// SPDX-License-Identifier: MIT
pragma solidity 0.8.13;

/// @title ClonesWithImmutableArgs
/// @author wighawag, zefram.eth
/// @notice Enables creating clone contracts with immutable args
library ClonesWithImmutableArgs {
    error CreateFail();

    /// @notice Creates a clone proxy of the implementation contract, with immutable args
    /// @dev data cannot exceed 65535 bytes, since 2 bytes are used to store the data length
    /// @param implementation The implementation contract to clone
    /// @param data Encoded immutable args
    /// @return instance The address of the created clone
    function clone(address implementation, bytes memory data)
        internal
        returns (address payable instance)
    {
        // unrealistic for memory ptr or data length to exceed 256 bits
        unchecked {
            uint256 extraLength = data.length + 2; // +2 bytes for telling how much data there is appended to the call
            uint256 creationSize = 0x41 + extraLength;
            uint256 runSize = creationSize - 10;
            uint256 dataPtr;
            uint256 ptr;
            // solhint-disable-next-line no-inline-assembly
            assembly {
                ptr := mload(0x40)

                // -------------------------------------------------------------------------------------------------------------
                // CREATION (10 bytes)
                // -------------------------------------------------------------------------------------------------------------

                // 61 runtime  | PUSH2 runtime (r)     | r                       | –
                mstore(
                    ptr,
                    0x6100000000000000000000000000000000000000000000000000000000000000
                )
                mstore(add(ptr, 0x01), shl(240, runSize)) // size of the contract running bytecode (16 bits)

                // creation size = 0a
                // 3d          | RETURNDATASIZE        | 0 r                     | –
                // 81          | DUP2                  | r 0 r                   | –
                // 60 creation | PUSH1 creation (c)    | c r 0 r                 | –
                // 3d          | RETURNDATASIZE        | 0 c r 0 r               | –
                // 39          | CODECOPY              | 0 r                     | [0-runSize): runtime code
                // f3          | RETURN                |                         | [0-runSize): runtime code

                // -------------------------------------------------------------------------------------------------------------
                // RUNTIME (55 bytes + extraLength)
                // -------------------------------------------------------------------------------------------------------------

                // 3d          | RETURNDATASIZE        | 0                       | –
                // 3d          | RETURNDATASIZE        | 0 0                     | –
                // 3d          | RETURNDATASIZE        | 0 0 0                   | –
                // 3d          | RETURNDATASIZE        | 0 0 0 0                 | –
                // 36          | CALLDATASIZE          | cds 0 0 0 0             | –
                // 3d          | RETURNDATASIZE        | 0 cds 0 0 0 0           | –
                // 3d          | RETURNDATASIZE        | 0 0 cds 0 0 0 0         | –
                // 37          | CALLDATACOPY          | 0 0 0 0                 | [0, cds) = calldata
                // 61          | PUSH2 extra           | extra 0 0 0 0           | [0, cds) = calldata
                mstore(
                    add(ptr, 0x03),
                    0x3d81600a3d39f33d3d3d3d363d3d376100000000000000000000000000000000
                )
                mstore(add(ptr, 0x13), shl(240, extraLength))

                // 60 0x37     | PUSH1 0x37            | 0x37 extra 0 0 0 0      | [0, cds) = calldata // 0x37 (55) is runtime size - data
                // 36          | CALLDATASIZE          | cds 0x37 extra 0 0 0 0  | [0, cds) = calldata
                // 39          | CODECOPY              | 0 0 0 0                 | [0, cds) = calldata, [cds, cds+0x37) = extraData
                // 36          | CALLDATASIZE          | cds 0 0 0 0             | [0, cds) = calldata, [cds, cds+0x37) = extraData
                // 61 extra    | PUSH2 extra           | extra cds 0 0 0 0       | [0, cds) = calldata, [cds, cds+0x37) = extraData
                mstore(
                    add(ptr, 0x15),
                    0x6037363936610000000000000000000000000000000000000000000000000000
                )
                mstore(add(ptr, 0x1b), shl(240, extraLength))

                // 01          | ADD                   | cds+extra 0 0 0 0       | [0, cds) = calldata, [cds, cds+0x37) = extraData
                // 3d          | RETURNDATASIZE        | 0 cds 0 0 0 0           | [0, cds) = calldata, [cds, cds+0x37) = extraData
                // 73 addr     | PUSH20 0x123…         | addr 0 cds 0 0 0 0      | [0, cds) = calldata, [cds, cds+0x37) = extraData
                mstore(
                    add(ptr, 0x1d),
                    0x013d730000000000000000000000000000000000000000000000000000000000
                )
                mstore(add(ptr, 0x20), shl(0x60, implementation))

