// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (access/Ownable.sol)
pragma solidity ^0.8.0;
import "../utils/Context.sol";
/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract Ownable is Context {
    address private _owner;
    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);
    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor() {
        _transferOwnership(_msgSender());
    }
    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }
    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }
    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }
    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }
    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }
    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (interfaces/draft-IERC1822.sol)
pragma solidity ^0.8.0;
/**
 * @dev ERC1822: Universal Upgradeable Proxy Standard (UUPS) documents a method for upgradeability through a simplified
 * proxy whose upgrades are fully controlled by the current implementation.
 */
interface IERC1822Proxiable {
    /**
     * @dev Returns the storage slot that the proxiable contract assumes is being used to store the implementation
     * address.
     *
     * IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
     * bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
     * function revert if invoked through a proxy.
     */
    function proxiableUUID() external view returns (bytes32);
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.3) (interfaces/IERC1967.sol)
pragma solidity ^0.8.0;
/**
 * @dev ERC-1967: Proxy Storage Slots. This interface contains the events defined in the ERC.
 *
 * _Available since v4.9._
 */
interface IERC1967 {
    /**
     * @dev Emitted when the implementation is upgraded.
     */
    event Upgraded(address indexed implementation);
    /**
     * @dev Emitted when the admin account has changed.
     */
    event AdminChanged(address previousAdmin, address newAdmin);
    /**
     * @dev Emitted when the beacon is changed.
     */
    event BeaconUpgraded(address indexed beacon);
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (proxy/beacon/BeaconProxy.sol)
pragma solidity ^0.8.0;
import "./IBeacon.sol";
import "../Proxy.sol";
import "../ERC1967/ERC1967Upgrade.sol";
/**
 * @dev This contract implements a proxy that gets the implementation address for each call from an {UpgradeableBeacon}.
 *
 * The beacon address is stored in storage slot `uint256(keccak256('eip1967.proxy.beacon')) - 1`, so that it doesn't
 * conflict with the storage layout of the implementation behind the proxy.
 *
 * _Available since v3.4._
 */
contract BeaconProxy is Proxy, ERC1967Upgrade {
    /**
     * @dev Initializes the proxy with `beacon`.
     *
     * If `data` is nonempty, it's used as data in a delegate call to the implementation returned by the beacon. This
     * will typically be an encoded function call, and allows initializing the storage of the proxy like a Solidity
     * constructor.
     *
     * Requirements:
     *
     * - `beacon` must be a contract with the interface {IBeacon}.
     */
    constructor(address beacon, bytes memory data) payable {
        _upgradeBeaconToAndCall(beacon, data, false);
    }
    /**
     * @dev Returns the current beacon address.
     */
    function _beacon() internal view virtual returns (address) {
        return _getBeacon();
    }
    /**
     * @dev Returns the current implementation address of the associated beacon.
     */
    function _implementation() internal view virtual override returns (address) {
        return IBeacon(_getBeacon()).implementation();
    }
    /**
     * @dev Changes the proxy to use a new beacon. Deprecated: see {_upgradeBeaconToAndCall}.
     *
     * If `data` is nonempty, it's used as data in a delegate call to the implementation returned by the beacon.
     *
     * Requirements:
     *
     * - `beacon` must be a contract.
     * - The implementation returned by `beacon` must be a contract.
     */
    function _setBeacon(address beacon, bytes memory data) internal virtual {
        _upgradeBeaconToAndCall(beacon, data, false);
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (proxy/beacon/IBeacon.sol)
pragma solidity ^0.8.0;
/**
 * @dev This is the interface that {BeaconProxy} expects of its beacon.
 */
interface IBeacon {
    /**
     * @dev Must return an address that can be used as a delegate call target.
     *
     * {BeaconProxy} will check that this address is a contract.
     */
    function implementation() external view returns (address);
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (proxy/beacon/UpgradeableBeacon.sol)
pragma solidity ^0.8.0;
import "./IBeacon.sol";
import "../../access/Ownable.sol";
import "../../utils/Address.sol";
/**
 * @dev This contract is used in conjunction with one or more instances of {BeaconProxy} to determine their
 * implementation contract, which is where they will delegate all function calls.
 *
 * An owner is able to change the implementation the beacon points to, thus upgrading the proxies that use this beacon.
 */
contract UpgradeableBeacon is IBeacon, Ownable {
    address private _implementation;
    /**
     * @dev Emitted when the implementation returned by the beacon is changed.
     */
    event Upgraded(address indexed implementation);
    /**
     * @dev Sets the address of the initial implementation, and the deployer account as the owner who can upgrade the
     * beacon.
     */
    constructor(address implementation_) {
        _setImplementation(implementation_);
    }
    /**
     * @dev Returns the current implementation address.
     */
    function implementation() public view virtual override returns (address) {
        return _implementation;
    }
    /**
     * @dev Upgrades the beacon to a new implementation.
     *
     * Emits an {Upgraded} event.
     *
     * Requirements:
     *
     * - msg.sender must be the owner of the contract.
     * - `newImplementation` must be a contract.
     */
    function upgradeTo(address newImplementation) public virtual onlyOwner {
        _setImplementation(newImplementation);
        emit Upgraded(newImplementation);
    }
    /**
     * @dev Sets the implementation contract address for this beacon
     *
     * Requirements:
     *
     * - `newImplementation` must be a contract.
     */
    function _setImplementation(address newImplementation) private {
        require(Address.isContract(newImplementation), "UpgradeableBeacon: implementation is not a contract");
        _implementation = newImplementation;
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (proxy/ERC1967/ERC1967Proxy.sol)
pragma solidity ^0.8.0;
import "../Proxy.sol";
import "./ERC1967Upgrade.sol";
/**
 * @dev This contract implements an upgradeable proxy. It is upgradeable because calls are delegated to an
 * implementation address that can be changed. This address is stored in storage in the location specified by
 * https://eips.ethereum.org/EIPS/eip-1967[EIP1967], so that it doesn't conflict with the storage layout of the
 * implementation behind the proxy.
 */
contract ERC1967Proxy is Proxy, ERC1967Upgrade {
    /**
     * @dev Initializes the upgradeable proxy with an initial implementation specified by `_logic`.
     *
     * If `_data` is nonempty, it's used as data in a delegate call to `_logic`. This will typically be an encoded
     * function call, and allows initializing the storage of the proxy like a Solidity constructor.
     */
    constructor(address _logic, bytes memory _data) payable {
        _upgradeToAndCall(_logic, _data, false);
    }
    /**
     * @dev Returns the current implementation address.
     */
    function _implementation() internal view virtual override returns (address impl) {
        return ERC1967Upgrade._getImplementation();
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.3) (proxy/ERC1967/ERC1967Upgrade.sol)
pragma solidity ^0.8.2;
import "../beacon/IBeacon.sol";
import "../../interfaces/IERC1967.sol";
import "../../interfaces/draft-IERC1822.sol";
import "../../utils/Address.sol";
import "../../utils/StorageSlot.sol";
/**
 * @dev This abstract contract provides getters and event emitting update functions for
 * https://eips.ethereum.org/EIPS/eip-1967[EIP1967] slots.
 *
 * _Available since v4.1._
 *
 * @custom:oz-upgrades-unsafe-allow delegatecall
 */
abstract contract ERC1967Upgrade is IERC1967 {
    // This is the keccak-256 hash of "eip1967.proxy.rollback" subtracted by 1
    bytes32 private constant _ROLLBACK_SLOT = 0x4910fdfa16fed3260ed0e7147f7cc6da11a60208b5b9406d12a635614ffd9143;
    /**
     * @dev Storage slot with the address of the current implementation.
     * This is the keccak-256 hash of "eip1967.proxy.implementation" subtracted by 1, and is
     * validated in the constructor.
     */
    bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
    /**
     * @dev Returns the current implementation address.
     */
    function _getImplementation() internal view returns (address) {
        return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
    }
    /**
     * @dev Stores a new address in the EIP1967 implementation slot.
     */
    function _setImplementation(address newImplementation) private {
        require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
        StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
    }
    /**
     * @dev Perform implementation upgrade
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeTo(address newImplementation) internal {
        _setImplementation(newImplementation);
        emit Upgraded(newImplementation);
    }
    /**
     * @dev Perform implementation upgrade with additional setup call.
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeToAndCall(
        address newImplementation,
        bytes memory data,
        bool forceCall
    ) internal {
        _upgradeTo(newImplementation);
        if (data.length > 0 || forceCall) {
            Address.functionDelegateCall(newImplementation, data);
        }
    }
    /**
     * @dev Perform implementation upgrade with security checks for UUPS proxies, and additional setup call.
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeToAndCallUUPS(
        address newImplementation,
        bytes memory data,
        bool forceCall
    ) internal {
        // Upgrades from old implementations will perform a rollback test. This test requires the new
        // implementation to upgrade back to the old, non-ERC1822 compliant, implementation. Removing
        // this special case will break upgrade paths from old UUPS implementation to new ones.
        if (StorageSlot.getBooleanSlot(_ROLLBACK_SLOT).value) {
            _setImplementation(newImplementation);
        } else {
            try IERC1822Proxiable(newImplementation).proxiableUUID() returns (bytes32 slot) {
                require(slot == _IMPLEMENTATION_SLOT, "ERC1967Upgrade: unsupported proxiableUUID");
            } catch {
                revert("ERC1967Upgrade: new implementation is not UUPS");
            }
            _upgradeToAndCall(newImplementation, data, forceCall);
        }
    }
    /**
     * @dev Storage slot with the admin of the contract.
     * This is the keccak-256 hash of "eip1967.proxy.admin" subtracted by 1, and is
     * validated in the constructor.
     */
    bytes32 internal constant _ADMIN_SLOT = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;
    /**
     * @dev Returns the current admin.
     */
    function _getAdmin() internal view returns (address) {
        return StorageSlot.getAddressSlot(_ADMIN_SLOT).value;
    }
    /**
     * @dev Stores a new address in the EIP1967 admin slot.
     */
    function _setAdmin(address newAdmin) private {
        require(newAdmin != address(0), "ERC1967: new admin is the zero address");
        StorageSlot.getAddressSlot(_ADMIN_SLOT).value = newAdmin;
    }
    /**
     * @dev Changes the admin of the proxy.
     *
     * Emits an {AdminChanged} event.
     */
    function _changeAdmin(address newAdmin) internal {
        emit AdminChanged(_getAdmin(), newAdmin);
        _setAdmin(newAdmin);
    }
    /**
     * @dev The storage slot of the UpgradeableBeacon contract which defines the implementation for this proxy.
     * This is bytes32(uint256(keccak256('eip1967.proxy.beacon')) - 1)) and is validated in the constructor.
     */
    bytes32 internal constant _BEACON_SLOT = 0xa3f0ad74e5423aebfd80d3ef4346578335a9a72aeaee59ff6cb3582b35133d50;
    /**
     * @dev Returns the current beacon.
     */
    function _getBeacon() internal view returns (address) {
        return StorageSlot.getAddressSlot(_BEACON_SLOT).value;
    }
    /**
     * @dev Stores a new beacon in the EIP1967 beacon slot.
     */
    function _setBeacon(address newBeacon) private {
        require(Address.isContract(newBeacon), "ERC1967: new beacon is not a contract");
        require(
            Address.isContract(IBeacon(newBeacon).implementation()),
            "ERC1967: beacon implementation is not a contract"
        );
        StorageSlot.getAddressSlot(_BEACON_SLOT).value = newBeacon;
    }
    /**
     * @dev Perform beacon upgrade with additional setup call. Note: This upgrades the address of the beacon, it does
     * not upgrade the implementation contained in the beacon (see {UpgradeableBeacon-_setImplementation} for that).
     *
     * Emits a {BeaconUpgraded} event.
     */
    function _upgradeBeaconToAndCall(
        address newBeacon,
        bytes memory data,
        bool forceCall
    ) internal {
        _setBeacon(newBeacon);
        emit BeaconUpgraded(newBeacon);
        if (data.length > 0 || forceCall) {
            Address.functionDelegateCall(IBeacon(newBeacon).implementation(), data);
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (proxy/Proxy.sol)
pragma solidity ^0.8.0;
/**
 * @dev This abstract contract provides a fallback function that delegates all calls to another contract using the EVM
 * instruction `delegatecall`. We refer to the second contract as the _implementation_ behind the proxy, and it has to
 * be specified by overriding the virtual {_implementation} function.
 *
 * Additionally, delegation to the implementation can be triggered manually through the {_fallback} function, or to a
 * different contract through the {_delegate} function.
 *
 * The success and return data of the delegated call will be returned back to the caller of the proxy.
 */
abstract contract Proxy {
    /**
     * @dev Delegates the current call to `implementation`.
     *
     * This function does not return to its internal call site, it will return directly to the external caller.
     */
    function _delegate(address implementation) internal virtual {
        assembly {
            // Copy msg.data. We take full control of memory in this inline assembly
            // block because it will not return to Solidity code. We overwrite the
            // Solidity scratch pad at memory position 0.
            calldatacopy(0, 0, calldatasize())
            // Call the implementation.
            // out and outsize are 0 because we don't know the size yet.
            let result := delegatecall(gas(), implementation, 0, calldatasize(), 0, 0)
            // Copy the returned data.
            returndatacopy(0, 0, returndatasize())
            switch result
            // delegatecall returns 0 on error.
            case 0 {
                revert(0, returndatasize())
            }
            default {
                return(0, returndatasize())
            }
        }
    }
    /**
     * @dev This is a virtual function that should be overridden so it returns the address to which the fallback function
     * and {_fallback} should delegate.
     */
    function _implementation() internal view virtual returns (address);
    /**
     * @dev Delegates the current call to the address returned by `_implementation()`.
     *
     * This function does not return to its internal call site, it will return directly to the external caller.
     */
    function _fallback() internal virtual {
        _beforeFallback();
        _delegate(_implementation());
    }
    /**
     * @dev Fallback function that delegates calls to the address returned by `_implementation()`. Will run if no other
     * function in the contract matches the call data.
     */
    fallback() external payable virtual {
        _fallback();
    }
    /**
     * @dev Fallback function that delegates calls to the address returned by `_implementation()`. Will run if call data
     * is empty.
     */
    receive() external payable virtual {
        _fallback();
    }
    /**
     * @dev Hook that is called before falling back to the implementation. Can happen as part of a manual `_fallback`
     * call, or as part of the Solidity `fallback` or `receive` functions.
     *
     * If overridden should call `super._beforeFallback()`.
     */
    function _beforeFallback() internal virtual {}
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.3) (proxy/transparent/ProxyAdmin.sol)
pragma solidity ^0.8.0;
import "./TransparentUpgradeableProxy.sol";
import "../../access/Ownable.sol";
/**
 * @dev This is an auxiliary contract meant to be assigned as the admin of a {TransparentUpgradeableProxy}. For an
 * explanation of why you would want to use this see the documentation for {TransparentUpgradeableProxy}.
 */
contract ProxyAdmin is Ownable {
    /**
     * @dev Returns the current implementation of `proxy`.
     *
     * Requirements:
     *
     * - This contract must be the admin of `proxy`.
     */
    function getProxyImplementation(ITransparentUpgradeableProxy proxy) public view virtual returns (address) {
        // We need to manually run the static call since the getter cannot be flagged as view
        // bytes4(keccak256("implementation()")) == 0x5c60da1b
        (bool success, bytes memory returndata) = address(proxy).staticcall(hex"5c60da1b");
        require(success);
        return abi.decode(returndata, (address));
    }
    /**
     * @dev Returns the current admin of `proxy`.
     *
     * Requirements:
     *
     * - This contract must be the admin of `proxy`.
     */
    function getProxyAdmin(ITransparentUpgradeableProxy proxy) public view virtual returns (address) {
        // We need to manually run the static call since the getter cannot be flagged as view
        // bytes4(keccak256("admin()")) == 0xf851a440
        (bool success, bytes memory returndata) = address(proxy).staticcall(hex"f851a440");
        require(success);
        return abi.decode(returndata, (address));
    }
    /**
     * @dev Changes the admin of `proxy` to `newAdmin`.
     *
     * Requirements:
     *
     * - This contract must be the current admin of `proxy`.
     */
    function changeProxyAdmin(ITransparentUpgradeableProxy proxy, address newAdmin) public virtual onlyOwner {
        proxy.changeAdmin(newAdmin);
    }
    /**
     * @dev Upgrades `proxy` to `implementation`. See {TransparentUpgradeableProxy-upgradeTo}.
     *
     * Requirements:
     *
     * - This contract must be the admin of `proxy`.
     */
    function upgrade(ITransparentUpgradeableProxy proxy, address implementation) public virtual onlyOwner {
        proxy.upgradeTo(implementation);
    }
    /**
     * @dev Upgrades `proxy` to `implementation` and calls a function on the new implementation. See
     * {TransparentUpgradeableProxy-upgradeToAndCall}.
     *
     * Requirements:
     *
     * - This contract must be the admin of `proxy`.
     */
    function upgradeAndCall(
        ITransparentUpgradeableProxy proxy,
        address implementation,
        bytes memory data
    ) public payable virtual onlyOwner {
        proxy.upgradeToAndCall{value: msg.value}(implementation, data);
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.3) (proxy/transparent/TransparentUpgradeableProxy.sol)
pragma solidity ^0.8.0;
import "../ERC1967/ERC1967Proxy.sol";
/**
 * @dev Interface for {TransparentUpgradeableProxy}. In order to implement transparency, {TransparentUpgradeableProxy}
 * does not implement this interface directly, and some of its functions are implemented by an internal dispatch
 * mechanism. The compiler is unaware that these functions are implemented by {TransparentUpgradeableProxy} and will not
 * include them in the ABI so this interface must be used to interact with it.
 */
interface ITransparentUpgradeableProxy is IERC1967 {
    function admin() external view returns (address);
    function implementation() external view returns (address);
    function changeAdmin(address) external;
    function upgradeTo(address) external;
    function upgradeToAndCall(address, bytes memory) external payable;
}
/**
 * @dev This contract implements a proxy that is upgradeable by an admin.
 *
 * To avoid https://medium.com/nomic-labs-blog/malicious-backdoors-in-ethereum-proxies-62629adf3357[proxy selector
 * clashing], which can potentially be used in an attack, this contract uses the
 * https://blog.openzeppelin.com/the-transparent-proxy-pattern/[transparent proxy pattern]. This pattern implies two
 * things that go hand in hand:
 *
 * 1. If any account other than the admin calls the proxy, the call will be forwarded to the implementation, even if
 * that call matches one of the admin functions exposed by the proxy itself.
 * 2. If the admin calls the proxy, it can access the admin functions, but its calls will never be forwarded to the
 * implementation. If the admin tries to call a function on the implementation it will fail with an error that says
 * "admin cannot fallback to proxy target".
