privileged function.
    error Unauthorized();
    /// @notice Thrown when trying to add an already registered owner.
    ///
    /// @param owner The owner bytes.
    error AlreadyOwner(bytes owner);
    /// @notice Thrown when trying to remove an owner from an index that is empty.
    ///
    /// @param index The targeted index for removal.
    error NoOwnerAtIndex(uint256 index);
    /// @notice Thrown when `owner` argument does not match owner found at index.
    ///
    /// @param index         The index of the owner to be removed.
    /// @param expectedOwner The owner passed in the remove call.
    /// @param actualOwner   The actual owner at `index`.
    error WrongOwnerAtIndex(uint256 index, bytes expectedOwner, bytes actualOwner);
    /// @notice Thrown when a provided owner is neither 64 bytes long (for public key)
    ///         nor a ABI encoded address.
    ///
    /// @param owner The invalid owner.
    error InvalidOwnerBytesLength(bytes owner);
    /// @notice Thrown if a provided owner is 32 bytes long but does not fit in an `address` type.
    ///
    /// @param owner The invalid owner.
    error InvalidEthereumAddressOwner(bytes owner);
    /// @notice Thrown when removeOwnerAtIndex is called and there is only one current owner.
    error LastOwner();
    /// @notice Thrown when removeLastOwner is called and there is more than one current owner.
    ///
    /// @param ownersRemaining The number of current owners.
    error NotLastOwner(uint256 ownersRemaining);
    /// @notice Emitted when a new owner is registered.
    ///
    /// @param index The owner index of the owner added.
    /// @param owner The owner added.
    event AddOwner(uint256 indexed index, bytes owner);
    /// @notice Emitted when an owner is removed.
    ///
    /// @param index The owner index of the owner removed.
    /// @param owner The owner removed.
    event RemoveOwner(uint256 indexed index, bytes owner);
    /// @notice Access control modifier ensuring the caller is an authorized owner
    modifier onlyOwner() virtual {
        _checkOwner();
        _;
    }
    /// @notice Adds a new Ethereum-address owner.
    ///
    /// @param owner The owner address.
    function addOwnerAddress(address owner) external virtual onlyOwner {
        _addOwnerAtIndex(abi.encode(owner), _getMultiOwnableStorage().nextOwnerIndex++);
    }
    /// @notice Adds a new public-key owner.
    ///
    /// @param x The owner public key x coordinate.
    /// @param y The owner public key y coordinate.
    function addOwnerPublicKey(bytes32 x, bytes32 y) external virtual onlyOwner {
        _addOwnerAtIndex(abi.encode(x, y), _getMultiOwnableStorage().nextOwnerIndex++);
    }
    /// @notice Removes owner at the given `index`.
    ///
    /// @dev Reverts if the owner is not registered at `index`.
    /// @dev Reverts if there is currently only one owner.
    /// @dev Reverts if `owner` does not match bytes found at `index`.
    ///
    /// @param index The index of the owner to be removed.
    /// @param owner The ABI encoded bytes of the owner to be removed.
    function removeOwnerAtIndex(uint256 index, bytes calldata owner) external virtual onlyOwner {
        if (ownerCount() == 1) {
            revert LastOwner();
        }
        _removeOwnerAtIndex(index, owner);
    }
    /// @notice Removes owner at the given `index`, which should be the only current owner.
    ///
    /// @dev Reverts if the owner is not registered at `index`.
    /// @dev Reverts if there is currently more than one owner.
    /// @dev Reverts if `owner` does not match bytes found at `index`.
    ///
    /// @param index The index of the owner to be removed.
    /// @param owner The ABI encoded bytes of the owner to be removed.
    function removeLastOwner(uint256 index, bytes calldata owner) external virtual onlyOwner {
        uint256 ownersRemaining = ownerCount();
        if (ownersRemaining > 1) {
            revert NotLastOwner(ownersRemaining);
        }
        _removeOwnerAtIndex(index, owner);
    }
    /// @notice Checks if the given `account` address is registered as owner.
    ///
    /// @param account The account address to check.
    ///
    /// @return `true` if the account is an owner else `false`.
    function isOwnerAddress(address account) public view virtual returns (bool) {
        return _getMultiOwnableStorage().isOwner[abi.encode(account)];
    }
    /// @notice Checks if the given `x`, `y` public key is registered as owner.
    ///
    /// @param x The public key x coordinate.
    /// @param y The public key y coordinate.
    ///
    /// @return `true` if the account is an owner else `false`.
    function isOwnerPublicKey(bytes32 x, bytes32 y) public view virtual returns (bool) {
        return _getMultiOwnableStorage().isOwner[abi.encode(x, y)];
    }
    /// @notice Checks if the given `account` bytes is registered as owner.
    ///
    /// @param account The account, should be ABI encoded address or public key.
    ///
    /// @return `true` if the account is an owner else `false`.
    function isOwnerBytes(bytes memory account) public view virtual returns (bool) {
        return _getMultiOwnableStorage().isOwner[account];
    }
    /// @notice Returns the owner bytes at the given `index`.
    ///
    /// @param index The index to lookup.
    ///
    /// @return The owner bytes (empty if no owner is registered at this `index`).
    function ownerAtIndex(uint256 index) public view virtual returns (bytes memory) {
        return _getMultiOwnableStorage().ownerAtIndex[index];
    }
    /// @notice Returns the next index that will be used to add a new owner.
    ///
    /// @return The next index that will be used to add a new owner.
    function nextOwnerIndex() public view virtual returns (uint256) {
        return _getMultiOwnableStorage().nextOwnerIndex;
    }
    /// @notice Returns the current number of owners
    ///
    /// @return The current owner count
    function ownerCount() public view virtual returns (uint256) {
        MultiOwnableStorage storage $ = _getMultiOwnableStorage();
        return $.nextOwnerIndex - $.removedOwnersCount;
    }
    /// @notice Tracks the number of owners removed
    ///
    /// @dev Used with `this.nextOwnerIndex` to avoid removing all owners
    ///
    /// @return The number of owners that have been removed.
    function removedOwnersCount() public view virtual returns (uint256) {
        return _getMultiOwnableStorage().removedOwnersCount;
    }
    /// @notice Initialize the owners of this contract.
    ///
    /// @dev Intended to be called contract is first deployed and never again.
    /// @dev Reverts if a provided owner is neither 64 bytes long (for public key) nor a valid address.
    ///
    /// @param owners The initial set of owners.
    function _initializeOwners(bytes[] memory owners) internal virtual {
        MultiOwnableStorage storage $ = _getMultiOwnableStorage();
        uint256 nextOwnerIndex_ = $.nextOwnerIndex;
        for (uint256 i; i < owners.length; i++) {
            if (owners[i].length != 32 && owners[i].length != 64) {
                revert InvalidOwnerBytesLength(owners[i]);
            }
            if (owners[i].length == 32 && uint256(bytes32(owners[i])) > type(uint160).max) {
                revert InvalidEthereumAddressOwner(owners[i]);
            }
            _addOwnerAtIndex(owners[i], nextOwnerIndex_++);
        }
        $.nextOwnerIndex = nextOwnerIndex_;
    }
    /// @notice Adds an owner at the given `index`.
    ///
    /// @dev Reverts if `owner` is already registered as an owner.
    ///
    /// @param owner The owner raw bytes to register.
    /// @param index The index to write to.
    function _addOwnerAtIndex(bytes memory owner, uint256 index) internal virtual {
        if (isOwnerBytes(owner)) revert AlreadyOwner(owner);
        MultiOwnableStorage storage $ = _getMultiOwnableStorage();
        $.isOwner[owner] = true;
        $.ownerAtIndex[index] = owner;
        emit AddOwner(index, owner);
    }
    /// @notice Removes owner at the given `index`.
    ///
    /// @dev Reverts if the owner is not registered at `index`.
    /// @dev Reverts if `owner` does not match bytes found at `index`.
    ///
    /// @param index The index of the owner to be removed.
    /// @param owner The ABI encoded bytes of the owner to be removed.
    function _removeOwnerAtIndex(uint256 index, bytes calldata owner) internal virtual {
        bytes memory owner_ = ownerAtIndex(index);
        if (owner_.length == 0) revert NoOwnerAtIndex(index);
        if (keccak256(owner_) != keccak256(owner)) {
            revert WrongOwnerAtIndex({index: index, expectedOwner: owner, actualOwner: owner_});
        }
        MultiOwnableStorage storage $ = _getMultiOwnableStorage();
        delete $.isOwner[owner];
        delete $.ownerAtIndex[index];
        $.removedOwnersCount++;
        emit RemoveOwner(index, owner);
    }
    /// @notice Checks if the sender is an owner of this contract or the contract itself.
    ///
    /// @dev Revert if the sender is not an owner fo the contract itself.
    function _checkOwner() internal view virtual {
        if (isOwnerAddress(msg.sender) || (msg.sender == address(this))) {
            return;
        }
        revert Unauthorized();
    }
    /// @notice Helper function to get a storage reference to the `MultiOwnableStorage` struct.
    ///
    /// @return $ A storage reference to the `MultiOwnableStorage` struct.
    function _getMultiOwnableStorage() internal pure returns (MultiOwnableStorage storage $) {
        assembly ("memory-safe") {
            $.slot := MUTLI_OWNABLE_STORAGE_LOCATION
        }
    }
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
/* solhint-disable no-inline-assembly */
/**
 * returned data from validateUserOp.
 * validateUserOp returns a uint256, with is created by `_packedValidationData` and parsed by `_parseValidationData`
 * @param aggregator - address(0) - the account validated the signature by itself.
 *              address(1) - the account failed to validate the signature.
 *              otherwise - this is an address of a signature aggregator that must be used to validate the signature.
 * @param validAfter - this UserOp is valid only after this timestamp.
 * @param validaUntil - this UserOp is valid only up to this timestamp.
 */
    struct ValidationData {
        address aggregator;
        uint48 validAfter;
        uint48 validUntil;
    }
//extract sigFailed, validAfter, validUntil.
// also convert zero validUntil to type(uint48).max
    function _parseValidationData(uint validationData) pure returns (ValidationData memory data) {
        address aggregator = address(uint160(validationData));
        uint48 validUntil = uint48(validationData >> 160);
        if (validUntil == 0) {
            validUntil = type(uint48).max;
        }
        uint48 validAfter = uint48(validationData >> (48 + 160));
        return ValidationData(aggregator, validAfter, validUntil);
    }
// intersect account and paymaster ranges.
    function _intersectTimeRange(uint256 validationData, uint256 paymasterValidationData) pure returns (ValidationData memory) {
        ValidationData memory accountValidationData = _parseValidationData(validationData);
        ValidationData memory pmValidationData = _parseValidationData(paymasterValidationData);
        address aggregator = accountValidationData.aggregator;
        if (aggregator == address(0)) {
            aggregator = pmValidationData.aggregator;
        }
        uint48 validAfter = accountValidationData.validAfter;
        uint48 validUntil = accountValidationData.validUntil;
        uint48 pmValidAfter = pmValidationData.validAfter;
        uint48 pmValidUntil = pmValidationData.validUntil;
        if (validAfter < pmValidAfter) validAfter = pmValidAfter;
        if (validUntil > pmValidUntil) validUntil = pmValidUntil;
        return ValidationData(aggregator, validAfter, validUntil);
    }
/**
 * helper to pack the return value for validateUserOp
 * @param data - the ValidationData to pack
 */
    function _packValidationData(ValidationData memory data) pure returns (uint256) {
        return uint160(data.aggregator) | (uint256(data.validUntil) << 160) | (uint256(data.validAfter) << (160 + 48));
    }
/**
 * helper to pack the return value for validateUserOp, when not using an aggregator
 * @param sigFailed - true for signature failure, false for success
 * @param validUntil last timestamp this UserOperation is valid (or zero for infinite)
 * @param validAfter first timestamp this UserOperation is valid
 */
    function _packValidationData(bool sigFailed, uint48 validUntil, uint48 validAfter) pure returns (uint256) {
        return (sigFailed ? 1 : 0) | (uint256(validUntil) << 160) | (uint256(validAfter) << (160 + 48));
    }
/**
 * keccak function over calldata.
 * @dev copy calldata into memory, do keccak and drop allocated memory. Strangely, this is more efficient than letting solidity do it.
 */
    function calldataKeccak(bytes calldata data) pure returns (bytes32 ret) {
        assembly {
            let mem := mload(0x40)
            let len := data.length
            calldatacopy(mem, data.offset, len)
            ret := keccak256(mem, len)
        }
    }
//********************************************************************************************/
//  ___           _       ___               _         _    _ _
// | __| _ ___ __| |_    / __|_ _ _  _ _ __| |_ ___  | |  (_) |__
// | _| '_/ -_|_-< ' \\  | (__| '_| || | '_ \\  _/ _ \\ | |__| | '_ \\
// |_||_| \\___/__/_||_|  \\___|_|  \\_, | .__/\\__\\___/ |____|_|_.__/
//                                |__/|_|
///* Copyright (C) 2022 - Renaud Dubois - This file is part of FCL (Fresh CryptoLib) project
///* License: This software is licensed under MIT License
///* This Code may be reused including license and copyright notice.
///* See LICENSE file at the root folder of the project.
///* FILE: FCL_ecdsa.sol
///*
///*
///* DESCRIPTION: ecdsa verification implementation
///*
//**************************************************************************************/
//* WARNING: this code SHALL not be used for non prime order curves for security reasons.
// Code is optimized for a=-3 only curves with prime order, constant like -1, -2 shall be replaced
// if ever used for other curve than sec256R1
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19 <0.9.0;
import {FCL_Elliptic_ZZ} from "./FCL_elliptic.sol";
library FCL_ecdsa {
    // Set parameters for curve sec256r1.public
      //curve order (number of points)
    uint256 constant n = FCL_Elliptic_ZZ.n;
  
    /**
     * @dev ECDSA verification, given , signature, and public key.
     */
    /**
     * @dev ECDSA verification, given , signature, and public key, no calldata version
     */
    function ecdsa_verify(bytes32 message, uint256 r, uint256 s, uint256 Qx, uint256 Qy)  internal view returns (bool){
        if (r == 0 || r >= FCL_Elliptic_ZZ.n || s == 0 || s >= FCL_Elliptic_ZZ.n) {
            return false;
        }
        
        if (!FCL_Elliptic_ZZ.ecAff_isOnCurve(Qx, Qy)) {
            return false;
        }
        uint256 sInv = FCL_Elliptic_ZZ.FCL_nModInv(s);
        uint256 scalar_u = mulmod(uint256(message), sInv, FCL_Elliptic_ZZ.n);
        uint256 scalar_v = mulmod(r, sInv, FCL_Elliptic_ZZ.n);
        uint256 x1;
        x1 = FCL_Elliptic_ZZ.ecZZ_mulmuladd_S_asm(Qx, Qy, scalar_u, scalar_v);
        x1= addmod(x1, n-r,n );
    
        return x1 == 0;
    }
    function ec_recover_r1(uint256 h, uint256 v, uint256 r, uint256 s) internal view returns (address)
    {
         if (r == 0 || r >= FCL_Elliptic_ZZ.n || s == 0 || s >= FCL_Elliptic_ZZ.n) {
            return address(0);
        }
        uint256 y=FCL_Elliptic_ZZ.ec_Decompress(r, v-27);
        uint256 rinv=FCL_Elliptic_ZZ.FCL_nModInv(r);
        uint256 u1=mulmod(FCL_Elliptic_ZZ.n-addmod(0,h,FCL_Elliptic_ZZ.n), rinv,FCL_Elliptic_ZZ.n);//-hr^-1
        uint256 u2=mulmod(s, rinv,FCL_Elliptic_ZZ.n);//sr^-1
        uint256 Qx;
        uint256 Qy;
        (Qx,Qy)=FCL_Elliptic_ZZ.ecZZ_mulmuladd(r,y, u1, u2);
        return address(uint160(uint256(keccak256(abi.encodePacked(Qx, Qy)))));
    }
    function ecdsa_precomputed_verify(bytes32 message, uint256 r, uint256 s, address Shamir8)
        internal view
        returns (bool)
    {
       
        if (r == 0 || r >= n || s == 0 || s >= n) {
            return false;
        }
        /* Q is pushed via the contract at address Shamir8 assumed to be correct
        if (!isOnCurve(Q[0], Q[1])) {
            return false;
        }*/
        uint256 sInv = FCL_Elliptic_ZZ.FCL_nModInv(s);
        uint256 X;
        //Shamir 8 dimensions
        X = FCL_Elliptic_ZZ.ecZZ_mulmuladd_S8_extcode(mulmod(uint256(message), sInv, n), mulmod(r, sInv, n), Shamir8);
        X= addmod(X, n-r,n );
        return X == 0;
    } //end  ecdsa_precomputed_verify()
     function ecdsa_precomputed_verify(bytes32 message, uint256[2] calldata rs, address Shamir8)
        internal view
        returns (bool)
    {
        uint256 r = rs[0];
        uint256 s = rs[1];
        if (r == 0 || r >= n || s == 0 || s >= n) {
            return false;
        }
        /* Q is pushed via the contract at address Shamir8 assumed to be correct
        if (!isOnCurve(Q[0], Q[1])) {
            return false;
        }*/
        uint256 sInv = FCL_Elliptic_ZZ.FCL_nModInv(s);
        uint256 X;
        //Shamir 8 dimensions
        X = FCL_Elliptic_ZZ.ecZZ_mulmuladd_S8_extcode(mulmod(uint256(message), sInv, n), mulmod(r, sInv, n), Shamir8);
        X= addmod(X, n-r,n );
        return X == 0;
    } //end  ecdsa_precomputed_verify()
}
//********************************************************************************************/
//  ___           _       ___               _         _    _ _
// | __| _ ___ __| |_    / __|_ _ _  _ _ __| |_ ___  | |  (_) |__
// | _| '_/ -_|_-< ' \\  | (__| '_| || | '_ \\  _/ _ \\ | |__| | '_ \\
// |_||_| \\___/__/_||_|  \\___|_|  \\_, | .__/\\__\\___/ |____|_|_.__/
//                                |__/|_|
///* Copyright (C) 2022 - Renaud Dubois - This file is part of FCL (Fresh CryptoLib) project
///* License: This software is licensed under MIT License
///* This Code may be reused including license and copyright notice.
///* See LICENSE file at the root folder of the project.
///* FILE: FCL_elliptic.sol
///*
///*
///* DESCRIPTION: modified XYZZ system coordinates for EVM elliptic point multiplication
///*  optimization
///*
//**************************************************************************************/
//* WARNING: this code SHALL not be used for non prime order curves for security reasons.
// Code is optimized for a=-3 only curves with prime order, constant like -1, -2 shall be replaced
// if ever used for other curve than sec256R1
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19 <0.9.0;
library FCL_Elliptic_ZZ {
    // Set parameters for curve sec256r1.
    // address of the ModExp precompiled contract (Arbitrary-precision exponentiation under modulo)
    address constant MODEXP_PRECOMPILE = 0x0000000000000000000000000000000000000005;
    //curve prime field modulus
    uint256 constant p = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF;
    //short weierstrass first coefficient
    uint256 constant a = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC;
    //short weierstrass second coefficient
    uint256 constant b = 0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B;
    //generating point affine coordinates
    uint256 constant gx = 0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296;
    uint256 constant gy = 0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5;
    //curve order (number of points)
    uint256 constant n = 0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551;
    /* -2 mod p constant, used to speed up inversion and doubling (avoid negation)*/
    uint256 constant minus_2 = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFD;
    /* -2 mod n constant, used to speed up inversion*/
    uint256 constant minus_2modn = 0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC63254F;
    uint256 constant minus_1 = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
    //P+1 div 4
    uint256 constant pp1div4=0x3fffffffc0000000400000000000000000000000400000000000000000000000;
    //arbitrary constant to express no quadratic residuosity
    uint256 constant _NOTSQUARE=0xFFFFFFFF00000002000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF;
    uint256 constant _NOTONCURVE=0xFFFFFFFF00000003000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF;
    /**
     * /* inversion mod n via a^(n-2), use of precompiled using little Fermat theorem
     */
    function FCL_nModInv(uint256 u) internal view returns (uint256 result) {
        assembly {
            let pointer := mload(0x40)
            // Define length of base, exponent and modulus. 0x20 == 32 bytes
            mstore(pointer, 0x20)
            mstore(add(pointer, 0x20), 0x20)
            mstore(add(pointer, 0x40), 0x20)
            // Define variables base, exponent and modulus
            mstore(add(pointer, 0x60), u)
            mstore(add(pointer, 0x80), minus_2modn)
            mstore(add(pointer, 0xa0), n)
            // Call the precompiled contract 0x05 = ModExp
            if iszero(staticcall(not(0), 0x05, pointer, 0xc0, pointer, 0x20)) { revert(0, 0) }
            result := mload(pointer)
        }
    }
    /**
     * /* @dev inversion mod nusing little Fermat theorem via a^(n-2), use of precompiled
     */
    function FCL_pModInv(uint256 u) internal view returns (uint256 result) {
        assembly {
            let pointer := mload(0x40)
            // Define length of base, exponent and modulus. 0x20 == 32 bytes
            mstore(pointer, 0x20)
            mstore(add(pointer, 0x20), 0x20)
            mstore(add(pointer, 0x40), 0x20)
            // Define variables base, exponent and modulus
            mstore(add(pointer, 0x60), u)
            mstore(add(pointer, 0x80), minus_2)
            mstore(add(pointer, 0xa0), p)
            // Call the precompiled contract 0x05 = ModExp
            if iszero(staticcall(not(0), 0x05, pointer, 0xc0, pointer, 0x20)) { revert(0, 0) }
            result := mload(pointer)
        }
    }
    //Coron projective shuffling, take as input alpha as blinding factor
   function ecZZ_Coronize(uint256 alpha, uint256 x, uint256 y,  uint256 zz, uint256 zzz) internal pure  returns (uint256 x3, uint256 y3, uint256 zz3, uint256 zzz3)
   {
       
        uint256 alpha2=mulmod(alpha,alpha,p);
       
        x3=mulmod(alpha2, x,p); //alpha^-2.x
        y3=mulmod(mulmod(alpha, alpha2,p), y,p);
        zz3=mulmod(zz,alpha2,p);//alpha^2 zz
        zzz3=mulmod(zzz,mulmod(alpha, alpha2,p),p);//alpha^3 zzz
        
        return (x3, y3, zz3, zzz3);
   }
 function ecZZ_Add(uint256 x1, uint256 y1, uint256 zz1, uint256 zzz1, uint256 x2, uint256 y2, uint256 zz2, uint256 zzz2) internal pure  returns (uint256 x3, uint256 y3, uint256 zz3, uint256 zzz3)
  {
    uint256 u1=mulmod(x1,zz2,p); // U1 = X1*ZZ2
    uint256 u2=mulmod(x2, zz1,p);               //  U2 = X2*ZZ1
    u2=addmod(u2, p-u1, p);//  P = U2-U1
    x1=mulmod(u2, u2, p);//PP
    x2=mulmod(x1, u2, p);//PPP
    
    zz3=mulmod(x1, mulmod(zz1, zz2, p),p);//ZZ3 = ZZ1*ZZ2*PP  
    zzz3=mulmod(zzz1, mulmod(zzz2, x2, p),p);//ZZZ3 = ZZZ1*ZZZ2*PPP
    zz1=mulmod(y1, zzz2,p);  // S1 = Y1*ZZZ2
    zz2=mulmod(y2, zzz1, p);    // S2 = Y2*ZZZ1 
    zz2=addmod(zz2, p-zz1, p);//R = S2-S1
    zzz1=mulmod(u1, x1,p); //Q = U1*PP
    x3= addmod(addmod(mulmod(zz2, zz2, p), p-x2,p), mulmod(minus_2, zzz1,p),p); //X3 = R2-PPP-2*Q
    y3=addmod( mulmod(zz2, addmod(zzz1, p-x3, p),p), p-mulmod(zz1, x2, p),p);//R*(Q-X3)-S1*PPP
    return (x3, y3, zz3, zzz3);
  }
/// @notice Calculate one modular square root of a given integer. Assume that p=3 mod 4.
/// @dev Uses the ModExp precompiled contract at address 0x05 for fast computation using little Fermat theorem
/// @param self The integer of which to find the modular inverse
/// @return result The modular inverse of the input integer. If the modular inverse doesn't exist, it revert the tx
function SqrtMod(uint256 self) internal view returns (uint256 result){
 assembly ("memory-safe") {
        // load the free memory pointer value
        let pointer := mload(0x40)
        // Define length of base (Bsize)
        mstore(pointer, 0x20)
        // Define the exponent size (Esize)
        mstore(add(pointer, 0x20), 0x20)
        // Define the modulus size (Msize)
        mstore(add(pointer, 0x40), 0x20)
        // Define variables base (B)
        mstore(add(pointer, 0x60), self)
        // Define the exponent (E)
        mstore(add(pointer, 0x80), pp1div4)
        // We save the point of the last argument, it will be override by the result
        // of the precompile call in order to avoid paying for the memory expansion properly
        let _result := add(pointer, 0xa0)
        // Define the modulus (M)
        mstore(_result, p)
        // Call the precompiled ModExp (0x05) https://www.evm.codes/precompiled#0x05
        if iszero(
            staticcall(
                not(0), // amount of gas to send
                MODEXP_PRECOMPILE, // target
                pointer, // argsOffset
                0xc0, // argsSize (6 * 32 bytes)
                _result, // retOffset (we override M to avoid paying for the memory expansion)
                0x20 // retSize (32 bytes)
            )
        ) { revert(0, 0) }
  result := mload(_result)
//  result :=addmod(result,0,p)
 }
   if(mulmod(result,result,p)!=self){
     result=_NOTSQUARE;
   }
  