                // 5a          | GAS                   | gas addr 0 cds 0 0 0 0  | [0, cds) = calldata, [cds, cds+0x37) = extraData
                // f4          | DELEGATECALL          | success 0 0             | [0, cds) = calldata, [cds, cds+0x37) = extraData
                // 3d          | RETURNDATASIZE        | rds success 0 0         | [0, cds) = calldata, [cds, cds+0x37) = extraData
                // 3d          | RETURNDATASIZE        | rds rds success 0 0     | [0, cds) = calldata, [cds, cds+0x37) = extraData
                // 93          | SWAP4                 | 0 rds success 0 rds     | [0, cds) = calldata, [cds, cds+0x37) = extraData
                // 80          | DUP1                  | 0 0 rds success 0 rds   | [0, cds) = calldata, [cds, cds+0x37) = extraData
                // 3e          | RETURNDATACOPY        | success 0 rds           | [0, rds) = return data (there might be some irrelevant leftovers in memory [rds, cds+0x37) when rds < cds+0x37)
                // 60 0x35     | PUSH1 0x35            | 0x35 sucess 0 rds       | [0, rds) = return data
                // 57          | JUMPI                 | 0 rds                   | [0, rds) = return data
                // fd          | REVERT                | –                       | [0, rds) = return data
                // 5b          | JUMPDEST              | 0 rds                   | [0, rds) = return data
                // f3          | RETURN                | –                       | [0, rds) = return data
                mstore(
                    add(ptr, 0x34),
                    0x5af43d3d93803e603557fd5bf300000000000000000000000000000000000000
                )
            }

            // -------------------------------------------------------------------------------------------------------------
            // APPENDED DATA (Accessible from extcodecopy)
            // (but also send as appended data to the delegatecall)
            // -------------------------------------------------------------------------------------------------------------

            extraLength -= 2;
            uint256 counter = extraLength;
            uint256 copyPtr = ptr + 0x41;
            // solhint-disable-next-line no-inline-assembly
            assembly {
                dataPtr := add(data, 32)
            }
            for (; counter >= 32; counter -= 32) {
                // solhint-disable-next-line no-inline-assembly
                assembly {
                    mstore(copyPtr, mload(dataPtr))
                }

                copyPtr += 32;
                dataPtr += 32;
            }
            uint256 mask = ~(256**(32 - counter) - 1);
            // solhint-disable-next-line no-inline-assembly
            assembly {
                mstore(copyPtr, and(mload(dataPtr), mask))
            }
            copyPtr += counter;
            // solhint-disable-next-line no-inline-assembly
            assembly {
                mstore(copyPtr, shl(240, extraLength))
            }
            // solhint-disable-next-line no-inline-assembly
            assembly {
                instance := create(0, ptr, creationSize)
            }
            if (instance == address(0)) {
                revert CreateFail();
            }
        }
    }
}

/// @title Clone
/// @author zefram.eth
/// @notice Provides helper functions for reading immutable args from calldata
contract Clone {
    /// @notice Reads an immutable arg with type address
    /// @param argOffset The offset of the arg in the packed data
    /// @return arg The arg value
    function _getArgAddress(uint256 argOffset)
        internal
        pure
        returns (address arg)
    {
        uint256 offset = _getImmutableArgsOffset();
        // solhint-disable-next-line no-inline-assembly
        assembly {
            arg := shr(0x60, calldataload(add(offset, argOffset)))
        }
    }

    /// @notice Reads an immutable arg with type uint256
    /// @param argOffset The offset of the arg in the packed data
    /// @return arg The arg value
    function _getArgUint256(uint256 argOffset)
        internal
        pure
        returns (uint256 arg)
    {
        uint256 offset = _getImmutableArgsOffset();
        // solhint-disable-next-line no-inline-assembly
        assembly {
            arg := calldataload(add(offset, argOffset))
        }
    }

    /// @notice Reads an immutable arg with type bytes32
    /// @param argOffset The offset of the arg in the packed data
    /// @return arg The arg value
    function _getArgBytes32(uint256 argOffset)
        internal
        pure
        returns (bytes32 arg)
    {
        uint256 offset = _getImmutableArgsOffset();
        // solhint-disable-next-line no-inline-assembly
        assembly {
            arg := calldataload(add(offset, argOffset))
        }
    }

    /// @notice Reads a uint256 array stored in the immutable args.
    /// @param argOffset The offset of the arg in the packed data
    /// @param arrLen Number of elements in the array
    /// @return arr The array
    function _getArgUint256Array(uint256 argOffset, uint64 arrLen)
        internal
        pure
        returns (uint256[] memory arr)
    {
        uint256 offset = _getImmutableArgsOffset();
        uint256 el;
        arr = new uint256[](arrLen);
        for (uint64 i = 0; i < arrLen; i++) {
            assembly {
                // solhint-disable-next-line no-inline-assembly
                el := calldataload(add(add(offset, argOffset), mul(i, 32)))
            }
            arr[i] = el;
        }
        return arr;
    }