 *
 * These properties mean that the admin account can only be used for admin actions like upgrading the proxy or changing
 * the admin, so it's best if it's a dedicated account that is not used for anything else. This will avoid headaches due
 * to sudden errors when trying to call a function from the proxy implementation.
 *
 * Our recommendation is for the dedicated account to be an instance of the {ProxyAdmin} contract. If set up this way,
 * you should think of the `ProxyAdmin` instance as the real administrative interface of your proxy.
 *
 * NOTE: The real interface of this proxy is that defined in `ITransparentUpgradeableProxy`. This contract does not
 * inherit from that interface, and instead the admin functions are implicitly implemented using a custom dispatch
 * mechanism in `_fallback`. Consequently, the compiler will not produce an ABI for this contract. This is necessary to
 * fully implement transparency without decoding reverts caused by selector clashes between the proxy and the
 * implementation.
 *
 * WARNING: It is not recommended to extend this contract to add additional external functions. If you do so, the compiler
 * will not check that there are no selector conflicts, due to the note above. A selector clash between any new function
 * and the functions declared in {ITransparentUpgradeableProxy} will be resolved in favor of the new one. This could
 * render the admin operations inaccessible, which could prevent upgradeability. Transparency may also be compromised.
 */
contract TransparentUpgradeableProxy is ERC1967Proxy {
    /**
     * @dev Initializes an upgradeable proxy managed by `_admin`, backed by the implementation at `_logic`, and
     * optionally initialized with `_data` as explained in {ERC1967Proxy-constructor}.
     */
    constructor(
        address _logic,
        address admin_,
        bytes memory _data
    ) payable ERC1967Proxy(_logic, _data) {
        _changeAdmin(admin_);
    }
    /**
     * @dev Modifier used internally that will delegate the call to the implementation unless the sender is the admin.
     *
     * CAUTION: This modifier is deprecated, as it could cause issues if the modified function has arguments, and the
     * implementation provides a function with the same selector.
     */
    modifier ifAdmin() {
        if (msg.sender == _getAdmin()) {
            _;
        } else {
            _fallback();
        }
    }
    /**
     * @dev If caller is the admin process the call internally, otherwise transparently fallback to the proxy behavior
     */
    function _fallback() internal virtual override {
        if (msg.sender == _getAdmin()) {
            bytes memory ret;
            bytes4 selector = msg.sig;
            if (selector == ITransparentUpgradeableProxy.upgradeTo.selector) {
                ret = _dispatchUpgradeTo();
            } else if (selector == ITransparentUpgradeableProxy.upgradeToAndCall.selector) {
                ret = _dispatchUpgradeToAndCall();
            } else if (selector == ITransparentUpgradeableProxy.changeAdmin.selector) {
                ret = _dispatchChangeAdmin();
            } else if (selector == ITransparentUpgradeableProxy.admin.selector) {
                ret = _dispatchAdmin();
            } else if (selector == ITransparentUpgradeableProxy.implementation.selector) {
                ret = _dispatchImplementation();
            } else {
                revert("TransparentUpgradeableProxy: admin cannot fallback to proxy target");
            }
            assembly {
                return(add(ret, 0x20), mload(ret))
            }
        } else {
            super._fallback();
        }
    }
    /**
     * @dev Returns the current admin.
     *
     * TIP: To get this value clients can read directly from the storage slot shown below (specified by EIP1967) using the
     * https://eth.wiki/json-rpc/API#eth_getstorageat[`eth_getStorageAt`] RPC call.
     * `0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103`
     */
    function _dispatchAdmin() private returns (bytes memory) {
        _requireZeroValue();
        address admin = _getAdmin();
        return abi.encode(admin);
    }
    /**
     * @dev Returns the current implementation.
     *
     * TIP: To get this value clients can read directly from the storage slot shown below (specified by EIP1967) using the
     * https://eth.wiki/json-rpc/API#eth_getstorageat[`eth_getStorageAt`] RPC call.
     * `0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc`
     */
    function _dispatchImplementation() private returns (bytes memory) {
        _requireZeroValue();
        address implementation = _implementation();
        return abi.encode(implementation);
    }
    /**
     * @dev Changes the admin of the proxy.
     *
     * Emits an {AdminChanged} event.
     */
    function _dispatchChangeAdmin() private returns (bytes memory) {
        _requireZeroValue();
        address newAdmin = abi.decode(msg.data[4:], (address));
        _changeAdmin(newAdmin);
        return "";
    }
    /**
     * @dev Upgrade the implementation of the proxy.
     */
    function _dispatchUpgradeTo() private returns (bytes memory) {
        _requireZeroValue();
        address newImplementation = abi.decode(msg.data[4:], (address));
        _upgradeToAndCall(newImplementation, bytes(""), false);
        return "";
    }
    /**
     * @dev Upgrade the implementation of the proxy, and then call a function from the new implementation as specified
     * by `data`, which should be an encoded function call. This is useful to initialize new storage variables in the
     * proxied contract.
     */
    function _dispatchUpgradeToAndCall() private returns (bytes memory) {
        (address newImplementation, bytes memory data) = abi.decode(msg.data[4:], (address, bytes));
        _upgradeToAndCall(newImplementation, data, true);
        return "";
    }
    /**
     * @dev Returns the current admin.
     */
    function _admin() internal view virtual returns (address) {
        return _getAdmin();
    }
    /**
     * @dev To keep this contract fully transparent, all `ifAdmin` functions must be payable. This helper is here to
     * emulate some proxy functions being non-payable while still allowing value to pass through.
     */
    function _requireZeroValue() private {
        require(msg.value == 0);
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/Address.sol)
pragma solidity ^0.8.1;
/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.
        return account.code.length > 0;
    }
    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");
        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }
    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }
    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }
    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }
    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }
    function _revert(bytes memory returndata, string memory errorMessage) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert(errorMessage);
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)
pragma solidity ^0.8.0;
/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }
    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/StorageSlot.sol)
pragma solidity ^0.8.0;
/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC1967 implementation slot:
 * ```
 * contract ERC1967 {
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * _Available since v4.1 for `address`, `bool`, `bytes32`, and `uint256`._
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }
    struct BooleanSlot {
        bool value;
    }
    struct Bytes32Slot {
        bytes32 value;
    }
    struct Uint256Slot {
        uint256 value;
    }
    /**
     * @dev Returns an `AddressSlot` with member `value` located at `slot`.
     */
    function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }
    /**
     * @dev Returns an `BooleanSlot` with member `value` located at `slot`.
     */
    function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }
    /**
     * @dev Returns an `Bytes32Slot` with member `value` located at `slot`.
     */
    function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }
    /**
     * @dev Returns an `Uint256Slot` with member `value` located at `slot`.
     */
    function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (access/AccessControl.sol)
pragma solidity ^0.8.0;
import "./IAccessControlUpgradeable.sol";
import "../utils/ContextUpgradeable.sol";
import "../utils/StringsUpgradeable.sol";
import "../utils/introspection/ERC165Upgradeable.sol";
import "../proxy/utils/Initializable.sol";
/**
 * @dev Contract module that allows children to implement role-based access
 * control mechanisms. This is a lightweight version that doesn't allow enumerating role
 * members except through off-chain means by accessing the contract event logs. Some
 * applications may benefit from on-chain enumerability, for those cases see
 * {AccessControlEnumerable}.
 *
 * Roles are referred to by their `bytes32` identifier. These should be exposed
 * in the external API and be unique. The best way to achieve this is by
 * using `public constant` hash digests:
 *
 * ```solidity
 * bytes32 public constant MY_ROLE = keccak256("MY_ROLE");
 * ```
 *
 * Roles can be used to represent a set of permissions. To restrict access to a
 * function call, use {hasRole}:
 *
 * ```solidity
 * function foo() public {
 *     require(hasRole(MY_ROLE, msg.sender));
 *     ...
 * }
 * ```
 *
 * Roles can be granted and revoked dynamically via the {grantRole} and
 * {revokeRole} functions. Each role has an associated admin role, and only
 * accounts that have a role's admin role can call {grantRole} and {revokeRole}.
 *
 * By default, the admin role for all roles is `DEFAULT_ADMIN_ROLE`, which means
 * that only accounts with this role will be able to grant or revoke other
 * roles. More complex role relationships can be created by using
 * {_setRoleAdmin}.
 *
 * WARNING: The `DEFAULT_ADMIN_ROLE` is also its own admin: it has permission to
 * grant and revoke this role. Extra precautions should be taken to secure
 * accounts that have been granted it. We recommend using {AccessControlDefaultAdminRules}
 * to enforce additional security measures for this role.
 */
abstract contract AccessControlUpgradeable is Initializable, ContextUpgradeable, IAccessControlUpgradeable, ERC165Upgradeable {
    function __AccessControl_init() internal onlyInitializing {
    }
    function __AccessControl_init_unchained() internal onlyInitializing {
    }
    struct RoleData {
        mapping(address => bool) members;
        bytes32 adminRole;
    }
    mapping(bytes32 => RoleData) private _roles;
    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;
    /**
     * @dev Modifier that checks that an account has a specific role. Reverts
     * with a standardized message including the required role.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     *
     * _Available since v4.1._
     */
    modifier onlyRole(bytes32 role) {
        _checkRole(role);
        _;
    }
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IAccessControlUpgradeable).interfaceId || super.supportsInterface(interfaceId);
    }
    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) public view virtual override returns (bool) {
        return _roles[role].members[account];
    }
    /**
     * @dev Revert with a standard message if `_msgSender()` is missing `role`.
     * Overriding this function changes the behavior of the {onlyRole} modifier.
     *
     * Format of the revert message is described in {_checkRole}.
     *
     * _Available since v4.6._
     */
    function _checkRole(bytes32 role) internal view virtual {
        _checkRole(role, _msgSender());
    }
    /**
     * @dev Revert with a standard message if `account` is missing `role`.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     */
    function _checkRole(bytes32 role, address account) internal view virtual {
        if (!hasRole(role, account)) {
            revert(
                string(
                    abi.encodePacked(
                        "AccessControl: account ",
                        StringsUpgradeable.toHexString(account),
                        " is missing role ",
                        StringsUpgradeable.toHexString(uint256(role), 32)
                    )
                )
            );
        }
    }
    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) public view virtual override returns (bytes32) {
        return _roles[role].adminRole;
    }
    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     *
     * May emit a {RoleGranted} event.
     */
    function grantRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _grantRole(role, account);
    }
    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     *
     * May emit a {RoleRevoked} event.
     */
    function revokeRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _revokeRole(role, account);
    }
    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been revoked `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     *
     * May emit a {RoleRevoked} event.
     */
    function renounceRole(bytes32 role, address account) public virtual override {
        require(account == _msgSender(), "AccessControl: can only renounce roles for self");
        _revokeRole(role, account);
    }
    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event. Note that unlike {grantRole}, this function doesn't perform any
     * checks on the calling account.
     *
     * May emit a {RoleGranted} event.
     *
     * [WARNING]
     * ====
     * This function should only be called from the constructor when setting
     * up the initial roles for the system.
     *
     * Using this function in any other way is effectively circumventing the admin
     * system imposed by {AccessControl}.
     * ====
     *
     * NOTE: This function is deprecated in favor of {_grantRole}.
     */
    function _setupRole(bytes32 role, address account) internal virtual {
        _grantRole(role, account);
    }
    /**
     * @dev Sets `adminRole` as ``role``'s admin role.
     *
     * Emits a {RoleAdminChanged} event.
     */
    function _setRoleAdmin(bytes32 role, bytes32 adminRole) internal virtual {
        bytes32 previousAdminRole = getRoleAdmin(role);
        _roles[role].adminRole = adminRole;
        emit RoleAdminChanged(role, previousAdminRole, adminRole);
    }
    /**
     * @dev Grants `role` to `account`.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleGranted} event.
     */
    function _grantRole(bytes32 role, address account) internal virtual {
        if (!hasRole(role, account)) {
            _roles[role].members[account] = true;
            emit RoleGranted(role, account, _msgSender());
        }
    }
    /**
     * @dev Revokes `role` from `account`.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleRevoked} event.
     */
    function _revokeRole(bytes32 role, address account) internal virtual {
        if (hasRole(role, account)) {
            _roles[role].members[account] = false;
            emit RoleRevoked(role, account, _msgSender());
        }
    }
    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[49] private __gap;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (access/IAccessControl.sol)
pragma solidity ^0.8.0;
/**
 * @dev External interface of AccessControl declared to support ERC165 detection.
 */
interface IAccessControlUpgradeable {
    /**
     * @dev Emitted when `newAdminRole` is set as ``role``'s admin role, replacing `previousAdminRole`
     *
     * `DEFAULT_ADMIN_ROLE` is the starting admin for all roles, despite
     * {RoleAdminChanged} not being emitted signaling this.
     *
     * _Available since v3.1._
     */
    event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);
    /**
     * @dev Emitted when `account` is granted `role`.
     *
     * `sender` is the account that originated the contract call, an admin role
     * bearer except when using {AccessControl-_setupRole}.
     */
    event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);
    /**
     * @dev Emitted when `account` is revoked `role`.
     *
     * `sender` is the account that originated the contract call:
     *   - if using `revokeRole`, it is the admin role bearer
     *   - if using `renounceRole`, it is the role bearer (i.e. `account`)
     */
    event RoleRevoked(bytes32 indexed role, address indexed account, address indexed sender);
    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) external view returns (bool);
    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {AccessControl-_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) external view returns (bytes32);
    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) external;
    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) external;
    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been granted `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     */
    function renounceRole(bytes32 role, address account) external;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (proxy/utils/Initializable.sol)
pragma solidity ^0.8.2;
import "../../utils/AddressUpgradeable.sol";
/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```solidity
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 *
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;
    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;
    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);
    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts.
     *
     * Similar to `reinitializer(1)`, except that functions marked with `initializer` can be nested in the context of a
     * constructor.
     *
     * Emits an {Initialized} event.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!AddressUpgradeable.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }
    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * A reinitializer may be used after the original initialization step. This is essential to configure modules that
     * are added through upgrades and that require initialization.
     *
     * When `version` is 1, this modifier is similar to `initializer`, except that functions marked with `reinitializer`
     * cannot be nested. If one is invoked in the context of another, execution will revert.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     *
     * WARNING: setting the version to 255 will prevent any future reinitialization.
     *
     * Emits an {Initialized} event.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }
    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }
    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     *
     * Emits an {Initialized} event the first time it is successfully executed.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized != type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }
    /**
     * @dev Returns the highest version that has been initialized. See {reinitializer}.
     */
    function _getInitializedVersion() internal view returns (uint8) {
        return _initialized;
    }
    /**
     * @dev Returns `true` if the contract is currently initializing. See {onlyInitializing}.
     */
    function _isInitializing() internal view returns (bool) {
        return _initializing;
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (security/ReentrancyGuard.sol)
pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";
/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuardUpgradeable is Initializable {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.
    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;
    uint256 private _status;
    function __ReentrancyGuard_init() internal onlyInitializing {
        __ReentrancyGuard_init_unchained();
    }
    function __ReentrancyGuard_init_unchained() internal onlyInitializing {
        _status = _NOT_ENTERED;
    }
    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and making it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        _nonReentrantBefore();
        _;
        _nonReentrantAfter();
    }
    function _nonReentrantBefore() private {
        // On the first call to nonReentrant, _status will be _NOT_ENTERED
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");
        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;
    }
    function _nonReentrantAfter() private {
        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_ENTERED;
    }
    /**
     * @dev Returns true if the reentrancy guard is currently set to "entered", which indicates there is a
     * `nonReentrant` function in the call stack.
     */
    function _reentrancyGuardEntered() internal view returns (bool) {
        return _status == _ENTERED;
    }
    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[49] private __gap;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/Address.sol)
pragma solidity ^0.8.1;
/**
 * @dev Collection of functions related to the address type
 */
library AddressUpgradeable {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     *
     * Furthermore, `isContract` will also return true if the target contract within
     * the same transaction is already scheduled for destruction by `SELFDESTRUCT`,
     * which only has an effect at the end of a transaction.
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.
        return account.code.length > 0;
    }
    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.8.0/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");
        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }
    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }
    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }
    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }
    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }
    function _revert(bytes memory returndata, string memory errorMessage) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert(errorMessage);
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)
pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";
/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract ContextUpgradeable is Initializable {
    function __Context_init() internal onlyInitializing {
    }
    function __Context_init_unchained() internal onlyInitializing {
    }
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }
    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165.sol)
pragma solidity ^0.8.0;
import "./IERC165Upgradeable.sol";
import "../../proxy/utils/Initializable.sol";
/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 *
 * Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
 */
abstract contract ERC165Upgradeable is Initializable, IERC165Upgradeable {
    function __ERC165_init() internal onlyInitializing {
    }
    function __ERC165_init_unchained() internal onlyInitializing {
    }
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165Upgradeable).interfaceId;
    }
    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)
pragma solidity ^0.8.0;
/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165Upgradeable {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)
pragma solidity ^0.8.0;
/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library MathUpgradeable {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }
    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }
    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }
    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }
    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }
    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }
            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return prod0 / denominator;
            }
            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1, "Math: mulDiv overflow");
            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////
            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)
                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }
            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.
            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)
                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)
                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }
            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;
            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;
            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256
            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }
    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }
    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }
        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);
        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }
    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }
    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }
    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }
    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10 ** 64) {
                value /= 10 ** 64;
                result += 64;
            }
            if (value >= 10 ** 32) {
                value /= 10 ** 32;
                result += 32;
            }
            if (value >= 10 ** 16) {
                value /= 10 ** 16;
                result += 16;
            }
            if (value >= 10 ** 8) {
                value /= 10 ** 8;
                result += 8;
            }
            if (value >= 10 ** 4) {
                value /= 10 ** 4;
                result += 4;
            }
            if (value >= 10 ** 2) {
                value /= 10 ** 2;
                result += 2;
            }
            if (value >= 10 ** 1) {
                result += 1;
            }
        }
        return result;
    }
    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
        }
    }
    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }
    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SignedMath.sol)
pragma solidity ^0.8.0;
/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMathUpgradeable {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a > b ? a : b;
    }
    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }
    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }
    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/Strings.sol)
pragma solidity ^0.8.0;
import "./math/MathUpgradeable.sol";
import "./math/SignedMathUpgradeable.sol";
/**
 * @dev String operations.
 */
library StringsUpgradeable {
    bytes16 private constant _SYMBOLS = "0123456789abcdef";
    uint8 private constant _ADDRESS_LENGTH = 20;
    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = MathUpgradeable.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }
    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toString(int256 value) internal pure returns (string memory) {
        return string(abi.encodePacked(value < 0 ? "-" : "", toString(SignedMathUpgradeable.abs(value))));
    }
    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, MathUpgradeable.log256(value) + 1);
        }
    }
    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }
    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
    }
    /**
     * @dev Returns true if the two strings are equal.