   return result;
}
    /**
     * /* @dev Convert from affine rep to XYZZ rep
     */
    function ecAff_SetZZ(uint256 x0, uint256 y0) internal pure returns (uint256[4] memory P) {
        unchecked {
            P[2] = 1; //ZZ
            P[3] = 1; //ZZZ
            P[0] = x0;
            P[1] = y0;
        }
    }
    function ec_Decompress(uint256 x, uint256 parity) internal view returns(uint256 y){ 
        uint256 y2=mulmod(x,mulmod(x,x,p),p);//x3
        y2=addmod(b,addmod(y2,mulmod(x,a,p),p),p);//x3+ax+b
        y=SqrtMod(y2);
        if(y==_NOTSQUARE){
           return _NOTONCURVE;
        }
        if((y&1)!=(parity&1)){
            y=p-y;
        }
    }
    /**
     * /* @dev Convert from XYZZ rep to affine rep
     */
    /*    https://hyperelliptic.org/EFD/g1p/auto-shortw-xyzz-3.html#addition-add-2008-s*/
    function ecZZ_SetAff(uint256 x, uint256 y, uint256 zz, uint256 zzz) internal view returns (uint256 x1, uint256 y1) {
        uint256 zzzInv = FCL_pModInv(zzz); //1/zzz
        y1 = mulmod(y, zzzInv, p); //Y/zzz
        uint256 _b = mulmod(zz, zzzInv, p); //1/z
        zzzInv = mulmod(_b, _b, p); //1/zz
        x1 = mulmod(x, zzzInv, p); //X/zz
    }
    /**
     * /* @dev Sutherland2008 doubling
     */
    /* The "dbl-2008-s-1" doubling formulas */
    function ecZZ_Dbl(uint256 x, uint256 y, uint256 zz, uint256 zzz)
        internal
        pure
        returns (uint256 P0, uint256 P1, uint256 P2, uint256 P3)
    {
        unchecked {
            assembly {
                P0 := mulmod(2, y, p) //U = 2*Y1
                P2 := mulmod(P0, P0, p) // V=U^2
                P3 := mulmod(x, P2, p) // S = X1*V
                P1 := mulmod(P0, P2, p) // W=UV
                P2 := mulmod(P2, zz, p) //zz3=V*ZZ1
                zz := mulmod(3, mulmod(addmod(x, sub(p, zz), p), addmod(x, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                P0 := addmod(mulmod(zz, zz, p), mulmod(minus_2, P3, p), p) //X3=M^2-2S
                x := mulmod(zz, addmod(P3, sub(p, P0), p), p) //M(S-X3)
                P3 := mulmod(P1, zzz, p) //zzz3=W*zzz1
                P1 := addmod(x, sub(p, mulmod(P1, y, p)), p) //Y3= M(S-X3)-W*Y1
            }
        }
        return (P0, P1, P2, P3);
    }
    /**
     * @dev Sutherland2008 add a ZZ point with a normalized point and greedy formulae
     * warning: assume that P1(x1,y1)!=P2(x2,y2), true in multiplication loop with prime order (cofactor 1)
     */
    function ecZZ_AddN(uint256 x1, uint256 y1, uint256 zz1, uint256 zzz1, uint256 x2, uint256 y2)
        internal
        pure
        returns (uint256 P0, uint256 P1, uint256 P2, uint256 P3)
    {
        unchecked {
            if (y1 == 0) {
                return (x2, y2, 1, 1);
            }
            assembly {
                y1 := sub(p, y1)
                y2 := addmod(mulmod(y2, zzz1, p), y1, p)
                x2 := addmod(mulmod(x2, zz1, p), sub(p, x1), p)
                P0 := mulmod(x2, x2, p) //PP = P^2
                P1 := mulmod(P0, x2, p) //PPP = P*PP
                P2 := mulmod(zz1, P0, p) ////ZZ3 = ZZ1*PP
                P3 := mulmod(zzz1, P1, p) ////ZZZ3 = ZZZ1*PPP
                zz1 := mulmod(x1, P0, p) //Q = X1*PP
                P0 := addmod(addmod(mulmod(y2, y2, p), sub(p, P1), p), mulmod(minus_2, zz1, p), p) //R^2-PPP-2*Q
                P1 := addmod(mulmod(addmod(zz1, sub(p, P0), p), y2, p), mulmod(y1, P1, p), p) //R*(Q-X3)
            }
            //end assembly
        } //end unchecked
        return (P0, P1, P2, P3);
    }
    /**
     * @dev Return the zero curve in XYZZ coordinates.
     */
    function ecZZ_SetZero() internal pure returns (uint256 x, uint256 y, uint256 zz, uint256 zzz) {
        return (0, 0, 0, 0);
    }
    /**
     * @dev Check if point is the neutral of the curve
     */
    // uint256 x0, uint256 y0, uint256 zz0, uint256 zzz0
    function ecZZ_IsZero(uint256, uint256 y0, uint256, uint256) internal pure returns (bool) {
        return y0 == 0;
    }
    /**
     * @dev Return the zero curve in affine coordinates. Compatible with the double formulae (no special case)
     */
    function ecAff_SetZero() internal pure returns (uint256 x, uint256 y) {
        return (0, 0);
    }
    /**
     * @dev Check if the curve is the zero curve in affine rep.
     */
    // uint256 x, uint256 y)
    function ecAff_IsZero(uint256, uint256 y) internal pure returns (bool flag) {
        return (y == 0);
    }
    /**
     * @dev Check if a point in affine coordinates is on the curve (reject Neutral that is indeed on the curve).
     */
    function ecAff_isOnCurve(uint256 x, uint256 y) internal pure returns (bool) {
        if (x >= p || y >= p || ((x == 0) && (y == 0))) {
            return false;
        }
        unchecked {
            uint256 LHS = mulmod(y, y, p); // y^2
            uint256 RHS = addmod(mulmod(mulmod(x, x, p), x, p), mulmod(x, a, p), p); // x^3+ax
            RHS = addmod(RHS, b, p); // x^3 + a*x + b
            return LHS == RHS;
        }
    }
    /**
     * @dev Add two elliptic curve points in affine coordinates. Deal with P=Q
     */
    function ecAff_add(uint256 x0, uint256 y0, uint256 x1, uint256 y1) internal view returns (uint256, uint256) {
        uint256 zz0;
        uint256 zzz0;
        if (ecAff_IsZero(x0, y0)) return (x1, y1);
        if (ecAff_IsZero(x1, y1)) return (x0, y0);
        if((x0==x1)&&(y0==y1)) {
            (x0, y0, zz0, zzz0) = ecZZ_Dbl(x0, y0,1,1);
        }
        else{
            (x0, y0, zz0, zzz0) = ecZZ_AddN(x0, y0, 1, 1, x1, y1);
        }
        return ecZZ_SetAff(x0, y0, zz0, zzz0);
    }
    /**
     * @dev Computation of uG+vQ using Strauss-Shamir's trick, G basepoint, Q public key
     *       Returns only x for ECDSA use            
     *      */
    function ecZZ_mulmuladd_S_asm(
        uint256 Q0,
        uint256 Q1, //affine rep for input point Q
        uint256 scalar_u,
        uint256 scalar_v
    ) internal view returns (uint256 X) {
        uint256 zz;
        uint256 zzz;
        uint256 Y;
        uint256 index = 255;
        uint256 H0;
        uint256 H1;
        unchecked {
            if (scalar_u == 0 && scalar_v == 0) return 0;
            (H0, H1) = ecAff_add(gx, gy, Q0, Q1); 
            if((H0==0)&&(H1==0))//handling Q=-G
            {
                scalar_u=addmod(scalar_u, n-scalar_v, n);
                scalar_v=0;
                if (scalar_u == 0 && scalar_v == 0) return 0;
            }
            assembly {
                for { let T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1)) } eq(T4, 0) {
                    index := sub(index, 1)
                    T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                } {}
                zz := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                if eq(zz, 1) {
                    X := gx
                    Y := gy
                }
                if eq(zz, 2) {
                    X := Q0
                    Y := Q1
                }
                if eq(zz, 3) {
                    X := H0
                    Y := H1
                }
                index := sub(index, 1)
                zz := 1
                zzz := 1
                for {} gt(minus_1, index) { index := sub(index, 1) } {
                    // inlined EcZZ_Dbl
                    let T1 := mulmod(2, Y, p) //U = 2*Y1, y free
                    let T2 := mulmod(T1, T1, p) // V=U^2
                    let T3 := mulmod(X, T2, p) // S = X1*V
                    T1 := mulmod(T1, T2, p) // W=UV
                    let T4 := mulmod(3, mulmod(addmod(X, sub(p, zz), p), addmod(X, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                    zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                    zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                    X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                    T2 := mulmod(T4, addmod(X, sub(p, T3), p), p) //-M(S-X3)=M(X3-S)
                    Y := addmod(mulmod(T1, Y, p), T2, p) //-Y3= W*Y1-M(S-X3), we replace Y by -Y to avoid a sub in ecAdd
                    {
                        //value of dibit
                        T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                        if iszero(T4) {
                            Y := sub(p, Y) //restore the -Y inversion
                            continue
                        } // if T4!=0
                        if eq(T4, 1) {
                            T1 := gx
                            T2 := gy
                        }
                        if eq(T4, 2) {
                            T1 := Q0
                            T2 := Q1
                        }
                        if eq(T4, 3) {
                            T1 := H0
                            T2 := H1
                        }
                        if iszero(zz) {
                            X := T1
                            Y := T2
                            zz := 1
                            zzz := 1
                            continue
                        }
                        // inlined EcZZ_AddN
                        //T3:=sub(p, Y)
                        //T3:=Y
                        let y2 := addmod(mulmod(T2, zzz, p), Y, p) //R
                        T2 := addmod(mulmod(T1, zz, p), sub(p, X), p) //P
                        //special extremely rare case accumulator where EcAdd is replaced by EcDbl, no need to optimize this
                        //todo : construct edge vector case
                        if iszero(y2) {
                            if iszero(T2) {
                                T1 := mulmod(minus_2, Y, p) //U = 2*Y1, y free
                                T2 := mulmod(T1, T1, p) // V=U^2
                                T3 := mulmod(X, T2, p) // S = X1*V
                                T1 := mulmod(T1, T2, p) // W=UV
                                y2 := mulmod(addmod(X, zz, p), addmod(X, sub(p, zz), p), p) //(X-ZZ)(X+ZZ)
                                T4 := mulmod(3, y2, p) //M=3*(X-ZZ)(X+ZZ)
                                zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                                zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                                X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                                T2 := mulmod(T4, addmod(T3, sub(p, X), p), p) //M(S-X3)
                                Y := addmod(T2, mulmod(T1, Y, p), p) //Y3= M(S-X3)-W*Y1
                                continue
                            }
                        }
                        T4 := mulmod(T2, T2, p) //PP
                        let TT1 := mulmod(T4, T2, p) //PPP, this one could be spared, but adding this register spare gas
                        zz := mulmod(zz, T4, p)
                        zzz := mulmod(zzz, TT1, p) //zz3=V*ZZ1
                        let TT2 := mulmod(X, T4, p)
                        T4 := addmod(addmod(mulmod(y2, y2, p), sub(p, TT1), p), mulmod(minus_2, TT2, p), p)
                        Y := addmod(mulmod(addmod(TT2, sub(p, T4), p), y2, p), mulmod(Y, TT1, p), p)
                        X := T4
                    }
                } //end loop
                let T := mload(0x40)
                mstore(add(T, 0x60), zz)
                //(X,Y)=ecZZ_SetAff(X,Y,zz, zzz);
                //T[0] = inverseModp_Hard(T[0], p); //1/zzz, inline modular inversion using precompile:
                // Define length of base, exponent and modulus. 0x20 == 32 bytes
                mstore(T, 0x20)
                mstore(add(T, 0x20), 0x20)
                mstore(add(T, 0x40), 0x20)
                // Define variables base, exponent and modulus
                //mstore(add(pointer, 0x60), u)
                mstore(add(T, 0x80), minus_2)
                mstore(add(T, 0xa0), p)
                // Call the precompiled contract 0x05 = ModExp
                if iszero(staticcall(not(0), 0x05, T, 0xc0, T, 0x20)) { revert(0, 0) }
                //Y:=mulmod(Y,zzz,p)//Y/zzz
                //zz :=mulmod(zz, mload(T),p) //1/z
                //zz:= mulmod(zz,zz,p) //1/zz
                X := mulmod(X, mload(T), p) //X/zz
            } //end assembly
        } //end unchecked
        return X;
    }
    /**
     * @dev Computation of uG+vQ using Strauss-Shamir's trick, G basepoint, Q public key
     *       Returns affine representation of point (normalized)       
     *      */
    function ecZZ_mulmuladd(
        uint256 Q0,
        uint256 Q1, //affine rep for input point Q
        uint256 scalar_u,
        uint256 scalar_v
    ) internal view returns (uint256 X, uint256 Y) {
        uint256 zz;
        uint256 zzz;
        uint256 index = 255;
        uint256[6] memory T;
        uint256[2] memory H;
 
        unchecked {
            if (scalar_u == 0 && scalar_v == 0) return (0,0);
            (H[0], H[1]) = ecAff_add(gx, gy, Q0, Q1); //will not work if Q=P, obvious forbidden private key
            assembly {
                for { let T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1)) } eq(T4, 0) {
                    index := sub(index, 1)
                    T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                } {}
                zz := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                if eq(zz, 1) {
                    X := gx
                    Y := gy
                }
                if eq(zz, 2) {
                    X := Q0
                    Y := Q1
                }
                if eq(zz, 3) {
                    Y := mload(add(H,32))
                    X := mload(H)
                }
                index := sub(index, 1)
                zz := 1
                zzz := 1
                for {} gt(minus_1, index) { index := sub(index, 1) } {
                    // inlined EcZZ_Dbl
                    let T1 := mulmod(2, Y, p) //U = 2*Y1, y free
                    let T2 := mulmod(T1, T1, p) // V=U^2
                    let T3 := mulmod(X, T2, p) // S = X1*V
                    T1 := mulmod(T1, T2, p) // W=UV
                    let T4 := mulmod(3, mulmod(addmod(X, sub(p, zz), p), addmod(X, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                    zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                    zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                    X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                    T2 := mulmod(T4, addmod(X, sub(p, T3), p), p) //-M(S-X3)=M(X3-S)
                    Y := addmod(mulmod(T1, Y, p), T2, p) //-Y3= W*Y1-M(S-X3), we replace Y by -Y to avoid a sub in ecAdd
                    {
                        //value of dibit
                        T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                        if iszero(T4) {
                            Y := sub(p, Y) //restore the -Y inversion
                            continue
                        } // if T4!=0
                        if eq(T4, 1) {
                            T1 := gx
                            T2 := gy
                        }
                        if eq(T4, 2) {
                            T1 := Q0
                            T2 := Q1
                        }
                        if eq(T4, 3) {
                            T1 := mload(H)
                            T2 := mload(add(H,32))
                        }
                        if iszero(zz) {
                            X := T1
                            Y := T2
                            zz := 1
                            zzz := 1
                            continue
                        }
                        // inlined EcZZ_AddN
                        //T3:=sub(p, Y)
                        //T3:=Y
                        let y2 := addmod(mulmod(T2, zzz, p), Y, p) //R
                        T2 := addmod(mulmod(T1, zz, p), sub(p, X), p) //P
                        //special extremely rare case accumulator where EcAdd is replaced by EcDbl, no need to optimize this
                        //todo : construct edge vector case
                        if iszero(y2) {
                            if iszero(T2) {
                                T1 := mulmod(minus_2, Y, p) //U = 2*Y1, y free
                                T2 := mulmod(T1, T1, p) // V=U^2
                                T3 := mulmod(X, T2, p) // S = X1*V
                                T1 := mulmod(T1, T2, p) // W=UV
                                y2 := mulmod(addmod(X, zz, p), addmod(X, sub(p, zz), p), p) //(X-ZZ)(X+ZZ)
                                T4 := mulmod(3, y2, p) //M=3*(X-ZZ)(X+ZZ)
                                zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                                zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                                X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                                T2 := mulmod(T4, addmod(T3, sub(p, X), p), p) //M(S-X3)
                                Y := addmod(T2, mulmod(T1, Y, p), p) //Y3= M(S-X3)-W*Y1
                                continue
                            }
                        }
                        T4 := mulmod(T2, T2, p) //PP
                        let TT1 := mulmod(T4, T2, p) //PPP, this one could be spared, but adding this register spare gas
                        zz := mulmod(zz, T4, p)
                        zzz := mulmod(zzz, TT1, p) //zz3=V*ZZ1
                        let TT2 := mulmod(X, T4, p)
                        T4 := addmod(addmod(mulmod(y2, y2, p), sub(p, TT1), p), mulmod(minus_2, TT2, p), p)
                        Y := addmod(mulmod(addmod(TT2, sub(p, T4), p), y2, p), mulmod(Y, TT1, p), p)
                        X := T4
                    }
                } //end loop
                mstore(add(T, 0x60), zzz)
                //(X,Y)=ecZZ_SetAff(X,Y,zz, zzz);
                //T[0] = inverseModp_Hard(T[0], p); //1/zzz, inline modular inversion using precompile:
                // Define length of base, exponent and modulus. 0x20 == 32 bytes
                mstore(T, 0x20)
                mstore(add(T, 0x20), 0x20)
                mstore(add(T, 0x40), 0x20)
                // Define variables base, exponent and modulus
                //mstore(add(pointer, 0x60), u)
                mstore(add(T, 0x80), minus_2)
                mstore(add(T, 0xa0), p)
                // Call the precompiled contract 0x05 = ModExp
                if iszero(staticcall(not(0), 0x05, T, 0xc0, T, 0x20)) { revert(0, 0) }
                Y:=mulmod(Y,mload(T),p)//Y/zzz
                zz :=mulmod(zz, mload(T),p) //1/z
                zz:= mulmod(zz,zz,p) //1/zz
                X := mulmod(X, zz, p) //X/zz
            } //end assembly
        } //end unchecked
        return (X,Y);
    }
    //8 dimensions Shamir's trick, using precomputations stored in Shamir8,  stored as Bytecode of an external
    //contract at given address dataPointer
    //(thx to Lakhdar https://github.com/Kelvyne for EVM storage explanations and tricks)
    // the external tool to generate tables from public key is in the /sage directory
    function ecZZ_mulmuladd_S8_extcode(uint256 scalar_u, uint256 scalar_v, address dataPointer)
        internal view
        returns (uint256 X /*, uint Y*/ )
    {
        unchecked {
            uint256 zz; // third and  coordinates of the point
            uint256[6] memory T;
            zz = 256; //start index
            while (T[0] == 0) {
                zz = zz - 1;
                //tbd case of msb octobit is null
                T[0] = 64
                    * (
                        128 * ((scalar_v >> zz) & 1) + 64 * ((scalar_v >> (zz - 64)) & 1)
                            + 32 * ((scalar_v >> (zz - 128)) & 1) + 16 * ((scalar_v >> (zz - 192)) & 1)
                            + 8 * ((scalar_u >> zz) & 1) + 4 * ((scalar_u >> (zz - 64)) & 1)
                            + 2 * ((scalar_u >> (zz - 128)) & 1) + ((scalar_u >> (zz - 192)) & 1)
                    );
            }
            assembly {
                extcodecopy(dataPointer, T, mload(T), 64)
                let index := sub(zz, 1)
                X := mload(T)
                let Y := mload(add(T, 32))
                let zzz := 1
                zz := 1
                //loop over 1/4 of scalars thx to Shamir's trick over 8 points
                for {} gt(index, 191) { index := add(index, 191) } {
                    //inline Double
                    {
                        let TT1 := mulmod(2, Y, p) //U = 2*Y1, y free
                        let T2 := mulmod(TT1, TT1, p) // V=U^2
                        let T3 := mulmod(X, T2, p) // S = X1*V
                        let T1 := mulmod(TT1, T2, p) // W=UV
                        let T4 := mulmod(3, mulmod(addmod(X, sub(p, zz), p), addmod(X, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                        zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                        zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                        X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                        //T2:=mulmod(T4,addmod(T3, sub(p, X),p),p)//M(S-X3)
                        let T5 := mulmod(T4, addmod(X, sub(p, T3), p), p) //-M(S-X3)=M(X3-S)
                        //Y:= addmod(T2, sub(p, mulmod(T1, Y ,p)),p  )//Y3= M(S-X3)-W*Y1
                        Y := addmod(mulmod(T1, Y, p), T5, p) //-Y3= W*Y1-M(S-X3), we replace Y by -Y to avoid a sub in ecAdd
                        /* compute element to access in precomputed table */
                    }
                    {
                        let T4 := add(shl(13, and(shr(index, scalar_v), 1)), shl(9, and(shr(index, scalar_u), 1)))
                        let index2 := sub(index, 64)
                        let T3 :=
                            add(T4, add(shl(12, and(shr(index2, scalar_v), 1)), shl(8, and(shr(index2, scalar_u), 1))))
                        let index3 := sub(index2, 64)
                        let T2 :=
                            add(T3, add(shl(11, and(shr(index3, scalar_v), 1)), shl(7, and(shr(index3, scalar_u), 1))))
                        index := sub(index3, 64)
                        let T1 :=
                            add(T2, add(shl(10, and(shr(index, scalar_v), 1)), shl(6, and(shr(index, scalar_u), 1))))
                        //tbd: check validity of formulae with (0,1) to remove conditional jump
                        if iszero(T1) {
                            Y := sub(p, Y)
                            continue
                        }
                        extcodecopy(dataPointer, T, T1, 64)
                    }
                    {
                        /* Access to precomputed table using extcodecopy hack */
                        // inlined EcZZ_AddN
                        if iszero(zz) {
                            X := mload(T)
                            Y := mload(add(T, 32))
                            zz := 1
                            zzz := 1
                            continue
                        }
                        let y2 := addmod(mulmod(mload(add(T, 32)), zzz, p), Y, p)
                        let T2 := addmod(mulmod(mload(T), zz, p), sub(p, X), p)
                        //special case ecAdd(P,P)=EcDbl
                        if iszero(y2) {
                            if iszero(T2) {
                                let T1 := mulmod(minus_2, Y, p) //U = 2*Y1, y free
                                T2 := mulmod(T1, T1, p) // V=U^2
                                let T3 := mulmod(X, T2, p) // S = X1*V
                                T1 := mulmod(T1, T2, p) // W=UV
                                y2 := mulmod(addmod(X, zz, p), addmod(X, sub(p, zz), p), p) //(X-ZZ)(X+ZZ)
                                let T4 := mulmod(3, y2, p) //M=3*(X-ZZ)(X+ZZ)
                                zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                                zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                                X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                                T2 := mulmod(T4, addmod(T3, sub(p, X), p), p) //M(S-X3)
                                Y := addmod(T2, mulmod(T1, Y, p), p) //Y3= M(S-X3)-W*Y1
                                continue
                            }
                        }
                        let T4 := mulmod(T2, T2, p)
                        let T1 := mulmod(T4, T2, p) //
                        zz := mulmod(zz, T4, p)
                        //zzz3=V*ZZ1
                        zzz := mulmod(zzz, T1, p) // W=UV/
                        let zz1 := mulmod(X, T4, p)
                        X := addmod(addmod(mulmod(y2, y2, p), sub(p, T1), p), mulmod(minus_2, zz1, p), p)
                        Y := addmod(mulmod(addmod(zz1, sub(p, X), p), y2, p), mulmod(Y, T1, p), p)
                    }
                } //end loop
                mstore(add(T, 0x60), zz)
                //(X,Y)=ecZZ_SetAff(X,Y,zz, zzz);
                //T[0] = inverseModp_Hard(T[0], p); //1/zzz, inline modular inversion using precompile:
                // Define length of base, exponent and modulus. 0x20 == 32 bytes
                mstore(T, 0x20)
                mstore(add(T, 0x20), 0x20)
                mstore(add(T, 0x40), 0x20)
                // Define variables base, exponent and modulus
                //mstore(add(pointer, 0x60), u)
                mstore(add(T, 0x80), minus_2)
                mstore(add(T, 0xa0), p)
                // Call the precompiled contract 0x05 = ModExp
                if iszero(staticcall(not(0), 0x05, T, 0xc0, T, 0x20)) { revert(0, 0) }
                zz := mload(T)
                X := mulmod(X, zz, p) //X/zz
            }
        } //end unchecked
    }
   