     */
    function equal(string memory a, string memory b) internal pure returns (bool) {
        return keccak256(bytes(a)) == keccak256(bytes(b));
    }
}
// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.19;
interface IGenericErrors {
  /**
   * @dev Thrown when a parameter is the zero address.
   */
  error ZeroAddressNotAllowed();
}
// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.19;
interface IL1MessageManager {
  /**
   * @dev Emitted when L2->L1 message hashes have been added to L1 storage.
   */
  event L2L1MessageHashAddedToInbox(bytes32 indexed messageHash);
  /**
   * @dev Emitted when L1->L2 messages have been anchored on L2 and updated on L1.
   */
  event L1L2MessagesReceivedOnL2(bytes32[] messageHashes);
  /**
   * @dev Thrown when the message has been already sent.
   */
  error MessageAlreadySent();
  /**
   * @dev Thrown when the message has already been claimed.
   */
  error MessageDoesNotExistOrHasAlreadyBeenClaimed();
  /**
   * @dev Thrown when the message has already been received.
   */
  error MessageAlreadyReceived(bytes32 messageHash);
  /**
   * @dev Thrown when the L1->L2 message has not been sent.
   */
  error L1L2MessageNotSent(bytes32 messageHash);
}
// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.19;
interface IMessageService {
  /**
   * @dev Emitted when a message is sent.
   * @dev We include the message hash to save hashing costs on the rollup.
   */
  event MessageSent(
    address indexed _from,
    address indexed _to,
    uint256 _fee,
    uint256 _value,
    uint256 _nonce,
    bytes _calldata,
    bytes32 indexed _messageHash
  );
  /**
   * @dev Emitted when a message is claimed.
   */
  event MessageClaimed(bytes32 indexed _messageHash);
  /**
   * @dev Thrown when fees are lower than the minimum fee.
   */
  error FeeTooLow();
  /**
   * @dev Thrown when fees are lower than value.
   */
  error ValueShouldBeGreaterThanFee();
  /**
   * @dev Thrown when the value sent is less than the fee.
   * @dev Value to forward on is msg.value - _fee.
   */
  error ValueSentTooLow();
  /**
   * @dev Thrown when the destination address reverts.
   */
  error MessageSendingFailed(address destination);
  /**
   * @dev Thrown when the destination address reverts.
   */
  error FeePaymentFailed(address recipient);
  /**
   * @notice Sends a message for transporting from the given chain.
   * @dev This function should be called with a msg.value = _value + _fee. The fee will be paid on the destination chain.
   * @param _to The destination address on the destination chain.
   * @param _fee The message service fee on the origin chain.
   * @param _calldata The calldata used by the destination message service to call the destination contract.
   */
  function sendMessage(address _to, uint256 _fee, bytes calldata _calldata) external payable;
  /**
   * @notice Deliver a message to the destination chain.
   * @notice Is called automatically by the Postman, dApp or end user.
   * @param _from The msg.sender calling the origin message service.
   * @param _to The destination address on the destination chain.
   * @param _value The value to be transferred to the destination address.
   * @param _fee The message service fee on the origin chain.
   * @param _feeRecipient Address that will receive the fees.
   * @param _calldata The calldata used by the destination message service to call/forward to the destination contract.
   * @param _nonce Unique message number.
   */
  function claimMessage(
    address _from,
    address _to,
    uint256 _fee,
    uint256 _value,
    address payable _feeRecipient,
    bytes calldata _calldata,
    uint256 _nonce
  ) external;
  /**
   * @notice Returns the original sender of the message on the origin layer.
   * @return The original sender of the message on the origin layer.
   */
  function sender() external view returns (address);
}
// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.19;
interface IPauseManager {
  /**
   * @dev Thrown when a specific pause type is paused.
   */
  error IsPaused(bytes32 pauseType);
  /**
   * @dev Thrown when a specific pause type is not paused and expected to be.
   */
  error IsNotPaused(bytes32 pauseType);
  /**
   * @dev Emitted when a pause type is paused.
   */
  event Paused(address messageSender, bytes32 pauseType);
  /**
   * @dev Emitted when a pause type is unpaused.
   */
  event UnPaused(address messageSender, bytes32 pauseType);
}
// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.19;
/**
 * @title Contract to manage cross-chain messaging on L1 and rollup proving
 * @author ConsenSys Software Inc.
 */
interface IPlonkVerifier {
  /**
   * @notice Interface for verifier contracts.
   * @param _proof The proof used to verify.
   * @param _public_inputs The computed public inputs for the proof verification.
   */
  function Verify(bytes memory _proof, uint256[] memory _public_inputs) external returns (bool);
}
// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.19;
interface IRateLimiter {
  /**
   * @dev Thrown when an amount breaches the limit in the period.
   */
  error RateLimitExceeded();
  /**
   * @dev Thrown when the period is initialised to zero.
   */
  error PeriodIsZero();
  /**
   * @dev Thrown when the limit is initialised to zero.
   */
  error LimitIsZero();
  /**
   * @dev Emitted when the amount in the period is reset to zero.
   */
  event AmountUsedInPeriodReset(address indexed resettingAddress);
  /**
   * @dev Emitted when the limit is changed.
   * @dev If the current used amount is higher than the new limit, the used amount is lowered to the limit.
   */
  event LimitAmountChanged(
    address indexed amountChangeBy,
    uint256 amount,
    bool amountUsedLoweredToLimit,
    bool usedAmountResetToZero
  );
  /**
   * @notice Resets the rate limit amount to the amount specified.
   * @param _amount New message hashes.
   */
  function resetRateLimitAmount(uint256 _amount) external;
  /**
   * @notice Resets the amount used in the period to zero.
   */
  function resetAmountUsedInPeriod() external;
}
// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.19;
interface IZkEvmV2 {
  struct BlockData {
    bytes32 blockRootHash;
    uint32 l2BlockTimestamp;
    bytes[] transactions;
    bytes32[] l2ToL1MsgHashes;
    bytes fromAddresses;
    uint16[] batchReceptionIndices;
  }
  /**
   * @dev Emitted when a L2 block has been finalized on L1
   */
  event BlockFinalized(uint256 indexed blockNumber, bytes32 indexed stateRootHash);
  /**
   * @dev Emitted when a L2 blocks have been finalized on L1
   */
  event BlocksVerificationDone(uint256 indexed lastBlockFinalized, bytes32 startingRootHash, bytes32 finalRootHash);
  /**
   * @dev Emitted when a verifier is set for a particular proof type
   */
  event VerifierAddressChanged(
    address indexed verifierAddress,
    uint256 indexed proofType,
    address indexed verifierSetBy
  );
  /**
   * @dev Thrown when l2 block timestamp is not correct
   */
  error BlockTimestampError();
  /**
   * @dev Thrown when the starting rootHash does not match the existing state
   */
  error StartingRootHashDoesNotMatch();
  /**
   * @dev Thrown when block contains zero transactions
   */
  error EmptyBlock();
  /**
   * @dev Thrown when zk proof is empty bytes
   */
  error ProofIsEmpty();
  /**
   * @dev Thrown when zk proof type is invalid
   */
  error InvalidProofType();
  /**
   * @dev Thrown when zk proof is invalid
   */
  error InvalidProof();
  /**
   * @notice Adds or updated the verifier contract address for a proof type
   * @dev DEFAULT_ADMIN_ROLE is required to execute
   * @param _newVerifierAddress The address for the verifier contract
   * @param _proofType The proof type being set/updated
   **/
  function setVerifierAddress(address _newVerifierAddress, uint256 _proofType) external;
  /**
   * @notice Finalizes blocks without using a proof
   * @dev DEFAULT_ADMIN_ROLE is required to execute
   * @param _calldata The full BlockData collection - block, transaction and log data
   **/
  function finalizeBlocksWithoutProof(BlockData[] calldata _calldata) external;
  /**
   * @notice Finalizes blocks without using a proof
   * @dev OPERATOR_ROLE is required to execute
   * @dev If the verifier based on proof type is not found, it defaults to the default verifier type
   * @param _calldata The full BlockData collection - block, transaction and log data
   * @param _proof The proof to verified with the proof type verifier contract
   * @param _proofType The proof type to determine which verifier contract to use
   * @param _parentStateRootHash The beginning roothash to start with
   **/
  function finalizeBlocks(
    BlockData[] calldata _calldata,
    bytes calldata _proof,
    uint256 _proofType,
    bytes32 _parentStateRootHash
  ) external;
}
// SPDX-License-Identifier: AGPL-3.0
pragma solidity ^0.8.19;
import { IL1MessageManager } from "../../interfaces/IL1MessageManager.sol";
/**
 * @title Contract to manage cross-chain message hashes storage and status on L1.
 * @author ConsenSys Software Inc.
 */
abstract contract L1MessageManager is IL1MessageManager {
  uint8 public constant INBOX_STATUS_UNKNOWN = 0;
  uint8 public constant INBOX_STATUS_RECEIVED = 1;
  uint8 public constant OUTBOX_STATUS_UNKNOWN = 0;
  uint8 public constant OUTBOX_STATUS_SENT = 1;
  uint8 public constant OUTBOX_STATUS_RECEIVED = 2;
  /// @dev There is a uint216 worth of storage layout here.
  /// @dev Mapping to store L1->L2 message hashes status.
  /// @dev messageHash => messageStatus (0: unknown, 1: sent, 2: received).
  mapping(bytes32 => uint256) public outboxL1L2MessageStatus;
  /// @dev Mapping to store L2->L1 message hashes status.
  /// @dev messageHash => messageStatus (0: unknown, 1: received).
  mapping(bytes32 => uint256) public inboxL2L1MessageStatus;
  /// @dev Keep free storage slots for future implementation updates to avoid storage collision.
  // *******************************************************************************************
  // NB: THIS GAP HAS BEEN PUSHED OUT IN FAVOUR OF THE GAP INSIDE THE REENTRANCY CODE
  //uint256[50] private __gap;
  // NB: DO NOT USE THIS GAP
  // *******************************************************************************************
  /**
   * @notice Add a cross-chain L2->L1 message hash in storage.
   * @dev Once the event is emitted, it should be ready for claiming (post block finalization).
   * @param  _messageHash Hash of the message.
   */
  function _addL2L1MessageHash(bytes32 _messageHash) internal {
    if (inboxL2L1MessageStatus[_messageHash] != INBOX_STATUS_UNKNOWN) {
      revert MessageAlreadyReceived(_messageHash);
    }
    inboxL2L1MessageStatus[_messageHash] = INBOX_STATUS_RECEIVED;
    emit L2L1MessageHashAddedToInbox(_messageHash);
  }
  /**
   * @notice Update the status of L2->L1 message when a user claims a message on L1.
   * @dev The L2->L1 message is removed from storage.
   * @dev Due to the nature of the rollup, we should not get a second entry of this.
   * @param  _messageHash Hash of the message.
   */
  function _updateL2L1MessageStatusToClaimed(bytes32 _messageHash) internal {
    if (inboxL2L1MessageStatus[_messageHash] != INBOX_STATUS_RECEIVED) {
      revert MessageDoesNotExistOrHasAlreadyBeenClaimed();
    }
    delete inboxL2L1MessageStatus[_messageHash];
  }
  /**
   * @notice Add L1->L2 message hash in storage when a message is sent on L1.
   * @param  _messageHash Hash of the message.
   */
  function _addL1L2MessageHash(bytes32 _messageHash) internal {
    outboxL1L2MessageStatus[_messageHash] = OUTBOX_STATUS_SENT;
  }
  /**
   * @notice Update the status of L1->L2 messages as received when messages has been stored on L2.
   * @dev The expectation here is that the rollup is limited to 100 hashes being added here - array is not open ended.
   * @param  _messageHashes List of message hashes.
   */
  function _updateL1L2MessageStatusToReceived(bytes32[] memory _messageHashes) internal {
    uint256 messageHashArrayLength = _messageHashes.length;
    for (uint256 i; i < messageHashArrayLength; ) {
      bytes32 messageHash = _messageHashes[i];
      uint256 existingStatus = outboxL1L2MessageStatus[messageHash];
      if (existingStatus == OUTBOX_STATUS_UNKNOWN) {
        revert L1L2MessageNotSent(messageHash);
      }
      if (existingStatus != OUTBOX_STATUS_RECEIVED) {
        outboxL1L2MessageStatus[messageHash] = OUTBOX_STATUS_RECEIVED;
      }
      unchecked {
        i++;
      }
    }
    emit L1L2MessagesReceivedOnL2(_messageHashes);
  }
}
// SPDX-License-Identifier: AGPL-3.0
pragma solidity ^0.8.19;
import { Initializable } from "@openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol";
import { ReentrancyGuardUpgradeable } from "@openzeppelin/contracts-upgradeable/security/ReentrancyGuardUpgradeable.sol";
import { IMessageService } from "../../interfaces/IMessageService.sol";
import { IGenericErrors } from "../../interfaces/IGenericErrors.sol";
import { PauseManager } from "../lib/PauseManager.sol";
import { RateLimiter } from "../lib/RateLimiter.sol";
import { L1MessageManager } from "./L1MessageManager.sol";
/**
 * @title Contract to manage cross-chain messaging on L1.
 * @author ConsenSys Software Inc.
 */
abstract contract L1MessageService is
  Initializable,
  RateLimiter,
  L1MessageManager,
  ReentrancyGuardUpgradeable,
  PauseManager,
  IMessageService,
  IGenericErrors
{
  // @dev This is initialised to save user cost with existing slot.
  uint256 public nextMessageNumber;
  address private _messageSender;
  // Keep free storage slots for future implementation updates to avoid storage collision.
  uint256[50] private __gap;
  // @dev adding these should not affect storage as they are constants and are store in bytecode
  uint256 private constant REFUND_OVERHEAD_IN_GAS = 42000;
  /**
   * @notice Initialises underlying message service dependencies.
   * @dev _messageSender is initialised to a non-zero value for gas efficiency on claiming.
   * @param _limitManagerAddress The address owning the rate limiting management role.
   * @param _pauseManagerAddress The address owning the pause management role.
   * @param _rateLimitPeriod The period to rate limit against.
   * @param _rateLimitAmount The limit allowed for withdrawing the period.
   **/
  function __MessageService_init(
    address _limitManagerAddress,
    address _pauseManagerAddress,
    uint256 _rateLimitPeriod,
    uint256 _rateLimitAmount
  ) internal onlyInitializing {
    if (_limitManagerAddress == address(0)) {
      revert ZeroAddressNotAllowed();
    }
    if (_pauseManagerAddress == address(0)) {
      revert ZeroAddressNotAllowed();
    }
    __ERC165_init();
    __Context_init();
    __AccessControl_init();
    __RateLimiter_init(_rateLimitPeriod, _rateLimitAmount);
    _grantRole(RATE_LIMIT_SETTER_ROLE, _limitManagerAddress);
    _grantRole(PAUSE_MANAGER_ROLE, _pauseManagerAddress);
    nextMessageNumber = 1;
    _messageSender = address(123456789);
  }
  /**
   * @notice Adds a message for sending cross-chain and emits MessageSent.
   * @dev The message number is preset (nextMessageNumber) and only incremented at the end if successful for the next caller.
   * @dev This function should be called with a msg.value = _value + _fee. The fee will be paid on the destination chain.
   * @param _to The address the message is intended for.
   * @param _fee The fee being paid for the message delivery.
   * @param _calldata The calldata to pass to the recipient.
   **/
  function sendMessage(
    address _to,
    uint256 _fee,
    bytes calldata _calldata
  ) external payable whenTypeNotPaused(L1_L2_PAUSE_TYPE) whenTypeNotPaused(GENERAL_PAUSE_TYPE) {
    if (_to == address(0)) {
      revert ZeroAddressNotAllowed();
    }
    if (_fee > msg.value) {
      revert ValueSentTooLow();
    }
    uint256 messageNumber = nextMessageNumber;
    uint256 valueSent = msg.value - _fee;
    bytes32 messageHash = keccak256(abi.encode(msg.sender, _to, _fee, valueSent, messageNumber, _calldata));
    // @dev Status check and revert is in the message manager
    _addL1L2MessageHash(messageHash);
    nextMessageNumber++;
    emit MessageSent(msg.sender, _to, _fee, valueSent, messageNumber, _calldata, messageHash);
  }
  /**
   * @notice Claims and delivers a cross-chain message.
   * @dev _feeRecipient can be set to address(0) to receive as msg.sender.
   * @dev _messageSender is set temporarily when claiming and reset post. Used in sender().
   * @dev _messageSender is reset to address(123456789) to be more gas efficient.
   * @param _from The address of the original sender.
   * @param _to The address the message is intended for.
   * @param _fee The fee being paid for the message delivery.
   * @param _value The value to be transferred to the destination address.
   * @param _feeRecipient The recipient for the fee.
   * @param _calldata The calldata to pass to the recipient.
   * @param _nonce The unique auto generated nonce used when sending the message.
   **/
  function claimMessage(
    address _from,
    address _to,
    uint256 _fee,
    uint256 _value,
    address payable _feeRecipient,
    bytes calldata _calldata,
    uint256 _nonce
  ) external nonReentrant distributeFees(_fee, _to, _calldata, _feeRecipient) {
    _requireTypeNotPaused(L2_L1_PAUSE_TYPE);
    _requireTypeNotPaused(GENERAL_PAUSE_TYPE);
    bytes32 messageHash = keccak256(abi.encode(_from, _to, _fee, _value, _nonce, _calldata));
    // @dev Status check and revert is in the message manager.
    _updateL2L1MessageStatusToClaimed(messageHash);
    _addUsedAmount(_fee + _value);
    _messageSender = _from;
    (bool callSuccess, bytes memory returnData) = _to.call{ value: _value }(_calldata);
    if (!callSuccess) {
      if (returnData.length > 0) {
        assembly {
          let data_size := mload(returnData)
          revert(add(32, returnData), data_size)
        }
      } else {
        revert MessageSendingFailed(_to);
      }
    }
    _messageSender = address(123456789);
    emit MessageClaimed(messageHash);
  }
  /**
   * @notice Claims and delivers a cross-chain message.
   * @dev _messageSender is set temporarily when claiming.
   **/
  function sender() external view returns (address) {
    return _messageSender;
  }
  /**
   * @notice Function to receive funds for liquidity purposes.
   **/
  receive() external payable virtual {}
  /**
   * @notice The unspent fee is refunded if applicable.
   * @param _feeInWei The fee paid for delivery in Wei.
   * @param _to The recipient of the message and gas refund.
   * @param _calldata The calldata of the message.
   **/
  modifier distributeFees(
    uint256 _feeInWei,
    address _to,
    bytes calldata _calldata,
    address _feeRecipient
  ) {
    //pre-execution
    uint256 startingGas = gasleft();
    _;
    //post-execution
    // we have a fee
    if (_feeInWei > 0) {
      // default postman fee
      uint256 deliveryFee = _feeInWei;
      // do we have empty calldata?
      if (_calldata.length == 0) {
        bool isDestinationEOA;
        assembly {
          isDestinationEOA := iszero(extcodesize(_to))
        }
        // are we calling an EOA
        if (isDestinationEOA) {
          // initial + cost to call and refund minus gasleft
          deliveryFee = (startingGas + REFUND_OVERHEAD_IN_GAS - gasleft()) * tx.gasprice;
          if (_feeInWei > deliveryFee) {
            payable(_to).send(_feeInWei - deliveryFee);
          } else {
            deliveryFee = _feeInWei;
          }
        }
      }
      address feeReceiver = _feeRecipient == address(0) ? msg.sender : _feeRecipient;
      bool callSuccess = payable(feeReceiver).send(deliveryFee);
      if (!callSuccess) {
        revert FeePaymentFailed(feeReceiver);
      }
    }
  }
}
// SPDX-License-Identifier: AGPL-3.0
pragma solidity ^0.8.19;
/**
 * @title Decoding functions for message service anchoring and bytes slicing.
 * @author ConsenSys Software Inc.
 * @notice You can use this to slice bytes and extract anchoring hashes from calldata.
 **/
library CodecV2 {
  /**
   * @notice Decodes a collection of bytes32 (hashes) from the calldata of a transaction.
   * @dev Extracts and decodes skipping the function selector (selector is expected in the input).
   * @dev A check beforehand must be performed to confirm this is the correct type of transaction.
   * @param _calldataWithSelector The calldata for the transaction.
   * @return bytes32[] - array of message hashes.
   **/
  function _extractXDomainAddHashes(bytes memory _calldataWithSelector) internal pure returns (bytes32[] memory) {
    assembly {
      let len := sub(mload(_calldataWithSelector), 4)
      _calldataWithSelector := add(_calldataWithSelector, 0x4)
      mstore(_calldataWithSelector, len)
    }
    return abi.decode(_calldataWithSelector, (bytes32[]));
  }
}
// SPDX-License-Identifier: AGPL-3.0
pragma solidity ^0.8.19;
import { Initializable } from "@openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol";
import { AccessControlUpgradeable } from "@openzeppelin/contracts-upgradeable/access/AccessControlUpgradeable.sol";
import { IPauseManager } from "../../interfaces/IPauseManager.sol";
/**
 * @title Contract to manage cross-chain function pausing.
 * @author ConsenSys Software Inc.
 */
abstract contract PauseManager is Initializable, IPauseManager, AccessControlUpgradeable {
  bytes32 public constant PAUSE_MANAGER_ROLE = keccak256("PAUSE_MANAGER_ROLE");
  bytes32 public constant GENERAL_PAUSE_TYPE = keccak256("GENERAL_PAUSE_TYPE");
  bytes32 public constant L1_L2_PAUSE_TYPE = keccak256("L1_L2_PAUSE_TYPE");
  bytes32 public constant L2_L1_PAUSE_TYPE = keccak256("L2_L1_PAUSE_TYPE");
  bytes32 public constant PROVING_SYSTEM_PAUSE_TYPE = keccak256("PROVING_SYSTEM_PAUSE_TYPE");
  mapping(bytes32 => bool) public pauseTypeStatuses;
  uint256[10] private _gap;
  /**
   * @dev Modifier to make a function callable only when the type is not paused.
   *
   * Requirements:
   *
   * - The type must not be paused.
   */
  modifier whenTypeNotPaused(bytes32 _pauseType) {
    _requireTypeNotPaused(_pauseType);
    _;
  }
  /**
   * @dev Modifier to make a function callable only when the type is paused.
   *
   * Requirements:
   *
   * - The type must not be paused.
   */
  modifier whenTypePaused(bytes32 _pauseType) {
    _requireTypePaused(_pauseType);
    _;
  }
  /**
   * @dev Throws if the type is not paused.
   * @param _pauseType The keccak256 pause type being checked,
   */
  function _requireTypePaused(bytes32 _pauseType) internal view virtual {
    if (!pauseTypeStatuses[_pauseType]) {
      revert IsNotPaused(_pauseType);
    }
  }
  /**
   * @dev Throws if the type is paused.
   * @param _pauseType The keccak256 pause type being checked,
   */
  function _requireTypeNotPaused(bytes32 _pauseType) internal view virtual {
    if (pauseTypeStatuses[_pauseType]) {
      revert IsPaused(_pauseType);
    }
  }
  /**
   * @notice Pauses functionality by specific type.
   * @dev Requires PAUSE_MANAGER_ROLE.
   * @param _pauseType keccak256 pause type.
   **/
  function pauseByType(bytes32 _pauseType) external whenTypeNotPaused(_pauseType) onlyRole(PAUSE_MANAGER_ROLE) {
    pauseTypeStatuses[_pauseType] = true;
    emit Paused(_msgSender(), _pauseType);
  }
  /**
   * @notice Unpauses functionality by specific type.
   * @dev Requires PAUSE_MANAGER_ROLE.
   * @param _pauseType keccak256 pause type.
   **/
  function unPauseByType(bytes32 _pauseType) external whenTypePaused(_pauseType) onlyRole(PAUSE_MANAGER_ROLE) {
    pauseTypeStatuses[_pauseType] = false;
    emit UnPaused(_msgSender(), _pauseType);
  }
}
// SPDX-License-Identifier: AGPL-3.0
pragma solidity ^0.8.19;
import { Initializable } from "@openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol";
import { AccessControlUpgradeable } from "@openzeppelin/contracts-upgradeable/access/AccessControlUpgradeable.sol";
import { IRateLimiter } from "../../interfaces/IRateLimiter.sol";
/**
 * @title Rate Limiter by period and amount using the block timestamp.
 * @author ConsenSys Software Inc.
 * @notice You can use this control numeric limits over a period using timestamp.
 **/
contract RateLimiter is Initializable, IRateLimiter, AccessControlUpgradeable {
  bytes32 public constant RATE_LIMIT_SETTER_ROLE = keccak256("RATE_LIMIT_SETTER_ROLE");
  uint256 public periodInSeconds; // how much time before limit resets.
  uint256 public limitInWei; // max ether to withdraw per period.
  // @dev Public for ease of consumption.
  // @notice The time at which the current period ends at.
  uint256 public currentPeriodEnd;
  // @dev Public for ease of consumption.
  // @notice Amounts already withdrawn this period.
  uint256 public currentPeriodAmountInWei;
  uint256[10] private _gap;
  /**
   * @notice Initialises the limits and period for the rate limiter.
   * @param _periodInSeconds The length of the period in seconds.
   * @param _limitInWei The limit allowed in the period in Wei.
   **/
  function __RateLimiter_init(uint256 _periodInSeconds, uint256 _limitInWei) internal onlyInitializing {
    if (_periodInSeconds == 0) {
      revert PeriodIsZero();
    }
    if (_limitInWei == 0) {
      revert LimitIsZero();
    }
    periodInSeconds = _periodInSeconds;
    limitInWei = _limitInWei;
    currentPeriodEnd = block.timestamp + _periodInSeconds;
  }
  /**
   * @notice Increments the amount used in the period.
   * @dev The amount determining logic is external to this (e.g. fees are included when calling here).
   * @dev Reverts if the limit is breached.
   * @param _usedAmount The amount used to be added.
   **/
  function _addUsedAmount(uint256 _usedAmount) internal {
    uint256 currentPeriodAmountTemp;
    if (currentPeriodEnd < block.timestamp) {
      currentPeriodEnd = block.timestamp + periodInSeconds;
      currentPeriodAmountTemp = _usedAmount;
    } else {
      currentPeriodAmountTemp = currentPeriodAmountInWei + _usedAmount;
    }
    if (currentPeriodAmountTemp > limitInWei) {
      revert RateLimitExceeded();
    }
    currentPeriodAmountInWei = currentPeriodAmountTemp;
  }
  /**
   * @notice Resets the rate limit amount.
   * @dev If the used amount is higher, it is set to the limit to avoid confusion/issues.
   * @dev Only the RATE_LIMIT_SETTER_ROLE is allowed to execute this function.
   * @dev Emits the LimitAmountChanged event.
   * @dev usedLimitAmountToSet will use the default value of zero if period has expired
   * @param _amount The amount to reset the limit to.
   **/
  function resetRateLimitAmount(uint256 _amount) external onlyRole(RATE_LIMIT_SETTER_ROLE) {
    uint256 usedLimitAmountToSet;
    bool amountUsedLoweredToLimit;
    bool usedAmountResetToZero;
    if (currentPeriodEnd < block.timestamp) {
      currentPeriodEnd = block.timestamp + periodInSeconds;
      usedAmountResetToZero = true;
    } else {
      if (_amount < currentPeriodAmountInWei) {
        usedLimitAmountToSet = _amount;
        amountUsedLoweredToLimit = true;
      }
    }
    limitInWei = _amount;
    if (usedAmountResetToZero || amountUsedLoweredToLimit) {
      currentPeriodAmountInWei = usedLimitAmountToSet;
    }
    emit LimitAmountChanged(_msgSender(), _amount, amountUsedLoweredToLimit, usedAmountResetToZero);
  }
  /**
   * @notice Resets the amount used to zero.
   * @dev Only the RATE_LIMIT_SETTER_ROLE is allowed to execute this function.
   * @dev Emits the AmountUsedInPeriodReset event.
   **/
  function resetAmountUsedInPeriod() external onlyRole(RATE_LIMIT_SETTER_ROLE) {
    currentPeriodAmountInWei = 0;
    emit AmountUsedInPeriodReset(_msgSender());
  }
}
// SPDX-License-Identifier: Apache-2.0
/**
 * @author Hamdi Allam [email protected]
 * @notice Please reach out with any questions or concerns.
 */
pragma solidity ^0.8.19;
error NotList();
error WrongBytesLength();
error NoNext();
error MemoryOutOfBounds(uint256 inde);
library RLPReader {
  uint8 internal constant STRING_SHORT_START = 0x80;
  uint8 internal constant STRING_LONG_START = 0xb8;
  uint8 internal constant LIST_SHORT_START = 0xc0;
  uint8 internal constant LIST_LONG_START = 0xf8;
  uint8 internal constant LIST_SHORT_START_MAX = 0xf7;
  uint8 internal constant WORD_SIZE = 32;
  struct RLPItem {
    uint256 len;
    uint256 memPtr;
  }
  struct Iterator {
    RLPItem item; // Item that's being iterated over.
    uint256 nextPtr; // Position of the next item in the list.
  }
  /**
   * @dev Returns the next element in the iteration. Reverts if it has no next element.
   * @param _self The iterator.
   * @return nextItem The next element in the iteration.
   */
  function _next(Iterator memory _self) internal pure returns (RLPItem memory nextItem) {
    if (!_hasNext(_self)) {
      revert NoNext();
    }
    uint256 ptr = _self.nextPtr;
    uint256 itemLength = _itemLength(ptr);
    _self.nextPtr = ptr + itemLength;
    nextItem.len = itemLength;
    nextItem.memPtr = ptr;
  }
  /**
   * @dev Returns the number 'skiptoNum' element in the iteration.
   * @param _self The iterator.
   * @param _skipToNum Element position in the RLP item iterator to return.
   * @return item The number 'skipToNum' element in the iteration.
   */
  function _skipTo(Iterator memory _self, uint256 _skipToNum) internal pure returns (RLPItem memory item) {
    uint256 lenX;
    uint256 memPtrStart = _self.item.memPtr;
    uint256 endPtr;
    uint256 byte0;
    uint256 byteLen;
    assembly {
      // get first byte to know if it is a short/long list
      byte0 := byte(0, mload(memPtrStart))
      // yul has no if/else so if it a short list ( < long list start )
      switch lt(byte0, LIST_LONG_START)
      case 1 {
        // the length is just the difference in bytes
        lenX := sub(byte0, 0xc0)
      }
      case 0 {
        // at this point we care only about lists, so this is the default
        // get how many next bytes indicate the list length
        byteLen := sub(byte0, 0xf7)
        // move one over to the list length start
        memPtrStart := add(memPtrStart, 1)
        // shift over grabbing the bytelen elements
        lenX := div(mload(memPtrStart), exp(256, sub(32, byteLen)))
      }
      // get the end
      endPtr := add(memPtrStart, lenX)
    }
    uint256 ptr = _self.nextPtr;
    uint256 itemLength = _itemLength(ptr);
    _self.nextPtr = ptr + itemLength;
    for (uint256 i; i < _skipToNum - 1; ) {
      ptr = _self.nextPtr;
      if (ptr > endPtr) revert MemoryOutOfBounds(endPtr);
      itemLength = _itemLength(ptr);
      _self.nextPtr = ptr + itemLength;
      unchecked {
        i++;
      }
    }
    item.len = itemLength;
    item.memPtr = ptr;
  }
  /**
   * @dev Returns true if the iteration has more elements.
   * @param _self The iterator.
   * @return True if the iteration has more elements.
   */
  function _hasNext(Iterator memory _self) internal pure returns (bool) {
    RLPItem memory item = _self.item;
    return _self.nextPtr < item.memPtr + item.len;
  }
  /**
   * @param item RLP encoded bytes.
   * @return newItem The RLP item.
   */
  function _toRlpItem(bytes memory item) internal pure returns (RLPItem memory newItem) {
    uint256 memPtr;
    assembly {
      memPtr := add(item, 0x20)
    }
    newItem.len = item.length;
    newItem.memPtr = memPtr;
  }
  /**
   * @dev Creates an iterator. Reverts if item is not a list.
   * @param _self The RLP item.
   * @return iterator 'Iterator' over the item.
   */
  function _iterator(RLPItem memory _self) internal pure returns (Iterator memory iterator) {
    if (!_isList(_self)) {
      revert NotList();
    }
    uint256 ptr = _self.memPtr + _payloadOffset(_self.memPtr);
    iterator.item = _self;
    iterator.nextPtr = ptr;
  }
  /**
   * @param _item The RLP item.
   * @return (memPtr, len) Tuple: Location of the item's payload in memory.
   */
  function _payloadLocation(RLPItem memory _item) internal pure returns (uint256, uint256) {
    uint256 offset = _payloadOffset(_item.memPtr);
    uint256 memPtr = _item.memPtr + offset;
    uint256 len = _item.len - offset; // data length
    return (memPtr, len);
  }
  /**
   * @param _item The RLP item.
   * @return Indicator whether encoded payload is a list.
   */
  function _isList(RLPItem memory _item) internal pure returns (bool) {
    if (_item.len == 0) return false;
    uint8 byte0;
    uint256 memPtr = _item.memPtr;
    assembly {
      byte0 := byte(0, mload(memPtr))
    }
    if (byte0 < LIST_SHORT_START) return false;
    return true;
  }
  /**
   * @param _item The RLP item.
   * @return result Returns the item as an address.
   */
  function _toAddress(RLPItem memory _item) internal pure returns (address) {
    // 1 byte for the length prefix
    if (_item.len != 21) {
      revert WrongBytesLength();
    }
    return address(uint160(_toUint(_item)));
  }
  /**
   * @param _item The RLP item.
   * @return result Returns the item as a uint256.
   */
  function _toUint(RLPItem memory _item) internal pure returns (uint256 result) {
    if (_item.len == 0 || _item.len > 33) {
      revert WrongBytesLength();
    }
    (uint256 memPtr, uint256 len) = _payloadLocation(_item);
    assembly {
      result := mload(memPtr)
      // Shfit to the correct location if neccesary.
      if lt(len, 32) {
        result := div(result, exp(256, sub(32, len)))
      }
    }
  }
  /**
   * @param _item The RLP item.
   * @return result Returns the item as bytes.
   */
  function _toBytes(RLPItem memory _item) internal pure returns (bytes memory result) {
    if (_item.len == 0) {
      revert WrongBytesLength();
    }
    (uint256 memPtr, uint256 len) = _payloadLocation(_item);
    result = new bytes(len);
    uint256 destPtr;
    assembly {
      destPtr := add(0x20, result)
    }
    _copy(memPtr, destPtr, len);
  }
  /*
   * Private Helpers
   */
  /**
   * @param _memPtr Item memory pointer.
   * @return Entire RLP item byte length.
   */
  function _itemLength(uint256 _memPtr) private pure returns (uint256) {
    uint256 itemLen;
    uint256 dataLen;
    uint256 byte0;
    assembly {
      byte0 := byte(0, mload(_memPtr))
    }
    if (byte0 < STRING_SHORT_START) itemLen = 1;
    else if (byte0 < STRING_LONG_START) itemLen = byte0 - STRING_SHORT_START + 1;
    else if (byte0 < LIST_SHORT_START) {
      assembly {
        let byteLen := sub(byte0, 0xb7) // # Of bytes the actual length is.
        _memPtr := add(_memPtr, 1) // Skip over the first byte.
        /* 32 byte word size */
        dataLen := div(mload(_memPtr), exp(256, sub(32, byteLen))) // Right shifting to get the len.
        itemLen := add(dataLen, add(byteLen, 1))
      }
    } else if (byte0 < LIST_LONG_START) {
      itemLen = byte0 - LIST_SHORT_START + 1;
    } else {
      assembly {
        let byteLen := sub(byte0, 0xf7)
        _memPtr := add(_memPtr, 1)
        dataLen := div(mload(_memPtr), exp(256, sub(32, byteLen))) // Right shifting to the correct length.
        itemLen := add(dataLen, add(byteLen, 1))
      }
    }
    return itemLen;
  }
  /**
   * @param _memPtr Item memory pointer.
   * @return Number of bytes until the data.
   */
  function _payloadOffset(uint256 _memPtr) private pure returns (uint256) {
    uint256 byte0;
    assembly {
      byte0 := byte(0, mload(_memPtr))
    }
    if (byte0 < STRING_SHORT_START) return 0;
    else if (byte0 < STRING_LONG_START || (byte0 >= LIST_SHORT_START && byte0 < LIST_LONG_START)) return 1;
    else if (byte0 < LIST_SHORT_START)
      // being explicit
      return byte0 - (STRING_LONG_START - 1) + 1;
    else return byte0 - (LIST_LONG_START - 1) + 1;
  }
  /**
   * @param _src Pointer to source.
   * @param _dest Pointer to destination.
   * @param _len Amount of memory to copy from the source.
   */
  function _copy(uint256 _src, uint256 _dest, uint256 _len) private pure {
    if (_len == 0) return;
    // copy as many word sizes as possible
    for (; _len >= WORD_SIZE; _len -= WORD_SIZE) {
      assembly {
        mstore(_dest, mload(_src))
      }
      _src += WORD_SIZE;
      _dest += WORD_SIZE;
    }
    if (_len > 0) {
      // Left over bytes. Mask is used to remove unwanted bytes from the word.
      uint256 mask = 256 ** (WORD_SIZE - _len) - 1;
      assembly {
        let srcpart := and(mload(_src), not(mask)) // Zero out src.
        let destpart := and(mload(_dest), mask) // Retrieve the bytes.
        mstore(_dest, or(destpart, srcpart))
      }
    }
  }
}
// SPDX-License-Identifier: AGPL-3.0
pragma solidity ^0.8.19;
import { RLPReader } from "./Rlp.sol";
using RLPReader for RLPReader.RLPItem;
using RLPReader for RLPReader.Iterator;
using RLPReader for bytes;
/*
 * dev Thrown when the transaction data length is too short.