    // improving the extcodecopy trick : append array at end of contract
    function ecZZ_mulmuladd_S8_hackmem(uint256 scalar_u, uint256 scalar_v, uint256 dataPointer)
        internal view
        returns (uint256 X /*, uint Y*/ )
    {
        uint256 zz; // third and  coordinates of the point
        uint256[6] memory T;
        zz = 256; //start index
        unchecked {
            while (T[0] == 0) {
                zz = zz - 1;
                //tbd case of msb octobit is null
                T[0] = 64
                    * (
                        128 * ((scalar_v >> zz) & 1) + 64 * ((scalar_v >> (zz - 64)) & 1)
                            + 32 * ((scalar_v >> (zz - 128)) & 1) + 16 * ((scalar_v >> (zz - 192)) & 1)
                            + 8 * ((scalar_u >> zz) & 1) + 4 * ((scalar_u >> (zz - 64)) & 1)
                            + 2 * ((scalar_u >> (zz - 128)) & 1) + ((scalar_u >> (zz - 192)) & 1)
                    );
            }
            assembly {
                codecopy(T, add(mload(T), dataPointer), 64)
                X := mload(T)
                let Y := mload(add(T, 32))
                let zzz := 1
                zz := 1
                //loop over 1/4 of scalars thx to Shamir's trick over 8 points
                for { let index := 254 } gt(index, 191) { index := add(index, 191) } {
                    let T1 := mulmod(2, Y, p) //U = 2*Y1, y free
                    let T2 := mulmod(T1, T1, p) // V=U^2
                    let T3 := mulmod(X, T2, p) // S = X1*V
                    T1 := mulmod(T1, T2, p) // W=UV
                    let T4 := mulmod(3, mulmod(addmod(X, sub(p, zz), p), addmod(X, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                    zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                    zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                    X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                    //T2:=mulmod(T4,addmod(T3, sub(p, X),p),p)//M(S-X3)
                    T2 := mulmod(T4, addmod(X, sub(p, T3), p), p) //-M(S-X3)=M(X3-S)
                    //Y:= addmod(T2, sub(p, mulmod(T1, Y ,p)),p  )//Y3= M(S-X3)-W*Y1
                    Y := addmod(mulmod(T1, Y, p), T2, p) //-Y3= W*Y1-M(S-X3), we replace Y by -Y to avoid a sub in ecAdd
                    /* compute element to access in precomputed table */
                    T4 := add(shl(13, and(shr(index, scalar_v), 1)), shl(9, and(shr(index, scalar_u), 1)))
                    index := sub(index, 64)
                    T4 := add(T4, add(shl(12, and(shr(index, scalar_v), 1)), shl(8, and(shr(index, scalar_u), 1))))
                    index := sub(index, 64)
                    T4 := add(T4, add(shl(11, and(shr(index, scalar_v), 1)), shl(7, and(shr(index, scalar_u), 1))))
                    index := sub(index, 64)
                    T4 := add(T4, add(shl(10, and(shr(index, scalar_v), 1)), shl(6, and(shr(index, scalar_u), 1))))
                    //index:=add(index,192), restore index, interleaved with loop
                    //tbd: check validity of formulae with (0,1) to remove conditional jump
                    if iszero(T4) {
                        Y := sub(p, Y)
                        continue
                    }
                    {
                        /* Access to precomputed table using extcodecopy hack */
                        codecopy(T, add(T4, dataPointer), 64)
                        // inlined EcZZ_AddN
                        let y2 := addmod(mulmod(mload(add(T, 32)), zzz, p), Y, p)
                        T2 := addmod(mulmod(mload(T), zz, p), sub(p, X), p)
                        T4 := mulmod(T2, T2, p)
                        T1 := mulmod(T4, T2, p)
                        T2 := mulmod(zz, T4, p) // W=UV
                        zzz := mulmod(zzz, T1, p) //zz3=V*ZZ1
                        let zz1 := mulmod(X, T4, p)
                        T4 := addmod(addmod(mulmod(y2, y2, p), sub(p, T1), p), mulmod(minus_2, zz1, p), p)
                        Y := addmod(mulmod(addmod(zz1, sub(p, T4), p), y2, p), mulmod(Y, T1, p), p)
                        zz := T2
                        X := T4
                    }
                } //end loop
                mstore(add(T, 0x60), zz)
                //(X,Y)=ecZZ_SetAff(X,Y,zz, zzz);
                //T[0] = inverseModp_Hard(T[0], p); //1/zzz, inline modular inversion using precompile:
                // Define length of base, exponent and modulus. 0x20 == 32 bytes
                mstore(T, 0x20)
                mstore(add(T, 0x20), 0x20)
                mstore(add(T, 0x40), 0x20)
                // Define variables base, exponent and modulus
                //mstore(add(pointer, 0x60), u)
                mstore(add(T, 0x80), minus_2)
                mstore(add(T, 0xa0), p)
                // Call the precompiled contract 0x05 = ModExp
                if iszero(staticcall(not(0), 0x05, T, 0xc0, T, 0x20)) { revert(0, 0) }
                zz := mload(T)
                X := mulmod(X, zz, p) //X/zz
            }
        } //end unchecked
    }
    /**
     * @dev ECDSA verification using a precomputed table of multiples of P and Q stored in contract at address Shamir8
     *     generation of contract bytecode for precomputations is done using sagemath code
     *     (see sage directory, WebAuthn_precompute.sage)
     */
    /**
     * @dev ECDSA verification using a precomputed table of multiples of P and Q appended at end of contract at address endcontract
     *     generation of contract bytecode for precomputations is done using sagemath code
     *     (see sage directory, WebAuthn_precompute.sage)
     */
    function ecdsa_precomputed_hackmem(bytes32 message, uint256[2] calldata rs, uint256 endcontract)
        internal view
        returns (bool)
    {
        uint256 r = rs[0];
        uint256 s = rs[1];
        if (r == 0 || r >= n || s == 0 || s >= n) {
            return false;
        }
        /* Q is pushed via bytecode assumed to be correct
        if (!isOnCurve(Q[0], Q[1])) {
            return false;
        }*/
        uint256 sInv = FCL_nModInv(s);
        uint256 X;
        //Shamir 8 dimensions
        X = ecZZ_mulmuladd_S8_hackmem(mulmod(uint256(message), sInv, n), mulmod(r, sInv, n), endcontract);
        assembly {
            X := addmod(X, sub(n, r), n)
        }
        return X == 0;
    } //end  ecdsa_precomputed_verify()
} //EOF
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.2) (utils/Base64.sol)
pragma solidity ^0.8.20;
/**
 * @dev Provides a set of functions to operate with Base64 strings.
 */
library Base64 {
    /**
     * @dev Base64 Encoding/Decoding Table
     * See sections 4 and 5 of https://datatracker.ietf.org/doc/html/rfc4648
     */
    string internal constant _TABLE = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
    string internal constant _TABLE_URL = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789-_";
    /**
     * @dev Converts a `bytes` to its Bytes64 `string` representation.
     */
    function encode(bytes memory data) internal pure returns (string memory) {
        return _encode(data, _TABLE, true);
    }
    /**
     * @dev Converts a `bytes` to its Bytes64Url `string` representation.
     */
    function encodeURL(bytes memory data) internal pure returns (string memory) {
        return _encode(data, _TABLE_URL, false);
    }
    /**
     * @dev Internal table-agnostic conversion
     */
    function _encode(bytes memory data, string memory table, bool withPadding) private pure returns (string memory) {
        /**
         * Inspired by Brecht Devos (Brechtpd) implementation - MIT licence
         * https://github.com/Brechtpd/base64/blob/e78d9fd951e7b0977ddca77d92dc85183770daf4/base64.sol
         */
        if (data.length == 0) return "";
        // If padding is enabled, the final length should be `bytes` data length divided by 3 rounded up and then
        // multiplied by 4 so that it leaves room for padding the last chunk
        // - `data.length + 2`  -> Round up
        // - `/ 3`              -> Number of 3-bytes chunks
        // - `4 *`              -> 4 characters for each chunk
        // If padding is disabled, the final length should be `bytes` data length multiplied by 4/3 rounded up as
        // opposed to when padding is required to fill the last chunk.
        // - `4 *`              -> 4 characters for each chunk
        // - `data.length + 2`  -> Round up
        // - `/ 3`              -> Number of 3-bytes chunks
        uint256 resultLength = withPadding ? 4 * ((data.length + 2) / 3) : (4 * data.length + 2) / 3;
        string memory result = new string(resultLength);
        /// @solidity memory-safe-assembly
        assembly {
            // Prepare the lookup table (skip the first "length" byte)
            let tablePtr := add(table, 1)
            // Prepare result pointer, jump over length
            let resultPtr := add(result, 0x20)
            let dataPtr := data
            let endPtr := add(data, mload(data))
            // In some cases, the last iteration will read bytes after the end of the data. We cache the value, and
            // set it to zero to make sure no dirty bytes are read in that section.
            let afterPtr := add(endPtr, 0x20)
            let afterCache := mload(afterPtr)
            mstore(afterPtr, 0x00)
            // Run over the input, 3 bytes at a time
            for {
            } lt(dataPtr, endPtr) {
            } {
                // Advance 3 bytes
                dataPtr := add(dataPtr, 3)
                let input := mload(dataPtr)
                // To write each character, shift the 3 byte (24 bits) chunk
                // 4 times in blocks of 6 bits for each character (18, 12, 6, 0)
                // and apply logical AND with 0x3F to bitmask the least significant 6 bits.
                // Use this as an index into the lookup table, mload an entire word
                // so the desired character is in the least significant byte, and
                // mstore8 this least significant byte into the result and continue.
                mstore8(resultPtr, mload(add(tablePtr, and(shr(18, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
                mstore8(resultPtr, mload(add(tablePtr, and(shr(12, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
                mstore8(resultPtr, mload(add(tablePtr, and(shr(6, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
                mstore8(resultPtr, mload(add(tablePtr, and(input, 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
            }
            // Reset the value that was cached
            mstore(afterPtr, afterCache)
            if withPadding {
                // When data `bytes` is not exactly 3 bytes long
                // it is padded with `=` characters at the end
                switch mod(mload(data), 3)
                case 1 {
                    mstore8(sub(resultPtr, 1), 0x3d)
                    mstore8(sub(resultPtr, 2), 0x3d)
                }
                case 2 {
                    mstore8(sub(resultPtr, 1), 0x3d)
                }
            }
        }
        return result;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Library for converting numbers into strings and other string operations.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/LibString.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/LibString.sol)
///
/// @dev Note:
/// For performance and bytecode compactness, most of the string operations are restricted to
/// byte strings (7-bit ASCII), except where otherwise specified.
/// Usage of byte string operations on charsets with runes spanning two or more bytes
/// can lead to undefined behavior.
library LibString {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                        CUSTOM ERRORS                       */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev The length of the output is too small to contain all the hex digits.
    error HexLengthInsufficient();
    /// @dev The length of the string is more than 32 bytes.
    error TooBigForSmallString();
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev The constant returned when the `search` is not found in the string.
    uint256 internal constant NOT_FOUND = type(uint256).max;
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     DECIMAL OPERATIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns the base 10 decimal representation of `value`.
    function toString(uint256 value) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            // The maximum value of a uint256 contains 78 digits (1 byte per digit), but
            // we allocate 0xa0 bytes to keep the free memory pointer 32-byte word aligned.
            // We will need 1 word for the trailing zeros padding, 1 word for the length,
            // and 3 words for a maximum of 78 digits.
            str := add(mload(0x40), 0x80)
            // Update the free memory pointer to allocate.
            mstore(0x40, add(str, 0x20))
            // Zeroize the slot after the string.
            mstore(str, 0)
            // Cache the end of the memory to calculate the length later.
            let end := str
            let w := not(0) // Tsk.
            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            for { let temp := value } 1 {} {
                str := add(str, w) // `sub(str, 1)`.
                // Write the character to the pointer.
                // The ASCII index of the '0' character is 48.
                mstore8(str, add(48, mod(temp, 10)))
                // Keep dividing `temp` until zero.
                temp := div(temp, 10)
                if iszero(temp) { break }
            }
            let length := sub(end, str)
            // Move the pointer 32 bytes leftwards to make room for the length.
            str := sub(str, 0x20)
            // Store the length.
            mstore(str, length)
        }
    }
    /// @dev Returns the base 10 decimal representation of `value`.
    function toString(int256 value) internal pure returns (string memory str) {
        if (value >= 0) {
            return toString(uint256(value));
        }
        unchecked {
            str = toString(~uint256(value) + 1);
        }
        /// @solidity memory-safe-assembly
        assembly {
            // We still have some spare memory space on the left,
            // as we have allocated 3 words (96 bytes) for up to 78 digits.
            let length := mload(str) // Load the string length.
            mstore(str, 0x2d) // Store the '-' character.
            str := sub(str, 1) // Move back the string pointer by a byte.
            mstore(str, add(length, 1)) // Update the string length.
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   HEXADECIMAL OPERATIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns the hexadecimal representation of `value`,
    /// left-padded to an input length of `length` bytes.
    /// The output is prefixed with "0x" encoded using 2 hexadecimal digits per byte,
    /// giving a total length of `length * 2 + 2` bytes.
    /// Reverts if `length` is too small for the output to contain all the digits.
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value, length);
        /// @solidity memory-safe-assembly
        assembly {
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(str, 0x3078) // Write the "0x" prefix.
            str := sub(str, 2) // Move the pointer.
            mstore(str, strLength) // Write the length.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`,
    /// left-padded to an input length of `length` bytes.
    /// The output is prefixed with "0x" encoded using 2 hexadecimal digits per byte,
    /// giving a total length of `length * 2` bytes.
    /// Reverts if `length` is too small for the output to contain all the digits.
    function toHexStringNoPrefix(uint256 value, uint256 length)
        internal
        pure
        returns (string memory str)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // We need 0x20 bytes for the trailing zeros padding, `length * 2` bytes
            // for the digits, 0x02 bytes for the prefix, and 0x20 bytes for the length.
            // We add 0x20 to the total and round down to a multiple of 0x20.
            // (0x20 + 0x20 + 0x02 + 0x20) = 0x62.
            str := add(mload(0x40), and(add(shl(1, length), 0x42), not(0x1f)))
            // Allocate the memory.
            mstore(0x40, add(str, 0x20))
            // Zeroize the slot after the string.
            mstore(str, 0)
            // Cache the end to calculate the length later.
            let end := str
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)
            let start := sub(str, add(length, length))
            let w := not(1) // Tsk.
            let temp := value
            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            for {} 1 {} {
                str := add(str, w) // `sub(str, 2)`.
                mstore8(add(str, 1), mload(and(temp, 15)))
                mstore8(str, mload(and(shr(4, temp), 15)))
                temp := shr(8, temp)
                if iszero(xor(str, start)) { break }
            }
            if temp {
                mstore(0x00, 0x2194895a) // `HexLengthInsufficient()`.
                revert(0x1c, 0x04)
            }
            // Compute the string's length.
            let strLength := sub(end, str)
            // Move the pointer and write the length.
            str := sub(str, 0x20)
            mstore(str, strLength)
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is prefixed with "0x" and encoded using 2 hexadecimal digits per byte.
    /// As address are 20 bytes long, the output will left-padded to have
    /// a length of `20 * 2 + 2` bytes.
    function toHexString(uint256 value) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(str, 0x3078) // Write the "0x" prefix.
            str := sub(str, 2) // Move the pointer.
            mstore(str, strLength) // Write the length.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is prefixed with "0x".
    /// The output excludes leading "0" from the `toHexString` output.
    /// `0x00: "0x0", 0x01: "0x1", 0x12: "0x12", 0x123: "0x123"`.
    function toMinimalHexString(uint256 value) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let o := eq(byte(0, mload(add(str, 0x20))), 0x30) // Whether leading zero is present.
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(add(str, o), 0x3078) // Write the "0x" prefix, accounting for leading zero.
            str := sub(add(str, o), 2) // Move the pointer, accounting for leading zero.
            mstore(str, sub(strLength, o)) // Write the length, accounting for leading zero.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output excludes leading "0" from the `toHexStringNoPrefix` output.
    /// `0x00: "0", 0x01: "1", 0x12: "12", 0x123: "123"`.
    function toMinimalHexStringNoPrefix(uint256 value) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let o := eq(byte(0, mload(add(str, 0x20))), 0x30) // Whether leading zero is present.
            let strLength := mload(str) // Get the length.
            str := add(str, o) // Move the pointer, accounting for leading zero.
            mstore(str, sub(strLength, o)) // Write the length, accounting for leading zero.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is encoded using 2 hexadecimal digits per byte.
    /// As address are 20 bytes long, the output will left-padded to have
    /// a length of `20 * 2` bytes.
    function toHexStringNoPrefix(uint256 value) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            // We need 0x20 bytes for the trailing zeros padding, 0x20 bytes for the length,
            // 0x02 bytes for the prefix, and 0x40 bytes for the digits.
            // The next multiple of 0x20 above (0x20 + 0x20 + 0x02 + 0x40) is 0xa0.
            str := add(mload(0x40), 0x80)
            // Allocate the memory.
            mstore(0x40, add(str, 0x20))
            // Zeroize the slot after the string.
            mstore(str, 0)
            // Cache the end to calculate the length later.
            let end := str
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)
            let w := not(1) // Tsk.
            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            for { let temp := value } 1 {} {
                str := add(str, w) // `sub(str, 2)`.
                mstore8(add(str, 1), mload(and(temp, 15)))
                mstore8(str, mload(and(shr(4, temp), 15)))
                temp := shr(8, temp)
                if iszero(temp) { break }
            }
            // Compute the string's length.
            let strLength := sub(end, str)
            // Move the pointer and write the length.
            str := sub(str, 0x20)
            mstore(str, strLength)
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is prefixed with "0x", encoded using 2 hexadecimal digits per byte,
    /// and the alphabets are capitalized conditionally according to
    /// https://eips.ethereum.org/EIPS/eip-55
    function toHexStringChecksummed(address value) internal pure returns (string memory str) {
        str = toHexString(value);
        /// @solidity memory-safe-assembly
        assembly {
            let mask := shl(6, div(not(0), 255)) // `0b010000000100000000 ...`
            let o := add(str, 0x22)
            let hashed := and(keccak256(o, 40), mul(34, mask)) // `0b10001000 ... `
            let t := shl(240, 136) // `0b10001000 << 240`
            for { let i := 0 } 1 {} {
                mstore(add(i, i), mul(t, byte(i, hashed)))
                i := add(i, 1)
                if eq(i, 20) { break }
            }
            mstore(o, xor(mload(o), shr(1, and(mload(0x00), and(mload(o), mask)))))
            o := add(o, 0x20)
            mstore(o, xor(mload(o), shr(1, and(mload(0x20), and(mload(o), mask)))))
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is prefixed with "0x" and encoded using 2 hexadecimal digits per byte.
    function toHexString(address value) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(str, 0x3078) // Write the "0x" prefix.
            str := sub(str, 2) // Move the pointer.
            mstore(str, strLength) // Write the length.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is encoded using 2 hexadecimal digits per byte.
    function toHexStringNoPrefix(address value) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            str := mload(0x40)
            // Allocate the memory.
            // We need 0x20 bytes for the trailing zeros padding, 0x20 bytes for the length,
            // 0x02 bytes for the prefix, and 0x28 bytes for the digits.
            // The next multiple of 0x20 above (0x20 + 0x20 + 0x02 + 0x28) is 0x80.
            mstore(0x40, add(str, 0x80))
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)
            str := add(str, 2)
            mstore(str, 40)
            let o := add(str, 0x20)
            mstore(add(o, 40), 0)
            value := shl(96, value)
            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            for { let i := 0 } 1 {} {
                let p := add(o, add(i, i))
                let temp := byte(i, value)
                mstore8(add(p, 1), mload(and(temp, 15)))
                mstore8(p, mload(shr(4, temp)))
                i := add(i, 1)
                if eq(i, 20) { break }
            }
        }
    }
    /// @dev Returns the hex encoded string from the raw bytes.
    /// The output is encoded using 2 hexadecimal digits per byte.
    function toHexString(bytes memory raw) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(raw);
        /// @solidity memory-safe-assembly
        assembly {
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(str, 0x3078) // Write the "0x" prefix.
            str := sub(str, 2) // Move the pointer.
            mstore(str, strLength) // Write the length.
        }
    }
    /// @dev Returns the hex encoded string from the raw bytes.
    /// The output is encoded using 2 hexadecimal digits per byte.
    function toHexStringNoPrefix(bytes memory raw) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            let length := mload(raw)
            str := add(mload(0x40), 2) // Skip 2 bytes for the optional prefix.
            mstore(str, add(length, length)) // Store the length of the output.
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)
            let o := add(str, 0x20)
            let end := add(raw, length)
            for {} iszero(eq(raw, end)) {} {
                raw := add(raw, 1)
                mstore8(add(o, 1), mload(and(mload(raw), 15)))
                mstore8(o, mload(and(shr(4, mload(raw)), 15)))
                o := add(o, 2)
            }
            mstore(o, 0) // Zeroize the slot after the string.
            mstore(0x40, add(o, 0x20)) // Allocate the memory.
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   RUNE STRING OPERATIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns the number of UTF characters in the string.
    function runeCount(string memory s) internal pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            if mload(s) {
                mstore(0x00, div(not(0), 255))
                mstore(0x20, 0x0202020202020202020202020202020202020202020202020303030304040506)
                let o := add(s, 0x20)
                let end := add(o, mload(s))
                for { result := 1 } 1 { result := add(result, 1) } {
                    o := add(o, byte(0, mload(shr(250, mload(o)))))
                    if iszero(lt(o, end)) { break }
                }
            }
        }
    }
    /// @dev Returns if this string is a 7-bit ASCII string.
    /// (i.e. all characters codes are in [0..127])
    function is7BitASCII(string memory s) internal pure returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            let mask := shl(7, div(not(0), 255))
            result := 1
            let n := mload(s)
            if n {
                let o := add(s, 0x20)
                let end := add(o, n)
                let last := mload(end)
                mstore(end, 0)
                for {} 1 {} {
                    if and(mask, mload(o)) {
                        result := 0
                        break
                    }
                    o := add(o, 0x20)
                    if iszero(lt(o, end)) { break }
                }
                mstore(end, last)
            }
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   BYTE STRING OPERATIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    // For performance and bytecode compactness, byte string operations are restricted
    // to 7-bit ASCII strings. All offsets are byte offsets, not UTF character offsets.
    // Usage of byte string operations on charsets with runes spanning two or more bytes
    // can lead to undefined behavior.
    /// @dev Returns `subject` all occurrences of `search` replaced with `replacement`.
    function replace(string memory subject, string memory search, string memory replacement)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLength := mload(subject)
            let searchLength := mload(search)
            let replacementLength := mload(replacement)
            subject := add(subject, 0x20)
            search := add(search, 0x20)
            replacement := add(replacement, 0x20)
            result := add(mload(0x40), 0x20)
            let subjectEnd := add(subject, subjectLength)
            if iszero(gt(searchLength, subjectLength)) {
                let subjectSearchEnd := add(sub(subjectEnd, searchLength), 1)
                let h := 0
                if iszero(lt(searchLength, 0x20)) { h := keccak256(search, searchLength) }
                let m := shl(3, sub(0x20, and(searchLength, 0x1f)))
                let s := mload(search)
                for {} 1 {} {
                    let t := mload(subject)
                    // Whether the first `searchLength % 32` bytes of
                    // `subject` and `search` matches.
                    if iszero(shr(m, xor(t, s))) {
                        if h {
                            if iszero(eq(keccak256(subject, searchLength), h)) {
                                mstore(result, t)
                                result := add(result, 1)
                                subject := add(subject, 1)
                                if iszero(lt(subject, subjectSearchEnd)) { break }
                                continue
                            }
                        }
                        // Copy the `replacement` one word at a time.
                        for { let o := 0 } 1 {} {
                            mstore(add(result, o), mload(add(replacement, o)))
                            o := add(o, 0x20)
                            if iszero(lt(o, replacementLength)) { break }
                        }
                        result := add(result, replacementLength)
                        subject := add(subject, searchLength)
                        if searchLength {
                            if iszero(lt(subject, subjectSearchEnd)) { break }
                            continue
                        }
                    }
                    mstore(result, t)
                    result := add(result, 1)
                    subject := add(subject, 1)
                    if iszero(lt(subject, subjectSearchEnd)) { break }
                }
            }
            let resultRemainder := result
            result := add(mload(0x40), 0x20)
            let k := add(sub(resultRemainder, result), sub(subjectEnd, subject))
            // Copy the rest of the string one word at a time.
            for {} lt(subject, subjectEnd) {} {
                mstore(resultRemainder, mload(subject))
                resultRemainder := add(resultRemainder, 0x20)
                subject := add(subject, 0x20)
            }
            result := sub(result, 0x20)
            let last := add(add(result, 0x20), k) // Zeroize the slot after the string.
            mstore(last, 0)
            mstore(0x40, add(last, 0x20)) // Allocate the memory.
            mstore(result, k) // Store the length.
        }
    }
    /// @dev Returns the byte index of the first location of `search` in `subject`,
    /// searching from left to right, starting from `from`.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `search` is not found.
    function indexOf(string memory subject, string memory search, uint256 from)
        internal
        pure
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            for { let subjectLength := mload(subject) } 1 {} {
                if iszero(mload(search)) {
                    if iszero(gt(from, subjectLength)) {
                        result := from
                        break
                    }
                    result := subjectLength
                    break
                }
                let searchLength := mload(search)
                let subjectStart := add(subject, 0x20)
                result := not(0) // Initialize to `NOT_FOUND`.
                subject := add(subjectStart, from)
                let end := add(sub(add(subjectStart, subjectLength), searchLength), 1)
                let m := shl(3, sub(0x20, and(searchLength, 0x1f)))
                let s := mload(add(search, 0x20))
                if iszero(and(lt(subject, end), lt(from, subjectLength))) { break }
                if iszero(lt(searchLength, 0x20)) {
                    for { let h := keccak256(add(search, 0x20), searchLength) } 1 {} {
                        if iszero(shr(m, xor(mload(subject), s))) {
                            if eq(keccak256(subject, searchLength), h) {
                                result := sub(subject, subjectStart)
                                break
                            }
                        }
                        subject := add(subject, 1)
                        if iszero(lt(subject, end)) { break }
                    }
                    break
                }
                for {} 1 {} {
                    if iszero(shr(m, xor(mload(subject), s))) {
                        result := sub(subject, subjectStart)
                        break
                    }
                    subject := add(subject, 1)
                    if iszero(lt(subject, end)) { break }
                }
                break
            }
        }
    }
    /// @dev Returns the byte index of the first location of `search` in `subject`,
    /// searching from left to right.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `search` is not found.
    function indexOf(string memory subject, string memory search)
        internal
        pure
        returns (uint256 result)
    {
        result = indexOf(subject, search, 0);
    }
    /// @dev Returns the byte index of the first location of `search` in `subject`,
    /// searching from right to left, starting from `from`.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `search` is not found.
    function lastIndexOf(string memory subject, string memory search, uint256 from)
        internal
        pure
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            for {} 1 {} {
                result := not(0) // Initialize to `NOT_FOUND`.
                let searchLength := mload(search)
                if gt(searchLength, mload(subject)) { break }
                let w := result
                let fromMax := sub(mload(subject), searchLength)
                if iszero(gt(fromMax, from)) { from := fromMax }
                let end := add(add(subject, 0x20), w)
                subject := add(add(subject, 0x20), from)
                if iszero(gt(subject, end)) { break }
                // As this function is not too often used,
                // we shall simply use keccak256 for smaller bytecode size.
                for { let h := keccak256(add(search, 0x20), searchLength) } 1 {} {
                    if eq(keccak256(subject, searchLength), h) {
                        result := sub(subject, add(end, 1))
                        break
                    }
                    subject := add(subject, w) // `sub(subject, 1)`.
                    if iszero(gt(subject, end)) { break }
                }
                break
            }
        }
    }
    /// @dev Returns the byte index of the first location of `search` in `subject`,
    /// searching from right to left.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `search` is not found.
    function lastIndexOf(string memory subject, string memory search)
        internal
        pure
        returns (uint256 result)
    {
        result = lastIndexOf(subject, search, uint256(int256(-1)));
    }
    /// @dev Returns true if `search` is found in `subject`, false otherwise.
    function contains(string memory subject, string memory search) internal pure returns (bool) {
        return indexOf(subject, search) != NOT_FOUND;
    }
    /// @dev Returns whether `subject` starts with `search`.
    function startsWith(string memory subject, string memory search)
        internal
        pure
        returns (bool result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let searchLength := mload(search)
            // Just using keccak256 directly is actually cheaper.
            // forgefmt: disable-next-item
            result := and(
                iszero(gt(searchLength, mload(subject))),
                eq(
                    keccak256(add(subject, 0x20), searchLength),
                    keccak256(add(search, 0x20), searchLength)
                )
            )
        }
    }
    /// @dev Returns whether `subject` ends with `search`.
    function endsWith(string memory subject, string memory search)
        internal
        pure
        returns (bool result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let searchLength := mload(search)
            let subjectLength := mload(subject)
            // Whether `search` is not longer than `subject`.
            let withinRange := iszero(gt(searchLength, subjectLength))
            // Just using keccak256 directly is actually cheaper.
            // forgefmt: disable-next-item
            result := and(
                withinRange,
                eq(
                    keccak256(
                        // `subject + 0x20 + max(subjectLength - searchLength, 0)`.
                        add(add(subject, 0x20), mul(withinRange, sub(subjectLength, searchLength))),
                        searchLength
                    ),
                    keccak256(add(search, 0x20), searchLength)
                )
            )
        }
    }
    /// @dev Returns `subject` repeated `times`.
    function repeat(string memory subject, uint256 times)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLength := mload(subject)
            if iszero(or(iszero(times), iszero(subjectLength))) {
                subject := add(subject, 0x20)
                result := mload(0x40)
                let output := add(result, 0x20)
                for {} 1 {} {
                    // Copy the `subject` one word at a time.
                    for { let o := 0 } 1 {} {
                        mstore(add(output, o), mload(add(subject, o)))
                        o := add(o, 0x20)
                        if iszero(lt(o, subjectLength)) { break }
                    }
                    output := add(output, subjectLength)
                    times := sub(times, 1)
                    if iszero(times) { break }
                }
                mstore(output, 0) // Zeroize the slot after the string.
                let resultLength := sub(output, add(result, 0x20))
                mstore(result, resultLength) // Store the length.
                // Allocate the memory.
                mstore(0x40, add(result, add(resultLength, 0x20)))
            }
        }
    }
    /// @dev Returns a copy of `subject` sliced from `start` to `end` (exclusive).
    /// `start` and `end` are byte offsets.
    function slice(string memory subject, uint256 start, uint256 end)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLength := mload(subject)
            if iszero(gt(subjectLength, end)) { end := subjectLength }
            if iszero(gt(subjectLength, start)) { start := subjectLength }
            if lt(start, end) {
                result := mload(0x40)
                let resultLength := sub(end, start)
                mstore(result, resultLength)
                subject := add(subject, start)
                let w := not(0x1f)
                // Copy the `subject` one word at a time, backwards.
                for { let o := and(add(resultLength, 0x1f), w) } 1 {} {
                    mstore(add(result, o), mload(add(subject, o)))
                    o := add(o, w) // `sub(o, 0x20)`.
                    if iszero(o) { break }
                }
                // Zeroize the slot after the string.
                mstore(add(add(result, 0x20), resultLength), 0)
                // Allocate memory for the length and the bytes,
                // rounded up to a multiple of 32.
                mstore(0x40, add(result, and(add(resultLength, 0x3f), w)))
            }
        }
    }
    /// @dev Returns a copy of `subject` sliced from `start` to the end of the string.
    /// `start` is a byte offset.
    function slice(string memory subject, uint256 start)
        internal
        pure
        returns (string memory result)
    {
        result = slice(subject, start, uint256(int256(-1)));
    }
    /// @dev Returns all the indices of `search` in `subject`.
    /// The indices are byte offsets.
    function indicesOf(string memory subject, string memory search)
        internal
        pure
        returns (uint256[] memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLength := mload(subject)
            let searchLength := mload(search)
            if iszero(gt(searchLength, subjectLength)) {
                subject := add(subject, 0x20)
                search := add(search, 0x20)
                result := add(mload(0x40), 0x20)
                let subjectStart := subject
                let subjectSearchEnd := add(sub(add(subject, subjectLength), searchLength), 1)
                let h := 0
                if iszero(lt(searchLength, 0x20)) { h := keccak256(search, searchLength) }
                let m := shl(3, sub(0x20, and(searchLength, 0x1f)))
                let s := mload(search)
                for {} 1 {} {
                    let t := mload(subject)
                    // Whether the first `searchLength % 32` bytes of
                    // `subject` and `search` matches.
                    if iszero(shr(m, xor(t, s))) {
                        if h {
                            if iszero(eq(keccak256(subject, searchLength), h)) {
                                subject := add(subject, 1)
                                if iszero(lt(subject, subjectSearchEnd)) { break }
                                continue
                            }
                        }
                        // Append to `result`.
                        mstore(result, sub(subject, subjectStart))
                        result := add(result, 0x20)
                        // Advance `subject` by `searchLength`.
                        subject := add(subject, searchLength)
                        if searchLength {
                            if iszero(lt(subject, subjectSearchEnd)) { break }
                            continue
                        }
                    }
                    subject := add(subject, 1)
                    if iszero(lt(subject, subjectSearchEnd)) { break }
                }
                let resultEnd := result
                // Assign `result` to the free memory pointer.
                result := mload(0x40)
                // Store the length of `result`.
                mstore(result, shr(5, sub(resultEnd, add(result, 0x20))))
                // Allocate memory for result.
                // We allocate one more word, so this array can be recycled for {split}.
                mstore(0x40, add(resultEnd, 0x20))
            }
        }
    }
    /// @dev Returns a arrays of strings based on the `delimiter` inside of the `subject` string.
    function split(string memory subject, string memory delimiter)
        internal
        pure
        returns (string[] memory result)
    {
        uint256[] memory indices = indicesOf(subject, delimiter);
        /// @solidity memory-safe-assembly
        assembly {
            let w := not(0x1f)
            let indexPtr := add(indices, 0x20)
            let indicesEnd := add(indexPtr, shl(5, add(mload(indices), 1)))
            mstore(add(indicesEnd, w), mload(subject))
            mstore(indices, add(mload(indices), 1))
            let prevIndex := 0
            for {} 1 {} {
                let index := mload(indexPtr)
                mstore(indexPtr, 0x60)
                if iszero(eq(index, prevIndex)) {
                    let element := mload(0x40)
                    let elementLength := sub(index, prevIndex)
                    mstore(element, elementLength)
                    // Copy the `subject` one word at a time, backwards.
                    for { let o := and(add(elementLength, 0x1f), w) } 1 {} {
                        mstore(add(element, o), mload(add(add(subject, prevIndex), o)))
                        o := add(o, w) // `sub(o, 0x20)`.
                        if iszero(o) { break }
                    }
                    // Zeroize the slot after the string.
                    mstore(add(add(element, 0x20), elementLength), 0)
                    // Allocate memory for the length and the bytes,
                    // rounded up to a multiple of 32.
                    mstore(0x40, add(element, and(add(elementLength, 0x3f), w)))
                    // Store the `element` into the array.
                    mstore(indexPtr, element)
                }
                prevIndex := add(index, mload(delimiter))
                indexPtr := add(indexPtr, 0x20)
                if iszero(lt(indexPtr, indicesEnd)) { break }
            }
            result := indices
            if iszero(mload(delimiter)) {
                result := add(indices, 0x20)
                mstore(result, sub(mload(indices), 2))
            }
        }
    }
    /// @dev Returns a concatenated string of `a` and `b`.
    /// Cheaper than `string.concat()` and does not de-align the free memory pointer.
    function concat(string memory a, string memory b)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let w := not(0x1f)
            result := mload(0x40)
            let aLength := mload(a)
            // Copy `a` one word at a time, backwards.
            for { let o := and(add(aLength, 0x20), w) } 1 {} {
                mstore(add(result, o), mload(add(a, o)))
                o := add(o, w) // `sub(o, 0x20)`.
                if iszero(o) { break }
            }
            let bLength := mload(b)
            let output := add(result, aLength)
            // Copy `b` one word at a time, backwards.
            for { let o := and(add(bLength, 0x20), w) } 1 {} {
                mstore(add(output, o), mload(add(b, o)))
                o := add(o, w) // `sub(o, 0x20)`.
                if iszero(o) { break }
            }
            let totalLength := add(aLength, bLength)
            let last := add(add(result, 0x20), totalLength)
            // Zeroize the slot after the string.
            mstore(last, 0)
            // Stores the length.
            mstore(result, totalLength)
            // Allocate memory for the length and the bytes,
            // rounded up to a multiple of 32.
            mstore(0x40, and(add(last, 0x1f), w))
        }
    }
    /// @dev Returns a copy of the string in either lowercase or UPPERCASE.
    /// WARNING! This function is only compatible with 7-bit ASCII strings.
    function toCase(string memory subject, bool toUpper)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let length := mload(subject)
            if length {
                result := add(mload(0x40), 0x20)
                subject := add(subject, 1)
                let flags := shl(add(70, shl(5, toUpper)), 0x3ffffff)
                let w := not(0)
                for { let o := length } 1 {} {
                    o := add(o, w)
                    let b := and(0xff, mload(add(subject, o)))
                    mstore8(add(result, o), xor(b, and(shr(b, flags), 0x20)))
                    if iszero(o) { break }
                }
                result := mload(0x40)
                mstore(result, length) // Store the length.
                let last := add(add(result, 0x20), length)
                mstore(last, 0) // Zeroize the slot after the string.
                mstore(0x40, add(last, 0x20)) // Allocate the memory.
            }
        }
    }
    /// @dev Returns a string from a small bytes32 string.
    /// `s` must be null-terminated, or behavior will be undefined.
    function fromSmallString(bytes32 s) internal pure returns (string memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40)
            let n := 0
            for {} byte(n, s) { n := add(n, 1) } {} // Scan for '\\0'.
            mstore(result, n)
            let o := add(result, 0x20)
            mstore(o, s)
            mstore(add(o, n), 0)
            mstore(0x40, add(result, 0x40))
        }
    }
    /// @dev Returns the small string, with all bytes after the first null byte zeroized.