 */
error TransactionShort();
/*
 * dev Thrown when the transaction type is unknown.
 */
error UnknownTransactionType();
/**
 * @title Contract to decode RLP formatted transactions.
 * @author ConsenSys Software Inc.
 */
library TransactionDecoder {
  /**
   * @notice Decodes the transaction extracting the calldata.
   * @param _transaction The RLP transaction.
   * @return data Returns the transaction calldata as bytes.
   */
  function decodeTransaction(bytes calldata _transaction) internal pure returns (bytes memory) {
    if (_transaction.length < 1) {
      revert TransactionShort();
    }
    bytes1 version = _transaction[0];
    if (version == 0x01) {
      return _decodeEIP2930Transaction(_transaction);
    }
    if (version == 0x02) {
      return _decodeEIP1559Transaction(_transaction);
    }
    if (version >= 0xc0) {
      return _decodeLegacyTransaction(_transaction);
    }
    revert UnknownTransactionType();
  }
  /**
   * @notice Decodes the EIP1559 transaction extracting the calldata.
   * @param _transaction The RLP transaction.
   * @return data Returns the transaction calldata as bytes.
   */
  function _decodeEIP1559Transaction(bytes calldata _transaction) private pure returns (bytes memory data) {
    bytes memory txData = _transaction[1:]; // skip the version byte
    RLPReader.RLPItem memory rlp = txData._toRlpItem();
    RLPReader.Iterator memory it = rlp._iterator();
    data = it._skipTo(8)._toBytes();
  }
  /**
   * @notice Decodes the EIP29230 transaction extracting the calldata.
   * @param _transaction The RLP transaction.
   * @return data Returns the transaction calldata as bytes.
   */
  function _decodeEIP2930Transaction(bytes calldata _transaction) private pure returns (bytes memory data) {
    bytes memory txData = _transaction[1:]; // skip the version byte
    RLPReader.RLPItem memory rlp = txData._toRlpItem();
    RLPReader.Iterator memory it = rlp._iterator();
    data = it._skipTo(7)._toBytes();
  }
  /**
   * @notice Decodes the legacy transaction extracting the calldata.
   * @param _transaction The RLP transaction.
   * @return data Returns the transaction calldata as bytes.
   */
  function _decodeLegacyTransaction(bytes calldata _transaction) private pure returns (bytes memory data) {
    bytes memory txData = _transaction;
    RLPReader.RLPItem memory rlp = txData._toRlpItem();
    RLPReader.Iterator memory it = rlp._iterator();
    data = it._skipTo(6)._toBytes();
  }
}
// SPDX-License-Identifier: AGPL-3.0
pragma solidity ^0.8.19;
import { Initializable } from "@openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol";
import { AccessControlUpgradeable } from "@openzeppelin/contracts-upgradeable/access/AccessControlUpgradeable.sol";
import { L1MessageService } from "./messageService/l1/L1MessageService.sol";
import { TransactionDecoder } from "./messageService/lib/TransactionDecoder.sol";
import { IZkEvmV2 } from "./interfaces/IZkEvmV2.sol";
import { IPlonkVerifier } from "./interfaces/IPlonkVerifier.sol";
import { CodecV2 } from "./messageService/lib/Codec.sol";
/**
 * @title Contract to manage cross-chain messaging on L1 and rollup proving.
 * @author ConsenSys Software Inc.
 */
contract ZkEvmV2 is IZkEvmV2, Initializable, AccessControlUpgradeable, L1MessageService {
  using TransactionDecoder for *;
  using CodecV2 for *;
  uint256 private constant MODULO_R = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
  bytes32 public constant OPERATOR_ROLE = keccak256("OPERATOR_ROLE");
  uint256 public currentTimestamp;
  uint256 public currentL2BlockNumber;
  mapping(uint256 => bytes32) public stateRootHashes;
  mapping(uint256 => address) public verifiers;
  uint256[50] private __gap;
  /// @custom:oz-upgrades-unsafe-allow constructor
  constructor() {
    _disableInitializers();
  }
  /**
   * @notice Initializes zkEvm and underlying service dependencies.
   * @dev DEFAULT_ADMIN_ROLE is set for the security council.
   * @dev OPERATOR_ROLE is set for operators.
   * @param _initialStateRootHash The initial hash at migration used for proof verification.
   * @param _initialL2BlockNumber The initial block number at migration.
   * @param _defaultVerifier The default verifier for rollup proofs.
   * @param _securityCouncil The address for the security council performing admin operations.
   * @param _operators The allowed rollup operators at initialization.
   * @param _rateLimitPeriodInSeconds The period in which withdrawal amounts and fees will be accumulated.
   * @param _rateLimitAmountInWei The limit allowed for withdrawing in the period.
   **/
  function initialize(
    bytes32 _initialStateRootHash,
    uint256 _initialL2BlockNumber,
    address _defaultVerifier,
    address _securityCouncil,
    address[] calldata _operators,
    uint256 _rateLimitPeriodInSeconds,
    uint256 _rateLimitAmountInWei
  ) public initializer {
    if (_defaultVerifier == address(0)) {
      revert ZeroAddressNotAllowed();
    }
    for (uint256 i; i < _operators.length; ) {
      if (_operators[i] == address(0)) {
        revert ZeroAddressNotAllowed();
      }
      _grantRole(OPERATOR_ROLE, _operators[i]);
      unchecked {
        i++;
      }
    }
    _grantRole(DEFAULT_ADMIN_ROLE, _securityCouncil);
    __MessageService_init(_securityCouncil, _securityCouncil, _rateLimitPeriodInSeconds, _rateLimitAmountInWei);
    verifiers[0] = _defaultVerifier;
    currentL2BlockNumber = _initialL2BlockNumber;
    stateRootHashes[_initialL2BlockNumber] = _initialStateRootHash;
  }
  /**
   * @notice Adds or updates the verifier contract address for a proof type.
   * @dev DEFAULT_ADMIN_ROLE is required to execute.
   * @param _newVerifierAddress The address for the verifier contract.
   * @param _proofType The proof type being set/updated.
   **/
  function setVerifierAddress(address _newVerifierAddress, uint256 _proofType) external onlyRole(DEFAULT_ADMIN_ROLE) {
    if (_newVerifierAddress == address(0)) {
      revert ZeroAddressNotAllowed();
    }
    emit VerifierAddressChanged(_newVerifierAddress, _proofType, msg.sender);
    verifiers[_proofType] = _newVerifierAddress;
  }
  /**
   * @notice Finalizes blocks without using a proof.
   * @dev DEFAULT_ADMIN_ROLE is required to execute.
   * @param _blocksData The full BlockData collection - block, transaction and log data.
   **/
  function finalizeBlocksWithoutProof(
    BlockData[] calldata _blocksData
  ) external whenTypeNotPaused(GENERAL_PAUSE_TYPE) onlyRole(DEFAULT_ADMIN_ROLE) {
    _finalizeBlocks(_blocksData, new bytes(0), 0, bytes32(0), false);
  }
  /**
   * @notice Finalizes blocks using a proof.
   * @dev OPERATOR_ROLE is required to execute.
   * @dev If the verifier based on proof type is not found, it reverts.
   * @param _blocksData The full BlockData collection - block, transaction and log data.
   * @param _proof The proof to be verified with the proof type verifier contract.
   * @param _proofType The proof type to determine which verifier contract to use.
   * @param _parentStateRootHash The starting roothash for the last known block.
   **/
  function finalizeBlocks(
    BlockData[] calldata _blocksData,
    bytes calldata _proof,
    uint256 _proofType,
    bytes32 _parentStateRootHash
  )
    external
    whenTypeNotPaused(PROVING_SYSTEM_PAUSE_TYPE)
    whenTypeNotPaused(GENERAL_PAUSE_TYPE)
    onlyRole(OPERATOR_ROLE)
  {
    if (stateRootHashes[currentL2BlockNumber] != _parentStateRootHash) {
      revert StartingRootHashDoesNotMatch();
    }
    _finalizeBlocks(_blocksData, _proof, _proofType, _parentStateRootHash, true);
  }
  /**
   * @notice Finalizes blocks with or without using a proof depending on _shouldProve
   * @dev If the verifier based on proof type is not found, it reverts.
   * @param _blocksData The full BlockData collection - block, transaction and log data.
   * @param _proof The proof to be verified with the proof type verifier contract.
   * @param _proofType The proof type to determine which verifier contract to use.
   * @param _parentStateRootHash The starting roothash for the last known block.
   **/
  function _finalizeBlocks(
    BlockData[] calldata _blocksData,
    bytes memory _proof,
    uint256 _proofType,
    bytes32 _parentStateRootHash,
    bool _shouldProve
  ) private {
    uint256 currentBlockNumberTemp = currentL2BlockNumber;
    uint256 firstBlockNumber = currentBlockNumberTemp + 1;
    uint256[] memory timestamps = new uint256[](_blocksData.length);
    bytes32[] memory blockHashes = new bytes32[](_blocksData.length);
    bytes32[] memory hashOfRootHashes = new bytes32[](_blocksData.length + 1);
    hashOfRootHashes[0] = _parentStateRootHash;
    bytes32 hashOfTxHashes;
    bytes32 hashOfMessageHashes;
    for (uint256 i; i < _blocksData.length; ) {
      BlockData calldata blockInfo = _blocksData[i];
      if (blockInfo.l2BlockTimestamp >= block.timestamp) {
        revert BlockTimestampError();
      }
      hashOfTxHashes = _processBlockTransactions(blockInfo.transactions, blockInfo.batchReceptionIndices);
      hashOfMessageHashes = _processMessageHashes(blockInfo.l2ToL1MsgHashes);
      ++currentBlockNumberTemp;
      blockHashes[i] = keccak256(
        abi.encodePacked(
          hashOfTxHashes,
          hashOfMessageHashes,
          keccak256(abi.encodePacked(blockInfo.batchReceptionIndices)),
          keccak256(blockInfo.fromAddresses)
        )
      );
      timestamps[i] = blockInfo.l2BlockTimestamp;
      hashOfRootHashes[i + 1] = blockInfo.blockRootHash;
      emit BlockFinalized(currentBlockNumberTemp, blockInfo.blockRootHash);
      unchecked {
        i++;
      }
    }
    stateRootHashes[currentBlockNumberTemp] = _blocksData[_blocksData.length - 1].blockRootHash;
    currentTimestamp = _blocksData[_blocksData.length - 1].l2BlockTimestamp;
    currentL2BlockNumber = currentBlockNumberTemp;
    if (_shouldProve) {
      _verifyProof(
        uint256(
          keccak256(
            abi.encode(
              keccak256(abi.encodePacked(blockHashes)),
              firstBlockNumber,
              keccak256(abi.encodePacked(timestamps)),
              keccak256(abi.encodePacked(hashOfRootHashes))
            )
          )
        ) % MODULO_R,
        _proofType,
        _proof,
        _parentStateRootHash
      );
    }
  }
  /**
   * @notice Hashes all transactions individually and then hashes the packed hash array.
   * @dev Updates the outbox status on L1 as received.
   * @param _transactions The transactions in a particular block.
   * @param _batchReceptionIndices The indexes where the transaction type is the L1->L2 achoring message hashes transaction.
   **/
  function _processBlockTransactions(
    bytes[] calldata _transactions,
    uint16[] calldata _batchReceptionIndices
  ) internal returns (bytes32 hashOfTxHashes) {
    bytes32[] memory transactionHashes = new bytes32[](_transactions.length);
    if (_transactions.length == 0) {
      revert EmptyBlock();
    }
    for (uint256 i; i < _batchReceptionIndices.length; ) {
      _updateL1L2MessageStatusToReceived(
        TransactionDecoder.decodeTransaction(_transactions[_batchReceptionIndices[i]])._extractXDomainAddHashes()
      );
      unchecked {
        i++;
      }
    }
    for (uint256 i; i < _transactions.length; ) {
      transactionHashes[i] = keccak256(_transactions[i]);
      unchecked {
        i++;
      }
    }
    hashOfTxHashes = keccak256(abi.encodePacked(transactionHashes));
  }
  /**
   * @notice Anchors message hashes and hashes the packed hash array.
   * @dev Also adds L2->L1 sent message hashes for later claiming.
   * @param _messageHashes The hashes in the message sent event logs.
   **/
  function _processMessageHashes(bytes32[] calldata _messageHashes) internal returns (bytes32 hashOfLogHashes) {
    for (uint256 i; i < _messageHashes.length; ) {
      _addL2L1MessageHash(_messageHashes[i]);
      unchecked {
        i++;
      }
    }
    hashOfLogHashes = keccak256(abi.encodePacked(_messageHashes));
  }
  /**
   * @notice Verifies the proof with locally computed public inputs.
   * @dev If the verifier based on proof type is not found, it reverts with InvalidProofType.
   * @param _publicInputHash The full BlockData collection - block, transaction and log data.
   * @param _proofType The proof type to determine which verifier contract to use.
   * @param _proof The proof to be verified with the proof type verifier contract.
   * @param _parentStateRootHash The beginning roothash to start with.
   **/
  function _verifyProof(
    uint256 _publicInputHash,
    uint256 _proofType,
    bytes memory _proof,
    bytes32 _parentStateRootHash
  ) private {
    uint256[] memory input = new uint256[](1);
    input[0] = _publicInputHash;
    address verifierToUse = verifiers[_proofType];
    if (verifierToUse == address(0)) {
      revert InvalidProofType();
    }
    bool success = IPlonkVerifier(verifierToUse).Verify(_proof, input);
    if (!success) {
      revert InvalidProof();
    }
    emit BlocksVerificationDone(currentL2BlockNumber, _parentStateRootHash, stateRootHashes[currentL2BlockNumber]);
  }
}

// SPDX-License-Identifier: Apache-2.0
// Copyright 2023 Consensys Software Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// Code generated by gnark DO NOT EDIT
pragma solidity ^0.8.19;
import { Utils } from "./Utils.sol";
contract PlonkVerifierFull {
  using Utils for *;
  uint256 private constant r_mod = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
  uint256 private constant p_mod = 21888242871839275222246405745257275088696311157297823662689037894645226208583;
  uint256 private constant g2_srs_0_x_0 = 11559732032986387107991004021392285783925812861821192530917403151452391805634;
  uint256 private constant g2_srs_0_x_1 = 10857046999023057135944570762232829481370756359578518086990519993285655852781;
  uint256 private constant g2_srs_0_y_0 = 4082367875863433681332203403145435568316851327593401208105741076214120093531;
  uint256 private constant g2_srs_0_y_1 = 8495653923123431417604973247489272438418190587263600148770280649306958101930;
  uint256 private constant g2_srs_1_x_0 = 15805639136721018565402881920352193254830339253282065586954346329754995870280;
  uint256 private constant g2_srs_1_x_1 = 19089565590083334368588890253123139704298730990782503769911324779715431555531;
  uint256 private constant g2_srs_1_y_0 = 9779648407879205346559610309258181044130619080926897934572699915909528404984;
  uint256 private constant g2_srs_1_y_1 = 6779728121489434657638426458390319301070371227460768374343986326751507916979;
  // ----------------------- vk ---------------------
  uint256 private constant vk_domain_size = 67108864;
  uint256 private constant vk_inv_domain_size =
    21888242545679039938882419398440172875981108180010270949818755658014750055173;
  uint256 private constant vk_omega = 7419588552507395652481651088034484897579724952953562618697845598160172257810;
  uint256 private constant vk_ql_com_x = 13525709715452455298954926042894212564628036321399789360566793694715937771352;
  uint256 private constant vk_ql_com_y = 16585249180591675138941559203780511979245575412908714775636958360987383792239;
  uint256 private constant vk_qr_com_x = 14148572045886251945792876173080813556116314088794324579574660284762914941669;
  uint256 private constant vk_qr_com_y = 13842239550691491428464191545817225601597189810026701643462638680503957744889;
  uint256 private constant vk_qm_com_x = 13522897959955119652865784834835976361490133655994054434262671514193248404625;
  uint256 private constant vk_qm_com_y = 13493447428329441420851370602159948706574248532218034239617820929323277518001;
  uint256 private constant vk_qo_com_x = 7060690164887603180822709561299613895672597716510049606680499562908505132709;
  uint256 private constant vk_qo_com_y = 17132453280808170663140286188647213203791535181032438058770464109374337899153;
  uint256 private constant vk_qk_com_x = 15216401052757890774219228156239863879308845760439647233724618177408901913570;
  uint256 private constant vk_qk_com_y = 12451956943068853170449619051211352834650857556519559497734074793907719431916;
  uint256 private constant vk_s1_com_x = 14256405778767051587276133608837021203518255961898101394303537378002866419040;
  uint256 private constant vk_s1_com_y = 21038700968212297875313747694611083193187035592187569106720411730639905255252;
  uint256 private constant vk_s2_com_x = 1019109700203543492729048562641359612628812305695299058467746496950485325794;
  uint256 private constant vk_s2_com_y = 490278430319379230242443848913755358662702057338304277498471180434097991836;
  uint256 private constant vk_s3_com_x = 2969427075258365849777260383285616082152301055041585820485498518017437026548;
  uint256 private constant vk_s3_com_y = 16099347285202727295431946911322450887583714417016216619148080599766330871066;
  uint256 private constant vk_coset_shift = 5;
  uint256 private constant vk_selector_commitments_commit_api_0_x =
    21788360697493106829785246939901744021456836473452930837314992369057900122018;
  uint256 private constant vk_selector_commitments_commit_api_0_y =
    16125341249761668633747631072985421243468892447965413965887015388783528206032;
  uint256 private constant vk_selector_commitments_commit_api_1_x =
    9369801914206014217445122279591521815449013590744042826207321226401456655568;
  uint256 private constant vk_selector_commitments_commit_api_1_y =
    20403534275150672051547282308343985824042675377185536764459718189767081861844;
  uint256 private constant vk_selector_commitments_commit_api_2_x =
    15085855314213485493120090850643571722324905485327671636383375594981366630616;
  uint256 private constant vk_selector_commitments_commit_api_2_y =
    9694401959517714837257605548316168182563966590362894961003011860886804708060;
  function load_vk_commitments_indices_commit_api(uint256[] memory v) internal pure {
    assembly {
      let _v := add(v, 0x20)
      mstore(_v, 22612113)
      _v := add(_v, 0x20)
      mstore(_v, 27501766)
      _v := add(_v, 0x20)
      mstore(_v, 60589135)
      _v := add(_v, 0x20)
    }
  }
  uint256 private constant vk_nb_commitments_commit_api = 3;
  // ------------------------------------------------
  // offset proof
  uint256 private constant proof_l_com_x = 0x20;
  uint256 private constant proof_l_com_y = 0x40;
  uint256 private constant proof_r_com_x = 0x60;
  uint256 private constant proof_r_com_y = 0x80;
  uint256 private constant proof_o_com_x = 0xa0;
  uint256 private constant proof_o_com_y = 0xc0;
  // h = h_0 + x^{n+2}h_1 + x^{2(n+2)}h_2
  uint256 private constant proof_h_0_x = 0xe0;
  uint256 private constant proof_h_0_y = 0x100;
  uint256 private constant proof_h_1_x = 0x120;
  uint256 private constant proof_h_1_y = 0x140;
  uint256 private constant proof_h_2_x = 0x160;
  uint256 private constant proof_h_2_y = 0x180;
  // wire values at zeta
  uint256 private constant proof_l_at_zeta = 0x1a0;
  uint256 private constant proof_r_at_zeta = 0x1c0;
  uint256 private constant proof_o_at_zeta = 0x1e0;
  //uint256[STATE_WIDTH-1] permutation_polynomials_at_zeta; // Sσ1(zeta),Sσ2(zeta)
  uint256 private constant proof_s1_at_zeta = 0x200; // Sσ1(zeta)
  uint256 private constant proof_s2_at_zeta = 0x220; // Sσ2(zeta)
  //Bn254.G1Point grand_product_commitment;                 // [z(x)]
  uint256 private constant proof_grand_product_commitment_x = 0x240;
  uint256 private constant proof_grand_product_commitment_y = 0x260;
  uint256 private constant proof_grand_product_at_zeta_omega = 0x280; // z(w*zeta)
  uint256 private constant proof_quotient_polynomial_at_zeta = 0x2a0; // t(zeta)
  uint256 private constant proof_linearised_polynomial_at_zeta = 0x2c0; // r(zeta)
  // Folded proof for the opening of H, linearised poly, l, r, o, s_1, s_2, qcp
  uint256 private constant proof_batch_opening_at_zeta_x = 0x2e0; // [Wzeta]
  uint256 private constant proof_batch_opening_at_zeta_y = 0x300;
  //Bn254.G1Point opening_at_zeta_omega_proof;      // [Wzeta*omega]
  uint256 private constant proof_opening_at_zeta_omega_x = 0x320;
  uint256 private constant proof_opening_at_zeta_omega_y = 0x340;
  uint256 private constant proof_openings_selector_commit_api_at_zeta = 0x360;
  // -> next part of proof is
  // [ openings_selector_commits || commitments_wires_commit_api]
  // -------- offset state
  // challenges to check the claimed quotient
  uint256 private constant state_alpha = 0x00;
  uint256 private constant state_beta = 0x20;
  uint256 private constant state_gamma = 0x40;
  uint256 private constant state_zeta = 0x60;
  // reusable value
  uint256 private constant state_alpha_square_lagrange_0 = 0x80;
  // commitment to H
  uint256 private constant state_folded_h_x = 0xa0;
  uint256 private constant state_folded_h_y = 0xc0;
  // commitment to the linearised polynomial
  uint256 private constant state_linearised_polynomial_x = 0xe0;
  uint256 private constant state_linearised_polynomial_y = 0x100;
  // Folded proof for the opening of H, linearised poly, l, r, o, s_1, s_2, qcp
  uint256 private constant state_folded_claimed_values = 0x120;
  // folded digests of H, linearised poly, l, r, o, s_1, s_2, qcp
  // Bn254.G1Point folded_digests;
  uint256 private constant state_folded_digests_x = 0x140;
  uint256 private constant state_folded_digests_y = 0x160;
  uint256 private constant state_pi = 0x180;
  uint256 private constant state_zeta_power_n_minus_one = 0x1a0;
  uint256 private constant state_gamma_kzg = 0x1c0;
  uint256 private constant state_success = 0x1e0;
  uint256 private constant state_check_var = 0x200; // /!\\ this slot is used for debugging only
  uint256 private constant state_last_mem = 0x220;
  // -------- errors
  uint256 private constant error_string_id = 0x08c379a000000000000000000000000000000000000000000000000000000000; // selector for function Error(string)
  // read the commitments to the wires related to the commit api and store them in wire_commitments.
  // The commitments are points on Bn254(Fp) so they are stored on 2 uint256.
  function load_wire_commitments_commit_api(uint256[] memory wire_commitments, bytes memory proof) internal pure {
    assembly {
      let w := add(wire_commitments, 0x20)
      let p := add(proof, proof_openings_selector_commit_api_at_zeta)
      p := add(p, mul(vk_nb_commitments_commit_api, 0x20))
      for {
        let i := 0
      } lt(i, vk_nb_commitments_commit_api) {
        i := add(i, 1)
      } {
        // x coordinate
        mstore(w, mload(p))
        w := add(w, 0x20)
        p := add(p, 0x20)
        // y coordinate
        mstore(w, mload(p))
        w := add(w, 0x20)
        p := add(p, 0x20)
      }
    }
  }
  function derive_gamma_beta_alpha_zeta(
    bytes memory proof,
    uint256[] memory public_inputs
  ) internal view returns (uint256, uint256, uint256, uint256) {
    uint256 gamma;
    uint256 beta;
    uint256 alpha;
    uint256 zeta;
    assembly {
      let mem := mload(0x40)
      derive_gamma(proof, public_inputs)
      gamma := mload(mem)
      derive_beta(proof, gamma)
      beta := mload(mem)
      derive_alpha(proof, beta)
      alpha := mload(mem)
      derive_zeta(proof, alpha)
      zeta := mload(mem)
      gamma := mod(gamma, r_mod)
      beta := mod(beta, r_mod)
      alpha := mod(alpha, r_mod)
      zeta := mod(zeta, r_mod)
      function error_sha2_256() {
        let ptError := mload(0x40)
        mstore(ptError, error_string_id) // selector for function Error(string)
        mstore(add(ptError, 0x4), 0x20)
        mstore(add(ptError, 0x24), 0x19)
        mstore(add(ptError, 0x44), "error staticcall sha2-256")
        revert(ptError, 0x64)
      }
      // Derive gamma as Sha256(<transcript>)
      // where transcript is the concatenation (in this order) of:
      // * the word "gamma" in ascii, equal to [0x67,0x61,0x6d, 0x6d, 0x61] and encoded as a uint256.
      // * the commitments to the permutation polynomials S1, S2, S3, where we concatenate the coordinates of those points
      // * the commitments of Ql, Qr, Qm, Qo, Qk
      // * the public inputs
      // * the commitments of the wires related to the custom gates (commitments_wires_commit_api)
      // * commitments to L, R, O (proof_<l,r,o>_com_<x,y>)
      // The data described above is written starting at mPtr. "gamma" lies on 5 bytes,
      // and is encoded as a uint256 number n. In basis b = 256, the number looks like this
      // [0 0 0 .. 0x67 0x61 0x6d, 0x6d, 0x61]. The first non zero entry is at position 27=0x1b
      function derive_gamma(aproof, pub_inputs) {
        let mPtr := mload(0x40)
        // gamma
        // gamma in ascii is [0x67,0x61,0x6d, 0x6d, 0x61]
        // (same for alpha, beta, zeta)
        mstore(mPtr, 0x67616d6d61) // "gamma"
        mstore(add(mPtr, 0x20), vk_s1_com_x)
        mstore(add(mPtr, 0x40), vk_s1_com_y)
        mstore(add(mPtr, 0x60), vk_s2_com_x)
        mstore(add(mPtr, 0x80), vk_s2_com_y)
        mstore(add(mPtr, 0xa0), vk_s3_com_x)
        mstore(add(mPtr, 0xc0), vk_s3_com_y)
        mstore(add(mPtr, 0xe0), vk_ql_com_x)
        mstore(add(mPtr, 0x100), vk_ql_com_y)
        mstore(add(mPtr, 0x120), vk_qr_com_x)
        mstore(add(mPtr, 0x140), vk_qr_com_y)
        mstore(add(mPtr, 0x160), vk_qm_com_x)
        mstore(add(mPtr, 0x180), vk_qm_com_y)
        mstore(add(mPtr, 0x1a0), vk_qo_com_x)
        mstore(add(mPtr, 0x1c0), vk_qo_com_y)
        mstore(add(mPtr, 0x1e0), vk_qk_com_x)
        mstore(add(mPtr, 0x200), vk_qk_com_y)
        let pi := add(pub_inputs, 0x20)
        let _mPtr := add(mPtr, 0x220)
        for {
          let i := 0
        } lt(i, mload(pub_inputs)) {
          i := add(i, 1)
        } {
          mstore(_mPtr, mload(pi))
          pi := add(pi, 0x20)
          _mPtr := add(_mPtr, 0x20)
        }
        let _proof := add(aproof, proof_openings_selector_commit_api_at_zeta)
        _proof := add(_proof, mul(vk_nb_commitments_commit_api, 0x20))
        for {
          let i := 0
        } lt(i, vk_nb_commitments_commit_api) {
          i := add(i, 1)
        } {
          mstore(_mPtr, mload(_proof))
          mstore(add(_mPtr, 0x20), mload(add(_proof, 0x20)))
          _mPtr := add(_mPtr, 0x40)
          _proof := add(_proof, 0x40)
        }
        mstore(_mPtr, mload(add(aproof, proof_l_com_x)))
        mstore(add(_mPtr, 0x20), mload(add(aproof, proof_l_com_y)))
        mstore(add(_mPtr, 0x40), mload(add(aproof, proof_r_com_x)))
        mstore(add(_mPtr, 0x60), mload(add(aproof, proof_r_com_y)))
        mstore(add(_mPtr, 0x80), mload(add(aproof, proof_o_com_x)))
        mstore(add(_mPtr, 0xa0), mload(add(aproof, proof_o_com_y)))
        let size := add(0x2c5, mul(mload(pub_inputs), 0x20)) // 0x2c5 = 22*32+5
        size := add(size, mul(vk_nb_commitments_commit_api, 0x40))
        let success := staticcall(sub(gas(), 2000), 0x2, add(mPtr, 0x1b), size, mPtr, 0x20) //0x1b -> 000.."gamma"
        if eq(success, 0) {
          error_sha2_256()
        }
      }
      function derive_beta(aproof, prev_challenge) {
        let mPtr := mload(0x40)
        // beta
        mstore(mPtr, 0x62657461) // "beta"
        mstore(add(mPtr, 0x20), prev_challenge)
        let success := staticcall(sub(gas(), 2000), 0x2, add(mPtr, 0x1c), 0x24, mPtr, 0x20) //0x1b -> 000.."gamma"
        if eq(success, 0) {
          error_sha2_256()
        }
      }
      // alpha depends on the previous challenge (beta) and on the commitment to the grand product polynomial
      function derive_alpha(aproof, prev_challenge) {
        let mPtr := mload(0x40)
        // alpha
        mstore(mPtr, 0x616C706861) // "alpha"
        mstore(add(mPtr, 0x20), prev_challenge)
        mstore(add(mPtr, 0x40), mload(add(aproof, proof_grand_product_commitment_x)))
        mstore(add(mPtr, 0x60), mload(add(aproof, proof_grand_product_commitment_y)))
        let success := staticcall(sub(gas(), 2000), 0x2, add(mPtr, 0x1b), 0x65, mPtr, 0x20) //0x1b -> 000.."gamma"
        if eq(success, 0) {
          error_sha2_256()
        }
      }
      // zeta depends on the previous challenge (alpha) and on the commitment to the quotient polynomial
      function derive_zeta(aproof, prev_challenge) {
        let mPtr := mload(0x40)
        // zeta
        mstore(mPtr, 0x7a657461) // "zeta"
        mstore(add(mPtr, 0x20), prev_challenge)
        mstore(add(mPtr, 0x40), mload(add(aproof, proof_h_0_x)))
        mstore(add(mPtr, 0x60), mload(add(aproof, proof_h_0_y)))
        mstore(add(mPtr, 0x80), mload(add(aproof, proof_h_1_x)))
        mstore(add(mPtr, 0xa0), mload(add(aproof, proof_h_1_y)))
        mstore(add(mPtr, 0xc0), mload(add(aproof, proof_h_2_x)))
        mstore(add(mPtr, 0xe0), mload(add(aproof, proof_h_2_y)))
        let success := staticcall(sub(gas(), 2000), 0x2, add(mPtr, 0x1c), 0xe4, mPtr, 0x20)
        if eq(success, 0) {
          error_sha2_256()
        }
      }
    }
    return (gamma, beta, alpha, zeta);
  }
  // Computes L_i(zeta) =  ωⁱ/n * (ζⁿ-1)/(ζ-ωⁱ) where:
  // * n = vk_domain_size
  // * ω = vk_omega (generator of the multiplicative cyclic group of order n in (ℤ/rℤ)*)
  // * ζ = zeta (challenge derived with Fiat Shamir)
  function compute_ith_lagrange_at_z(uint256 zeta, uint256 i) internal view returns (uint256) {
    uint256 res;
    assembly {
      function error_pow_local() {
        let ptError := mload(0x40)
        mstore(ptError, error_string_id)
        mstore(add(ptError, 0x4), 0x20)
        mstore(add(ptError, 0x24), 0x17)
        mstore(add(ptError, 0x44), "error staticcall modexp")
        revert(ptError, 0x64)
      }
      // _n^_i [r]
      function pow_local(x, e) -> result {
        let mPtr := mload(0x40)
        mstore(mPtr, 0x20)
        mstore(add(mPtr, 0x20), 0x20)
        mstore(add(mPtr, 0x40), 0x20)
        mstore(add(mPtr, 0x60), x)
        mstore(add(mPtr, 0x80), e)
        mstore(add(mPtr, 0xa0), r_mod)
        let success := staticcall(sub(gas(), 2000), 0x05, mPtr, 0xc0, 0x00, 0x20)
        if eq(success, 0) {
          error_pow_local()
        }
        result := mload(0x00)
      }
      let w := pow_local(vk_omega, i) // w**i
      i := addmod(zeta, sub(r_mod, w), r_mod) // z-w**i
      zeta := pow_local(zeta, vk_domain_size) // z**n
      zeta := addmod(zeta, sub(r_mod, 1), r_mod) // z**n-1
      w := mulmod(w, vk_inv_domain_size, r_mod) // w**i/n
      i := pow_local(i, sub(r_mod, 2)) // (z-w**i)**-1
      w := mulmod(w, i, r_mod) // w**i/n*(z-w)**-1
      res := mulmod(w, zeta, r_mod)
    }
    return res;
  }
  function compute_pi(
    uint256[] memory public_inputs,
    uint256 zeta,
    bytes memory proof
  ) internal view returns (uint256) {
    // evaluation of Z=Xⁿ⁻¹ at ζ
    // uint256 zeta_power_n_minus_one = Fr.pow(zeta, vk_domain_size);
    // zeta_power_n_minus_one = Fr.sub(zeta_power_n_minus_one, 1);
    uint256 zeta_power_n_minus_one;
    uint256 pi;
    assembly {
      function error_pow() {
        let ptError := mload(0x40)
        mstore(ptError, error_string_id) // selector for function Error(string)
        mstore(add(ptError, 0x4), 0x20)
        mstore(add(ptError, 0x24), 0x17)
        mstore(add(ptError, 0x44), "error staticcall modexp")
        revert(ptError, 0x64)
      }
      sum_pi_wo_api_commit(add(public_inputs, 0x20), mload(public_inputs), zeta)
      pi := mload(mload(0x40))
      function sum_pi_wo_api_commit(ins, n, z) {
        let li := mload(0x40)
        batch_compute_lagranges_at_z(z, n, li)
        let res := 0
        let tmp := 0
        for {
          let i := 0
        } lt(i, n) {
          i := add(i, 1)
        } {
          tmp := mulmod(mload(li), mload(ins), r_mod)
          res := addmod(res, tmp, r_mod)
          li := add(li, 0x20)
          ins := add(ins, 0x20)
        }
        mstore(mload(0x40), res)
      }
      // mPtr <- [L_0(z), .., L_{n-1}(z)]
      //
      // Here L_i(zeta) =  ωⁱ/n * (ζⁿ-1)/(ζ-ωⁱ) where:
      // * n = vk_domain_size
      // * ω = vk_omega (generator of the multiplicative cyclic group of order n in (ℤ/rℤ)*)
      // * ζ = zeta (challenge derived with Fiat Shamir)
      function batch_compute_lagranges_at_z(z, n, mPtr) {
        let zn := addmod(pow(z, vk_domain_size, mPtr), sub(r_mod, 1), r_mod)
        zn := mulmod(zn, vk_inv_domain_size, r_mod)
        let _w := 1
        let _mPtr := mPtr
        for {
          let i := 0
        } lt(i, n) {
          i := add(i, 1)
        } {
          mstore(_mPtr, addmod(z, sub(r_mod, _w), r_mod))
          _w := mulmod(_w, vk_omega, r_mod)
          _mPtr := add(_mPtr, 0x20)
        }
        batch_invert(mPtr, n, _mPtr)
        _mPtr := mPtr
        _w := 1
        for {
          let i := 0
        } lt(i, n) {
          i := add(i, 1)
        } {
          mstore(_mPtr, mulmod(mulmod(mload(_mPtr), zn, r_mod), _w, r_mod))
          _mPtr := add(_mPtr, 0x20)
          _w := mulmod(_w, vk_omega, r_mod)
        }
      }
      // batch invert (modulo r) in place the nb_ins uint256 inputs starting at ins.