    function normalizeSmallString(bytes32 s) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            for {} byte(result, s) { result := add(result, 1) } {} // Scan for '\\0'.
            mstore(0x00, s)
            mstore(result, 0x00)
            result := mload(0x00)
        }
    }
    /// @dev Returns the string as a normalized null-terminated small string.
    function toSmallString(string memory s) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(s)
            if iszero(lt(result, 33)) {
                mstore(0x00, 0xec92f9a3) // `TooBigForSmallString()`.
                revert(0x1c, 0x04)
            }
            result := shl(shl(3, sub(32, result)), mload(add(s, result)))
        }
    }
    /// @dev Returns a lowercased copy of the string.
    /// WARNING! This function is only compatible with 7-bit ASCII strings.
    function lower(string memory subject) internal pure returns (string memory result) {
        result = toCase(subject, false);
    }
    /// @dev Returns an UPPERCASED copy of the string.
    /// WARNING! This function is only compatible with 7-bit ASCII strings.
    function upper(string memory subject) internal pure returns (string memory result) {
        result = toCase(subject, true);
    }
    /// @dev Escapes the string to be used within HTML tags.
    function escapeHTML(string memory s) internal pure returns (string memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            let end := add(s, mload(s))
            result := add(mload(0x40), 0x20)
            // Store the bytes of the packed offsets and strides into the scratch space.
            // `packed = (stride << 5) | offset`. Max offset is 20. Max stride is 6.
            mstore(0x1f, 0x900094)
            mstore(0x08, 0xc0000000a6ab)
            // Store "&quot;&amp;&#39;&lt;&gt;" into the scratch space.
            mstore(0x00, shl(64, 0x2671756f743b26616d703b262333393b266c743b2667743b))
            for {} iszero(eq(s, end)) {} {
                s := add(s, 1)
                let c := and(mload(s), 0xff)
                // Not in `["\\"","'","&","<",">"]`.
                if iszero(and(shl(c, 1), 0x500000c400000000)) {
                    mstore8(result, c)
                    result := add(result, 1)
                    continue
                }
                let t := shr(248, mload(c))
                mstore(result, mload(and(t, 0x1f)))
                result := add(result, shr(5, t))
            }
            let last := result
            mstore(last, 0) // Zeroize the slot after the string.
            result := mload(0x40)
            mstore(result, sub(last, add(result, 0x20))) // Store the length.
            mstore(0x40, add(last, 0x20)) // Allocate the memory.
        }
    }
    /// @dev Escapes the string to be used within double-quotes in a JSON.
    /// If `addDoubleQuotes` is true, the result will be enclosed in double-quotes.
    function escapeJSON(string memory s, bool addDoubleQuotes)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let end := add(s, mload(s))
            result := add(mload(0x40), 0x20)
            if addDoubleQuotes {
                mstore8(result, 34)
                result := add(1, result)
            }
            // Store "\\\\u0000" in scratch space.
            // Store "0123456789abcdef" in scratch space.
            // Also, store `{0x08:"b", 0x09:"t", 0x0a:"n", 0x0c:"f", 0x0d:"r"}`.
            // into the scratch space.
            mstore(0x15, 0x5c75303030303031323334353637383961626364656662746e006672)
            // Bitmask for detecting `["\\"","\\\\"]`.
            let e := or(shl(0x22, 1), shl(0x5c, 1))
            for {} iszero(eq(s, end)) {} {
                s := add(s, 1)
                let c := and(mload(s), 0xff)
                if iszero(lt(c, 0x20)) {
                    if iszero(and(shl(c, 1), e)) {
                        // Not in `["\\"","\\\\"]`.
                        mstore8(result, c)
                        result := add(result, 1)
                        continue
                    }
                    mstore8(result, 0x5c) // "\\\\".
                    mstore8(add(result, 1), c)
                    result := add(result, 2)
                    continue
                }
                if iszero(and(shl(c, 1), 0x3700)) {
                    // Not in `["\\b","\\t","\
","\\f","\\d"]`.
                    mstore8(0x1d, mload(shr(4, c))) // Hex value.
                    mstore8(0x1e, mload(and(c, 15))) // Hex value.
                    mstore(result, mload(0x19)) // "\\\\u00XX".
                    result := add(result, 6)
                    continue
                }
                mstore8(result, 0x5c) // "\\\\".
                mstore8(add(result, 1), mload(add(c, 8)))
                result := add(result, 2)
            }
            if addDoubleQuotes {
                mstore8(result, 34)
                result := add(1, result)
            }
            let last := result
            mstore(last, 0) // Zeroize the slot after the string.
            result := mload(0x40)
            mstore(result, sub(last, add(result, 0x20))) // Store the length.
            mstore(0x40, add(last, 0x20)) // Allocate the memory.
        }
    }
    /// @dev Escapes the string to be used within double-quotes in a JSON.
    function escapeJSON(string memory s) internal pure returns (string memory result) {
        result = escapeJSON(s, false);
    }
    /// @dev Returns whether `a` equals `b`.
    function eq(string memory a, string memory b) internal pure returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := eq(keccak256(add(a, 0x20), mload(a)), keccak256(add(b, 0x20), mload(b)))
        }
    }
    /// @dev Returns whether `a` equals `b`, where `b` is a null-terminated small string.
    function eqs(string memory a, bytes32 b) internal pure returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            // These should be evaluated on compile time, as far as possible.
            let m := not(shl(7, div(not(iszero(b)), 255))) // `0x7f7f ...`.
            let x := not(or(m, or(b, add(m, and(b, m)))))
            let r := shl(7, iszero(iszero(shr(128, x))))
            r := or(r, shl(6, iszero(iszero(shr(64, shr(r, x))))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            // forgefmt: disable-next-item
            result := gt(eq(mload(a), add(iszero(x), xor(31, shr(3, r)))),
                xor(shr(add(8, r), b), shr(add(8, r), mload(add(a, 0x20)))))
        }
    }
    /// @dev Packs a single string with its length into a single word.
    /// Returns `bytes32(0)` if the length is zero or greater than 31.
    function packOne(string memory a) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            // We don't need to zero right pad the string,
            // since this is our own custom non-standard packing scheme.
            result :=
                mul(
                    // Load the length and the bytes.
                    mload(add(a, 0x1f)),
                    // `length != 0 && length < 32`. Abuses underflow.
                    // Assumes that the length is valid and within the block gas limit.
                    lt(sub(mload(a), 1), 0x1f)
                )
        }
    }
    /// @dev Unpacks a string packed using {packOne}.
    /// Returns the empty string if `packed` is `bytes32(0)`.
    /// If `packed` is not an output of {packOne}, the output behavior is undefined.
    function unpackOne(bytes32 packed) internal pure returns (string memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            // Grab the free memory pointer.
            result := mload(0x40)
            // Allocate 2 words (1 for the length, 1 for the bytes).
            mstore(0x40, add(result, 0x40))
            // Zeroize the length slot.
            mstore(result, 0)
            // Store the length and bytes.
            mstore(add(result, 0x1f), packed)
            // Right pad with zeroes.
            mstore(add(add(result, 0x20), mload(result)), 0)
        }
    }
    /// @dev Packs two strings with their lengths into a single word.
    /// Returns `bytes32(0)` if combined length is zero or greater than 30.
    function packTwo(string memory a, string memory b) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            let aLength := mload(a)
            // We don't need to zero right pad the strings,
            // since this is our own custom non-standard packing scheme.
            result :=
                mul(
                    // Load the length and the bytes of `a` and `b`.
                    or(
                        shl(shl(3, sub(0x1f, aLength)), mload(add(a, aLength))),
                        mload(sub(add(b, 0x1e), aLength))
                    ),
                    // `totalLength != 0 && totalLength < 31`. Abuses underflow.
                    // Assumes that the lengths are valid and within the block gas limit.
                    lt(sub(add(aLength, mload(b)), 1), 0x1e)
                )
        }
    }
    /// @dev Unpacks strings packed using {packTwo}.
    /// Returns the empty strings if `packed` is `bytes32(0)`.
    /// If `packed` is not an output of {packTwo}, the output behavior is undefined.
    function unpackTwo(bytes32 packed)
        internal
        pure
        returns (string memory resultA, string memory resultB)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Grab the free memory pointer.
            resultA := mload(0x40)
            resultB := add(resultA, 0x40)
            // Allocate 2 words for each string (1 for the length, 1 for the byte). Total 4 words.
            mstore(0x40, add(resultB, 0x40))
            // Zeroize the length slots.
            mstore(resultA, 0)
            mstore(resultB, 0)
            // Store the lengths and bytes.
            mstore(add(resultA, 0x1f), packed)
            mstore(add(resultB, 0x1f), mload(add(add(resultA, 0x20), mload(resultA))))
            // Right pad with zeroes.
            mstore(add(add(resultA, 0x20), mload(resultA)), 0)
            mstore(add(add(resultB, 0x20), mload(resultB)), 0)
        }
    }
    /// @dev Directly returns `a` without copying.
    function directReturn(string memory a) internal pure {
        assembly {
            // Assumes that the string does not start from the scratch space.
            let retStart := sub(a, 0x20)
            let retSize := add(mload(a), 0x40)
            // Right pad with zeroes. Just in case the string is produced
            // by a method that doesn't zero right pad.
            mstore(add(retStart, retSize), 0)
            // Store the return offset.
            mstore(retStart, 0x20)
            // End the transaction, returning the string.
            return(retStart, retSize)
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.23;
import {IAccount} from "account-abstraction/interfaces/IAccount.sol";
import {UserOperation, UserOperationLib} from "account-abstraction/interfaces/UserOperation.sol";
import {Receiver} from "solady/accounts/Receiver.sol";
import {SignatureCheckerLib} from "solady/utils/SignatureCheckerLib.sol";
import {UUPSUpgradeable} from "solady/utils/UUPSUpgradeable.sol";
import {WebAuthn} from "webauthn-sol/WebAuthn.sol";
import {ERC1271} from "./ERC1271.sol";
import {MultiOwnable} from "./MultiOwnable.sol";
/// @title Coinbase Smart Wallet
///
/// @notice ERC-4337-compatible smart account, based on Solady's ERC4337 account implementation
///         with inspiration from Alchemy's LightAccount and Daimo's DaimoAccount. Verified by z0r0z.eth from (⌘) NANI.eth
///
/// @author Coinbase (https://github.com/coinbase/smart-wallet)
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/accounts/ERC4337.sol)
contract CoinbaseSmartWallet is ERC1271, IAccount, MultiOwnable, UUPSUpgradeable, Receiver {
    /// @notice A wrapper struct used for signature validation so that callers
    ///         can identify the owner that signed.
    struct SignatureWrapper {
        /// @dev The index of the owner that signed, see `MultiOwnable.ownerAtIndex`
        uint256 ownerIndex;
        /// @dev If `MultiOwnable.ownerAtIndex` is an Ethereum address, this should be `abi.encodePacked(r, s, v)`
        ///      If `MultiOwnable.ownerAtIndex` is a public key, this should be `abi.encode(WebAuthnAuth)`.
        bytes signatureData;
    }
    /// @notice Represents a call to make.
    struct Call {
        /// @dev The address to call.
        address target;
        /// @dev The value to send when making the call.
        uint256 value;
        /// @dev The data of the call.
        bytes data;
    }
    /// @notice Reserved nonce key (upper 192 bits of `UserOperation.nonce`) for cross-chain replayable
    ///         transactions.
    ///
    /// @dev MUST BE the `UserOperation.nonce` key when `UserOperation.calldata` is calling
    ///      `executeWithoutChainIdValidation`and MUST NOT BE `UserOperation.nonce` key when `UserOperation.calldata` is
    ///      NOT calling `executeWithoutChainIdValidation`.
    ///
    /// @dev Helps enforce sequential sequencing of replayable transactions.
    uint256 public constant REPLAYABLE_NONCE_KEY = 8453;
    /// @notice Thrown when `initialize` is called but the account already has had at least one owner.
    error Initialized();
    /// @notice Thrown when a call is passed to `executeWithoutChainIdValidation` that is not allowed by
    ///         `canSkipChainIdValidation`
    ///
    /// @param selector The selector of the call.
    error SelectorNotAllowed(bytes4 selector);
    /// @notice Thrown in validateUserOp if the key of `UserOperation.nonce` does not match the calldata.
    ///
    /// @dev Calls to `this.executeWithoutChainIdValidation` MUST use `REPLAYABLE_NONCE_KEY` and
    ///      calls NOT to `this.executeWithoutChainIdValidation` MUST NOT use `REPLAYABLE_NONCE_KEY`.
    ///
    /// @param key The invalid `UserOperation.nonce` key.
    error InvalidNonceKey(uint256 key);
    /// @notice Reverts if the caller is not the EntryPoint.
    modifier onlyEntryPoint() virtual {
        if (msg.sender != entryPoint()) {
            revert Unauthorized();
        }
        _;
    }
    /// @notice Reverts if the caller is neither the EntryPoint, the owner, nor the account itself.
    modifier onlyEntryPointOrOwner() virtual {
        if (msg.sender != entryPoint()) {
            _checkOwner();
        }
        _;
    }
    /// @notice Sends to the EntryPoint (i.e. `msg.sender`) the missing funds for this transaction.
    ///
    /// @dev Subclass MAY override this modifier for better funds management (e.g. send to the
    ///      EntryPoint more than the minimum required, so that in future transactions it will not
    ///      be required to send again).
    ///
    /// @param missingAccountFunds The minimum value this modifier should send the EntryPoint which
    ///                            MAY be zero, in case there is enough deposit, or the userOp has a
    ///                            paymaster.
    modifier payPrefund(uint256 missingAccountFunds) virtual {
        _;
        assembly ("memory-safe") {
            if missingAccountFunds {
                // Ignore failure (it's EntryPoint's job to verify, not the account's).
                pop(call(gas(), caller(), missingAccountFunds, codesize(), 0x00, codesize(), 0x00))
            }
        }
    }
    constructor() {
        // Implementation should not be initializable (does not affect proxies which use their own storage).
        bytes[] memory owners = new bytes[](1);
        owners[0] = abi.encode(address(0));
        _initializeOwners(owners);
    }
    /// @notice Initializes the account with the `owners`.
    ///
    /// @dev Reverts if the account has had at least one owner, i.e. has been initialized.
    ///
    /// @param owners Array of initial owners for this account. Each item should be
    ///               an ABI encoded Ethereum address, i.e. 32 bytes with 12 leading 0 bytes,
    ///               or a 64 byte public key.
    function initialize(bytes[] calldata owners) external payable virtual {
        if (nextOwnerIndex() != 0) {
            revert Initialized();
        }
        _initializeOwners(owners);
    }
    /// @inheritdoc IAccount
    ///
    /// @notice ERC-4337 `validateUserOp` method. The EntryPoint will
    ///         call `UserOperation.sender.call(UserOperation.callData)` only if this validation call returns
    ///         successfully.
    ///
    /// @dev Signature failure should be reported by returning 1 (see: `this._isValidSignature`). This
    ///      allows making a "simulation call" without a valid signature. Other failures (e.g. invalid signature format)
    ///      should still revert to signal failure.
    /// @dev Reverts if the `UserOperation.nonce` key is invalid for `UserOperation.calldata`.
    /// @dev Reverts if the signature format is incorrect or invalid for owner type.
    ///
    /// @param userOp              The `UserOperation` to validate.
    /// @param userOpHash          The `UserOperation` hash, as computed by `EntryPoint.getUserOpHash(UserOperation)`.
    /// @param missingAccountFunds The missing account funds that must be deposited on the Entrypoint.
    ///
    /// @return validationData The encoded `ValidationData` structure:
    ///                        `(uint256(validAfter) << (160 + 48)) | (uint256(validUntil) << 160) | (success ? 0 : 1)`
    ///                        where `validUntil` is 0 (indefinite) and `validAfter` is 0.
    function validateUserOp(UserOperation calldata userOp, bytes32 userOpHash, uint256 missingAccountFunds)
        external
        virtual
        onlyEntryPoint
        payPrefund(missingAccountFunds)
        returns (uint256 validationData)
    {
        uint256 key = userOp.nonce >> 64;
        if (bytes4(userOp.callData) == this.executeWithoutChainIdValidation.selector) {
            userOpHash = getUserOpHashWithoutChainId(userOp);
            if (key != REPLAYABLE_NONCE_KEY) {
                revert InvalidNonceKey(key);
            }
        } else {
            if (key == REPLAYABLE_NONCE_KEY) {
                revert InvalidNonceKey(key);
            }
        }
        // Return 0 if the recovered address matches the owner.
        if (_isValidSignature(userOpHash, userOp.signature)) {
            return 0;
        }
        // Else return 1
        return 1;
    }
    /// @notice Executes `calls` on this account (i.e. self call).
    ///
    /// @dev Can only be called by the Entrypoint.
    /// @dev Reverts if the given call is not authorized to skip the chain ID validtion.
    /// @dev `validateUserOp()` will recompute the `userOpHash` without the chain ID before validating
    ///      it if the `UserOperation.calldata` is calling this function. This allows certain UserOperations
    ///      to be replayed for all accounts sharing the same address across chains. E.g. This may be
    ///      useful for syncing owner changes.
    ///
    /// @param calls An array of calldata to use for separate self calls.
    function executeWithoutChainIdValidation(bytes[] calldata calls) external payable virtual onlyEntryPoint {
        for (uint256 i; i < calls.length; i++) {
            bytes calldata call = calls[i];
            bytes4 selector = bytes4(call);
            if (!canSkipChainIdValidation(selector)) {
                revert SelectorNotAllowed(selector);
            }
            _call(address(this), 0, call);
        }
    }
    /// @notice Executes the given call from this account.
    ///
    /// @dev Can only be called by the Entrypoint or an owner of this account (including itself).
    ///
    /// @param target The address to call.
    /// @param value  The value to send with the call.
    /// @param data   The data of the call.
    function execute(address target, uint256 value, bytes calldata data)
        external
        payable
        virtual
        onlyEntryPointOrOwner
    {
        _call(target, value, data);
    }
    /// @notice Executes batch of `Call`s.
    ///
    /// @dev Can only be called by the Entrypoint or an owner of this account (including itself).
    ///
    /// @param calls The list of `Call`s to execute.
    function executeBatch(Call[] calldata calls) external payable virtual onlyEntryPointOrOwner {
        for (uint256 i; i < calls.length; i++) {
            _call(calls[i].target, calls[i].value, calls[i].data);
        }
    }
    /// @notice Returns the address of the EntryPoint v0.6.
    ///
    /// @return The address of the EntryPoint v0.6
    function entryPoint() public view virtual returns (address) {
        return 0x5FF137D4b0FDCD49DcA30c7CF57E578a026d2789;
    }
    /// @notice Computes the hash of the `UserOperation` in the same way as EntryPoint v0.6, but
    ///         leaves out the chain ID.
    ///
    /// @dev This allows accounts to sign a hash that can be used on many chains.
    ///
    /// @param userOp The `UserOperation` to compute the hash for.
    ///
    /// @return The `UserOperation` hash, which does not depend on chain ID.
    function getUserOpHashWithoutChainId(UserOperation calldata userOp) public view virtual returns (bytes32) {
        return keccak256(abi.encode(UserOperationLib.hash(userOp), entryPoint()));
    }
    /// @notice Returns the implementation of the ERC1967 proxy.
    ///
    /// @return $ The address of implementation contract.
    function implementation() public view returns (address $) {
        assembly {
            $ := sload(_ERC1967_IMPLEMENTATION_SLOT)
        }
    }
    /// @notice Returns whether `functionSelector` can be called in `executeWithoutChainIdValidation`.
    ///
    /// @param functionSelector The function selector to check.
    ////
    /// @return `true` is the function selector is allowed to skip the chain ID validation, else `false`.
    function canSkipChainIdValidation(bytes4 functionSelector) public pure returns (bool) {
        if (
            functionSelector == MultiOwnable.addOwnerPublicKey.selector
                || functionSelector == MultiOwnable.addOwnerAddress.selector
                || functionSelector == MultiOwnable.removeOwnerAtIndex.selector
                || functionSelector == MultiOwnable.removeLastOwner.selector
                || functionSelector == UUPSUpgradeable.upgradeToAndCall.selector
        ) {
            return true;
        }
        return false;
    }
    /// @notice Executes the given call from this account.
    ///
    /// @dev Reverts if the call reverted.
    /// @dev Implementation taken from
    /// https://github.com/alchemyplatform/light-account/blob/43f625afdda544d5e5af9c370c9f4be0943e4e90/src/common/BaseLightAccount.sol#L125
    ///
    /// @param target The target call address.
    /// @param value  The call value to user.
    /// @param data   The raw call data.
    function _call(address target, uint256 value, bytes memory data) internal {
        (bool success, bytes memory result) = target.call{value: value}(data);
        if (!success) {
            assembly ("memory-safe") {
                revert(add(result, 32), mload(result))
            }
        }
    }
    /// @inheritdoc ERC1271
    ///
    /// @dev Used by both `ERC1271.isValidSignature` AND `IAccount.validateUserOp` signature validation.
    /// @dev Reverts if owner at `ownerIndex` is not compatible with `signature` format.
    ///
    /// @param signature ABI encoded `SignatureWrapper`.
    function _isValidSignature(bytes32 hash, bytes calldata signature) internal view virtual override returns (bool) {
        SignatureWrapper memory sigWrapper = abi.decode(signature, (SignatureWrapper));
        bytes memory ownerBytes = ownerAtIndex(sigWrapper.ownerIndex);
        if (ownerBytes.length == 32) {
            if (uint256(bytes32(ownerBytes)) > type(uint160).max) {
                // technically should be impossible given owners can only be added with
                // addOwnerAddress and addOwnerPublicKey, but we leave incase of future changes.
                revert InvalidEthereumAddressOwner(ownerBytes);
            }
            address owner;
            assembly ("memory-safe") {
                owner := mload(add(ownerBytes, 32))
            }
            return SignatureCheckerLib.isValidSignatureNow(owner, hash, sigWrapper.signatureData);
        }
        if (ownerBytes.length == 64) {
            (uint256 x, uint256 y) = abi.decode(ownerBytes, (uint256, uint256));
            WebAuthn.WebAuthnAuth memory auth = abi.decode(sigWrapper.signatureData, (WebAuthn.WebAuthnAuth));
            return WebAuthn.verify({challenge: abi.encode(hash), requireUV: false, webAuthnAuth: auth, x: x, y: y});
        }
        revert InvalidOwnerBytesLength(ownerBytes);
    }
    /// @inheritdoc UUPSUpgradeable
    ///
    /// @dev Authorization logic is only based on the `msg.sender` being an owner of this account,
    ///      or `address(this)`.
    function _authorizeUpgrade(address) internal view virtual override(UUPSUpgradeable) onlyOwner {}
    /// @inheritdoc ERC1271
    function _domainNameAndVersion() internal pure override(ERC1271) returns (string memory, string memory) {
        return ("Coinbase Smart Wallet", "1");
    }
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
import "./UserOperation.sol";
interface IAccount {
    /**
     * Validate user's signature and nonce
     * the entryPoint will make the call to the recipient only if this validation call returns successfully.
     * signature failure should be reported by returning SIG_VALIDATION_FAILED (1).
     * This allows making a "simulation call" without a valid signature
     * Other failures (e.g. nonce mismatch, or invalid signature format) should still revert to signal failure.
     *
     * @dev Must validate caller is the entryPoint.
     *      Must validate the signature and nonce
     * @param userOp the operation that is about to be executed.
     * @param userOpHash hash of the user's request data. can be used as the basis for signature.
     * @param missingAccountFunds missing funds on the account's deposit in the entrypoint.
     *      This is the minimum amount to transfer to the sender(entryPoint) to be able to make the call.
     *      The excess is left as a deposit in the entrypoint, for future calls.
     *      can be withdrawn anytime using "entryPoint.withdrawTo()"
     *      In case there is a paymaster in the request (or the current deposit is high enough), this value will be zero.
     * @return validationData packaged ValidationData structure. use `_packValidationData` and `_unpackValidationData` to encode and decode
     *      <20-byte> sigAuthorizer - 0 for valid signature, 1 to mark signature failure,
     *         otherwise, an address of an "authorizer" contract.
     *      <6-byte> validUntil - last timestamp this operation is valid. 0 for "indefinite"
     *      <6-byte> validAfter - first timestamp this operation is valid
     *      If an account doesn't use time-range, it is enough to return SIG_VALIDATION_FAILED value (1) for signature failure.
     *      Note that the validation code cannot use block.timestamp (or block.number) directly.
     */
    function validateUserOp(UserOperation calldata userOp, bytes32 userOpHash, uint256 missingAccountFunds)
    external returns (uint256 validationData);
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
/* solhint-disable no-inline-assembly */
import {calldataKeccak} from "../core/Helpers.sol";
/**
 * User Operation struct
 * @param sender the sender account of this request.
     * @param nonce unique value the sender uses to verify it is not a replay.
     * @param initCode if set, the account contract will be created by this constructor/
     * @param callData the method call to execute on this account.
     * @param callGasLimit the gas limit passed to the callData method call.
     * @param verificationGasLimit gas used for validateUserOp and validatePaymasterUserOp.
     * @param preVerificationGas gas not calculated by the handleOps method, but added to the gas paid. Covers batch overhead.
     * @param maxFeePerGas same as EIP-1559 gas parameter.
     * @param maxPriorityFeePerGas same as EIP-1559 gas parameter.
     * @param paymasterAndData if set, this field holds the paymaster address and paymaster-specific data. the paymaster will pay for the transaction instead of the sender.
     * @param signature sender-verified signature over the entire request, the EntryPoint address and the chain ID.
     */
    struct UserOperation {
        address sender;
        uint256 nonce;
        bytes initCode;
        bytes callData;
        uint256 callGasLimit;
        uint256 verificationGasLimit;
        uint256 preVerificationGas;
        uint256 maxFeePerGas;
        uint256 maxPriorityFeePerGas;
        bytes paymasterAndData;
        bytes signature;
    }
/**
 * Utility functions helpful when working with UserOperation structs.
 */
library UserOperationLib {
    function getSender(UserOperation calldata userOp) internal pure returns (address) {
        address data;
        //read sender from userOp, which is first userOp member (saves 800 gas...)
        assembly {data := calldataload(userOp)}
        return address(uint160(data));
    }
    //relayer/block builder might submit the TX with higher priorityFee, but the user should not
    // pay above what he signed for.
    function gasPrice(UserOperation calldata userOp) internal view returns (uint256) {
    unchecked {
        uint256 maxFeePerGas = userOp.maxFeePerGas;
        uint256 maxPriorityFeePerGas = userOp.maxPriorityFeePerGas;
        if (maxFeePerGas == maxPriorityFeePerGas) {
            //legacy mode (for networks that don't support basefee opcode)
            return maxFeePerGas;
        }
        return min(maxFeePerGas, maxPriorityFeePerGas + block.basefee);
    }
    }
    function pack(UserOperation calldata userOp) internal pure returns (bytes memory ret) {
        address sender = getSender(userOp);
        uint256 nonce = userOp.nonce;
        bytes32 hashInitCode = calldataKeccak(userOp.initCode);
        bytes32 hashCallData = calldataKeccak(userOp.callData);
        uint256 callGasLimit = userOp.callGasLimit;
        uint256 verificationGasLimit = userOp.verificationGasLimit;
        uint256 preVerificationGas = userOp.preVerificationGas;
        uint256 maxFeePerGas = userOp.maxFeePerGas;
        uint256 maxPriorityFeePerGas = userOp.maxPriorityFeePerGas;
        bytes32 hashPaymasterAndData = calldataKeccak(userOp.paymasterAndData);
        return abi.encode(
            sender, nonce,
            hashInitCode, hashCallData,
            callGasLimit, verificationGasLimit, preVerificationGas,
            maxFeePerGas, maxPriorityFeePerGas,
            hashPaymasterAndData
        );
    }
    function hash(UserOperation calldata userOp) internal pure returns (bytes32) {
        return keccak256(pack(userOp));
    }
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Receiver mixin for ETH and safe-transferred ERC721 and ERC1155 tokens.
/// @author Solady (https://github.com/Vectorized/solady/blob/main/src/accounts/Receiver.sol)
///
/// @dev Note:
/// - Handles all ERC721 and ERC1155 token safety callbacks.
/// - Collapses function table gas overhead and code size.
/// - Utilizes fallback so unknown calldata will pass on.
abstract contract Receiver {
    /// @dev For receiving ETH.
    receive() external payable virtual {}
    /// @dev Fallback function with the `receiverFallback` modifier.
    fallback() external payable virtual receiverFallback {}
    /// @dev Modifier for the fallback function to handle token callbacks.
    modifier receiverFallback() virtual {
        /// @solidity memory-safe-assembly
        assembly {
            let s := shr(224, calldataload(0))
            // 0x150b7a02: `onERC721Received(address,address,uint256,bytes)`.
            // 0xf23a6e61: `onERC1155Received(address,address,uint256,uint256,bytes)`.
            // 0xbc197c81: `onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)`.
            if or(eq(s, 0x150b7a02), or(eq(s, 0xf23a6e61), eq(s, 0xbc197c81))) {
                mstore(0x20, s) // Store `msg.sig`.
                return(0x3c, 0x20) // Return `msg.sig`.
            }
        }
        _;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Signature verification helper that supports both ECDSA signatures from EOAs
/// and ERC1271 signatures from smart contract wallets like Argent and Gnosis safe.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/SignatureCheckerLib.sol)
/// @author Modified from OpenZeppelin (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/utils/cryptography/SignatureChecker.sol)
///
/// @dev Note:
/// - The signature checking functions use the ecrecover precompile (0x1).
/// - The `bytes memory signature` variants use the identity precompile (0x4)
///   to copy memory internally.
/// - Unlike ECDSA signatures, contract signatures are revocable.
/// - As of Solady version 0.0.134, all `bytes signature` variants accept both
///   regular 65-byte `(r, s, v)` and EIP-2098 `(r, vs)` short form signatures.
///   See: https://eips.ethereum.org/EIPS/eip-2098
///   This is for calldata efficiency on smart accounts prevalent on L2s.
///
/// WARNING! Do NOT use signatures as unique identifiers:
/// - Use a nonce in the digest to prevent replay attacks on the same contract.
/// - Use EIP-712 for the digest to prevent replay attacks across different chains and contracts.
///   EIP-712 also enables readable signing of typed data for better user safety.
/// This implementation does NOT check if a signature is non-malleable.
library SignatureCheckerLib {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*               SIGNATURE CHECKING OPERATIONS                */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns whether `signature` is valid for `signer` and `hash`.
    /// If `signer` is a smart contract, the signature is validated with ERC1271.
    /// Otherwise, the signature is validated with `ECDSA.recover`.
    function isValidSignatureNow(address signer, bytes32 hash, bytes memory signature)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits of `signer` in case they are dirty.
            for { signer := shr(96, shl(96, signer)) } signer {} {
                let m := mload(0x40)
                mstore(0x00, hash)
                mstore(0x40, mload(add(signature, 0x20))) // `r`.
                if eq(mload(signature), 64) {
                    let vs := mload(add(signature, 0x40))
                    mstore(0x20, add(shr(255, vs), 27)) // `v`.
                    mstore(0x60, shr(1, shl(1, vs))) // `s`.
                    let t :=
                        staticcall(
                            gas(), // Amount of gas left for the transaction.
                            1, // Address of `ecrecover`.
                            0x00, // Start of input.
                            0x80, // Size of input.
                            0x01, // Start of output.
                            0x20 // Size of output.
                        )
                    // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                    if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                        isValid := 1
                        mstore(0x60, 0) // Restore the zero slot.
                        mstore(0x40, m) // Restore the free memory pointer.
                        break
                    }
                }
                if eq(mload(signature), 65) {
                    mstore(0x20, byte(0, mload(add(signature, 0x60)))) // `v`.
                    mstore(0x60, mload(add(signature, 0x40))) // `s`.
                    let t :=
                        staticcall(
                            gas(), // Amount of gas left for the transaction.
                            1, // Address of `ecrecover`.
                            0x00, // Start of input.
                            0x80, // Size of input.
                            0x01, // Start of output.
                            0x20 // Size of output.
                        )
                    // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                    if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                        isValid := 1
                        mstore(0x60, 0) // Restore the zero slot.
                        mstore(0x40, m) // Restore the free memory pointer.
                        break
                    }
                }
                mstore(0x60, 0) // Restore the zero slot.
                mstore(0x40, m) // Restore the free memory pointer.
                let f := shl(224, 0x1626ba7e)
                mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
                mstore(add(m, 0x04), hash)
                let d := add(m, 0x24)
                mstore(d, 0x40) // The offset of the `signature` in the calldata.
                // Copy the `signature` over.
                let n := add(0x20, mload(signature))
                pop(staticcall(gas(), 4, signature, n, add(m, 0x44), n))
                // forgefmt: disable-next-item
                isValid := and(
                    // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                    eq(mload(d), f),
                    // Whether the staticcall does not revert.
                    // This must be placed at the end of the `and` clause,
                    // as the arguments are evaluated from right to left.
                    staticcall(
                        gas(), // Remaining gas.
                        signer, // The `signer` address.
                        m, // Offset of calldata in memory.
                        add(returndatasize(), 0x44), // Length of calldata in memory.
                        d, // Offset of returndata.
                        0x20 // Length of returndata to write.
                    )
                )
                break
            }
        }
    }
    /// @dev Returns whether `signature` is valid for `signer` and `hash`.
    /// If `signer` is a smart contract, the signature is validated with ERC1271.
    /// Otherwise, the signature is validated with `ECDSA.recover`.
    function isValidSignatureNowCalldata(address signer, bytes32 hash, bytes calldata signature)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits of `signer` in case they are dirty.
            for { signer := shr(96, shl(96, signer)) } signer {} {
                let m := mload(0x40)
                mstore(0x00, hash)
                if eq(signature.length, 64) {
                    let vs := calldataload(add(signature.offset, 0x20))
                    mstore(0x20, add(shr(255, vs), 27)) // `v`.
                    mstore(0x40, calldataload(signature.offset)) // `r`.
                    mstore(0x60, shr(1, shl(1, vs))) // `s`.
                    let t :=
                        staticcall(
                            gas(), // Amount of gas left for the transaction.
                            1, // Address of `ecrecover`.
                            0x00, // Start of input.
                            0x80, // Size of input.
                            0x01, // Start of output.
                            0x20 // Size of output.
                        )
                    // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                    if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                        isValid := 1
                        mstore(0x60, 0) // Restore the zero slot.
                        mstore(0x40, m) // Restore the free memory pointer.
                        break
                    }
                }
                if eq(signature.length, 65) {
                    mstore(0x20, byte(0, calldataload(add(signature.offset, 0x40)))) // `v`.
                    calldatacopy(0x40, signature.offset, 0x40) // `r`, `s`.
                    let t :=
                        staticcall(
                            gas(), // Amount of gas left for the transaction.
                            1, // Address of `ecrecover`.
                            0x00, // Start of input.
                            0x80, // Size of input.
                            0x01, // Start of output.
                            0x20 // Size of output.
                        )
                    // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                    if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                        isValid := 1
                        mstore(0x60, 0) // Restore the zero slot.
                        mstore(0x40, m) // Restore the free memory pointer.
                        break
                    }
                }
                mstore(0x60, 0) // Restore the zero slot.
                mstore(0x40, m) // Restore the free memory pointer.
                let f := shl(224, 0x1626ba7e)
                mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
                mstore(add(m, 0x04), hash)
                let d := add(m, 0x24)
                mstore(d, 0x40) // The offset of the `signature` in the calldata.
                mstore(add(m, 0x44), signature.length)
                // Copy the `signature` over.
                calldatacopy(add(m, 0x64), signature.offset, signature.length)
                // forgefmt: disable-next-item
                isValid := and(
                    // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                    eq(mload(d), f),
                    // Whether the staticcall does not revert.
                    // This must be placed at the end of the `and` clause,
                    // as the arguments are evaluated from right to left.
                    staticcall(
                        gas(), // Remaining gas.
                        signer, // The `signer` address.
                        m, // Offset of calldata in memory.
                        add(signature.length, 0x64), // Length of calldata in memory.
                        d, // Offset of returndata.
                        0x20 // Length of returndata to write.
                    )
                )
                break
            }
        }
    }
    /// @dev Returns whether the signature (`r`, `vs`) is valid for `signer` and `hash`.
    /// If `signer` is a smart contract, the signature is validated with ERC1271.
    /// Otherwise, the signature is validated with `ECDSA.recover`.
    function isValidSignatureNow(address signer, bytes32 hash, bytes32 r, bytes32 vs)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits of `signer` in case they are dirty.
            for { signer := shr(96, shl(96, signer)) } signer {} {
                let m := mload(0x40)
                mstore(0x00, hash)
                mstore(0x20, add(shr(255, vs), 27)) // `v`.
                mstore(0x40, r) // `r`.
                mstore(0x60, shr(1, shl(1, vs))) // `s`.
                let t :=
                    staticcall(
                        gas(), // Amount of gas left for the transaction.
                        1, // Address of `ecrecover`.
                        0x00, // Start of input.
                        0x80, // Size of input.
                        0x01, // Start of output.
                        0x20 // Size of output.
                    )
                // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                    isValid := 1
                    mstore(0x60, 0) // Restore the zero slot.
                    mstore(0x40, m) // Restore the free memory pointer.
                    break
                }
                let f := shl(224, 0x1626ba7e)
                mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
                mstore(add(m, 0x04), hash)
                let d := add(m, 0x24)
                mstore(d, 0x40) // The offset of the `signature` in the calldata.
                mstore(add(m, 0x44), 65) // Length of the signature.
                mstore(add(m, 0x64), r) // `r`.
                mstore(add(m, 0x84), mload(0x60)) // `s`.
                mstore8(add(m, 0xa4), mload(0x20)) // `v`.
                // forgefmt: disable-next-item
                isValid := and(
                    // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                    eq(mload(d), f),
                    // Whether the staticcall does not revert.
                    // This must be placed at the end of the `and` clause,
                    // as the arguments are evaluated from right to left.
                    staticcall(
                        gas(), // Remaining gas.
                        signer, // The `signer` address.
                        m, // Offset of calldata in memory.
                        0xa5, // Length of calldata in memory.
                        d, // Offset of returndata.
                        0x20 // Length of returndata to write.
                    )
                )
                mstore(0x60, 0) // Restore the zero slot.
                mstore(0x40, m) // Restore the free memory pointer.
                break
            }
        }
    }
    /// @dev Returns whether the signature (`v`, `r`, `s`) is valid for `signer` and `hash`.
    /// If `signer` is a smart contract, the signature is validated with ERC1271.
    /// Otherwise, the signature is validated with `ECDSA.recover`.
    function isValidSignatureNow(address signer, bytes32 hash, uint8 v, bytes32 r, bytes32 s)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits of `signer` in case they are dirty.
            for { signer := shr(96, shl(96, signer)) } signer {} {
                let m := mload(0x40)
                mstore(0x00, hash)
                mstore(0x20, and(v, 0xff)) // `v`.
                mstore(0x40, r) // `r`.
                mstore(0x60, s) // `s`.
                let t :=
                    staticcall(
                        gas(), // Amount of gas left for the transaction.
                        1, // Address of `ecrecover`.
                        0x00, // Start of input.
                        0x80, // Size of input.
                        0x01, // Start of output.
                        0x20 // Size of output.
                    )
                // `returndatasize()` will be `0x20` upon success, and `0x00` otherwise.
                if iszero(or(iszero(returndatasize()), xor(signer, mload(t)))) {
                    isValid := 1
                    mstore(0x60, 0) // Restore the zero slot.
                    mstore(0x40, m) // Restore the free memory pointer.
                    break
                }
                let f := shl(224, 0x1626ba7e)
                mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
                mstore(add(m, 0x04), hash)
                let d := add(m, 0x24)
                mstore(d, 0x40) // The offset of the `signature` in the calldata.
                mstore(add(m, 0x44), 65) // Length of the signature.
                mstore(add(m, 0x64), r) // `r`.
                mstore(add(m, 0x84), s) // `s`.
                mstore8(add(m, 0xa4), v) // `v`.
                // forgefmt: disable-next-item
                isValid := and(
                    // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                    eq(mload(d), f),
                    // Whether the staticcall does not revert.
                    // This must be placed at the end of the `and` clause,
                    // as the arguments are evaluated from right to left.
                    staticcall(
                        gas(), // Remaining gas.
                        signer, // The `signer` address.
                        m, // Offset of calldata in memory.
                        0xa5, // Length of calldata in memory.
                        d, // Offset of returndata.
                        0x20 // Length of returndata to write.
                    )
                )
                mstore(0x60, 0) // Restore the zero slot.
                mstore(0x40, m) // Restore the free memory pointer.
                break
            }
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     ERC1271 OPERATIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns whether `signature` is valid for `hash` for an ERC1271 `signer` contract.
    function isValidERC1271SignatureNow(address signer, bytes32 hash, bytes memory signature)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40)
            let f := shl(224, 0x1626ba7e)
            mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
            mstore(add(m, 0x04), hash)
            let d := add(m, 0x24)
            mstore(d, 0x40) // The offset of the `signature` in the calldata.
            // Copy the `signature` over.
            let n := add(0x20, mload(signature))
            pop(staticcall(gas(), 4, signature, n, add(m, 0x44), n))
            // forgefmt: disable-next-item
            isValid := and(
                // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                eq(mload(d), f),
                // Whether the staticcall does not revert.
                // This must be placed at the end of the `and` clause,
                // as the arguments are evaluated from right to left.
                staticcall(
                    gas(), // Remaining gas.
                    signer, // The `signer` address.
                    m, // Offset of calldata in memory.
                    add(returndatasize(), 0x44), // Length of calldata in memory.
                    d, // Offset of returndata.
                    0x20 // Length of returndata to write.
                )
            )
        }
    }
    /// @dev Returns whether `signature` is valid for `hash` for an ERC1271 `signer` contract.
    function isValidERC1271SignatureNowCalldata(
        address signer,
        bytes32 hash,
        bytes calldata signature
    ) internal view returns (bool isValid) {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40)
            let f := shl(224, 0x1626ba7e)
            mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
            mstore(add(m, 0x04), hash)
            let d := add(m, 0x24)
            mstore(d, 0x40) // The offset of the `signature` in the calldata.
            mstore(add(m, 0x44), signature.length)
            // Copy the `signature` over.
            calldatacopy(add(m, 0x64), signature.offset, signature.length)
            // forgefmt: disable-next-item
            isValid := and(
                // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                eq(mload(d), f),
                // Whether the staticcall does not revert.
                // This must be placed at the end of the `and` clause,
                // as the arguments are evaluated from right to left.
                staticcall(
                    gas(), // Remaining gas.
                    signer, // The `signer` address.
                    m, // Offset of calldata in memory.
                    add(signature.length, 0x64), // Length of calldata in memory.
                    d, // Offset of returndata.
                    0x20 // Length of returndata to write.
                )
            )
        }
    }
    /// @dev Returns whether the signature (`r`, `vs`) is valid for `hash`
    /// for an ERC1271 `signer` contract.
    function isValidERC1271SignatureNow(address signer, bytes32 hash, bytes32 r, bytes32 vs)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40)
            let f := shl(224, 0x1626ba7e)
            mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
            mstore(add(m, 0x04), hash)
            let d := add(m, 0x24)
            mstore(d, 0x40) // The offset of the `signature` in the calldata.
            mstore(add(m, 0x44), 65) // Length of the signature.
            mstore(add(m, 0x64), r) // `r`.
            mstore(add(m, 0x84), shr(1, shl(1, vs))) // `s`.
            mstore8(add(m, 0xa4), add(shr(255, vs), 27)) // `v`.
            // forgefmt: disable-next-item
            isValid := and(
                // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                eq(mload(d), f),
                // Whether the staticcall does not revert.
                // This must be placed at the end of the `and` clause,
                // as the arguments are evaluated from right to left.
                staticcall(
                    gas(), // Remaining gas.
                    signer, // The `signer` address.
                    m, // Offset of calldata in memory.
                    0xa5, // Length of calldata in memory.
                    d, // Offset of returndata.
                    0x20 // Length of returndata to write.
                )
            )
        }
    }
    /// @dev Returns whether the signature (`v`, `r`, `s`) is valid for `hash`
    /// for an ERC1271 `signer` contract.
    function isValidERC1271SignatureNow(address signer, bytes32 hash, uint8 v, bytes32 r, bytes32 s)
        internal
        view
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40)
            let f := shl(224, 0x1626ba7e)
            mstore(m, f) // `bytes4(keccak256("isValidSignature(bytes32,bytes)"))`.
            mstore(add(m, 0x04), hash)
            let d := add(m, 0x24)
            mstore(d, 0x40) // The offset of the `signature` in the calldata.
            mstore(add(m, 0x44), 65) // Length of the signature.
            mstore(add(m, 0x64), r) // `r`.
            mstore(add(m, 0x84), s) // `s`.
            mstore8(add(m, 0xa4), v) // `v`.
            // forgefmt: disable-next-item
            isValid := and(
                // Whether the returndata is the magic value `0x1626ba7e` (left-aligned).
                eq(mload(d), f),
                // Whether the staticcall does not revert.
                // This must be placed at the end of the `and` clause,
                // as the arguments are evaluated from right to left.
                staticcall(
                    gas(), // Remaining gas.
                    signer, // The `signer` address.
                    m, // Offset of calldata in memory.
                    0xa5, // Length of calldata in memory.
                    d, // Offset of returndata.
                    0x20 // Length of returndata to write.
                )
            )
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     HASHING OPERATIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns an Ethereum Signed Message, created from a `hash`.
    /// This produces a hash corresponding to the one signed with the
    /// [`eth_sign`](https://eth.wiki/json-rpc/API#eth_sign)
    /// JSON-RPC method as part of EIP-191.
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x20, hash) // Store into scratch space for keccak256.
            mstore(0x00, "\\x00\\x00\\x00\\x00\\x19Ethereum Signed Message:\
32") // 28 bytes.
            result := keccak256(0x04, 0x3c) // `32 * 2 - (32 - 28) = 60 = 0x3c`.
        }
    }
    /// @dev Returns an Ethereum Signed Message, created from `s`.
    /// This produces a hash corresponding to the one signed with the
    /// [`eth_sign`](https://eth.wiki/json-rpc/API#eth_sign)
    /// JSON-RPC method as part of EIP-191.
    /// Note: Supports lengths of `s` up to 999999 bytes.
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            let sLength := mload(s)
            let o := 0x20
            mstore(o, "\\x19Ethereum Signed Message:\
") // 26 bytes, zero-right-padded.
            mstore(0x00, 0x00)
            // Convert the `s.length` to ASCII decimal representation: `base10(s.length)`.
            for { let temp := sLength } 1 {} {
                o := sub(o, 1)
                mstore8(o, add(48, mod(temp, 10)))
                temp := div(temp, 10)
                if iszero(temp) { break }
            }
            let n := sub(0x3a, o) // Header length: `26 + 32 - o`.
            // Throw an out-of-offset error (consumes all gas) if the header exceeds 32 bytes.
            returndatacopy(returndatasize(), returndatasize(), gt(n, 0x20))
            mstore(s, or(mload(0x00), mload(n))) // Temporarily store the header.
            result := keccak256(add(s, sub(0x20, n)), add(n, sLength))
            mstore(s, sLength) // Restore the length.
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   EMPTY CALLDATA HELPERS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns an empty calldata bytes.
    function emptySignature() internal pure returns (bytes calldata signature) {
        /// @solidity memory-safe-assembly
        assembly {
            signature.length := 0
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice UUPS proxy mixin.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/UUPSUpgradeable.sol)
/// @author Modified from OpenZeppelin
/// (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/proxy/utils/UUPSUpgradeable.sol)
///
/// Note:
/// - This implementation is intended to be used with ERC1967 proxies.
/// See: `LibClone.deployERC1967` and related functions.
/// - This implementation is NOT compatible with legacy OpenZeppelin proxies
/// which do not store the implementation at `_ERC1967_IMPLEMENTATION_SLOT`.
abstract contract UUPSUpgradeable {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev The upgrade failed.
    error UpgradeFailed();
    /// @dev The call is from an unauthorized call context.
    error UnauthorizedCallContext();
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         IMMUTABLES                         */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev For checking if the context is a delegate call.
    uint256 private immutable __self = uint256(uint160(address(this)));
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                           EVENTS                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Emitted when the proxy's implementation is upgraded.
    event Upgraded(address indexed implementation);
    /// @dev `keccak256(bytes("Upgraded(address)"))`.
    uint256 private constant _UPGRADED_EVENT_SIGNATURE =
        0xbc7cd75a20ee27fd9adebab32041f755214dbc6bffa90cc0225b39da2e5c2d3b;
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                          STORAGE                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev The ERC-1967 storage slot for the implementation in the proxy.
    /// `uint256(keccak256("eip1967.proxy.implementation")) - 1`.
    bytes32 internal constant _ERC1967_IMPLEMENTATION_SLOT =
        0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                      UUPS OPERATIONS                       */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Please override this function to check if `msg.sender` is authorized
    /// to upgrade the proxy to `newImplementation`, reverting if not.
    /// ```
    ///     function _authorizeUpgrade(address) internal override onlyOwner {}
    /// ```
    function _authorizeUpgrade(address newImplementation) internal virtual;
    /// @dev Returns the storage slot used by the implementation,
    /// as specified in [ERC1822](https://eips.ethereum.org/EIPS/eip-1822).
    ///
    /// Note: The `notDelegated` modifier prevents accidental upgrades to
    /// an implementation that is a proxy contract.
    function proxiableUUID() public view virtual notDelegated returns (bytes32) {
        // This function must always return `_ERC1967_IMPLEMENTATION_SLOT` to comply with ERC1967.
        return _ERC1967_IMPLEMENTATION_SLOT;
    }
    /// @dev Upgrades the proxy's implementation to `newImplementation`.
    /// Emits a {Upgraded} event.
    ///
    /// Note: Passing in empty `data` skips the delegatecall to `newImplementation`.
    function upgradeToAndCall(address newImplementation, bytes calldata data)
        public
        payable
        virtual
        onlyProxy
    {
        _authorizeUpgrade(newImplementation);
        /// @solidity memory-safe-assembly
        assembly {
            newImplementation := shr(96, shl(96, newImplementation)) // Clears upper 96 bits.
            mstore(0x01, 0x52d1902d) // `proxiableUUID()`.
            let s := _ERC1967_IMPLEMENTATION_SLOT
            // Check if `newImplementation` implements `proxiableUUID` correctly.
            if iszero(eq(mload(staticcall(gas(), newImplementation, 0x1d, 0x04, 0x01, 0x20)), s)) {
                mstore(0x01, 0x55299b49) // `UpgradeFailed()`.
                revert(0x1d, 0x04)
            }
            // Emit the {Upgraded} event.
            log2(codesize(), 0x00, _UPGRADED_EVENT_SIGNATURE, newImplementation)
            sstore(s, newImplementation) // Updates the implementation.
            // Perform a delegatecall to `newImplementation` if `data` is non-empty.
            if data.length {
                // Forwards the `data` to `newImplementation` via delegatecall.
                let m := mload(0x40)
                calldatacopy(m, data.offset, data.length)
                if iszero(delegatecall(gas(), newImplementation, m, data.length, codesize(), 0x00))
                {
                    // Bubble up the revert if the call reverts.
                    returndatacopy(m, 0x00, returndatasize())
                    revert(m, returndatasize())
                }
            }
        }
    }
    /// @dev Requires that the execution is performed through a proxy.
    modifier onlyProxy() {
        uint256 s = __self;
        /// @solidity memory-safe-assembly
        assembly {
            // To enable use cases with an immutable default implementation in the bytecode,
            // (see: ERC6551Proxy), we don't require that the proxy address must match the
            // value stored in the implementation slot, which may not be initialized.
            if eq(s, address()) {
                mstore(0x00, 0x9f03a026) // `UnauthorizedCallContext()`.
                revert(0x1c, 0x04)
            }
        }
        _;
    }
    /// @dev Requires that the execution is NOT performed via delegatecall.
    /// This is the opposite of `onlyProxy`.
    modifier notDelegated() {
        uint256 s = __self;
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(eq(s, address())) {
                mstore(0x00, 0x9f03a026) // `UnauthorizedCallContext()`.
                revert(0x1c, 0x04)
            }
        }
        _;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import {FCL_ecdsa} from "FreshCryptoLib/FCL_ecdsa.sol";
import {FCL_Elliptic_ZZ} from "FreshCryptoLib/FCL_elliptic.sol";
import {Base64} from "openzeppelin-contracts/contracts/utils/Base64.sol";
import {LibString} from "solady/utils/LibString.sol";
/// @title WebAuthn
///
/// @notice A library for verifying WebAuthn Authentication Assertions, built off the work
///         of Daimo.
///
/// @dev Attempts to use the RIP-7212 precompile for signature verification.
///      If precompile verification fails, it falls back to FreshCryptoLib.
///
/// @author Coinbase (https://github.com/base-org/webauthn-sol)
/// @author Daimo (https://github.com/daimo-eth/p256-verifier/blob/master/src/WebAuthn.sol)
library WebAuthn {
    using LibString for string;
    struct WebAuthnAuth {
        /// @dev The WebAuthn authenticator data.
        ///      See https://www.w3.org/TR/webauthn-2/#dom-authenticatorassertionresponse-authenticatordata.
        bytes authenticatorData;
        /// @dev The WebAuthn client data JSON.
        ///      See https://www.w3.org/TR/webauthn-2/#dom-authenticatorresponse-clientdatajson.
        string clientDataJSON;
        /// @dev The index at which "challenge":"..." occurs in `clientDataJSON`.
        uint256 challengeIndex;
        /// @dev The index at which "type":"..." occurs in `clientDataJSON`.
        uint256 typeIndex;
        /// @dev The r value of secp256r1 signature
        uint256 r;
        /// @dev The s value of secp256r1 signature
        uint256 s;
    }
    /// @dev Bit 0 of the authenticator data struct, corresponding to the "User Present" bit.
    ///      See https://www.w3.org/TR/webauthn-2/#flags.
    bytes1 private constant _AUTH_DATA_FLAGS_UP = 0x01;
    /// @dev Bit 2 of the authenticator data struct, corresponding to the "User Verified" bit.
    ///      See https://www.w3.org/TR/webauthn-2/#flags.
    bytes1 private constant _AUTH_DATA_FLAGS_UV = 0x04;
    /// @dev Secp256r1 curve order / 2 used as guard to prevent signature malleability issue.
    uint256 private constant _P256_N_DIV_2 = FCL_Elliptic_ZZ.n / 2;
    /// @dev The precompiled contract address to use for signature verification in the “secp256r1” elliptic curve.
    ///      See https://github.com/ethereum/RIPs/blob/master/RIPS/rip-7212.md.
    address private constant _VERIFIER = address(0x100);
    /// @dev The expected type (hash) in the client data JSON when verifying assertion signatures.
    ///      See https://www.w3.org/TR/webauthn-2/#dom-collectedclientdata-type
    bytes32 private constant _EXPECTED_TYPE_HASH = keccak256('"type":"webauthn.get"');
    ///
    /// @notice Verifies a Webauthn Authentication Assertion as described
    /// in https://www.w3.org/TR/webauthn-2/#sctn-verifying-assertion.
    ///
    /// @dev We do not verify all the steps as described in the specification, only ones relevant to our context.
    ///      Please carefully read through this list before usage.
    ///
    ///      Specifically, we do verify the following:
    ///         - Verify that authenticatorData (which comes from the authenticator, such as iCloud Keychain) indicates
    ///           a well-formed assertion with the user present bit set. If `requireUV` is set, checks that the authenticator
    ///           enforced user verification. User verification should be required if, and only if, options.userVerification
    ///           is set to required in the request.
    ///         - Verifies that the client JSON is of type "webauthn.get", i.e. the client was responding to a request to
    ///           assert authentication.
    ///         - Verifies that the client JSON contains the requested challenge.
    ///         - Verifies that (r, s) constitute a valid signature over both the authenicatorData and client JSON, for public
    ///            key (x, y).
    ///
    ///      We make some assumptions about the particular use case of this verifier, so we do NOT verify the following:
    ///         - Does NOT verify that the origin in the `clientDataJSON` matches the Relying Party's origin: tt is considered
    ///           the authenticator's responsibility to ensure that the user is interacting with the correct RP. This is
    ///           enforced by most high quality authenticators properly, particularly the iCloud Keychain and Google Password
    ///           Manager were tested.
    ///         - Does NOT verify That `topOrigin` in `clientDataJSON` is well-formed: We assume it would never be present, i.e.
    ///           the credentials are never used in a cross-origin/iframe context. The website/app set up should disallow
    ///           cross-origin usage of the credentials. This is the default behaviour for created credentials in common settings.
    ///         - Does NOT verify that the `rpIdHash` in `authenticatorData` is the SHA-256 hash of the RP ID expected by the Relying
    ///           Party: this means that we rely on the authenticator to properly enforce credentials to be used only by the correct RP.
    ///           This is generally enforced with features like Apple App Site Association and Google Asset Links. To protect from
    ///           edge cases in which a previously-linked RP ID is removed from the authorised RP IDs, we recommend that messages
    ///           signed by the authenticator include some expiry mechanism.
    ///         - Does NOT verify the credential backup state: this assumes the credential backup state is NOT used as part of Relying
    ///           Party business logic or policy.
    ///         - Does NOT verify the values of the client extension outputs: this assumes that the Relying Party does not use client
    ///           extension outputs.
    ///         - Does NOT verify the signature counter: signature counters are intended to enable risk scoring for the Relying Party.
    ///           This assumes risk scoring is not used as part of Relying Party business logic or policy.
    ///         - Does NOT verify the attestation object: this assumes that response.attestationObject is NOT present in the response,
    ///           i.e. the RP does not intend to verify an attestation.
    ///
    /// @param challenge    The challenge that was provided by the relying party.
    /// @param requireUV    A boolean indicating whether user verification is required.
    /// @param webAuthnAuth The `WebAuthnAuth` struct.
    /// @param x            The x coordinate of the public key.
    /// @param y            The y coordinate of the public key.
    ///
    /// @return `true` if the authentication assertion passed validation, else `false`.
    function verify(bytes memory challenge, bool requireUV, WebAuthnAuth memory webAuthnAuth, uint256 x, uint256 y)
        internal
        view
        returns (bool)
    {
        if (webAuthnAuth.s > _P256_N_DIV_2) {
            // guard against signature malleability
            return false;
        }
        // 11. Verify that the value of C.type is the string webauthn.get.
        //     bytes("type":"webauthn.get").length = 21
        string memory _type = webAuthnAuth.clientDataJSON.slice(webAuthnAuth.typeIndex, webAuthnAuth.typeIndex + 21);
        if (keccak256(bytes(_type)) != _EXPECTED_TYPE_HASH) {
            return false;
        }
        // 12. Verify that the value of C.challenge equals the base64url encoding of options.challenge.
        bytes memory expectedChallenge = bytes(string.concat('"challenge":"', Base64.encodeURL(challenge), '"'));
        string memory actualChallenge =
            webAuthnAuth.clientDataJSON.slice(webAuthnAuth.challengeIndex, webAuthnAuth.challengeIndex + expectedChallenge.length);
        if (keccak256(bytes(actualChallenge)) != keccak256(expectedChallenge)) {
            return false;
        }
        // Skip 13., 14., 15.
        // 16. Verify that the UP bit of the flags in authData is set.
        if (webAuthnAuth.authenticatorData[32] & _AUTH_DATA_FLAGS_UP != _AUTH_DATA_FLAGS_UP) {
            return false;
        }
        // 17. If user verification is required for this assertion, verify that the User Verified bit of the flags in
        //     authData is set.
        if (requireUV && (webAuthnAuth.authenticatorData[32] & _AUTH_DATA_FLAGS_UV) != _AUTH_DATA_FLAGS_UV) {
            return false;
        }
        // skip 18.
        // 19. Let hash be the result of computing a hash over the cData using SHA-256.
        bytes32 clientDataJSONHash = sha256(bytes(webAuthnAuth.clientDataJSON));
        // 20. Using credentialPublicKey, verify that sig is a valid signature over the binary concatenation of authData
        //     and hash.
        bytes32 messageHash = sha256(abi.encodePacked(webAuthnAuth.authenticatorData, clientDataJSONHash));
        bytes memory args = abi.encode(messageHash, webAuthnAuth.r, webAuthnAuth.s, x, y);
        // try the RIP-7212 precompile address
        (bool success, bytes memory ret) = _VERIFIER.staticcall(args);
        // staticcall will not revert if address has no code
        // check return length
        // note that even if precompile exists, ret.length is 0 when verification returns false
        // so an invalid signature will be checked twice: once by the precompile and once by FCL.
        // Ideally this signature failure is simulated offchain and no one actually pay this gas.
        bool valid = ret.length > 0;
        if (success && valid) return abi.decode(ret, (uint256)) == 1;
        return FCL_ecdsa.ecdsa_verify(messageHash, webAuthnAuth.r, webAuthnAuth.s, x, y);
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @title ERC-1271
///
/// @notice Abstract ERC-1271 implementation (based on Solady's) with guards to handle the same
///         signer being used on multiple accounts.
///
/// @dev To prevent the same signature from being validated on different accounts owned by the samer signer,
///      we introduce an anti cross-account-replay layer: the original hash is input into a new EIP-712 compliant
///      hash. The domain separator of this outer hash contains the chain id and address of this contract, so that
///      it cannot be used on two accounts (see `replaySafeHash()` for the implementation details).
///
/// @author Coinbase (https://github.com/coinbase/smart-wallet)
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/accounts/ERC1271.sol)
abstract contract ERC1271 {
    /// @dev Precomputed `typeHash` used to produce EIP-712 compliant hash when applying the anti
    ///      cross-account-replay layer.
    ///
    ///      The original hash must either be:
    ///         - An EIP-191 hash: keccak256("\\x19Ethereum Signed Message:\
" || len(someMessage) || someMessage)
    ///         - An EIP-712 hash: keccak256("\\x19\\x01" || someDomainSeparator || hashStruct(someStruct))
    bytes32 private constant _MESSAGE_TYPEHASH = keccak256("CoinbaseSmartWalletMessage(bytes32 hash)");
    /// @notice Returns information about the `EIP712Domain` used to create EIP-712 compliant hashes.
    ///
    /// @dev Follows ERC-5267 (see https://eips.ethereum.org/EIPS/eip-5267).
    ///
    /// @return fields The bitmap of used fields.
    /// @return name The value of the `EIP712Domain.name` field.
    /// @return version The value of the `EIP712Domain.version` field.
    /// @return chainId The value of the `EIP712Domain.chainId` field.
    /// @return verifyingContract The value of the `EIP712Domain.verifyingContract` field.
    /// @return salt The value of the `EIP712Domain.salt` field.
    /// @return extensions The list of EIP numbers, that extends EIP-712 with new domain fields.
    function eip712Domain()
        external
        view
        virtual
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        )
    {
        fields = hex"0f"; // `0b1111`.
        (name, version) = _domainNameAndVersion();
        chainId = block.chainid;
        verifyingContract = address(this);
        salt = salt; // `bytes32(0)`.
        extensions = extensions; // `new uint256[](0)`.
    }
    /// @notice Validates the `signature` against the given `hash`.
    ///
    /// @dev This implementation follows ERC-1271. See https://eips.ethereum.org/EIPS/eip-1271.
    /// @dev IMPORTANT: Signature verification is performed on the hash produced AFTER applying the anti
    ///      cross-account-replay layer on the given `hash` (i.e., verification is run on the replay-safe
    ///      hash version).
    ///
    /// @param hash      The original hash.
    /// @param signature The signature of the replay-safe hash to validate.
    ///
    /// @return result `0x1626ba7e` if validation succeeded, else `0xffffffff`.
    function isValidSignature(bytes32 hash, bytes calldata signature) public view virtual returns (bytes4 result) {
        if (_isValidSignature({hash: replaySafeHash(hash), signature: signature})) {
            // bytes4(keccak256("isValidSignature(bytes32,bytes)"))
            return 0x1626ba7e;
        }
        return 0xffffffff;
    }
    /// @notice Wrapper around `_eip712Hash()` to produce a replay-safe hash fron the given `hash`.
    ///
    /// @dev The returned EIP-712 compliant replay-safe hash is the result of:
    ///      keccak256(
    ///         \\x19\\x01 ||
    ///         this.domainSeparator ||
    ///         hashStruct(CoinbaseSmartWalletMessage({ hash: `hash`}))
    ///      )
    ///
    /// @param hash The original hash.
    ///
    /// @return The corresponding replay-safe hash.
    function replaySafeHash(bytes32 hash) public view virtual returns (bytes32) {
        return _eip712Hash(hash);
    }
    /// @notice Returns the `domainSeparator` used to create EIP-712 compliant hashes.
    ///
    /// @dev Implements domainSeparator = hashStruct(eip712Domain).
    ///      See https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator.
    ///
    /// @return The 32 bytes domain separator result.
    function domainSeparator() public view returns (bytes32) {
        (string memory name, string memory version) = _domainNameAndVersion();
        return keccak256(
            abi.encode(
                keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"),
                keccak256(bytes(name)),
                keccak256(bytes(version)),
                block.chainid,
                address(this)
            )
        );
    }
    /// @notice Returns the EIP-712 typed hash of the `CoinbaseSmartWalletMessage(bytes32 hash)` data structure.
    ///
    /// @dev Implements encode(domainSeparator : 𝔹²⁵⁶, message : 𝕊) = "\\x19\\x01" || domainSeparator ||
    ///      hashStruct(message).
    /// @dev See https://eips.ethereum.org/EIPS/eip-712#specification.
    ///
    /// @param hash The `CoinbaseSmartWalletMessage.hash` field to hash.
    ////
    /// @return The resulting EIP-712 hash.
    function _eip712Hash(bytes32 hash) internal view virtual returns (bytes32) {
        return keccak256(abi.encodePacked("\\x19\\x01", domainSeparator(), _hashStruct(hash)));
    }
    /// @notice Returns the EIP-712 `hashStruct` result of the `CoinbaseSmartWalletMessage(bytes32 hash)` data
    ///         structure.
    ///
    /// @dev Implements hashStruct(s : 𝕊) = keccak256(typeHash || encodeData(s)).
    /// @dev See https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct.
    ///
    /// @param hash The `CoinbaseSmartWalletMessage.hash` field.
    ///
    /// @return The EIP-712 `hashStruct` result.
    function _hashStruct(bytes32 hash) internal view virtual returns (bytes32) {
        return keccak256(abi.encode(_MESSAGE_TYPEHASH, hash));
    }
    /// @notice Returns the domain name and version to use when creating EIP-712 signatures.
    ///
    /// @dev MUST be defined by the implementation.
    ///
    /// @return name    The user readable name of signing domain.
    /// @return version The current major version of the signing domain.
    function _domainNameAndVersion() internal view virtual returns (string memory name, string memory version);
    /// @notice Validates the `signature` against the given `hash`.
    ///
    /// @dev MUST be defined by the implementation.
    ///
    /// @param hash      The hash whose signature has been performed on.
    /// @param signature The signature associated with `hash`.
    ///
    /// @return `true` is the signature is valid, else `false`.
    function _isValidSignature(bytes32 hash, bytes calldata signature) internal view virtual returns (bool);
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.18;
/// @notice Storage layout used by this contract.
///
/// @custom:storage-location erc7201:coinbase.storage.MultiOwnable
struct MultiOwnableStorage {
    /// @dev Tracks the index of the next owner to add.
    uint256 nextOwnerIndex;
    /// @dev Tracks number of owners that have been removed.
    uint256 removedOwnersCount;
    /// @dev Maps index to owner bytes, used to idenfitied owners via a uint256 index.
    ///
    ///      Some uses—-such as signature validation for secp256r1 public key owners—-
    ///      requires the caller to assert the public key of the caller. To economize calldata,
    ///      we allow an index to identify an owner, so that the full owner bytes do
    ///      not need to be passed.
    ///
    ///      The `owner` bytes should either be
    ///         - An ABI encoded Ethereum address
    ///         - An ABI encoded public key
    mapping(uint256 index => bytes owner) ownerAtIndex;
    /// @dev Mapping of bytes to booleans indicating whether or not
    ///      bytes_ is an owner of this contract.
    mapping(bytes bytes_ => bool isOwner_) isOwner;
}
/// @title Multi Ownable
///
/// @notice Auth contract allowing multiple owners, each identified as bytes.
///
/// @author Coinbase (https://github.com/coinbase/smart-wallet)
contract MultiOwnable {
    /// @dev Slot for the `MultiOwnableStorage` struct in storage.
    ///      Computed from
    ///      keccak256(abi.encode(uint256(keccak256("coinbase.storage.MultiOwnable")) - 1)) & ~bytes32(uint256(0xff))
    ///      Follows ERC-7201 (see https://eips.ethereum.org/EIPS/eip-7201).
    bytes32 private constant MUTLI_OWNABLE_STORAGE_LOCATION =
        0x97e2c6aad4ce5d562ebfaa00db6b9e0fb66ea5d8162ed5b243f51a2e03086f00;
    /// @notice Thrown when the `msg.sender` is not an owner and is trying to call a privileged function.
    error Unauthorized();
    /// @notice Thrown when trying to add an already registered owner.
    ///
    /// @param owner The owner bytes.
    error AlreadyOwner(bytes owner);
    /// @notice Thrown when trying to remove an owner from an index that is empty.
    ///
    /// @param index The targeted index for removal.
    error NoOwnerAtIndex(uint256 index);
    /// @notice Thrown when `owner` argument does not match owner found at index.
    ///
    /// @param index         The index of the owner to be removed.
    /// @param expectedOwner The owner passed in the remove call.
    /// @param actualOwner   The actual owner at `index`.
    error WrongOwnerAtIndex(uint256 index, bytes expectedOwner, bytes actualOwner);
    /// @notice Thrown when a provided owner is neither 64 bytes long (for public key)
    ///         nor a ABI encoded address.
    ///
    /// @param owner The invalid owner.
    error InvalidOwnerBytesLength(bytes owner);
    /// @notice Thrown if a provided owner is 32 bytes long but does not fit in an `address` type.
    ///
    /// @param owner The invalid owner.
    error InvalidEthereumAddressOwner(bytes owner);
    /// @notice Thrown when removeOwnerAtIndex is called and there is only one current owner.
    error LastOwner();
    /// @notice Thrown when removeLastOwner is called and there is more than one current owner.
    ///
    /// @param ownersRemaining The number of current owners.
    error NotLastOwner(uint256 ownersRemaining);
    /// @notice Emitted when a new owner is registered.
    ///
    /// @param index The owner index of the owner added.
    /// @param owner The owner added.
    event AddOwner(uint256 indexed index, bytes owner);
    /// @notice Emitted when an owner is removed.
    ///
    /// @param index The owner index of the owner removed.
    /// @param owner The owner removed.
    event RemoveOwner(uint256 indexed index, bytes owner);
    /// @notice Access control modifier ensuring the caller is an authorized owner
    modifier onlyOwner() virtual {
        _checkOwner();
        _;
    }
    /// @notice Adds a new Ethereum-address owner.
    ///
    /// @param owner The owner address.
    function addOwnerAddress(address owner) external virtual onlyOwner {
        _addOwnerAtIndex(abi.encode(owner), _getMultiOwnableStorage().nextOwnerIndex++);
    }
    /// @notice Adds a new public-key owner.
    ///
    /// @param x The owner public key x coordinate.
    /// @param y The owner public key y coordinate.
    function addOwnerPublicKey(bytes32 x, bytes32 y) external virtual onlyOwner {
        _addOwnerAtIndex(abi.encode(x, y), _getMultiOwnableStorage().nextOwnerIndex++);
    }
    /// @notice Removes owner at the given `index`.
    ///
    /// @dev Reverts if the owner is not registered at `index`.
    /// @dev Reverts if there is currently only one owner.
    /// @dev Reverts if `owner` does not match bytes found at `index`.
    ///
    /// @param index The index of the owner to be removed.
    /// @param owner The ABI encoded bytes of the owner to be removed.
    function removeOwnerAtIndex(uint256 index, bytes calldata owner) external virtual onlyOwner {
        if (ownerCount() == 1) {
            revert LastOwner();
        }
        _removeOwnerAtIndex(index, owner);
    }
    /// @notice Removes owner at the given `index`, which should be the only current owner.
    ///
    /// @dev Reverts if the owner is not registered at `index`.
    /// @dev Reverts if there is currently more than one owner.
    /// @dev Reverts if `owner` does not match bytes found at `index`.
    ///
    /// @param index The index of the owner to be removed.
    /// @param owner The ABI encoded bytes of the owner to be removed.
    function removeLastOwner(uint256 index, bytes calldata owner) external virtual onlyOwner {
        uint256 ownersRemaining = ownerCount();
        if (ownersRemaining > 1) {
            revert NotLastOwner(ownersRemaining);
        }
        _removeOwnerAtIndex(index, owner);
    }
    /// @notice Checks if the given `account` address is registered as owner.
    ///
    /// @param account The account address to check.
    ///
    /// @return `true` if the account is an owner else `false`.
    function isOwnerAddress(address account) public view virtual returns (bool) {
        return _getMultiOwnableStorage().isOwner[abi.encode(account)];
    }
    /// @notice Checks if the given `x`, `y` public key is registered as owner.
    ///
    /// @param x The public key x coordinate.
    /// @param y The public key y coordinate.
    ///
    /// @return `true` if the account is an owner else `false`.
    function isOwnerPublicKey(bytes32 x, bytes32 y) public view virtual returns (bool) {
        return _getMultiOwnableStorage().isOwner[abi.encode(x, y)];
    }
    /// @notice Checks if the given `account` bytes is registered as owner.
    ///
    /// @param account The account, should be ABI encoded address or public key.
    ///
    /// @return `true` if the account is an owner else `false`.
    function isOwnerBytes(bytes memory account) public view virtual returns (bool) {
        return _getMultiOwnableStorage().isOwner[account];
    }
    /// @notice Returns the owner bytes at the given `index`.
    ///
    /// @param index The index to lookup.
    ///
    /// @return The owner bytes (empty if no owner is registered at this `index`).
    function ownerAtIndex(uint256 index) public view virtual returns (bytes memory) {
        return _getMultiOwnableStorage().ownerAtIndex[index];
    }
    /// @notice Returns the next index that will be used to add a new owner.
    ///
    /// @return The next index that will be used to add a new owner.
    function nextOwnerIndex() public view virtual returns (uint256) {
        return _getMultiOwnableStorage().nextOwnerIndex;
    }
    /// @notice Returns the current number of owners
    ///
    /// @return The current owner count
    function ownerCount() public view virtual returns (uint256) {
        MultiOwnableStorage storage $ = _getMultiOwnableStorage();
        return $.nextOwnerIndex - $.removedOwnersCount;
    }
    /// @notice Tracks the number of owners removed
    ///
    /// @dev Used with `this.nextOwnerIndex` to avoid removing all owners
    ///
    /// @return The number of owners that have been removed.
    function removedOwnersCount() public view virtual returns (uint256) {
        return _getMultiOwnableStorage().removedOwnersCount;
    }
    /// @notice Initialize the owners of this contract.
    ///
    /// @dev Intended to be called contract is first deployed and never again.
    /// @dev Reverts if a provided owner is neither 64 bytes long (for public key) nor a valid address.
    ///
    /// @param owners The initial set of owners.
    function _initializeOwners(bytes[] memory owners) internal virtual {
        MultiOwnableStorage storage $ = _getMultiOwnableStorage();
        uint256 nextOwnerIndex_ = $.nextOwnerIndex;
        for (uint256 i; i < owners.length; i++) {
            if (owners[i].length != 32 && owners[i].length != 64) {
                revert InvalidOwnerBytesLength(owners[i]);
            }
            if (owners[i].length == 32 && uint256(bytes32(owners[i])) > type(uint160).max) {
                revert InvalidEthereumAddressOwner(owners[i]);
            }
            _addOwnerAtIndex(owners[i], nextOwnerIndex_++);
        }
        $.nextOwnerIndex = nextOwnerIndex_;
    }
    /// @notice Adds an owner at the given `index`.
    ///
    /// @dev Reverts if `owner` is already registered as an owner.
    ///
    /// @param owner The owner raw bytes to register.
    /// @param index The index to write to.
    function _addOwnerAtIndex(bytes memory owner, uint256 index) internal virtual {
        if (isOwnerBytes(owner)) revert AlreadyOwner(owner);
        MultiOwnableStorage storage $ = _getMultiOwnableStorage();
        $.isOwner[owner] = true;
        $.ownerAtIndex[index] = owner;
        emit AddOwner(index, owner);
    }
    /// @notice Removes owner at the given `index`.
    ///
    /// @dev Reverts if the owner is not registered at `index`.
    /// @dev Reverts if `owner` does not match bytes found at `index`.
    ///
    /// @param index The index of the owner to be removed.
    /// @param owner The ABI encoded bytes of the owner to be removed.
    function _removeOwnerAtIndex(uint256 index, bytes calldata owner) internal virtual {
        bytes memory owner_ = ownerAtIndex(index);
        if (owner_.length == 0) revert NoOwnerAtIndex(index);
        if (keccak256(owner_) != keccak256(owner)) {
            revert WrongOwnerAtIndex({index: index, expectedOwner: owner, actualOwner: owner_});
        }
        MultiOwnableStorage storage $ = _getMultiOwnableStorage();
        delete $.isOwner[owner];
        delete $.ownerAtIndex[index];
        $.removedOwnersCount++;
        emit RemoveOwner(index, owner);
    }
    /// @notice Checks if the sender is an owner of this contract or the contract itself.
    ///
    /// @dev Revert if the sender is not an owner fo the contract itself.
    function _checkOwner() internal view virtual {
        if (isOwnerAddress(msg.sender) || (msg.sender == address(this))) {
            return;
        }
        revert Unauthorized();
    }
    /// @notice Helper function to get a storage reference to the `MultiOwnableStorage` struct.
    ///
    /// @return $ A storage reference to the `MultiOwnableStorage` struct.
    function _getMultiOwnableStorage() internal pure returns (MultiOwnableStorage storage $) {
        assembly ("memory-safe") {
            $.slot := MUTLI_OWNABLE_STORAGE_LOCATION
        }
    }
}
// SPDX-License-Identifier: GPL-3.0
pragma solidity ^0.8.12;
/* solhint-disable no-inline-assembly */
/**
 * returned data from validateUserOp.
 * validateUserOp returns a uint256, with is created by `_packedValidationData` and parsed by `_parseValidationData`
 * @param aggregator - address(0) - the account validated the signature by itself.
 *              address(1) - the account failed to validate the signature.
 *              otherwise - this is an address of a signature aggregator that must be used to validate the signature.
 * @param validAfter - this UserOp is valid only after this timestamp.
 * @param validaUntil - this UserOp is valid only up to this timestamp.
 */
    struct ValidationData {
        address aggregator;
        uint48 validAfter;
        uint48 validUntil;
    }
//extract sigFailed, validAfter, validUntil.
// also convert zero validUntil to type(uint48).max
    function _parseValidationData(uint validationData) pure returns (ValidationData memory data) {
        address aggregator = address(uint160(validationData));
        uint48 validUntil = uint48(validationData >> 160);
        if (validUntil == 0) {
            validUntil = type(uint48).max;
        }
        uint48 validAfter = uint48(validationData >> (48 + 160));
        return ValidationData(aggregator, validAfter, validUntil);
    }
// intersect account and paymaster ranges.
    function _intersectTimeRange(uint256 validationData, uint256 paymasterValidationData) pure returns (ValidationData memory) {
        ValidationData memory accountValidationData = _parseValidationData(validationData);
        ValidationData memory pmValidationData = _parseValidationData(paymasterValidationData);
        address aggregator = accountValidationData.aggregator;
        if (aggregator == address(0)) {
            aggregator = pmValidationData.aggregator;
        }
        uint48 validAfter = accountValidationData.validAfter;
        uint48 validUntil = accountValidationData.validUntil;
        uint48 pmValidAfter = pmValidationData.validAfter;
        uint48 pmValidUntil = pmValidationData.validUntil;
        if (validAfter < pmValidAfter) validAfter = pmValidAfter;
        if (validUntil > pmValidUntil) validUntil = pmValidUntil;
        return ValidationData(aggregator, validAfter, validUntil);
    }
/**
 * helper to pack the return value for validateUserOp
 * @param data - the ValidationData to pack
 */
    function _packValidationData(ValidationData memory data) pure returns (uint256) {
        return uint160(data.aggregator) | (uint256(data.validUntil) << 160) | (uint256(data.validAfter) << (160 + 48));
    }
/**
 * helper to pack the return value for validateUserOp, when not using an aggregator
 * @param sigFailed - true for signature failure, false for success
 * @param validUntil last timestamp this UserOperation is valid (or zero for infinite)
 * @param validAfter first timestamp this UserOperation is valid
 */
    function _packValidationData(bool sigFailed, uint48 validUntil, uint48 validAfter) pure returns (uint256) {
        return (sigFailed ? 1 : 0) | (uint256(validUntil) << 160) | (uint256(validAfter) << (160 + 48));
    }
/**
 * keccak function over calldata.
 * @dev copy calldata into memory, do keccak and drop allocated memory. Strangely, this is more efficient than letting solidity do it.
 */
    function calldataKeccak(bytes calldata data) pure returns (bytes32 ret) {
        assembly {
            let mem := mload(0x40)
            let len := data.length
            calldatacopy(mem, data.offset, len)
            ret := keccak256(mem, len)
        }
    }
//********************************************************************************************/
//  ___           _       ___               _         _    _ _
// | __| _ ___ __| |_    / __|_ _ _  _ _ __| |_ ___  | |  (_) |__
// | _| '_/ -_|_-< ' \\  | (__| '_| || | '_ \\  _/ _ \\ | |__| | '_ \\
// |_||_| \\___/__/_||_|  \\___|_|  \\_, | .__/\\__\\___/ |____|_|_.__/
//                                |__/|_|
///* Copyright (C) 2022 - Renaud Dubois - This file is part of FCL (Fresh CryptoLib) project
///* License: This software is licensed under MIT License
///* This Code may be reused including license and copyright notice.
///* See LICENSE file at the root folder of the project.
///* FILE: FCL_ecdsa.sol
///*
///*
///* DESCRIPTION: ecdsa verification implementation
///*
//**************************************************************************************/
//* WARNING: this code SHALL not be used for non prime order curves for security reasons.
// Code is optimized for a=-3 only curves with prime order, constant like -1, -2 shall be replaced
// if ever used for other curve than sec256R1
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19 <0.9.0;
import {FCL_Elliptic_ZZ} from "./FCL_elliptic.sol";
library FCL_ecdsa {
    // Set parameters for curve sec256r1.public
      //curve order (number of points)
    uint256 constant n = FCL_Elliptic_ZZ.n;
  