      function batch_invert(ins, nb_ins, mPtr) {
        mstore(mPtr, 1)
        let offset := 0
        for {
          let i := 0
        } lt(i, nb_ins) {
          i := add(i, 1)
        } {
          let prev := mload(add(mPtr, offset))
          let cur := mload(add(ins, offset))
          cur := mulmod(prev, cur, r_mod)
          offset := add(offset, 0x20)
          mstore(add(mPtr, offset), cur)
        }
        ins := add(ins, sub(offset, 0x20))
        mPtr := add(mPtr, offset)
        let inv := pow(mload(mPtr), sub(r_mod, 2), add(mPtr, 0x20))
        for {
          let i := 0
        } lt(i, nb_ins) {
          i := add(i, 1)
        } {
          mPtr := sub(mPtr, 0x20)
          let tmp := mload(ins)
          let cur := mulmod(inv, mload(mPtr), r_mod)
          mstore(ins, cur)
          inv := mulmod(inv, tmp, r_mod)
          ins := sub(ins, 0x20)
        }
      }
      // res <- x^e mod r
      function pow(x, e, mPtr) -> res {
        mstore(mPtr, 0x20)
        mstore(add(mPtr, 0x20), 0x20)
        mstore(add(mPtr, 0x40), 0x20)
        mstore(add(mPtr, 0x60), x)
        mstore(add(mPtr, 0x80), e)
        mstore(add(mPtr, 0xa0), r_mod)
        let success := staticcall(sub(gas(), 2000), 0x05, mPtr, 0xc0, mPtr, 0x20)
        if eq(success, 0) {
          error_pow()
        }
        res := mload(mPtr)
      }
      zeta_power_n_minus_one := pow(zeta, vk_domain_size, mload(0x40))
      zeta_power_n_minus_one := addmod(zeta_power_n_minus_one, sub(r_mod, 1), r_mod)
    }
    // compute the contribution of the public inputs whose indices are in commitment_indices,
    // and whose value is hash_fr of the corresponding commitme
    uint256[] memory commitment_indices = new uint256[](vk_nb_commitments_commit_api);
    load_vk_commitments_indices_commit_api(commitment_indices);
    uint256[] memory wire_committed_commitments;
    wire_committed_commitments = new uint256[](2 * vk_nb_commitments_commit_api);
    load_wire_commitments_commit_api(wire_committed_commitments, proof);
    for (uint256 i = 0; i < vk_nb_commitments_commit_api; i++) {
      uint256 hash_res = Utils.hash_fr(wire_committed_commitments[2 * i], wire_committed_commitments[2 * i + 1]);
      uint256 a = compute_ith_lagrange_at_z(zeta, commitment_indices[i] + public_inputs.length);
      assembly {
        a := mulmod(hash_res, a, r_mod)
        pi := addmod(pi, a, r_mod)
      }
    }
    return pi;
  }
  function check_inputs_size(uint256[] memory public_inputs) internal pure {
    bool input_checks = true;
    assembly {
      let s := mload(public_inputs)
      let p := add(public_inputs, 0x20)
      for {
        let i
      } lt(i, s) {
        i := add(i, 1)
      } {
        input_checks := and(input_checks, lt(mload(p), r_mod))
        p := add(p, 0x20)
      }
    }
    require(input_checks, "some inputs are bigger than r");
  }
  function check_proof_size(bytes memory proof) internal pure {
    uint256 expected_proof_size = 0x340 + vk_nb_commitments_commit_api * 0x60;
    uint256 actual_proof_size;
    assembly {
      actual_proof_size := mload(proof)
    }
    require(actual_proof_size == expected_proof_size, "wrong proof size");
  }
  function check_proof_openings_size(bytes memory proof) internal pure {
    bool openings_check = true;
    assembly {
      // linearised polynomial at zeta
      let p := add(proof, proof_linearised_polynomial_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))
      // quotient polynomial at zeta
      p := add(proof, proof_quotient_polynomial_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))
      // proof_l_at_zeta
      p := add(proof, proof_l_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))
      // proof_r_at_zeta
      p := add(proof, proof_r_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))
      // proof_o_at_zeta
      p := add(proof, proof_o_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))
      // proof_s1_at_zeta
      p := add(proof, proof_s1_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))
      // proof_s2_at_zeta
      p := add(proof, proof_s2_at_zeta)
      openings_check := and(openings_check, lt(mload(p), r_mod))
      // proof_grand_product_at_zeta_omega
      p := add(proof, proof_grand_product_at_zeta_omega)
      openings_check := and(openings_check, lt(mload(p), r_mod))
      // proof_openings_selector_commit_api_at_zeta
      p := add(proof, proof_openings_selector_commit_api_at_zeta)
      for {
        let i := 0
      } lt(i, vk_nb_commitments_commit_api) {
        i := add(i, 1)
      } {
        openings_check := and(openings_check, lt(mload(p), r_mod))
        p := add(p, 0x20)
      }
    }
    require(openings_check, "some openings are bigger than r");
  }
  function Verify(bytes memory proof, uint256[] memory public_inputs) public view returns (bool) {
    check_inputs_size(public_inputs);
    check_proof_size(proof);
    check_proof_openings_size(proof);
    uint256 gamma;
    uint256 beta;
    uint256 alpha;
    uint256 zeta;
    (gamma, beta, alpha, zeta) = derive_gamma_beta_alpha_zeta(proof, public_inputs);
    uint256 pi = compute_pi(public_inputs, zeta, proof);
    uint256 check;
    bool success = false;
    // uint256 success;
    assembly {
      let mem := mload(0x40)
      mstore(add(mem, state_alpha), alpha)
      mstore(add(mem, state_gamma), gamma)
      mstore(add(mem, state_zeta), zeta)
      mstore(add(mem, state_beta), beta)
      mstore(add(mem, state_pi), pi)
      compute_alpha_square_lagrange_0()
      verify_quotient_poly_eval_at_zeta(proof)
      fold_h(proof)
      compute_commitment_linearised_polynomial(proof)
      compute_gamma_kzg(proof)
      fold_state(proof)
      batch_verify_multi_points(proof)
      success := mload(add(mem, state_success))
      check := mload(add(mem, state_check_var))
      function error_verify() {
        let ptError := mload(0x40)
        mstore(ptError, error_string_id) // selector for function Error(string)
        mstore(add(ptError, 0x4), 0x20)
        mstore(add(ptError, 0x24), 0xc)
        mstore(add(ptError, 0x44), "error verify")
        revert(ptError, 0x64)
      }
      // compute α² * 1/n * (ζ{n}-1)/(ζ - 1) where
      // * α = challenge derived in derive_gamma_beta_alpha_zeta
      // * n = vk_domain_size
      // * ω = vk_omega (generator of the multiplicative cyclic group of order n in (ℤ/rℤ)*)
      // * ζ = zeta (challenge derived with Fiat Shamir)
      function compute_alpha_square_lagrange_0() {
        let state := mload(0x40)
        let mPtr := add(mload(0x40), state_last_mem)
        // zeta**n - 1
        let res := pow(mload(add(state, state_zeta)), vk_domain_size, mPtr)
        res := addmod(res, sub(r_mod, 1), r_mod)
        mstore(add(state, state_zeta_power_n_minus_one), res)
        // let res := mload(add(state, state_zeta_power_n_minus_one))
        let den := addmod(mload(add(state, state_zeta)), sub(r_mod, 1), r_mod)
        den := pow(den, sub(r_mod, 2), mPtr)
        den := mulmod(den, vk_inv_domain_size, r_mod)
        res := mulmod(den, res, r_mod)
        let l_alpha := mload(add(state, state_alpha))
        res := mulmod(res, l_alpha, r_mod)
        res := mulmod(res, l_alpha, r_mod)
        mstore(add(state, state_alpha_square_lagrange_0), res)
      }
      // follows alg. p.13 of https://eprint.iacr.org/2019/953.pdf
      // with t₁ = t₂ = 1, and the proofs are ([digest] + [quotient] +purported evaluation):
      // * [state_folded_state_digests], [proof_batch_opening_at_zeta_x], state_folded_evals
      // * [proof_grand_product_commitment], [proof_opening_at_zeta_omega_x], [proof_grand_product_at_zeta_omega]
      function batch_verify_multi_points(aproof) {
        let state := mload(0x40)
        let mPtr := add(state, state_last_mem)
        // here the random is not a challenge, hence no need to use Fiat Shamir, we just
        // need an unpredictible result.
        let random := mod(keccak256(state, 0x20), r_mod)
        let folded_quotients := mPtr
        mPtr := add(folded_quotients, 0x40)
        mstore(folded_quotients, mload(add(aproof, proof_batch_opening_at_zeta_x)))
        mstore(add(folded_quotients, 0x20), mload(add(aproof, proof_batch_opening_at_zeta_y)))
        point_acc_mul(folded_quotients, add(aproof, proof_opening_at_zeta_omega_x), random, mPtr)
        let folded_digests := add(state, state_folded_digests_x)
        point_acc_mul(folded_digests, add(aproof, proof_grand_product_commitment_x), random, mPtr)
        let folded_evals := add(state, state_folded_claimed_values)
        fr_acc_mul(folded_evals, add(aproof, proof_grand_product_at_zeta_omega), random)
        let folded_evals_commit := mPtr
        mPtr := add(folded_evals_commit, 0x40)
        mstore(folded_evals_commit, 14312776538779914388377568895031746459131577658076416373430523308756343304251)
        mstore(
          add(folded_evals_commit, 0x20),
          11763105256161367503191792604679297387056316997144156930871823008787082098465
        )
        mstore(add(folded_evals_commit, 0x40), mload(folded_evals))
        let check_staticcall := staticcall(sub(gas(), 2000), 7, folded_evals_commit, 0x60, folded_evals_commit, 0x40)
        if eq(check_staticcall, 0) {
          error_verify()
        }
        let folded_evals_commit_y := add(folded_evals_commit, 0x20)
        mstore(folded_evals_commit_y, sub(p_mod, mload(folded_evals_commit_y)))
        point_add(folded_digests, folded_digests, folded_evals_commit, mPtr)
        let folded_points_quotients := mPtr
        mPtr := add(mPtr, 0x40)
        point_mul(
          folded_points_quotients,
          add(aproof, proof_batch_opening_at_zeta_x),
          mload(add(state, state_zeta)),
          mPtr
        )
        let zeta_omega := mulmod(mload(add(state, state_zeta)), vk_omega, r_mod)
        random := mulmod(random, zeta_omega, r_mod)
        point_acc_mul(folded_points_quotients, add(aproof, proof_opening_at_zeta_omega_x), random, mPtr)
        point_add(folded_digests, folded_digests, folded_points_quotients, mPtr)
        let folded_quotients_y := add(folded_quotients, 0x20)
        mstore(folded_quotients_y, sub(p_mod, mload(folded_quotients_y)))
        mstore(mPtr, mload(folded_digests))
        mstore(add(mPtr, 0x20), mload(add(folded_digests, 0x20)))
        mstore(add(mPtr, 0x40), g2_srs_0_x_0) // the 4 lines are the canonical G2 point on BN254
        mstore(add(mPtr, 0x60), g2_srs_0_x_1)
        mstore(add(mPtr, 0x80), g2_srs_0_y_0)
        mstore(add(mPtr, 0xa0), g2_srs_0_y_1)
        mstore(add(mPtr, 0xc0), mload(folded_quotients))
        mstore(add(mPtr, 0xe0), mload(add(folded_quotients, 0x20)))
        mstore(add(mPtr, 0x100), g2_srs_1_x_0)
        mstore(add(mPtr, 0x120), g2_srs_1_x_1)
        mstore(add(mPtr, 0x140), g2_srs_1_y_0)
        mstore(add(mPtr, 0x160), g2_srs_1_y_1)
        check_pairing_kzg(mPtr)
      }
      // check_pairing_kzg checks the result of the final pairing product of the batched
      // kzg verification. The purpose of this function is too avoid exhausting the stack
      // in the function batch_verify_multi_points.
      // mPtr: pointer storing the tuple of pairs
      function check_pairing_kzg(mPtr) {
        let state := mload(0x40)
        // TODO test the staticcall using the method from audit_4-5
        let l_success := staticcall(sub(gas(), 2000), 8, mPtr, 0x180, 0x00, 0x20)
        let res_pairing := mload(0x00)
        let s_success := mload(add(state, state_success))
        res_pairing := and(and(res_pairing, l_success), s_success)
        mstore(add(state, state_success), res_pairing)
      }
      // Fold the opening proofs at ζ:
      // * at state+state_folded_digest we store: [H] + γ[Linearised_polynomial]+γ²[L] + γ³[R] + γ⁴[O] + γ⁵[S₁] +γ⁶[S₂] + ∑ᵢγ⁶⁺ⁱ[Pi_{i}]
      // * at state+state_folded_claimed_values we store: H(ζ) + γLinearised_polynomial(ζ)+γ²L(ζ) + γ³R(ζ)+ γ⁴O(ζ) + γ⁵S₁(ζ) +γ⁶S₂(ζ) + ∑ᵢγ⁶⁺ⁱPi_{i}(ζ)
      // acc_gamma stores the γⁱ
      function fold_state(aproof) {
        let state := mload(0x40)
        let mPtr := add(mload(0x40), state_last_mem)
        let l_gamma_kzg := mload(add(state, state_gamma_kzg))
        let acc_gamma := l_gamma_kzg
        let offset := add(0x200, mul(vk_nb_commitments_commit_api, 0x40)) // 0x40 = 2*0x20
        let mPtrOffset := add(mPtr, offset)
        mstore(add(state, state_folded_digests_x), mload(add(mPtr, 0x40)))
        mstore(add(state, state_folded_digests_y), mload(add(mPtr, 0x60)))
        mstore(add(state, state_folded_claimed_values), mload(add(aproof, proof_quotient_polynomial_at_zeta)))
        point_acc_mul(add(state, state_folded_digests_x), add(mPtr, 0x80), acc_gamma, mPtrOffset)
        fr_acc_mul(add(state, state_folded_claimed_values), add(aproof, proof_linearised_polynomial_at_zeta), acc_gamma)
        mstore(add(state, state_check_var), acc_gamma)
        acc_gamma := mulmod(acc_gamma, l_gamma_kzg, r_mod)
        point_acc_mul(add(state, state_folded_digests_x), add(mPtr, 0xc0), acc_gamma, mPtrOffset)
        fr_acc_mul(add(state, state_folded_claimed_values), add(aproof, proof_l_at_zeta), acc_gamma)
        acc_gamma := mulmod(acc_gamma, l_gamma_kzg, r_mod)
        point_acc_mul(add(state, state_folded_digests_x), add(mPtr, 0x100), acc_gamma, add(mPtr, offset))
        fr_acc_mul(add(state, state_folded_claimed_values), add(aproof, proof_r_at_zeta), acc_gamma)
        acc_gamma := mulmod(acc_gamma, l_gamma_kzg, r_mod)
        point_acc_mul(add(state, state_folded_digests_x), add(mPtr, 0x140), acc_gamma, add(mPtr, offset))
        fr_acc_mul(add(state, state_folded_claimed_values), add(aproof, proof_o_at_zeta), acc_gamma)
        acc_gamma := mulmod(acc_gamma, l_gamma_kzg, r_mod)
        point_acc_mul(add(state, state_folded_digests_x), add(mPtr, 0x180), acc_gamma, add(mPtr, offset))
        fr_acc_mul(add(state, state_folded_claimed_values), add(aproof, proof_s1_at_zeta), acc_gamma)
        acc_gamma := mulmod(acc_gamma, l_gamma_kzg, r_mod)
        point_acc_mul(add(state, state_folded_digests_x), add(mPtr, 0x1c0), acc_gamma, add(mPtr, offset))
        fr_acc_mul(add(state, state_folded_claimed_values), add(aproof, proof_s2_at_zeta), acc_gamma)
        let poscaz := add(aproof, proof_openings_selector_commit_api_at_zeta)
        let opca := add(mPtr, 0x200) // offset_proof_commits_api
        for {
          let i := 0
        } lt(i, vk_nb_commitments_commit_api) {
          i := add(i, 1)
        } {
          acc_gamma := mulmod(acc_gamma, l_gamma_kzg, r_mod)
          point_acc_mul(add(state, state_folded_digests_x), opca, acc_gamma, add(mPtr, offset))
          fr_acc_mul(add(state, state_folded_claimed_values), poscaz, acc_gamma)
          poscaz := add(poscaz, 0x20)
          opca := add(opca, 0x40)
        }
      }
      // generate the challenge (using Fiat Shamir) to fold the opening proofs
      // at ζ.
      // The process for deriving γ is the same as in derive_gamma but this time the inputs are
      // in this order (the [] means it's a commitment):
      // * ζ
      // * [H] ( = H₁ + ζᵐ⁺²*H₂ + ζ²⁽ᵐ⁺²⁾*H₃ )
      // * [Linearised polynomial]
      // * [L], [R], [O]
      // * [S₁] [S₂]
      // * [Pi_{i}] (wires associated to custom gates)
      // Then there are the purported evaluations of the previous committed polynomials:
      // * H(ζ)
      // * Linearised_polynomial(ζ)
      // * L(ζ), R(ζ), O(ζ), S₁(ζ), S₂(ζ)
      // * Pi_{i}(ζ)
      function compute_gamma_kzg(aproof) {
        let state := mload(0x40)
        let mPtr := add(mload(0x40), state_last_mem)
        mstore(mPtr, 0x67616d6d61) // "gamma"
        mstore(add(mPtr, 0x20), mload(add(state, state_zeta)))
        mstore(add(mPtr, 0x40), mload(add(state, state_folded_h_x)))
        mstore(add(mPtr, 0x60), mload(add(state, state_folded_h_y)))
        mstore(add(mPtr, 0x80), mload(add(state, state_linearised_polynomial_x)))
        mstore(add(mPtr, 0xa0), mload(add(state, state_linearised_polynomial_y)))
        mstore(add(mPtr, 0xc0), mload(add(aproof, proof_l_com_x)))
        mstore(add(mPtr, 0xe0), mload(add(aproof, proof_l_com_y)))
        mstore(add(mPtr, 0x100), mload(add(aproof, proof_r_com_x)))
        mstore(add(mPtr, 0x120), mload(add(aproof, proof_r_com_y)))
        mstore(add(mPtr, 0x140), mload(add(aproof, proof_o_com_x)))
        mstore(add(mPtr, 0x160), mload(add(aproof, proof_o_com_y)))
        mstore(add(mPtr, 0x180), vk_s1_com_x)
        mstore(add(mPtr, 0x1a0), vk_s1_com_y)
        mstore(add(mPtr, 0x1c0), vk_s2_com_x)
        mstore(add(mPtr, 0x1e0), vk_s2_com_y)
        let offset := 0x200
        mstore(add(mPtr, offset), vk_selector_commitments_commit_api_0_x)
        mstore(add(mPtr, add(offset, 0x20)), vk_selector_commitments_commit_api_0_y)
        offset := add(offset, 0x40)
        mstore(add(mPtr, offset), vk_selector_commitments_commit_api_1_x)
        mstore(add(mPtr, add(offset, 0x20)), vk_selector_commitments_commit_api_1_y)
        offset := add(offset, 0x40)
        mstore(add(mPtr, offset), vk_selector_commitments_commit_api_2_x)
        mstore(add(mPtr, add(offset, 0x20)), vk_selector_commitments_commit_api_2_y)
        offset := add(offset, 0x40)
        mstore(add(mPtr, offset), mload(add(aproof, proof_quotient_polynomial_at_zeta)))
        mstore(add(mPtr, add(offset, 0x20)), mload(add(aproof, proof_linearised_polynomial_at_zeta)))
        mstore(add(mPtr, add(offset, 0x40)), mload(add(aproof, proof_l_at_zeta)))
        mstore(add(mPtr, add(offset, 0x60)), mload(add(aproof, proof_r_at_zeta)))
        mstore(add(mPtr, add(offset, 0x80)), mload(add(aproof, proof_o_at_zeta)))
        mstore(add(mPtr, add(offset, 0xa0)), mload(add(aproof, proof_s1_at_zeta)))
        mstore(add(mPtr, add(offset, 0xc0)), mload(add(aproof, proof_s2_at_zeta)))
        let _mPtr := add(mPtr, add(offset, 0xe0))
        let _poscaz := add(aproof, proof_openings_selector_commit_api_at_zeta)
        for {
          let i := 0
        } lt(i, vk_nb_commitments_commit_api) {
          i := add(i, 1)
        } {
          mstore(_mPtr, mload(_poscaz))
          _poscaz := add(_poscaz, 0x20)
          _mPtr := add(_mPtr, 0x20)
        }
        let start_input := 0x1b // 00.."gamma"
        let size_input := add(0x16, mul(vk_nb_commitments_commit_api, 3)) // number of 32bytes elmts = 0x16 (zeta+2*7+7 for the digests+openings) + 2*vk_nb_commitments_commit_api (for the commitments of the selectors) + vk_nb_commitments_commit_api (for the openings of the selectors)
        size_input := add(0x5, mul(size_input, 0x20)) // size in bytes: 15*32 bytes + 5 bytes for gamma
        let check_staticcall := staticcall(
          sub(gas(), 2000),
          0x2,
          add(mPtr, start_input),
          size_input,
          add(state, state_gamma_kzg),
          0x20
        )
        if eq(check_staticcall, 0) {
          error_verify()
        }
        mstore(add(state, state_gamma_kzg), mod(mload(add(state, state_gamma_kzg)), r_mod))
      }
      function compute_commitment_linearised_polynomial_ec(aproof, s1, s2) {
        let state := mload(0x40)
        let mPtr := add(mload(0x40), state_last_mem)
        mstore(mPtr, vk_ql_com_x)
        mstore(add(mPtr, 0x20), vk_ql_com_y)
        point_mul(add(state, state_linearised_polynomial_x), mPtr, mload(add(aproof, proof_l_at_zeta)), add(mPtr, 0x40))
        mstore(mPtr, vk_qr_com_x)
        mstore(add(mPtr, 0x20), vk_qr_com_y)
        point_acc_mul(
          add(state, state_linearised_polynomial_x),
          mPtr,
          mload(add(aproof, proof_r_at_zeta)),
          add(mPtr, 0x40)
        )
        let rl := mulmod(mload(add(aproof, proof_l_at_zeta)), mload(add(aproof, proof_r_at_zeta)), r_mod)
        mstore(mPtr, vk_qm_com_x)
        mstore(add(mPtr, 0x20), vk_qm_com_y)
        point_acc_mul(add(state, state_linearised_polynomial_x), mPtr, rl, add(mPtr, 0x40))
        mstore(mPtr, vk_qo_com_x)
        mstore(add(mPtr, 0x20), vk_qo_com_y)
        point_acc_mul(
          add(state, state_linearised_polynomial_x),
          mPtr,
          mload(add(aproof, proof_o_at_zeta)),
          add(mPtr, 0x40)
        )
        mstore(mPtr, vk_qk_com_x)
        mstore(add(mPtr, 0x20), vk_qk_com_y)
        point_add(
          add(state, state_linearised_polynomial_x),
          add(state, state_linearised_polynomial_x),
          mPtr,
          add(mPtr, 0x40)
        )
        let commits_api_at_zeta := add(aproof, proof_openings_selector_commit_api_at_zeta)
        let commits_api := add(
          aproof,
          add(proof_openings_selector_commit_api_at_zeta, mul(vk_nb_commitments_commit_api, 0x20))
        )
        for {
          let i := 0
        } lt(i, vk_nb_commitments_commit_api) {
          i := add(i, 1)
        } {
          mstore(mPtr, mload(commits_api))
          mstore(add(mPtr, 0x20), mload(add(commits_api, 0x20)))
          point_acc_mul(add(state, state_linearised_polynomial_x), mPtr, mload(commits_api_at_zeta), add(mPtr, 0x40))
          commits_api_at_zeta := add(commits_api_at_zeta, 0x20)
          commits_api := add(commits_api, 0x40)
        }
        mstore(mPtr, vk_s3_com_x)
        mstore(add(mPtr, 0x20), vk_s3_com_y)
        point_acc_mul(add(state, state_linearised_polynomial_x), mPtr, s1, add(mPtr, 0x40))
        mstore(mPtr, mload(add(aproof, proof_grand_product_commitment_x)))
        mstore(add(mPtr, 0x20), mload(add(aproof, proof_grand_product_commitment_y)))
        point_acc_mul(add(state, state_linearised_polynomial_x), mPtr, s2, add(mPtr, 0x40))
      }
      // Compute the commitment to the linearized polynomial equal to
      //\tL(ζ)[Qₗ]+r(ζ)[Qᵣ]+R(ζ)L(ζ)[Qₘ]+O(ζ)[Qₒ]+[Qₖ]+Σᵢqc'ᵢ(ζ)[BsbCommitmentᵢ] +
      //\tα*( Z(μζ)(L(ζ)+β*S₁(ζ)+γ)*(R(ζ)+β*S₂(ζ)+γ)[S₃]-[Z](L(ζ)+β*id_{1}(ζ)+γ)*(R(ζ)+β*id_{2(ζ)+γ)*(O(ζ)+β*id_{3}(ζ)+γ) ) +
      //\tα²*L₁(ζ)[Z]
      // where
      // * id_1 = id, id_2 = vk_coset_shift*id, id_3 = vk_coset_shift^{2}*id
      // * the [] means that it's a commitment (i.e. a point on Bn254(F_p))
      function compute_commitment_linearised_polynomial(aproof) {
        let state := mload(0x40)
        let l_beta := mload(add(state, state_beta))
        let l_gamma := mload(add(state, state_gamma))
        let l_zeta := mload(add(state, state_zeta))
        let l_alpha := mload(add(state, state_alpha))
        let u := mulmod(mload(add(aproof, proof_grand_product_at_zeta_omega)), l_beta, r_mod)
        let v := mulmod(l_beta, mload(add(aproof, proof_s1_at_zeta)), r_mod)
        v := addmod(v, mload(add(aproof, proof_l_at_zeta)), r_mod)
        v := addmod(v, l_gamma, r_mod)
        let w := mulmod(l_beta, mload(add(aproof, proof_s2_at_zeta)), r_mod)
        w := addmod(w, mload(add(aproof, proof_r_at_zeta)), r_mod)
        w := addmod(w, l_gamma, r_mod)
        let s1 := mulmod(u, v, r_mod)
        s1 := mulmod(s1, w, r_mod)
        s1 := mulmod(s1, l_alpha, r_mod)
        let coset_square := mulmod(vk_coset_shift, vk_coset_shift, r_mod)
        let betazeta := mulmod(l_beta, l_zeta, r_mod)
        u := addmod(betazeta, mload(add(aproof, proof_l_at_zeta)), r_mod)
        u := addmod(u, l_gamma, r_mod)
        v := mulmod(betazeta, vk_coset_shift, r_mod)
        v := addmod(v, mload(add(aproof, proof_r_at_zeta)), r_mod)
        v := addmod(v, l_gamma, r_mod)
        w := mulmod(betazeta, coset_square, r_mod)
        w := addmod(w, mload(add(aproof, proof_o_at_zeta)), r_mod)
        w := addmod(w, l_gamma, r_mod)
        let s2 := mulmod(u, v, r_mod)
        s2 := mulmod(s2, w, r_mod)
        s2 := sub(r_mod, s2)
        s2 := mulmod(s2, l_alpha, r_mod)
        s2 := addmod(s2, mload(add(state, state_alpha_square_lagrange_0)), r_mod)
        // at this stage:
        // * s₁ = α*Z(μζ)(l(ζ)+β*s₁(ζ)+γ)*(r(ζ)+β*s₂(ζ)+γ)*β
        // * s₂ = -α*(l(ζ)+β*ζ+γ)*(r(ζ)+β*u*ζ+γ)*(o(ζ)+β*u²*ζ+γ) + α²*L₁(ζ)
        compute_commitment_linearised_polynomial_ec(aproof, s1, s2)
      }
      // compute H₁ + ζᵐ⁺²*H₂ + ζ²⁽ᵐ⁺²⁾*H₃ and store the result at
      // state + state_folded_h
      function fold_h(aproof) {
        let state := mload(0x40)
        let n_plus_two := add(vk_domain_size, 2)
        let mPtr := add(mload(0x40), state_last_mem)
        let zeta_power_n_plus_two := pow(mload(add(state, state_zeta)), n_plus_two, mPtr)
        point_mul(add(state, state_folded_h_x), add(aproof, proof_h_2_x), zeta_power_n_plus_two, mPtr)
        point_add(add(state, state_folded_h_x), add(state, state_folded_h_x), add(aproof, proof_h_1_x), mPtr)
        point_mul(add(state, state_folded_h_x), add(state, state_folded_h_x), zeta_power_n_plus_two, mPtr)
        point_add(add(state, state_folded_h_x), add(state, state_folded_h_x), add(aproof, proof_h_0_x), mPtr)
      }
      // check that
      //\tL(ζ)Qₗ(ζ)+r(ζ)Qᵣ(ζ)+R(ζ)L(ζ)Qₘ(ζ)+O(ζ)Qₒ(ζ)+Qₖ(ζ)+Σᵢqc'ᵢ(ζ)BsbCommitmentᵢ(ζ) +
      //  α*( Z(μζ)(l(ζ)+β*s₁(ζ)+γ)*(r(ζ)+β*s₂(ζ)+γ)*β*s₃(X)-Z(X)(l(ζ)+β*id_1(ζ)+γ)*(r(ζ)+β*id_2(ζ)+γ)*(o(ζ)+β*id_3(ζ)+γ) ) )
      // + α²*L₁(ζ) =
      // (ζⁿ-1)H(ζ)
      function verify_quotient_poly_eval_at_zeta(aproof) {
        let state := mload(0x40)
        // (l(ζ)+β*s1(ζ)+γ)
        let s1 := add(mload(0x40), state_last_mem)
        mstore(s1, mulmod(mload(add(aproof, proof_s1_at_zeta)), mload(add(state, state_beta)), r_mod))
        mstore(s1, addmod(mload(s1), mload(add(state, state_gamma)), r_mod))
        mstore(s1, addmod(mload(s1), mload(add(aproof, proof_l_at_zeta)), r_mod))
        // (r(ζ)+β*s2(ζ)+γ)
        let s2 := add(s1, 0x20)
        mstore(s2, mulmod(mload(add(aproof, proof_s2_at_zeta)), mload(add(state, state_beta)), r_mod))
        mstore(s2, addmod(mload(s2), mload(add(state, state_gamma)), r_mod))
        mstore(s2, addmod(mload(s2), mload(add(aproof, proof_r_at_zeta)), r_mod))
        // _s2 := mload(s2)
        // (o(ζ)+γ)
        let o := add(s1, 0x40)
        mstore(o, addmod(mload(add(aproof, proof_o_at_zeta)), mload(add(state, state_gamma)), r_mod))
        //  α*(Z(μζ))*(l(ζ)+β*s1(ζ)+γ)*(r(ζ)+β*s2(ζ)+γ)*(o(ζ)+γ)
        mstore(s1, mulmod(mload(s1), mload(s2), r_mod))
        mstore(s1, mulmod(mload(s1), mload(o), r_mod))
        mstore(s1, mulmod(mload(s1), mload(add(state, state_alpha)), r_mod))
        mstore(s1, mulmod(mload(s1), mload(add(aproof, proof_grand_product_at_zeta_omega)), r_mod))
        let computed_quotient := add(s1, 0x60)
        // linearizedpolynomial + pi(zeta)
        mstore(
          computed_quotient,
          addmod(mload(add(aproof, proof_linearised_polynomial_at_zeta)), mload(add(state, state_pi)), r_mod)
        )
        mstore(computed_quotient, addmod(mload(computed_quotient), mload(s1), r_mod))
        mstore(
          computed_quotient,
          addmod(mload(computed_quotient), sub(r_mod, mload(add(state, state_alpha_square_lagrange_0))), r_mod)
        )
        mstore(
          s2,
          mulmod(
            mload(add(aproof, proof_quotient_polynomial_at_zeta)),
            mload(add(state, state_zeta_power_n_minus_one)),
            r_mod
          )
        )
        mstore(add(state, state_success), eq(mload(computed_quotient), mload(s2)))
      }
      function point_add(dst, p, q, mPtr) {
        // let mPtr := add(mload(0x40), state_last_mem)
        let state := mload(0x40)
        mstore(mPtr, mload(p))
        mstore(add(mPtr, 0x20), mload(add(p, 0x20)))
        mstore(add(mPtr, 0x40), mload(q))
        mstore(add(mPtr, 0x60), mload(add(q, 0x20)))
        let l_success := staticcall(sub(gas(), 2000), 6, mPtr, 0x80, dst, 0x40)
        mstore(add(state, state_success), and(l_success, mload(add(state, state_success))))
      }
      // dst <- [s]src
      function point_mul(dst, src, s, mPtr) {
        // let mPtr := add(mload(0x40), state_last_mem)
        let state := mload(0x40)
        mstore(mPtr, mload(src))
        mstore(add(mPtr, 0x20), mload(add(src, 0x20)))
        mstore(add(mPtr, 0x40), s)
        let l_success := staticcall(sub(gas(), 2000), 7, mPtr, 0x60, dst, 0x40)
        mstore(add(state, state_success), and(l_success, mload(add(state, state_success))))
      }
      // dst <- dst + [s]src (Elliptic curve)
      function point_acc_mul(dst, src, s, mPtr) {
        let state := mload(0x40)
        mstore(mPtr, mload(src))
        mstore(add(mPtr, 0x20), mload(add(src, 0x20)))
        mstore(add(mPtr, 0x40), s)
        let l_success := staticcall(sub(gas(), 2000), 7, mPtr, 0x60, mPtr, 0x40)
        mstore(add(mPtr, 0x40), mload(dst))
        mstore(add(mPtr, 0x60), mload(add(dst, 0x20)))
        l_success := and(l_success, staticcall(sub(gas(), 2000), 6, mPtr, 0x80, dst, 0x40))
        mstore(add(state, state_success), and(l_success, mload(add(state, state_success))))
      }
      // dst <- dst + src (Fr) dst,src are addresses, s is a value
      function fr_acc_mul(dst, src, s) {
        let tmp := mulmod(mload(src), s, r_mod)
        mstore(dst, addmod(mload(dst), tmp, r_mod))
      }
      // dst <- x ** e mod r (x, e are values, not pointers)
      function pow(x, e, mPtr) -> res {
        mstore(mPtr, 0x20)
        mstore(add(mPtr, 0x20), 0x20)
        mstore(add(mPtr, 0x40), 0x20)
        mstore(add(mPtr, 0x60), x)
        mstore(add(mPtr, 0x80), e)
        mstore(add(mPtr, 0xa0), r_mod)
        let check_staticcall := staticcall(sub(gas(), 2000), 0x05, mPtr, 0xc0, mPtr, 0x20)
        if eq(check_staticcall, 0) {
          error_verify()
        }
        res := mload(mPtr)
      }
    }
    return success;
  }
}
// SPDX-License-Identifier: AGPL-3.0
// It has not been audited and is provided as-is, we make no guarantees or warranties to its safety and reliability.
//
// According to https://eprint.iacr.org/archive/2019/953/1585767119.pdf
pragma solidity ^0.8.19;
library Utils {
  uint256 private constant r_mod = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
  /**
   * @dev ExpandMsgXmd expands msg to a slice of lenInBytes bytes.
   *      https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-5
   *      https://tools.ietf.org/html/rfc8017#section-4.1 (I2OSP/O2ISP)
   */
  function expand_msg(uint256 x, uint256 y) public pure returns (uint8[48] memory res) {
    string memory dst = "BSB22-Plonk";
    //uint8[64] memory pad; // 64 is sha256 block size.
    // sha256(pad || msg || (0 || 48 || 0) || dst || 11)
    bytes memory tmp;
    uint8 zero = 0;
    uint8 lenInBytes = 48;
    uint8 sizeDomain = 11; // size of dst
    for (uint i = 0; i < 64; i++) {
      tmp = abi.encodePacked(tmp, zero);
    }
    tmp = abi.encodePacked(tmp, x, y, zero, lenInBytes, zero, dst, sizeDomain);
    bytes32 b0 = sha256(tmp);
    tmp = abi.encodePacked(b0, uint8(1), dst, sizeDomain);
    bytes32 b1 = sha256(tmp);
    for (uint i = 0; i < 32; i++) {
      res[i] = uint8(b1[i]);
    }
    tmp = abi.encodePacked(uint8(b0[0]) ^ uint8(b1[0]));
    for (uint i = 1; i < 32; i++) {
      tmp = abi.encodePacked(tmp, uint8(b0[i]) ^ uint8(b1[i]));
    }
    tmp = abi.encodePacked(tmp, uint8(2), dst, sizeDomain);
    b1 = sha256(tmp);
    // TODO handle the size of the dst (check gnark-crypto)
    for (uint i = 0; i < 16; i++) {
      res[i + 32] = uint8(b1[i]);
    }
    return res;
  }
  /**
   * @dev cf https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-5.2
   * corresponds to https://github.com/ConsenSys/gnark-crypto/blob/develop/ecc/bn254/fr/element.go
   */
  function hash_fr(uint256 x, uint256 y) internal pure returns (uint256 res) {
    // interpret a as a bigEndian integer and reduce it mod r
    uint8[48] memory xmsg = expand_msg(x, y);
    // uint8[48] memory xmsg = [0x44, 0x74, 0xb5, 0x29, 0xd7, 0xfb, 0x29, 0x88, 0x3a, 0x7a, 0xc1, 0x65, 0xfd, 0x72, 0xce, 0xd0, 0xd4, 0xd1, 0x3f, 0x9e, 0x85, 0x8a, 0x3, 0x86, 0x1c, 0x90, 0x83, 0x1e, 0x94, 0xdc, 0xfc, 0x1d, 0x70, 0x82, 0xf5, 0xbf, 0x30, 0x3, 0x39, 0x87, 0x21, 0x38, 0x15, 0xed, 0x12, 0x75, 0x44, 0x6a];
    // reduce xmsg mod r, where xmsg is intrepreted in big endian
    // (as SetBytes does for golang's Big.Int library).
    for (uint i = 0; i < 32; i++) {
      res += uint256(xmsg[47 - i]) << (8 * i);
    }
    res = res % r_mod;
    uint256 tmp;
    for (uint i = 0; i < 16; i++) {
      tmp += uint256(xmsg[15 - i]) << (8 * i);
    }
    // 2**256%r
    uint256 b = 6350874878119819312338956282401532410528162663560392320966563075034087161851;
    assembly {
      tmp := mulmod(tmp, b, r_mod)
      res := addmod(res, tmp, r_mod)
    }
    return res;
  }
}