    /**
     * @dev ECDSA verification, given , signature, and public key.
     */
    /**
     * @dev ECDSA verification, given , signature, and public key, no calldata version
     */
    function ecdsa_verify(bytes32 message, uint256 r, uint256 s, uint256 Qx, uint256 Qy)  internal view returns (bool){
        if (r == 0 || r >= FCL_Elliptic_ZZ.n || s == 0 || s >= FCL_Elliptic_ZZ.n) {
            return false;
        }
        
        if (!FCL_Elliptic_ZZ.ecAff_isOnCurve(Qx, Qy)) {
            return false;
        }
        uint256 sInv = FCL_Elliptic_ZZ.FCL_nModInv(s);
        uint256 scalar_u = mulmod(uint256(message), sInv, FCL_Elliptic_ZZ.n);
        uint256 scalar_v = mulmod(r, sInv, FCL_Elliptic_ZZ.n);
        uint256 x1;
        x1 = FCL_Elliptic_ZZ.ecZZ_mulmuladd_S_asm(Qx, Qy, scalar_u, scalar_v);
        x1= addmod(x1, n-r,n );
    
        return x1 == 0;
    }
    function ec_recover_r1(uint256 h, uint256 v, uint256 r, uint256 s) internal view returns (address)
    {
         if (r == 0 || r >= FCL_Elliptic_ZZ.n || s == 0 || s >= FCL_Elliptic_ZZ.n) {
            return address(0);
        }
        uint256 y=FCL_Elliptic_ZZ.ec_Decompress(r, v-27);
        uint256 rinv=FCL_Elliptic_ZZ.FCL_nModInv(r);
        uint256 u1=mulmod(FCL_Elliptic_ZZ.n-addmod(0,h,FCL_Elliptic_ZZ.n), rinv,FCL_Elliptic_ZZ.n);//-hr^-1
        uint256 u2=mulmod(s, rinv,FCL_Elliptic_ZZ.n);//sr^-1
        uint256 Qx;
        uint256 Qy;
        (Qx,Qy)=FCL_Elliptic_ZZ.ecZZ_mulmuladd(r,y, u1, u2);
        return address(uint160(uint256(keccak256(abi.encodePacked(Qx, Qy)))));
    }
    function ecdsa_precomputed_verify(bytes32 message, uint256 r, uint256 s, address Shamir8)
        internal view
        returns (bool)
    {
       
        if (r == 0 || r >= n || s == 0 || s >= n) {
            return false;
        }
        /* Q is pushed via the contract at address Shamir8 assumed to be correct
        if (!isOnCurve(Q[0], Q[1])) {
            return false;
        }*/
        uint256 sInv = FCL_Elliptic_ZZ.FCL_nModInv(s);
        uint256 X;
        //Shamir 8 dimensions
        X = FCL_Elliptic_ZZ.ecZZ_mulmuladd_S8_extcode(mulmod(uint256(message), sInv, n), mulmod(r, sInv, n), Shamir8);
        X= addmod(X, n-r,n );
        return X == 0;
    } //end  ecdsa_precomputed_verify()
     function ecdsa_precomputed_verify(bytes32 message, uint256[2] calldata rs, address Shamir8)
        internal view
        returns (bool)
    {
        uint256 r = rs[0];
        uint256 s = rs[1];
        if (r == 0 || r >= n || s == 0 || s >= n) {
            return false;
        }
        /* Q is pushed via the contract at address Shamir8 assumed to be correct
        if (!isOnCurve(Q[0], Q[1])) {
            return false;
        }*/
        uint256 sInv = FCL_Elliptic_ZZ.FCL_nModInv(s);
        uint256 X;
        //Shamir 8 dimensions
        X = FCL_Elliptic_ZZ.ecZZ_mulmuladd_S8_extcode(mulmod(uint256(message), sInv, n), mulmod(r, sInv, n), Shamir8);
        X= addmod(X, n-r,n );
        return X == 0;
    } //end  ecdsa_precomputed_verify()
}
//********************************************************************************************/
//  ___           _       ___               _         _    _ _
// | __| _ ___ __| |_    / __|_ _ _  _ _ __| |_ ___  | |  (_) |__
// | _| '_/ -_|_-< ' \\  | (__| '_| || | '_ \\  _/ _ \\ | |__| | '_ \\
// |_||_| \\___/__/_||_|  \\___|_|  \\_, | .__/\\__\\___/ |____|_|_.__/
//                                |__/|_|
///* Copyright (C) 2022 - Renaud Dubois - This file is part of FCL (Fresh CryptoLib) project
///* License: This software is licensed under MIT License
///* This Code may be reused including license and copyright notice.
///* See LICENSE file at the root folder of the project.
///* FILE: FCL_elliptic.sol
///*
///*
///* DESCRIPTION: modified XYZZ system coordinates for EVM elliptic point multiplication
///*  optimization
///*
//**************************************************************************************/
//* WARNING: this code SHALL not be used for non prime order curves for security reasons.
// Code is optimized for a=-3 only curves with prime order, constant like -1, -2 shall be replaced
// if ever used for other curve than sec256R1
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19 <0.9.0;
library FCL_Elliptic_ZZ {
    // Set parameters for curve sec256r1.
    // address of the ModExp precompiled contract (Arbitrary-precision exponentiation under modulo)
    address constant MODEXP_PRECOMPILE = 0x0000000000000000000000000000000000000005;
    //curve prime field modulus
    uint256 constant p = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF;
    //short weierstrass first coefficient
    uint256 constant a = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC;
    //short weierstrass second coefficient
    uint256 constant b = 0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B;
    //generating point affine coordinates
    uint256 constant gx = 0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296;
    uint256 constant gy = 0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5;
    //curve order (number of points)
    uint256 constant n = 0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551;
    /* -2 mod p constant, used to speed up inversion and doubling (avoid negation)*/
    uint256 constant minus_2 = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFD;
    /* -2 mod n constant, used to speed up inversion*/
    uint256 constant minus_2modn = 0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC63254F;
    uint256 constant minus_1 = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
    //P+1 div 4
    uint256 constant pp1div4=0x3fffffffc0000000400000000000000000000000400000000000000000000000;
    //arbitrary constant to express no quadratic residuosity
    uint256 constant _NOTSQUARE=0xFFFFFFFF00000002000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF;
    uint256 constant _NOTONCURVE=0xFFFFFFFF00000003000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF;
    /**
     * /* inversion mod n via a^(n-2), use of precompiled using little Fermat theorem
     */
    function FCL_nModInv(uint256 u) internal view returns (uint256 result) {
        assembly {
            let pointer := mload(0x40)
            // Define length of base, exponent and modulus. 0x20 == 32 bytes
            mstore(pointer, 0x20)
            mstore(add(pointer, 0x20), 0x20)
            mstore(add(pointer, 0x40), 0x20)
            // Define variables base, exponent and modulus
            mstore(add(pointer, 0x60), u)
            mstore(add(pointer, 0x80), minus_2modn)
            mstore(add(pointer, 0xa0), n)
            // Call the precompiled contract 0x05 = ModExp
            if iszero(staticcall(not(0), 0x05, pointer, 0xc0, pointer, 0x20)) { revert(0, 0) }
            result := mload(pointer)
        }
    }
    /**
     * /* @dev inversion mod nusing little Fermat theorem via a^(n-2), use of precompiled
     */
    function FCL_pModInv(uint256 u) internal view returns (uint256 result) {
        assembly {
            let pointer := mload(0x40)
            // Define length of base, exponent and modulus. 0x20 == 32 bytes
            mstore(pointer, 0x20)
            mstore(add(pointer, 0x20), 0x20)
            mstore(add(pointer, 0x40), 0x20)
            // Define variables base, exponent and modulus
            mstore(add(pointer, 0x60), u)
            mstore(add(pointer, 0x80), minus_2)
            mstore(add(pointer, 0xa0), p)
            // Call the precompiled contract 0x05 = ModExp
            if iszero(staticcall(not(0), 0x05, pointer, 0xc0, pointer, 0x20)) { revert(0, 0) }
            result := mload(pointer)
        }
    }
    //Coron projective shuffling, take as input alpha as blinding factor
   function ecZZ_Coronize(uint256 alpha, uint256 x, uint256 y,  uint256 zz, uint256 zzz) internal pure  returns (uint256 x3, uint256 y3, uint256 zz3, uint256 zzz3)
   {
       
        uint256 alpha2=mulmod(alpha,alpha,p);
       
        x3=mulmod(alpha2, x,p); //alpha^-2.x
        y3=mulmod(mulmod(alpha, alpha2,p), y,p);
        zz3=mulmod(zz,alpha2,p);//alpha^2 zz
        zzz3=mulmod(zzz,mulmod(alpha, alpha2,p),p);//alpha^3 zzz
        
        return (x3, y3, zz3, zzz3);
   }
 function ecZZ_Add(uint256 x1, uint256 y1, uint256 zz1, uint256 zzz1, uint256 x2, uint256 y2, uint256 zz2, uint256 zzz2) internal pure  returns (uint256 x3, uint256 y3, uint256 zz3, uint256 zzz3)
  {
    uint256 u1=mulmod(x1,zz2,p); // U1 = X1*ZZ2
    uint256 u2=mulmod(x2, zz1,p);               //  U2 = X2*ZZ1
    u2=addmod(u2, p-u1, p);//  P = U2-U1
    x1=mulmod(u2, u2, p);//PP
    x2=mulmod(x1, u2, p);//PPP
    
    zz3=mulmod(x1, mulmod(zz1, zz2, p),p);//ZZ3 = ZZ1*ZZ2*PP  
    zzz3=mulmod(zzz1, mulmod(zzz2, x2, p),p);//ZZZ3 = ZZZ1*ZZZ2*PPP
    zz1=mulmod(y1, zzz2,p);  // S1 = Y1*ZZZ2
    zz2=mulmod(y2, zzz1, p);    // S2 = Y2*ZZZ1 
    zz2=addmod(zz2, p-zz1, p);//R = S2-S1
    zzz1=mulmod(u1, x1,p); //Q = U1*PP
    x3= addmod(addmod(mulmod(zz2, zz2, p), p-x2,p), mulmod(minus_2, zzz1,p),p); //X3 = R2-PPP-2*Q
    y3=addmod( mulmod(zz2, addmod(zzz1, p-x3, p),p), p-mulmod(zz1, x2, p),p);//R*(Q-X3)-S1*PPP
    return (x3, y3, zz3, zzz3);
  }
/// @notice Calculate one modular square root of a given integer. Assume that p=3 mod 4.
/// @dev Uses the ModExp precompiled contract at address 0x05 for fast computation using little Fermat theorem
/// @param self The integer of which to find the modular inverse
/// @return result The modular inverse of the input integer. If the modular inverse doesn't exist, it revert the tx
function SqrtMod(uint256 self) internal view returns (uint256 result){
 assembly ("memory-safe") {
        // load the free memory pointer value
        let pointer := mload(0x40)
        // Define length of base (Bsize)
        mstore(pointer, 0x20)
        // Define the exponent size (Esize)
        mstore(add(pointer, 0x20), 0x20)
        // Define the modulus size (Msize)
        mstore(add(pointer, 0x40), 0x20)
        // Define variables base (B)
        mstore(add(pointer, 0x60), self)
        // Define the exponent (E)
        mstore(add(pointer, 0x80), pp1div4)
        // We save the point of the last argument, it will be override by the result
        // of the precompile call in order to avoid paying for the memory expansion properly
        let _result := add(pointer, 0xa0)
        // Define the modulus (M)
        mstore(_result, p)
        // Call the precompiled ModExp (0x05) https://www.evm.codes/precompiled#0x05
        if iszero(
            staticcall(
                not(0), // amount of gas to send
                MODEXP_PRECOMPILE, // target
                pointer, // argsOffset
                0xc0, // argsSize (6 * 32 bytes)
                _result, // retOffset (we override M to avoid paying for the memory expansion)
                0x20 // retSize (32 bytes)
            )
        ) { revert(0, 0) }
  result := mload(_result)
//  result :=addmod(result,0,p)
 }
   if(mulmod(result,result,p)!=self){
     result=_NOTSQUARE;
   }
  
   return result;
}
    /**
     * /* @dev Convert from affine rep to XYZZ rep
     */
    function ecAff_SetZZ(uint256 x0, uint256 y0) internal pure returns (uint256[4] memory P) {
        unchecked {
            P[2] = 1; //ZZ
            P[3] = 1; //ZZZ
            P[0] = x0;
            P[1] = y0;
        }
    }
    function ec_Decompress(uint256 x, uint256 parity) internal view returns(uint256 y){ 
        uint256 y2=mulmod(x,mulmod(x,x,p),p);//x3
        y2=addmod(b,addmod(y2,mulmod(x,a,p),p),p);//x3+ax+b
        y=SqrtMod(y2);
        if(y==_NOTSQUARE){
           return _NOTONCURVE;
        }
        if((y&1)!=(parity&1)){
            y=p-y;
        }
    }
    /**
     * /* @dev Convert from XYZZ rep to affine rep
     */
    /*    https://hyperelliptic.org/EFD/g1p/auto-shortw-xyzz-3.html#addition-add-2008-s*/
    function ecZZ_SetAff(uint256 x, uint256 y, uint256 zz, uint256 zzz) internal view returns (uint256 x1, uint256 y1) {
        uint256 zzzInv = FCL_pModInv(zzz); //1/zzz
        y1 = mulmod(y, zzzInv, p); //Y/zzz
        uint256 _b = mulmod(zz, zzzInv, p); //1/z
        zzzInv = mulmod(_b, _b, p); //1/zz
        x1 = mulmod(x, zzzInv, p); //X/zz
    }
    /**
     * /* @dev Sutherland2008 doubling
     */
    /* The "dbl-2008-s-1" doubling formulas */
    function ecZZ_Dbl(uint256 x, uint256 y, uint256 zz, uint256 zzz)
        internal
        pure
        returns (uint256 P0, uint256 P1, uint256 P2, uint256 P3)
    {
        unchecked {
            assembly {
                P0 := mulmod(2, y, p) //U = 2*Y1
                P2 := mulmod(P0, P0, p) // V=U^2
                P3 := mulmod(x, P2, p) // S = X1*V
                P1 := mulmod(P0, P2, p) // W=UV
                P2 := mulmod(P2, zz, p) //zz3=V*ZZ1
                zz := mulmod(3, mulmod(addmod(x, sub(p, zz), p), addmod(x, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                P0 := addmod(mulmod(zz, zz, p), mulmod(minus_2, P3, p), p) //X3=M^2-2S
                x := mulmod(zz, addmod(P3, sub(p, P0), p), p) //M(S-X3)
                P3 := mulmod(P1, zzz, p) //zzz3=W*zzz1
                P1 := addmod(x, sub(p, mulmod(P1, y, p)), p) //Y3= M(S-X3)-W*Y1
            }
        }
        return (P0, P1, P2, P3);
    }
    /**
     * @dev Sutherland2008 add a ZZ point with a normalized point and greedy formulae
     * warning: assume that P1(x1,y1)!=P2(x2,y2), true in multiplication loop with prime order (cofactor 1)
     */
    function ecZZ_AddN(uint256 x1, uint256 y1, uint256 zz1, uint256 zzz1, uint256 x2, uint256 y2)
        internal
        pure
        returns (uint256 P0, uint256 P1, uint256 P2, uint256 P3)
    {
        unchecked {
            if (y1 == 0) {
                return (x2, y2, 1, 1);
            }
            assembly {
                y1 := sub(p, y1)
                y2 := addmod(mulmod(y2, zzz1, p), y1, p)
                x2 := addmod(mulmod(x2, zz1, p), sub(p, x1), p)
                P0 := mulmod(x2, x2, p) //PP = P^2
                P1 := mulmod(P0, x2, p) //PPP = P*PP
                P2 := mulmod(zz1, P0, p) ////ZZ3 = ZZ1*PP
                P3 := mulmod(zzz1, P1, p) ////ZZZ3 = ZZZ1*PPP
                zz1 := mulmod(x1, P0, p) //Q = X1*PP
                P0 := addmod(addmod(mulmod(y2, y2, p), sub(p, P1), p), mulmod(minus_2, zz1, p), p) //R^2-PPP-2*Q
                P1 := addmod(mulmod(addmod(zz1, sub(p, P0), p), y2, p), mulmod(y1, P1, p), p) //R*(Q-X3)
            }
            //end assembly
        } //end unchecked
        return (P0, P1, P2, P3);
    }
    /**
     * @dev Return the zero curve in XYZZ coordinates.
     */
    function ecZZ_SetZero() internal pure returns (uint256 x, uint256 y, uint256 zz, uint256 zzz) {
        return (0, 0, 0, 0);
    }
    /**
     * @dev Check if point is the neutral of the curve
     */
    // uint256 x0, uint256 y0, uint256 zz0, uint256 zzz0
    function ecZZ_IsZero(uint256, uint256 y0, uint256, uint256) internal pure returns (bool) {
        return y0 == 0;
    }
    /**
     * @dev Return the zero curve in affine coordinates. Compatible with the double formulae (no special case)
     */
    function ecAff_SetZero() internal pure returns (uint256 x, uint256 y) {
        return (0, 0);
    }
    /**
     * @dev Check if the curve is the zero curve in affine rep.
     */
    // uint256 x, uint256 y)
    function ecAff_IsZero(uint256, uint256 y) internal pure returns (bool flag) {
        return (y == 0);
    }
    /**
     * @dev Check if a point in affine coordinates is on the curve (reject Neutral that is indeed on the curve).
     */
    function ecAff_isOnCurve(uint256 x, uint256 y) internal pure returns (bool) {
        if (x >= p || y >= p || ((x == 0) && (y == 0))) {
            return false;
        }
        unchecked {
            uint256 LHS = mulmod(y, y, p); // y^2
            uint256 RHS = addmod(mulmod(mulmod(x, x, p), x, p), mulmod(x, a, p), p); // x^3+ax
            RHS = addmod(RHS, b, p); // x^3 + a*x + b
            return LHS == RHS;
        }
    }
    /**
     * @dev Add two elliptic curve points in affine coordinates. Deal with P=Q
     */
    function ecAff_add(uint256 x0, uint256 y0, uint256 x1, uint256 y1) internal view returns (uint256, uint256) {
        uint256 zz0;
        uint256 zzz0;
        if (ecAff_IsZero(x0, y0)) return (x1, y1);
        if (ecAff_IsZero(x1, y1)) return (x0, y0);
        if((x0==x1)&&(y0==y1)) {
            (x0, y0, zz0, zzz0) = ecZZ_Dbl(x0, y0,1,1);
        }
        else{
            (x0, y0, zz0, zzz0) = ecZZ_AddN(x0, y0, 1, 1, x1, y1);
        }
        return ecZZ_SetAff(x0, y0, zz0, zzz0);
    }
    /**
     * @dev Computation of uG+vQ using Strauss-Shamir's trick, G basepoint, Q public key
     *       Returns only x for ECDSA use            
     *      */
    function ecZZ_mulmuladd_S_asm(
        uint256 Q0,
        uint256 Q1, //affine rep for input point Q
        uint256 scalar_u,
        uint256 scalar_v
    ) internal view returns (uint256 X) {
        uint256 zz;
        uint256 zzz;
        uint256 Y;
        uint256 index = 255;
        uint256 H0;
        uint256 H1;
        unchecked {
            if (scalar_u == 0 && scalar_v == 0) return 0;
            (H0, H1) = ecAff_add(gx, gy, Q0, Q1); 
            if((H0==0)&&(H1==0))//handling Q=-G
            {
                scalar_u=addmod(scalar_u, n-scalar_v, n);
                scalar_v=0;
                if (scalar_u == 0 && scalar_v == 0) return 0;
            }
            assembly {
                for { let T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1)) } eq(T4, 0) {
                    index := sub(index, 1)
                    T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                } {}
                zz := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                if eq(zz, 1) {
                    X := gx
                    Y := gy
                }
                if eq(zz, 2) {
                    X := Q0
                    Y := Q1
                }
                if eq(zz, 3) {
                    X := H0
                    Y := H1
                }
                index := sub(index, 1)
                zz := 1
                zzz := 1
                for {} gt(minus_1, index) { index := sub(index, 1) } {
                    // inlined EcZZ_Dbl
                    let T1 := mulmod(2, Y, p) //U = 2*Y1, y free
                    let T2 := mulmod(T1, T1, p) // V=U^2
                    let T3 := mulmod(X, T2, p) // S = X1*V
                    T1 := mulmod(T1, T2, p) // W=UV
                    let T4 := mulmod(3, mulmod(addmod(X, sub(p, zz), p), addmod(X, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                    zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                    zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                    X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                    T2 := mulmod(T4, addmod(X, sub(p, T3), p), p) //-M(S-X3)=M(X3-S)
                    Y := addmod(mulmod(T1, Y, p), T2, p) //-Y3= W*Y1-M(S-X3), we replace Y by -Y to avoid a sub in ecAdd
                    {
                        //value of dibit
                        T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                        if iszero(T4) {
                            Y := sub(p, Y) //restore the -Y inversion
                            continue
                        } // if T4!=0
                        if eq(T4, 1) {
                            T1 := gx
                            T2 := gy
                        }
                        if eq(T4, 2) {
                            T1 := Q0
                            T2 := Q1
                        }
                        if eq(T4, 3) {
                            T1 := H0
                            T2 := H1
                        }
                        if iszero(zz) {
                            X := T1
                            Y := T2
                            zz := 1
                            zzz := 1
                            continue
                        }
                        // inlined EcZZ_AddN
                        //T3:=sub(p, Y)
                        //T3:=Y
                        let y2 := addmod(mulmod(T2, zzz, p), Y, p) //R
                        T2 := addmod(mulmod(T1, zz, p), sub(p, X), p) //P
                        //special extremely rare case accumulator where EcAdd is replaced by EcDbl, no need to optimize this
                        //todo : construct edge vector case
                        if iszero(y2) {
                            if iszero(T2) {
                                T1 := mulmod(minus_2, Y, p) //U = 2*Y1, y free
                                T2 := mulmod(T1, T1, p) // V=U^2
                                T3 := mulmod(X, T2, p) // S = X1*V
                                T1 := mulmod(T1, T2, p) // W=UV
                                y2 := mulmod(addmod(X, zz, p), addmod(X, sub(p, zz), p), p) //(X-ZZ)(X+ZZ)
                                T4 := mulmod(3, y2, p) //M=3*(X-ZZ)(X+ZZ)
                                zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                                zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                                X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                                T2 := mulmod(T4, addmod(T3, sub(p, X), p), p) //M(S-X3)
                                Y := addmod(T2, mulmod(T1, Y, p), p) //Y3= M(S-X3)-W*Y1
                                continue
                            }
                        }
                        T4 := mulmod(T2, T2, p) //PP
                        let TT1 := mulmod(T4, T2, p) //PPP, this one could be spared, but adding this register spare gas
                        zz := mulmod(zz, T4, p)
                        zzz := mulmod(zzz, TT1, p) //zz3=V*ZZ1
                        let TT2 := mulmod(X, T4, p)
                        T4 := addmod(addmod(mulmod(y2, y2, p), sub(p, TT1), p), mulmod(minus_2, TT2, p), p)
                        Y := addmod(mulmod(addmod(TT2, sub(p, T4), p), y2, p), mulmod(Y, TT1, p), p)
                        X := T4
                    }
                } //end loop
                let T := mload(0x40)
                mstore(add(T, 0x60), zz)
                //(X,Y)=ecZZ_SetAff(X,Y,zz, zzz);
                //T[0] = inverseModp_Hard(T[0], p); //1/zzz, inline modular inversion using precompile:
                // Define length of base, exponent and modulus. 0x20 == 32 bytes
                mstore(T, 0x20)
                mstore(add(T, 0x20), 0x20)
                mstore(add(T, 0x40), 0x20)
                // Define variables base, exponent and modulus
                //mstore(add(pointer, 0x60), u)
                mstore(add(T, 0x80), minus_2)
                mstore(add(T, 0xa0), p)
                // Call the precompiled contract 0x05 = ModExp
                if iszero(staticcall(not(0), 0x05, T, 0xc0, T, 0x20)) { revert(0, 0) }
                //Y:=mulmod(Y,zzz,p)//Y/zzz
                //zz :=mulmod(zz, mload(T),p) //1/z
                //zz:= mulmod(zz,zz,p) //1/zz
                X := mulmod(X, mload(T), p) //X/zz
            } //end assembly
        } //end unchecked
        return X;
    }
    /**
     * @dev Computation of uG+vQ using Strauss-Shamir's trick, G basepoint, Q public key
     *       Returns affine representation of point (normalized)       
     *      */
    function ecZZ_mulmuladd(
        uint256 Q0,
        uint256 Q1, //affine rep for input point Q
        uint256 scalar_u,
        uint256 scalar_v
    ) internal view returns (uint256 X, uint256 Y) {
        uint256 zz;
        uint256 zzz;
        uint256 index = 255;
        uint256[6] memory T;
        uint256[2] memory H;
 
        unchecked {
            if (scalar_u == 0 && scalar_v == 0) return (0,0);
            (H[0], H[1]) = ecAff_add(gx, gy, Q0, Q1); //will not work if Q=P, obvious forbidden private key
            assembly {
                for { let T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1)) } eq(T4, 0) {
                    index := sub(index, 1)
                    T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                } {}
                zz := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                if eq(zz, 1) {
                    X := gx
                    Y := gy
                }
                if eq(zz, 2) {
                    X := Q0
                    Y := Q1
                }
                if eq(zz, 3) {
                    Y := mload(add(H,32))
                    X := mload(H)
                }
                index := sub(index, 1)
                zz := 1
                zzz := 1
                for {} gt(minus_1, index) { index := sub(index, 1) } {
                    // inlined EcZZ_Dbl
                    let T1 := mulmod(2, Y, p) //U = 2*Y1, y free
                    let T2 := mulmod(T1, T1, p) // V=U^2
                    let T3 := mulmod(X, T2, p) // S = X1*V
                    T1 := mulmod(T1, T2, p) // W=UV
                    let T4 := mulmod(3, mulmod(addmod(X, sub(p, zz), p), addmod(X, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                    zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                    zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                    X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                    T2 := mulmod(T4, addmod(X, sub(p, T3), p), p) //-M(S-X3)=M(X3-S)
                    Y := addmod(mulmod(T1, Y, p), T2, p) //-Y3= W*Y1-M(S-X3), we replace Y by -Y to avoid a sub in ecAdd
                    {
                        //value of dibit
                        T4 := add(shl(1, and(shr(index, scalar_v), 1)), and(shr(index, scalar_u), 1))
                        if iszero(T4) {
                            Y := sub(p, Y) //restore the -Y inversion
                            continue
                        } // if T4!=0
                        if eq(T4, 1) {
                            T1 := gx
                            T2 := gy
                        }
                        if eq(T4, 2) {
                            T1 := Q0
                            T2 := Q1
                        }
                        if eq(T4, 3) {
                            T1 := mload(H)
                            T2 := mload(add(H,32))
                        }
                        if iszero(zz) {
                            X := T1
                            Y := T2
                            zz := 1
                            zzz := 1
                            continue
                        }
                        // inlined EcZZ_AddN
                        //T3:=sub(p, Y)
                        //T3:=Y
                        let y2 := addmod(mulmod(T2, zzz, p), Y, p) //R
                        T2 := addmod(mulmod(T1, zz, p), sub(p, X), p) //P
                        //special extremely rare case accumulator where EcAdd is replaced by EcDbl, no need to optimize this
                        //todo : construct edge vector case
                        if iszero(y2) {
                            if iszero(T2) {
                                T1 := mulmod(minus_2, Y, p) //U = 2*Y1, y free
                                T2 := mulmod(T1, T1, p) // V=U^2
                                T3 := mulmod(X, T2, p) // S = X1*V
                                T1 := mulmod(T1, T2, p) // W=UV
                                y2 := mulmod(addmod(X, zz, p), addmod(X, sub(p, zz), p), p) //(X-ZZ)(X+ZZ)
                                T4 := mulmod(3, y2, p) //M=3*(X-ZZ)(X+ZZ)
                                zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                                zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                                X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                                T2 := mulmod(T4, addmod(T3, sub(p, X), p), p) //M(S-X3)
                                Y := addmod(T2, mulmod(T1, Y, p), p) //Y3= M(S-X3)-W*Y1
                                continue
                            }
                        }
                        T4 := mulmod(T2, T2, p) //PP
                        let TT1 := mulmod(T4, T2, p) //PPP, this one could be spared, but adding this register spare gas
                        zz := mulmod(zz, T4, p)
                        zzz := mulmod(zzz, TT1, p) //zz3=V*ZZ1
                        let TT2 := mulmod(X, T4, p)
                        T4 := addmod(addmod(mulmod(y2, y2, p), sub(p, TT1), p), mulmod(minus_2, TT2, p), p)
                        Y := addmod(mulmod(addmod(TT2, sub(p, T4), p), y2, p), mulmod(Y, TT1, p), p)
                        X := T4
                    }
                } //end loop
                mstore(add(T, 0x60), zzz)
                //(X,Y)=ecZZ_SetAff(X,Y,zz, zzz);
                //T[0] = inverseModp_Hard(T[0], p); //1/zzz, inline modular inversion using precompile:
                // Define length of base, exponent and modulus. 0x20 == 32 bytes
                mstore(T, 0x20)
                mstore(add(T, 0x20), 0x20)
                mstore(add(T, 0x40), 0x20)
                // Define variables base, exponent and modulus
                //mstore(add(pointer, 0x60), u)
                mstore(add(T, 0x80), minus_2)
                mstore(add(T, 0xa0), p)
                // Call the precompiled contract 0x05 = ModExp
                if iszero(staticcall(not(0), 0x05, T, 0xc0, T, 0x20)) { revert(0, 0) }
                Y:=mulmod(Y,mload(T),p)//Y/zzz
                zz :=mulmod(zz, mload(T),p) //1/z
                zz:= mulmod(zz,zz,p) //1/zz
                X := mulmod(X, zz, p) //X/zz
            } //end assembly
        } //end unchecked
        return (X,Y);
    }
    //8 dimensions Shamir's trick, using precomputations stored in Shamir8,  stored as Bytecode of an external
    //contract at given address dataPointer
    //(thx to Lakhdar https://github.com/Kelvyne for EVM storage explanations and tricks)
    // the external tool to generate tables from public key is in the /sage directory
    function ecZZ_mulmuladd_S8_extcode(uint256 scalar_u, uint256 scalar_v, address dataPointer)
        internal view
        returns (uint256 X /*, uint Y*/ )
    {
        unchecked {
            uint256 zz; // third and  coordinates of the point
            uint256[6] memory T;
            zz = 256; //start index
            while (T[0] == 0) {
                zz = zz - 1;
                //tbd case of msb octobit is null
                T[0] = 64
                    * (
                        128 * ((scalar_v >> zz) & 1) + 64 * ((scalar_v >> (zz - 64)) & 1)
                            + 32 * ((scalar_v >> (zz - 128)) & 1) + 16 * ((scalar_v >> (zz - 192)) & 1)
                            + 8 * ((scalar_u >> zz) & 1) + 4 * ((scalar_u >> (zz - 64)) & 1)
                            + 2 * ((scalar_u >> (zz - 128)) & 1) + ((scalar_u >> (zz - 192)) & 1)
                    );
            }
            assembly {
                extcodecopy(dataPointer, T, mload(T), 64)
                let index := sub(zz, 1)
                X := mload(T)
                let Y := mload(add(T, 32))
                let zzz := 1
                zz := 1
                //loop over 1/4 of scalars thx to Shamir's trick over 8 points
                for {} gt(index, 191) { index := add(index, 191) } {
                    //inline Double
                    {
                        let TT1 := mulmod(2, Y, p) //U = 2*Y1, y free
                        let T2 := mulmod(TT1, TT1, p) // V=U^2
                        let T3 := mulmod(X, T2, p) // S = X1*V
                        let T1 := mulmod(TT1, T2, p) // W=UV
                        let T4 := mulmod(3, mulmod(addmod(X, sub(p, zz), p), addmod(X, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                        zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                        zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                        X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                        //T2:=mulmod(T4,addmod(T3, sub(p, X),p),p)//M(S-X3)
                        let T5 := mulmod(T4, addmod(X, sub(p, T3), p), p) //-M(S-X3)=M(X3-S)
                        //Y:= addmod(T2, sub(p, mulmod(T1, Y ,p)),p  )//Y3= M(S-X3)-W*Y1
                        Y := addmod(mulmod(T1, Y, p), T5, p) //-Y3= W*Y1-M(S-X3), we replace Y by -Y to avoid a sub in ecAdd
                        /* compute element to access in precomputed table */
                    }
                    {
                        let T4 := add(shl(13, and(shr(index, scalar_v), 1)), shl(9, and(shr(index, scalar_u), 1)))
                        let index2 := sub(index, 64)
                        let T3 :=
                            add(T4, add(shl(12, and(shr(index2, scalar_v), 1)), shl(8, and(shr(index2, scalar_u), 1))))
                        let index3 := sub(index2, 64)
                        let T2 :=
                            add(T3, add(shl(11, and(shr(index3, scalar_v), 1)), shl(7, and(shr(index3, scalar_u), 1))))
                        index := sub(index3, 64)
                        let T1 :=
                            add(T2, add(shl(10, and(shr(index, scalar_v), 1)), shl(6, and(shr(index, scalar_u), 1))))
                        //tbd: check validity of formulae with (0,1) to remove conditional jump
                        if iszero(T1) {
                            Y := sub(p, Y)
                            continue
                        }
                        extcodecopy(dataPointer, T, T1, 64)
                    }
                    {
                        /* Access to precomputed table using extcodecopy hack */
                        // inlined EcZZ_AddN
                        if iszero(zz) {
                            X := mload(T)
                            Y := mload(add(T, 32))
                            zz := 1
                            zzz := 1
                            continue
                        }
                        let y2 := addmod(mulmod(mload(add(T, 32)), zzz, p), Y, p)
                        let T2 := addmod(mulmod(mload(T), zz, p), sub(p, X), p)
                        //special case ecAdd(P,P)=EcDbl
                        if iszero(y2) {
                            if iszero(T2) {
                                let T1 := mulmod(minus_2, Y, p) //U = 2*Y1, y free
                                T2 := mulmod(T1, T1, p) // V=U^2
                                let T3 := mulmod(X, T2, p) // S = X1*V
                                T1 := mulmod(T1, T2, p) // W=UV
                                y2 := mulmod(addmod(X, zz, p), addmod(X, sub(p, zz), p), p) //(X-ZZ)(X+ZZ)
                                let T4 := mulmod(3, y2, p) //M=3*(X-ZZ)(X+ZZ)
                                zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                                zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                                X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                                T2 := mulmod(T4, addmod(T3, sub(p, X), p), p) //M(S-X3)
                                Y := addmod(T2, mulmod(T1, Y, p), p) //Y3= M(S-X3)-W*Y1
                                continue
                            }
                        }
                        let T4 := mulmod(T2, T2, p)
                        let T1 := mulmod(T4, T2, p) //
                        zz := mulmod(zz, T4, p)
                        //zzz3=V*ZZ1
                        zzz := mulmod(zzz, T1, p) // W=UV/
                        let zz1 := mulmod(X, T4, p)
                        X := addmod(addmod(mulmod(y2, y2, p), sub(p, T1), p), mulmod(minus_2, zz1, p), p)
                        Y := addmod(mulmod(addmod(zz1, sub(p, X), p), y2, p), mulmod(Y, T1, p), p)
                    }
                } //end loop
                mstore(add(T, 0x60), zz)
                //(X,Y)=ecZZ_SetAff(X,Y,zz, zzz);
                //T[0] = inverseModp_Hard(T[0], p); //1/zzz, inline modular inversion using precompile:
                // Define length of base, exponent and modulus. 0x20 == 32 bytes
                mstore(T, 0x20)
                mstore(add(T, 0x20), 0x20)
                mstore(add(T, 0x40), 0x20)
                // Define variables base, exponent and modulus
                //mstore(add(pointer, 0x60), u)
                mstore(add(T, 0x80), minus_2)
                mstore(add(T, 0xa0), p)
                // Call the precompiled contract 0x05 = ModExp
                if iszero(staticcall(not(0), 0x05, T, 0xc0, T, 0x20)) { revert(0, 0) }
                zz := mload(T)
                X := mulmod(X, zz, p) //X/zz
            }
        } //end unchecked
    }
   
    // improving the extcodecopy trick : append array at end of contract
    function ecZZ_mulmuladd_S8_hackmem(uint256 scalar_u, uint256 scalar_v, uint256 dataPointer)
        internal view
        returns (uint256 X /*, uint Y*/ )
    {
        uint256 zz; // third and  coordinates of the point
        uint256[6] memory T;
        zz = 256; //start index
        unchecked {
            while (T[0] == 0) {
                zz = zz - 1;
                //tbd case of msb octobit is null
                T[0] = 64
                    * (
                        128 * ((scalar_v >> zz) & 1) + 64 * ((scalar_v >> (zz - 64)) & 1)
                            + 32 * ((scalar_v >> (zz - 128)) & 1) + 16 * ((scalar_v >> (zz - 192)) & 1)
                            + 8 * ((scalar_u >> zz) & 1) + 4 * ((scalar_u >> (zz - 64)) & 1)
                            + 2 * ((scalar_u >> (zz - 128)) & 1) + ((scalar_u >> (zz - 192)) & 1)
                    );
            }
            assembly {
                codecopy(T, add(mload(T), dataPointer), 64)
                X := mload(T)
                let Y := mload(add(T, 32))
                let zzz := 1
                zz := 1
                //loop over 1/4 of scalars thx to Shamir's trick over 8 points
                for { let index := 254 } gt(index, 191) { index := add(index, 191) } {
                    let T1 := mulmod(2, Y, p) //U = 2*Y1, y free
                    let T2 := mulmod(T1, T1, p) // V=U^2
                    let T3 := mulmod(X, T2, p) // S = X1*V
                    T1 := mulmod(T1, T2, p) // W=UV
                    let T4 := mulmod(3, mulmod(addmod(X, sub(p, zz), p), addmod(X, zz, p), p), p) //M=3*(X1-ZZ1)*(X1+ZZ1)
                    zzz := mulmod(T1, zzz, p) //zzz3=W*zzz1
                    zz := mulmod(T2, zz, p) //zz3=V*ZZ1, V free
                    X := addmod(mulmod(T4, T4, p), mulmod(minus_2, T3, p), p) //X3=M^2-2S
                    //T2:=mulmod(T4,addmod(T3, sub(p, X),p),p)//M(S-X3)
                    T2 := mulmod(T4, addmod(X, sub(p, T3), p), p) //-M(S-X3)=M(X3-S)
                    //Y:= addmod(T2, sub(p, mulmod(T1, Y ,p)),p  )//Y3= M(S-X3)-W*Y1
                    Y := addmod(mulmod(T1, Y, p), T2, p) //-Y3= W*Y1-M(S-X3), we replace Y by -Y to avoid a sub in ecAdd
                    /* compute element to access in precomputed table */
                    T4 := add(shl(13, and(shr(index, scalar_v), 1)), shl(9, and(shr(index, scalar_u), 1)))
                    index := sub(index, 64)
                    T4 := add(T4, add(shl(12, and(shr(index, scalar_v), 1)), shl(8, and(shr(index, scalar_u), 1))))
                    index := sub(index, 64)
                    T4 := add(T4, add(shl(11, and(shr(index, scalar_v), 1)), shl(7, and(shr(index, scalar_u), 1))))
                    index := sub(index, 64)
                    T4 := add(T4, add(shl(10, and(shr(index, scalar_v), 1)), shl(6, and(shr(index, scalar_u), 1))))
                    //index:=add(index,192), restore index, interleaved with loop
                    //tbd: check validity of formulae with (0,1) to remove conditional jump
                    if iszero(T4) {
                        Y := sub(p, Y)
                        continue
                    }
                    {
                        /* Access to precomputed table using extcodecopy hack */
                        codecopy(T, add(T4, dataPointer), 64)
                        // inlined EcZZ_AddN
                        let y2 := addmod(mulmod(mload(add(T, 32)), zzz, p), Y, p)
                        T2 := addmod(mulmod(mload(T), zz, p), sub(p, X), p)
                        T4 := mulmod(T2, T2, p)
                        T1 := mulmod(T4, T2, p)
                        T2 := mulmod(zz, T4, p) // W=UV
                        zzz := mulmod(zzz, T1, p) //zz3=V*ZZ1
                        let zz1 := mulmod(X, T4, p)
                        T4 := addmod(addmod(mulmod(y2, y2, p), sub(p, T1), p), mulmod(minus_2, zz1, p), p)
                        Y := addmod(mulmod(addmod(zz1, sub(p, T4), p), y2, p), mulmod(Y, T1, p), p)
                        zz := T2
                        X := T4
                    }
                } //end loop
                mstore(add(T, 0x60), zz)
                //(X,Y)=ecZZ_SetAff(X,Y,zz, zzz);
                //T[0] = inverseModp_Hard(T[0], p); //1/zzz, inline modular inversion using precompile:
                // Define length of base, exponent and modulus. 0x20 == 32 bytes
                mstore(T, 0x20)
                mstore(add(T, 0x20), 0x20)
                mstore(add(T, 0x40), 0x20)
                // Define variables base, exponent and modulus
                //mstore(add(pointer, 0x60), u)
                mstore(add(T, 0x80), minus_2)
                mstore(add(T, 0xa0), p)
                // Call the precompiled contract 0x05 = ModExp
                if iszero(staticcall(not(0), 0x05, T, 0xc0, T, 0x20)) { revert(0, 0) }
                zz := mload(T)
                X := mulmod(X, zz, p) //X/zz
            }
        } //end unchecked
    }
    /**
     * @dev ECDSA verification using a precomputed table of multiples of P and Q stored in contract at address Shamir8
     *     generation of contract bytecode for precomputations is done using sagemath code
     *     (see sage directory, WebAuthn_precompute.sage)
     */
    /**
     * @dev ECDSA verification using a precomputed table of multiples of P and Q appended at end of contract at address endcontract
     *     generation of contract bytecode for precomputations is done using sagemath code
     *     (see sage directory, WebAuthn_precompute.sage)
     */
    function ecdsa_precomputed_hackmem(bytes32 message, uint256[2] calldata rs, uint256 endcontract)
        internal view
        returns (bool)
    {
        uint256 r = rs[0];
        uint256 s = rs[1];
        if (r == 0 || r >= n || s == 0 || s >= n) {
            return false;
        }
        /* Q is pushed via bytecode assumed to be correct
        if (!isOnCurve(Q[0], Q[1])) {
            return false;
        }*/
        uint256 sInv = FCL_nModInv(s);
        uint256 X;
        //Shamir 8 dimensions
        X = ecZZ_mulmuladd_S8_hackmem(mulmod(uint256(message), sInv, n), mulmod(r, sInv, n), endcontract);
        assembly {
            X := addmod(X, sub(n, r), n)
        }
        return X == 0;
    } //end  ecdsa_precomputed_verify()
} //EOF
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.2) (utils/Base64.sol)
pragma solidity ^0.8.20;
/**
 * @dev Provides a set of functions to operate with Base64 strings.
 */
library Base64 {
    /**
     * @dev Base64 Encoding/Decoding Table
     * See sections 4 and 5 of https://datatracker.ietf.org/doc/html/rfc4648
     */
    string internal constant _TABLE = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
    string internal constant _TABLE_URL = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789-_";
    /**
     * @dev Converts a `bytes` to its Bytes64 `string` representation.
     */
    function encode(bytes memory data) internal pure returns (string memory) {
        return _encode(data, _TABLE, true);
    }
    /**
     * @dev Converts a `bytes` to its Bytes64Url `string` representation.
     */
    function encodeURL(bytes memory data) internal pure returns (string memory) {
        return _encode(data, _TABLE_URL, false);
    }
    /**
     * @dev Internal table-agnostic conversion
     */
    function _encode(bytes memory data, string memory table, bool withPadding) private pure returns (string memory) {
        /**
         * Inspired by Brecht Devos (Brechtpd) implementation - MIT licence
         * https://github.com/Brechtpd/base64/blob/e78d9fd951e7b0977ddca77d92dc85183770daf4/base64.sol
         */
        if (data.length == 0) return "";
        // If padding is enabled, the final length should be `bytes` data length divided by 3 rounded up and then
        // multiplied by 4 so that it leaves room for padding the last chunk
        // - `data.length + 2`  -> Round up
        // - `/ 3`              -> Number of 3-bytes chunks
        // - `4 *`              -> 4 characters for each chunk
        // If padding is disabled, the final length should be `bytes` data length multiplied by 4/3 rounded up as
        // opposed to when padding is required to fill the last chunk.
        // - `4 *`              -> 4 characters for each chunk
        // - `data.length + 2`  -> Round up
        // - `/ 3`              -> Number of 3-bytes chunks
        uint256 resultLength = withPadding ? 4 * ((data.length + 2) / 3) : (4 * data.length + 2) / 3;
        string memory result = new string(resultLength);
        /// @solidity memory-safe-assembly
        assembly {
            // Prepare the lookup table (skip the first "length" byte)
            let tablePtr := add(table, 1)
            // Prepare result pointer, jump over length
            let resultPtr := add(result, 0x20)
            let dataPtr := data
            let endPtr := add(data, mload(data))
            // In some cases, the last iteration will read bytes after the end of the data. We cache the value, and
            // set it to zero to make sure no dirty bytes are read in that section.
            let afterPtr := add(endPtr, 0x20)
            let afterCache := mload(afterPtr)
            mstore(afterPtr, 0x00)
            // Run over the input, 3 bytes at a time
            for {
            } lt(dataPtr, endPtr) {
            } {
                // Advance 3 bytes
                dataPtr := add(dataPtr, 3)
                let input := mload(dataPtr)
                // To write each character, shift the 3 byte (24 bits) chunk
                // 4 times in blocks of 6 bits for each character (18, 12, 6, 0)
                // and apply logical AND with 0x3F to bitmask the least significant 6 bits.
                // Use this as an index into the lookup table, mload an entire word
                // so the desired character is in the least significant byte, and
                // mstore8 this least significant byte into the result and continue.
                mstore8(resultPtr, mload(add(tablePtr, and(shr(18, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
                mstore8(resultPtr, mload(add(tablePtr, and(shr(12, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
                mstore8(resultPtr, mload(add(tablePtr, and(shr(6, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
                mstore8(resultPtr, mload(add(tablePtr, and(input, 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
            }
            // Reset the value that was cached
            mstore(afterPtr, afterCache)
            if withPadding {
                // When data `bytes` is not exactly 3 bytes long
                // it is padded with `=` characters at the end
                switch mod(mload(data), 3)
                case 1 {
                    mstore8(sub(resultPtr, 1), 0x3d)
                    mstore8(sub(resultPtr, 2), 0x3d)
                }
                case 2 {
                    mstore8(sub(resultPtr, 1), 0x3d)
                }
            }
        }
        return result;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Library for converting numbers into strings and other string operations.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/LibString.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/LibString.sol)
///
/// @dev Note:
/// For performance and bytecode compactness, most of the string operations are restricted to
/// byte strings (7-bit ASCII), except where otherwise specified.
/// Usage of byte string operations on charsets with runes spanning two or more bytes
/// can lead to undefined behavior.
library LibString {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                        CUSTOM ERRORS                       */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev The length of the output is too small to contain all the hex digits.
    error HexLengthInsufficient();
    /// @dev The length of the string is more than 32 bytes.
    error TooBigForSmallString();
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev The constant returned when the `search` is not found in the string.
    uint256 internal constant NOT_FOUND = type(uint256).max;
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     DECIMAL OPERATIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns the base 10 decimal representation of `value`.
    function toString(uint256 value) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            // The maximum value of a uint256 contains 78 digits (1 byte per digit), but
            // we allocate 0xa0 bytes to keep the free memory pointer 32-byte word aligned.
            // We will need 1 word for the trailing zeros padding, 1 word for the length,
            // and 3 words for a maximum of 78 digits.
            str := add(mload(0x40), 0x80)
            // Update the free memory pointer to allocate.
            mstore(0x40, add(str, 0x20))
            // Zeroize the slot after the string.
            mstore(str, 0)
            // Cache the end of the memory to calculate the length later.
            let end := str
            let w := not(0) // Tsk.
            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            for { let temp := value } 1 {} {
                str := add(str, w) // `sub(str, 1)`.
                // Write the character to the pointer.
                // The ASCII index of the '0' character is 48.
                mstore8(str, add(48, mod(temp, 10)))
                // Keep dividing `temp` until zero.
                temp := div(temp, 10)
                if iszero(temp) { break }
            }
            let length := sub(end, str)
            // Move the pointer 32 bytes leftwards to make room for the length.
            str := sub(str, 0x20)
            // Store the length.
            mstore(str, length)
        }
    }
    /// @dev Returns the base 10 decimal representation of `value`.
    function toString(int256 value) internal pure returns (string memory str) {
        if (value >= 0) {
            return toString(uint256(value));
        }
        unchecked {
            str = toString(~uint256(value) + 1);
        }
        /// @solidity memory-safe-assembly
        assembly {
            // We still have some spare memory space on the left,
            // as we have allocated 3 words (96 bytes) for up to 78 digits.
            let length := mload(str) // Load the string length.
            mstore(str, 0x2d) // Store the '-' character.
            str := sub(str, 1) // Move back the string pointer by a byte.
            mstore(str, add(length, 1)) // Update the string length.
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   HEXADECIMAL OPERATIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns the hexadecimal representation of `value`,
    /// left-padded to an input length of `length` bytes.
    /// The output is prefixed with "0x" encoded using 2 hexadecimal digits per byte,
    /// giving a total length of `length * 2 + 2` bytes.
    /// Reverts if `length` is too small for the output to contain all the digits.
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value, length);
        /// @solidity memory-safe-assembly
        assembly {
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(str, 0x3078) // Write the "0x" prefix.
            str := sub(str, 2) // Move the pointer.
            mstore(str, strLength) // Write the length.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`,
    /// left-padded to an input length of `length` bytes.
    /// The output is prefixed with "0x" encoded using 2 hexadecimal digits per byte,
    /// giving a total length of `length * 2` bytes.
    /// Reverts if `length` is too small for the output to contain all the digits.
    function toHexStringNoPrefix(uint256 value, uint256 length)
        internal
        pure
        returns (string memory str)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // We need 0x20 bytes for the trailing zeros padding, `length * 2` bytes
            // for the digits, 0x02 bytes for the prefix, and 0x20 bytes for the length.
            // We add 0x20 to the total and round down to a multiple of 0x20.
            // (0x20 + 0x20 + 0x02 + 0x20) = 0x62.
            str := add(mload(0x40), and(add(shl(1, length), 0x42), not(0x1f)))
            // Allocate the memory.
            mstore(0x40, add(str, 0x20))
            // Zeroize the slot after the string.
            mstore(str, 0)
            // Cache the end to calculate the length later.
            let end := str
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)
            let start := sub(str, add(length, length))
            let w := not(1) // Tsk.
            let temp := value
            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            for {} 1 {} {
                str := add(str, w) // `sub(str, 2)`.
                mstore8(add(str, 1), mload(and(temp, 15)))
                mstore8(str, mload(and(shr(4, temp), 15)))
                temp := shr(8, temp)
                if iszero(xor(str, start)) { break }
            }
            if temp {
                mstore(0x00, 0x2194895a) // `HexLengthInsufficient()`.
                revert(0x1c, 0x04)
            }
            // Compute the string's length.
            let strLength := sub(end, str)
            // Move the pointer and write the length.
            str := sub(str, 0x20)
            mstore(str, strLength)
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is prefixed with "0x" and encoded using 2 hexadecimal digits per byte.
    /// As address are 20 bytes long, the output will left-padded to have
    /// a length of `20 * 2 + 2` bytes.
    function toHexString(uint256 value) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(str, 0x3078) // Write the "0x" prefix.
            str := sub(str, 2) // Move the pointer.
            mstore(str, strLength) // Write the length.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is prefixed with "0x".
    /// The output excludes leading "0" from the `toHexString` output.
    /// `0x00: "0x0", 0x01: "0x1", 0x12: "0x12", 0x123: "0x123"`.
    function toMinimalHexString(uint256 value) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let o := eq(byte(0, mload(add(str, 0x20))), 0x30) // Whether leading zero is present.
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(add(str, o), 0x3078) // Write the "0x" prefix, accounting for leading zero.
            str := sub(add(str, o), 2) // Move the pointer, accounting for leading zero.
            mstore(str, sub(strLength, o)) // Write the length, accounting for leading zero.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output excludes leading "0" from the `toHexStringNoPrefix` output.
    /// `0x00: "0", 0x01: "1", 0x12: "12", 0x123: "123"`.
    function toMinimalHexStringNoPrefix(uint256 value) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let o := eq(byte(0, mload(add(str, 0x20))), 0x30) // Whether leading zero is present.
            let strLength := mload(str) // Get the length.
            str := add(str, o) // Move the pointer, accounting for leading zero.
            mstore(str, sub(strLength, o)) // Write the length, accounting for leading zero.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is encoded using 2 hexadecimal digits per byte.
    /// As address are 20 bytes long, the output will left-padded to have
    /// a length of `20 * 2` bytes.
    function toHexStringNoPrefix(uint256 value) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            // We need 0x20 bytes for the trailing zeros padding, 0x20 bytes for the length,
            // 0x02 bytes for the prefix, and 0x40 bytes for the digits.
            // The next multiple of 0x20 above (0x20 + 0x20 + 0x02 + 0x40) is 0xa0.
            str := add(mload(0x40), 0x80)
            // Allocate the memory.
            mstore(0x40, add(str, 0x20))
            // Zeroize the slot after the string.
            mstore(str, 0)
            // Cache the end to calculate the length later.
            let end := str
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)
            let w := not(1) // Tsk.
            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            for { let temp := value } 1 {} {
                str := add(str, w) // `sub(str, 2)`.
                mstore8(add(str, 1), mload(and(temp, 15)))
                mstore8(str, mload(and(shr(4, temp), 15)))
                temp := shr(8, temp)
                if iszero(temp) { break }
            }
            // Compute the string's length.
            let strLength := sub(end, str)
            // Move the pointer and write the length.
            str := sub(str, 0x20)
            mstore(str, strLength)
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is prefixed with "0x", encoded using 2 hexadecimal digits per byte,
    /// and the alphabets are capitalized conditionally according to
    /// https://eips.ethereum.org/EIPS/eip-55
    function toHexStringChecksummed(address value) internal pure returns (string memory str) {
        str = toHexString(value);
        /// @solidity memory-safe-assembly
        assembly {
            let mask := shl(6, div(not(0), 255)) // `0b010000000100000000 ...`
            let o := add(str, 0x22)
            let hashed := and(keccak256(o, 40), mul(34, mask)) // `0b10001000 ... `
            let t := shl(240, 136) // `0b10001000 << 240`
            for { let i := 0 } 1 {} {
                mstore(add(i, i), mul(t, byte(i, hashed)))
                i := add(i, 1)
                if eq(i, 20) { break }
            }
            mstore(o, xor(mload(o), shr(1, and(mload(0x00), and(mload(o), mask)))))
            o := add(o, 0x20)
            mstore(o, xor(mload(o), shr(1, and(mload(0x20), and(mload(o), mask)))))
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is prefixed with "0x" and encoded using 2 hexadecimal digits per byte.
    function toHexString(address value) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(value);
        /// @solidity memory-safe-assembly
        assembly {
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(str, 0x3078) // Write the "0x" prefix.
            str := sub(str, 2) // Move the pointer.
            mstore(str, strLength) // Write the length.
        }
    }
    /// @dev Returns the hexadecimal representation of `value`.
    /// The output is encoded using 2 hexadecimal digits per byte.
    function toHexStringNoPrefix(address value) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            str := mload(0x40)
            // Allocate the memory.
            // We need 0x20 bytes for the trailing zeros padding, 0x20 bytes for the length,
            // 0x02 bytes for the prefix, and 0x28 bytes for the digits.
            // The next multiple of 0x20 above (0x20 + 0x20 + 0x02 + 0x28) is 0x80.
            mstore(0x40, add(str, 0x80))
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)
            str := add(str, 2)
            mstore(str, 40)
            let o := add(str, 0x20)
            mstore(add(o, 40), 0)
            value := shl(96, value)
            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            for { let i := 0 } 1 {} {
                let p := add(o, add(i, i))
                let temp := byte(i, value)
                mstore8(add(p, 1), mload(and(temp, 15)))
                mstore8(p, mload(shr(4, temp)))
                i := add(i, 1)
                if eq(i, 20) { break }
            }
        }
    }
    /// @dev Returns the hex encoded string from the raw bytes.
    /// The output is encoded using 2 hexadecimal digits per byte.
    function toHexString(bytes memory raw) internal pure returns (string memory str) {
        str = toHexStringNoPrefix(raw);
        /// @solidity memory-safe-assembly
        assembly {
            let strLength := add(mload(str), 2) // Compute the length.
            mstore(str, 0x3078) // Write the "0x" prefix.
            str := sub(str, 2) // Move the pointer.
            mstore(str, strLength) // Write the length.
        }
    }
    /// @dev Returns the hex encoded string from the raw bytes.
    /// The output is encoded using 2 hexadecimal digits per byte.
    function toHexStringNoPrefix(bytes memory raw) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            let length := mload(raw)
            str := add(mload(0x40), 2) // Skip 2 bytes for the optional prefix.
            mstore(str, add(length, length)) // Store the length of the output.
            // Store "0123456789abcdef" in scratch space.
            mstore(0x0f, 0x30313233343536373839616263646566)
            let o := add(str, 0x20)
            let end := add(raw, length)
            for {} iszero(eq(raw, end)) {} {
                raw := add(raw, 1)
                mstore8(add(o, 1), mload(and(mload(raw), 15)))
                mstore8(o, mload(and(shr(4, mload(raw)), 15)))
                o := add(o, 2)
            }
            mstore(o, 0) // Zeroize the slot after the string.
            mstore(0x40, add(o, 0x20)) // Allocate the memory.
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   RUNE STRING OPERATIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns the number of UTF characters in the string.
    function runeCount(string memory s) internal pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            if mload(s) {
                mstore(0x00, div(not(0), 255))
                mstore(0x20, 0x0202020202020202020202020202020202020202020202020303030304040506)
                let o := add(s, 0x20)
                let end := add(o, mload(s))
                for { result := 1 } 1 { result := add(result, 1) } {
                    o := add(o, byte(0, mload(shr(250, mload(o)))))
                    if iszero(lt(o, end)) { break }
                }
            }
        }
    }
    /// @dev Returns if this string is a 7-bit ASCII string.
    /// (i.e. all characters codes are in [0..127])
    function is7BitASCII(string memory s) internal pure returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            let mask := shl(7, div(not(0), 255))
            result := 1
            let n := mload(s)
            if n {
                let o := add(s, 0x20)
                let end := add(o, n)
                let last := mload(end)
                mstore(end, 0)
                for {} 1 {} {
                    if and(mask, mload(o)) {
                        result := 0
                        break
                    }
                    o := add(o, 0x20)
                    if iszero(lt(o, end)) { break }
                }
                mstore(end, last)
            }
        }
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   BYTE STRING OPERATIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    // For performance and bytecode compactness, byte string operations are restricted
    // to 7-bit ASCII strings. All offsets are byte offsets, not UTF character offsets.
    // Usage of byte string operations on charsets with runes spanning two or more bytes
    // can lead to undefined behavior.
    /// @dev Returns `subject` all occurrences of `search` replaced with `replacement`.
    function replace(string memory subject, string memory search, string memory replacement)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLength := mload(subject)
            let searchLength := mload(search)
            let replacementLength := mload(replacement)
            subject := add(subject, 0x20)
            search := add(search, 0x20)
            replacement := add(replacement, 0x20)
            result := add(mload(0x40), 0x20)
            let subjectEnd := add(subject, subjectLength)
            if iszero(gt(searchLength, subjectLength)) {
                let subjectSearchEnd := add(sub(subjectEnd, searchLength), 1)
                let h := 0
                if iszero(lt(searchLength, 0x20)) { h := keccak256(search, searchLength) }
                let m := shl(3, sub(0x20, and(searchLength, 0x1f)))
                let s := mload(search)
                for {} 1 {} {
                    let t := mload(subject)
                    // Whether the first `searchLength % 32` bytes of
                    // `subject` and `search` matches.
                    if iszero(shr(m, xor(t, s))) {
                        if h {
                            if iszero(eq(keccak256(subject, searchLength), h)) {
                                mstore(result, t)
                                result := add(result, 1)
                                subject := add(subject, 1)
                                if iszero(lt(subject, subjectSearchEnd)) { break }
                                continue
                            }
                        }
                        // Copy the `replacement` one word at a time.
                        for { let o := 0 } 1 {} {
                            mstore(add(result, o), mload(add(replacement, o)))
                            o := add(o, 0x20)
                            if iszero(lt(o, replacementLength)) { break }
                        }
                        result := add(result, replacementLength)
                        subject := add(subject, searchLength)
                        if searchLength {
                            if iszero(lt(subject, subjectSearchEnd)) { break }
                            continue
                        }
                    }
                    mstore(result, t)
                    result := add(result, 1)
                    subject := add(subject, 1)
                    if iszero(lt(subject, subjectSearchEnd)) { break }
                }
            }
            let resultRemainder := result
            result := add(mload(0x40), 0x20)
            let k := add(sub(resultRemainder, result), sub(subjectEnd, subject))
            // Copy the rest of the string one word at a time.
            for {} lt(subject, subjectEnd) {} {
                mstore(resultRemainder, mload(subject))
                resultRemainder := add(resultRemainder, 0x20)
                subject := add(subject, 0x20)
            }
            result := sub(result, 0x20)
            let last := add(add(result, 0x20), k) // Zeroize the slot after the string.
            mstore(last, 0)
            mstore(0x40, add(last, 0x20)) // Allocate the memory.
            mstore(result, k) // Store the length.
        }
    }
    /// @dev Returns the byte index of the first location of `search` in `subject`,
    /// searching from left to right, starting from `from`.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `search` is not found.
    function indexOf(string memory subject, string memory search, uint256 from)
        internal
        pure
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            for { let subjectLength := mload(subject) } 1 {} {
                if iszero(mload(search)) {
                    if iszero(gt(from, subjectLength)) {
                        result := from
                        break
                    }
                    result := subjectLength
                    break
                }
                let searchLength := mload(search)
                let subjectStart := add(subject, 0x20)
                result := not(0) // Initialize to `NOT_FOUND`.
                subject := add(subjectStart, from)
                let end := add(sub(add(subjectStart, subjectLength), searchLength), 1)
                let m := shl(3, sub(0x20, and(searchLength, 0x1f)))
                let s := mload(add(search, 0x20))
                if iszero(and(lt(subject, end), lt(from, subjectLength))) { break }
                if iszero(lt(searchLength, 0x20)) {
                    for { let h := keccak256(add(search, 0x20), searchLength) } 1 {} {
                        if iszero(shr(m, xor(mload(subject), s))) {
                            if eq(keccak256(subject, searchLength), h) {
                                result := sub(subject, subjectStart)
                                break
                            }
                        }
                        subject := add(subject, 1)
                        if iszero(lt(subject, end)) { break }
                    }
                    break
                }
                for {} 1 {} {
                    if iszero(shr(m, xor(mload(subject), s))) {
                        result := sub(subject, subjectStart)
                        break
                    }
                    subject := add(subject, 1)
                    if iszero(lt(subject, end)) { break }
                }
                break
            }
        }
    }
    /// @dev Returns the byte index of the first location of `search` in `subject`,
    /// searching from left to right.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `search` is not found.
    function indexOf(string memory subject, string memory search)
        internal
        pure
        returns (uint256 result)
    {
        result = indexOf(subject, search, 0);
    }
    /// @dev Returns the byte index of the first location of `search` in `subject`,
    /// searching from right to left, starting from `from`.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `search` is not found.
    function lastIndexOf(string memory subject, string memory search, uint256 from)
        internal
        pure
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            for {} 1 {} {
                result := not(0) // Initialize to `NOT_FOUND`.
                let searchLength := mload(search)
                if gt(searchLength, mload(subject)) { break }
                let w := result
                let fromMax := sub(mload(subject), searchLength)
                if iszero(gt(fromMax, from)) { from := fromMax }
                let end := add(add(subject, 0x20), w)
                subject := add(add(subject, 0x20), from)
                if iszero(gt(subject, end)) { break }
                // As this function is not too often used,
                // we shall simply use keccak256 for smaller bytecode size.
                for { let h := keccak256(add(search, 0x20), searchLength) } 1 {} {
                    if eq(keccak256(subject, searchLength), h) {
                        result := sub(subject, add(end, 1))
                        break
                    }
                    subject := add(subject, w) // `sub(subject, 1)`.
                    if iszero(gt(subject, end)) { break }
                }
                break
            }
        }
    }
    /// @dev Returns the byte index of the first location of `search` in `subject`,
    /// searching from right to left.
    /// Returns `NOT_FOUND` (i.e. `type(uint256).max`) if the `search` is not found.
    function lastIndexOf(string memory subject, string memory search)
        internal
        pure
        returns (uint256 result)
    {
        result = lastIndexOf(subject, search, uint256(int256(-1)));
    }
    /// @dev Returns true if `search` is found in `subject`, false otherwise.
    function contains(string memory subject, string memory search) internal pure returns (bool) {
        return indexOf(subject, search) != NOT_FOUND;
    }
    /// @dev Returns whether `subject` starts with `search`.
    function startsWith(string memory subject, string memory search)
        internal
        pure
        returns (bool result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let searchLength := mload(search)
            // Just using keccak256 directly is actually cheaper.
            // forgefmt: disable-next-item
            result := and(
                iszero(gt(searchLength, mload(subject))),
                eq(
                    keccak256(add(subject, 0x20), searchLength),
                    keccak256(add(search, 0x20), searchLength)
                )
            )
        }
    }
    /// @dev Returns whether `subject` ends with `search`.
    function endsWith(string memory subject, string memory search)
        internal
        pure
        returns (bool result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let searchLength := mload(search)
            let subjectLength := mload(subject)
            // Whether `search` is not longer than `subject`.
            let withinRange := iszero(gt(searchLength, subjectLength))
            // Just using keccak256 directly is actually cheaper.
            // forgefmt: disable-next-item
            result := and(
                withinRange,
                eq(
                    keccak256(
                        // `subject + 0x20 + max(subjectLength - searchLength, 0)`.
                        add(add(subject, 0x20), mul(withinRange, sub(subjectLength, searchLength))),
                        searchLength
                    ),
                    keccak256(add(search, 0x20), searchLength)
                )
            )
        }
    }
    /// @dev Returns `subject` repeated `times`.
    function repeat(string memory subject, uint256 times)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLength := mload(subject)
            if iszero(or(iszero(times), iszero(subjectLength))) {
                subject := add(subject, 0x20)
                result := mload(0x40)
                let output := add(result, 0x20)
                for {} 1 {} {
                    // Copy the `subject` one word at a time.
                    for { let o := 0 } 1 {} {
                        mstore(add(output, o), mload(add(subject, o)))
                        o := add(o, 0x20)
                        if iszero(lt(o, subjectLength)) { break }
                    }
                    output := add(output, subjectLength)
                    times := sub(times, 1)
                    if iszero(times) { break }
                }
                mstore(output, 0) // Zeroize the slot after the string.
                let resultLength := sub(output, add(result, 0x20))
                mstore(result, resultLength) // Store the length.
                // Allocate the memory.
                mstore(0x40, add(result, add(resultLength, 0x20)))
            }
        }
    }
    /// @dev Returns a copy of `subject` sliced from `start` to `end` (exclusive).
    /// `start` and `end` are byte offsets.
    function slice(string memory subject, uint256 start, uint256 end)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLength := mload(subject)
            if iszero(gt(subjectLength, end)) { end := subjectLength }
            if iszero(gt(subjectLength, start)) { start := subjectLength }
            if lt(start, end) {
                result := mload(0x40)
                let resultLength := sub(end, start)
                mstore(result, resultLength)
                subject := add(subject, start)
                let w := not(0x1f)
                // Copy the `subject` one word at a time, backwards.
                for { let o := and(add(resultLength, 0x1f), w) } 1 {} {
                    mstore(add(result, o), mload(add(subject, o)))
                    o := add(o, w) // `sub(o, 0x20)`.
                    if iszero(o) { break }
                }
                // Zeroize the slot after the string.
                mstore(add(add(result, 0x20), resultLength), 0)
                // Allocate memory for the length and the bytes,
                // rounded up to a multiple of 32.
                mstore(0x40, add(result, and(add(resultLength, 0x3f), w)))
            }
        }
    }
    /// @dev Returns a copy of `subject` sliced from `start` to the end of the string.
    /// `start` is a byte offset.
    function slice(string memory subject, uint256 start)
        internal
        pure
        returns (string memory result)
    {
        result = slice(subject, start, uint256(int256(-1)));
    }
    /// @dev Returns all the indices of `search` in `subject`.
    /// The indices are byte offsets.
    function indicesOf(string memory subject, string memory search)
        internal
        pure
        returns (uint256[] memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let subjectLength := mload(subject)
            let searchLength := mload(search)
            if iszero(gt(searchLength, subjectLength)) {
                subject := add(subject, 0x20)
                search := add(search, 0x20)
                result := add(mload(0x40), 0x20)
                let subjectStart := subject
                let subjectSearchEnd := add(sub(add(subject, subjectLength), searchLength), 1)
                let h := 0
                if iszero(lt(searchLength, 0x20)) { h := keccak256(search, searchLength) }
                let m := shl(3, sub(0x20, and(searchLength, 0x1f)))
                let s := mload(search)
                for {} 1 {} {
                    let t := mload(subject)
                    // Whether the first `searchLength % 32` bytes of
                    // `subject` and `search` matches.
                    if iszero(shr(m, xor(t, s))) {
                        if h {
                            if iszero(eq(keccak256(subject, searchLength), h)) {
                                subject := add(subject, 1)
                                if iszero(lt(subject, subjectSearchEnd)) { break }
                                continue
                            }
                        }
                        // Append to `result`.
                        mstore(result, sub(subject, subjectStart))
                        result := add(result, 0x20)
                        // Advance `subject` by `searchLength`.
                        subject := add(subject, searchLength)
                        if searchLength {
                            if iszero(lt(subject, subjectSearchEnd)) { break }
                            continue
                        }
                    }
                    subject := add(subject, 1)
                    if iszero(lt(subject, subjectSearchEnd)) { break }
                }
                let resultEnd := result
                // Assign `result` to the free memory pointer.
                result := mload(0x40)
                // Store the length of `result`.
                mstore(result, shr(5, sub(resultEnd, add(result, 0x20))))
                // Allocate memory for result.
                // We allocate one more word, so this array can be recycled for {split}.
                mstore(0x40, add(resultEnd, 0x20))
            }
        }
    }
    /// @dev Returns a arrays of strings based on the `delimiter` inside of the `subject` string.
    function split(string memory subject, string memory delimiter)
        internal
        pure
        returns (string[] memory result)
    {
        uint256[] memory indices = indicesOf(subject, delimiter);
        /// @solidity memory-safe-assembly
        assembly {
            let w := not(0x1f)
            let indexPtr := add(indices, 0x20)
            let indicesEnd := add(indexPtr, shl(5, add(mload(indices), 1)))
            mstore(add(indicesEnd, w), mload(subject))
            mstore(indices, add(mload(indices), 1))
            let prevIndex := 0
            for {} 1 {} {
                let index := mload(indexPtr)
                mstore(indexPtr, 0x60)
                if iszero(eq(index, prevIndex)) {
                    let element := mload(0x40)
                    let elementLength := sub(index, prevIndex)
                    mstore(element, elementLength)
                    // Copy the `subject` one word at a time, backwards.
                    for { let o := and(add(elementLength, 0x1f), w) } 1 {} {
                        mstore(add(element, o), mload(add(add(subject, prevIndex), o)))
                        o := add(o, w) // `sub(o, 0x20)`.
                        if iszero(o) { break }
                    }
                    // Zeroize the slot after the string.
                    mstore(add(add(element, 0x20), elementLength), 0)
                    // Allocate memory for the length and the bytes,
                    // rounded up to a multiple of 32.
                    mstore(0x40, add(element, and(add(elementLength, 0x3f), w)))
                    // Store the `element` into the array.
                    mstore(indexPtr, element)
                }
                prevIndex := add(index, mload(delimiter))
                indexPtr := add(indexPtr, 0x20)
                if iszero(lt(indexPtr, indicesEnd)) { break }
            }
            result := indices
            if iszero(mload(delimiter)) {
                result := add(indices, 0x20)
                mstore(result, sub(mload(indices), 2))
            }
        }
    }
    /// @dev Returns a concatenated string of `a` and `b`.
    /// Cheaper than `string.concat()` and does not de-align the free memory pointer.
    function concat(string memory a, string memory b)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let w := not(0x1f)
            result := mload(0x40)
            let aLength := mload(a)
            // Copy `a` one word at a time, backwards.
            for { let o := and(add(aLength, 0x20), w) } 1 {} {
                mstore(add(result, o), mload(add(a, o)))
                o := add(o, w) // `sub(o, 0x20)`.
                if iszero(o) { break }
            }
            let bLength := mload(b)
            let output := add(result, aLength)
            // Copy `b` one word at a time, backwards.
            for { let o := and(add(bLength, 0x20), w) } 1 {} {
                mstore(add(output, o), mload(add(b, o)))
                o := add(o, w) // `sub(o, 0x20)`.
                if iszero(o) { break }
            }
            let totalLength := add(aLength, bLength)
            let last := add(add(result, 0x20), totalLength)
            // Zeroize the slot after the string.
            mstore(last, 0)
            // Stores the length.
            mstore(result, totalLength)
            // Allocate memory for the length and the bytes,
            // rounded up to a multiple of 32.
            mstore(0x40, and(add(last, 0x1f), w))
        }
    }
    /// @dev Returns a copy of the string in either lowercase or UPPERCASE.
    /// WARNING! This function is only compatible with 7-bit ASCII strings.
    function toCase(string memory subject, bool toUpper)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let length := mload(subject)
            if length {
                result := add(mload(0x40), 0x20)
                subject := add(subject, 1)
                let flags := shl(add(70, shl(5, toUpper)), 0x3ffffff)
                let w := not(0)
                for { let o := length } 1 {} {
                    o := add(o, w)
                    let b := and(0xff, mload(add(subject, o)))
                    mstore8(add(result, o), xor(b, and(shr(b, flags), 0x20)))
                    if iszero(o) { break }
                }
                result := mload(0x40)
                mstore(result, length) // Store the length.
                let last := add(add(result, 0x20), length)
                mstore(last, 0) // Zeroize the slot after the string.
                mstore(0x40, add(last, 0x20)) // Allocate the memory.
            }
        }
    }
    /// @dev Returns a string from a small bytes32 string.
    /// `s` must be null-terminated, or behavior will be undefined.
    function fromSmallString(bytes32 s) internal pure returns (string memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40)
            let n := 0
            for {} byte(n, s) { n := add(n, 1) } {} // Scan for '\\0'.
            mstore(result, n)
            let o := add(result, 0x20)
            mstore(o, s)
            mstore(add(o, n), 0)
            mstore(0x40, add(result, 0x40))
        }
    }
    /// @dev Returns the small string, with all bytes after the first null byte zeroized.
    function normalizeSmallString(bytes32 s) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            for {} byte(result, s) { result := add(result, 1) } {} // Scan for '\\0'.
            mstore(0x00, s)
            mstore(result, 0x00)
            result := mload(0x00)
        }
    }
    /// @dev Returns the string as a normalized null-terminated small string.
    function toSmallString(string memory s) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(s)
            if iszero(lt(result, 33)) {
                mstore(0x00, 0xec92f9a3) // `TooBigForSmallString()`.
                revert(0x1c, 0x04)
            }
            result := shl(shl(3, sub(32, result)), mload(add(s, result)))
        }
    }
    /// @dev Returns a lowercased copy of the string.
    /// WARNING! This function is only compatible with 7-bit ASCII strings.
    function lower(string memory subject) internal pure returns (string memory result) {
        result = toCase(subject, false);
    }
    /// @dev Returns an UPPERCASED copy of the string.
    /// WARNING! This function is only compatible with 7-bit ASCII strings.
    function upper(string memory subject) internal pure returns (string memory result) {
        result = toCase(subject, true);
    }
    /// @dev Escapes the string to be used within HTML tags.
    function escapeHTML(string memory s) internal pure returns (string memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            let end := add(s, mload(s))
            result := add(mload(0x40), 0x20)
            // Store the bytes of the packed offsets and strides into the scratch space.
            // `packed = (stride << 5) | offset`. Max offset is 20. Max stride is 6.
            mstore(0x1f, 0x900094)
            mstore(0x08, 0xc0000000a6ab)
            // Store "&quot;&amp;&#39;&lt;&gt;" into the scratch space.
            mstore(0x00, shl(64, 0x2671756f743b26616d703b262333393b266c743b2667743b))
            for {} iszero(eq(s, end)) {} {
                s := add(s, 1)
                let c := and(mload(s), 0xff)
                // Not in `["\\"","'","&","<",">"]`.
                if iszero(and(shl(c, 1), 0x500000c400000000)) {
                    mstore8(result, c)
                    result := add(result, 1)
                    continue
                }
                let t := shr(248, mload(c))
                mstore(result, mload(and(t, 0x1f)))
                result := add(result, shr(5, t))
            }
            let last := result
            mstore(last, 0) // Zeroize the slot after the string.
            result := mload(0x40)
            mstore(result, sub(last, add(result, 0x20))) // Store the length.
            mstore(0x40, add(last, 0x20)) // Allocate the memory.
        }
    }
    /// @dev Escapes the string to be used within double-quotes in a JSON.
    /// If `addDoubleQuotes` is true, the result will be enclosed in double-quotes.
    function escapeJSON(string memory s, bool addDoubleQuotes)
        internal
        pure
        returns (string memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let end := add(s, mload(s))
            result := add(mload(0x40), 0x20)
            if addDoubleQuotes {
                mstore8(result, 34)
                result := add(1, result)
            }
            // Store "\\\\u0000" in scratch space.
            // Store "0123456789abcdef" in scratch space.
            // Also, store `{0x08:"b", 0x09:"t", 0x0a:"n", 0x0c:"f", 0x0d:"r"}`.
            // into the scratch space.
            mstore(0x15, 0x5c75303030303031323334353637383961626364656662746e006672)
            // Bitmask for detecting `["\\"","\\\\"]`.
            let e := or(shl(0x22, 1), shl(0x5c, 1))
            for {} iszero(eq(s, end)) {} {
                s := add(s, 1)
                let c := and(mload(s), 0xff)
                if iszero(lt(c, 0x20)) {
                    if iszero(and(shl(c, 1), e)) {
                        // Not in `["\\"","\\\\"]`.
                        mstore8(result, c)
                        result := add(result, 1)
                        continue
                    }
                    mstore8(result, 0x5c) // "\\\\".
                    mstore8(add(result, 1), c)
                    result := add(result, 2)
                    continue
                }
                if iszero(and(shl(c, 1), 0x3700)) {
                    // Not in `["\\b","\\t","\
","\\f","\\d"]`.
                    mstore8(0x1d, mload(shr(4, c))) // Hex value.
                    mstore8(0x1e, mload(and(c, 15))) // Hex value.
                    mstore(result, mload(0x19)) // "\\\\u00XX".
                    result := add(result, 6)
                    continue
                }
                mstore8(result, 0x5c) // "\\\\".
                mstore8(add(result, 1), mload(add(c, 8)))
                result := add(result, 2)
            }
            if addDoubleQuotes {
                mstore8(result, 34)
                result := add(1, result)
            }
            let last := result
            mstore(last, 0) // Zeroize the slot after the string.
            result := mload(0x40)
            mstore(result, sub(last, add(result, 0x20))) // Store the length.
            mstore(0x40, add(last, 0x20)) // Allocate the memory.
        }
    }
    /// @dev Escapes the string to be used within double-quotes in a JSON.
    function escapeJSON(string memory s) internal pure returns (string memory result) {
        result = escapeJSON(s, false);
    }
    /// @dev Returns whether `a` equals `b`.
    function eq(string memory a, string memory b) internal pure returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := eq(keccak256(add(a, 0x20), mload(a)), keccak256(add(b, 0x20), mload(b)))
        }
    }
    /// @dev Returns whether `a` equals `b`, where `b` is a null-terminated small string.
    function eqs(string memory a, bytes32 b) internal pure returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            // These should be evaluated on compile time, as far as possible.
            let m := not(shl(7, div(not(iszero(b)), 255))) // `0x7f7f ...`.
            let x := not(or(m, or(b, add(m, and(b, m)))))
            let r := shl(7, iszero(iszero(shr(128, x))))
            r := or(r, shl(6, iszero(iszero(shr(64, shr(r, x))))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            // forgefmt: disable-next-item
            result := gt(eq(mload(a), add(iszero(x), xor(31, shr(3, r)))),
                xor(shr(add(8, r), b), shr(add(8, r), mload(add(a, 0x20)))))
        }
    }
    /// @dev Packs a single string with its length into a single word.
    /// Returns `bytes32(0)` if the length is zero or greater than 31.
    function packOne(string memory a) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            // We don't need to zero right pad the string,
            // since this is our own custom non-standard packing scheme.
            result :=
                mul(
                    // Load the length and the bytes.
                    mload(add(a, 0x1f)),
                    // `length != 0 && length < 32`. Abuses underflow.
                    // Assumes that the length is valid and within the block gas limit.
                    lt(sub(mload(a), 1), 0x1f)
                )
        }
    }
    /// @dev Unpacks a string packed using {packOne}.
    /// Returns the empty string if `packed` is `bytes32(0)`.
    /// If `packed` is not an output of {packOne}, the output behavior is undefined.
    function unpackOne(bytes32 packed) internal pure returns (string memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            // Grab the free memory pointer.
            result := mload(0x40)
            // Allocate 2 words (1 for the length, 1 for the bytes).
            mstore(0x40, add(result, 0x40))
            // Zeroize the length slot.
            mstore(result, 0)
            // Store the length and bytes.
            mstore(add(result, 0x1f), packed)
            // Right pad with zeroes.
            mstore(add(add(result, 0x20), mload(result)), 0)
        }
    }
    /// @dev Packs two strings with their lengths into a single word.
    /// Returns `bytes32(0)` if combined length is zero or greater than 30.
    function packTwo(string memory a, string memory b) internal pure returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            let aLength := mload(a)
            // We don't need to zero right pad the strings,
            // since this is our own custom non-standard packing scheme.
            result :=
                mul(
                    // Load the length and the bytes of `a` and `b`.
                    or(
                        shl(shl(3, sub(0x1f, aLength)), mload(add(a, aLength))),
                        mload(sub(add(b, 0x1e), aLength))
                    ),
                    // `totalLength != 0 && totalLength < 31`. Abuses underflow.
                    // Assumes that the lengths are valid and within the block gas limit.
                    lt(sub(add(aLength, mload(b)), 1), 0x1e)
                )
        }
    }
    /// @dev Unpacks strings packed using {packTwo}.
    /// Returns the empty strings if `packed` is `bytes32(0)`.
    /// If `packed` is not an output of {packTwo}, the output behavior is undefined.
    function unpackTwo(bytes32 packed)
        internal
        pure
        returns (string memory resultA, string memory resultB)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Grab the free memory pointer.
            resultA := mload(0x40)
            resultB := add(resultA, 0x40)
            // Allocate 2 words for each string (1 for the length, 1 for the byte). Total 4 words.
            mstore(0x40, add(resultB, 0x40))
            // Zeroize the length slots.
            mstore(resultA, 0)
            mstore(resultB, 0)
            // Store the lengths and bytes.
            mstore(add(resultA, 0x1f), packed)
            mstore(add(resultB, 0x1f), mload(add(add(resultA, 0x20), mload(resultA))))
            // Right pad with zeroes.
            mstore(add(add(resultA, 0x20), mload(resultA)), 0)
            mstore(add(add(resultB, 0x20), mload(resultB)), 0)
        }
    }
    /// @dev Directly returns `a` without copying.
    function directReturn(string memory a) internal pure {
        assembly {
            // Assumes that the string does not start from the scratch space.
            let retStart := sub(a, 0x20)
            let retSize := add(mload(a), 0x40)
            // Right pad with zeroes. Just in case the string is produced
            // by a method that doesn't zero right pad.
            mstore(add(retStart, retSize), 0)
            // Store the return offset.
            mstore(retStart, 0x20)
            // End the transaction, returning the string.
            return(retStart, retSize)
        }
    }
}