    /// @notice Reads a uint256 array stored in the immutable args.
    /// @param argOffset The offset of the arg in the packed data
    /// @param arrLen Number of elements in the array
    /// @return arr The array
    function _getArgBytes32Array(uint256 argOffset, uint64 arrLen)
        internal
        pure
        returns (bytes32[] memory arr)
    {
        uint256 offset = _getImmutableArgsOffset();
        bytes32 el;
        arr = new bytes32[](arrLen);
        for (uint64 i = 0; i < arrLen; i++) {
            assembly {
                // solhint-disable-next-line no-inline-assembly
                el := calldataload(add(add(offset, argOffset), mul(i, 32)))
            }
            arr[i] = el;
        }
        return arr;
    }

    /// @notice Reads an immutable arg with type uint64
    /// @param argOffset The offset of the arg in the packed data
    /// @return arg The arg value
    function _getArgUint64(uint256 argOffset)
        internal
        pure
        returns (uint64 arg)
    {
        uint256 offset = _getImmutableArgsOffset();
        // solhint-disable-next-line no-inline-assembly
        assembly {
            arg := shr(0xc0, calldataload(add(offset, argOffset)))
        }
    }

    /// @notice Reads an immutable arg with type uint8
    /// @param argOffset The offset of the arg in the packed data
    /// @return arg The arg value
    function _getArgUint8(uint256 argOffset) internal pure returns (uint8 arg) {
        uint256 offset = _getImmutableArgsOffset();
        // solhint-disable-next-line no-inline-assembly
        assembly {
            arg := shr(0xf8, calldataload(add(offset, argOffset)))
        }
    }

    /// @return offset The offset of the packed immutable args in calldata
    function _getImmutableArgsOffset() internal pure returns (uint256 offset) {
        // solhint-disable-next-line no-inline-assembly
        assembly {
            offset := sub(
                calldatasize(),
                add(shr(240, calldataload(sub(calldatasize(), 2))), 2)
            )
        }
    }
}

// OpenZeppelin Contracts (last updated v4.7.0) (utils/cryptography/ECDSA.sol)

// OpenZeppelin Contracts (last updated v4.7.0) (utils/Strings.sol)

// OpenZeppelin Contracts (last updated v4.7.0) (utils/math/Math.sol)

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    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) {
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1);

            ///////////////////////////////////////////////
            // 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 10, 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);
        }
    }
}

/**
 * @dev String operations.
 */
library Strings {
    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 = Math.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 `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.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 Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV // Deprecated in v4.8
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            /// @solidity memory-safe-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address, RecoverError) {
        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
        uint8 v = uint8((uint256(vs) >> 255) + 27);
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address, RecoverError) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n32", hash));
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n", Strings.toString(s.length), s));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", domainSeparator, structHash));
    }
}

/// @notice Minimalist and gas efficient standard ERC1155 implementation.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC1155.sol)
abstract contract ERC1155 {
    /*//////////////////////////////////////////////////////////////
                                 EVENTS
    //////////////////////////////////////////////////////////////*/

    event TransferSingle(
        address indexed operator,
        address indexed from,
        address indexed to,
        uint256 id,
        uint256 amount
    );

    event TransferBatch(
        address indexed operator,
        address indexed from,
        address indexed to,
        uint256[] ids,
        uint256[] amounts
    );

    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    event URI(string value, uint256 indexed id);

    /*//////////////////////////////////////////////////////////////
                             ERC1155 STORAGE
    //////////////////////////////////////////////////////////////*/

    mapping(address => mapping(uint256 => uint256)) public balanceOf;

    mapping(address => mapping(address => bool)) public isApprovedForAll;

    /*//////////////////////////////////////////////////////////////
                             METADATA LOGIC
    //////////////////////////////////////////////////////////////*/

    function uri(uint256 id) public view virtual returns (string memory);

    /*//////////////////////////////////////////////////////////////
                              ERC1155 LOGIC
    //////////////////////////////////////////////////////////////*/

    function setApprovalForAll(address operator, bool approved) public virtual {
        isApprovedForAll[msg.sender][operator] = approved;

        emit ApprovalForAll(msg.sender, operator, approved);
    }

    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes calldata data
    ) public virtual {
        require(msg.sender == from || isApprovedForAll[from][msg.sender], "NOT_AUTHORIZED");

        balanceOf[from][id] -= amount;
        balanceOf[to][id] += amount;

        emit TransferSingle(msg.sender, from, to, id, amount);

        require(
            to.code.length == 0
                ? to != address(0)
                : ERC1155TokenReceiver(to).onERC1155Received(msg.sender, from, id, amount, data) ==
                    ERC1155TokenReceiver.onERC1155Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] calldata ids,
        uint256[] calldata amounts,
        bytes calldata data
    ) public virtual {
        require(ids.length == amounts.length, "LENGTH_MISMATCH");

        require(msg.sender == from || isApprovedForAll[from][msg.sender], "NOT_AUTHORIZED");

        // Storing these outside the loop saves ~15 gas per iteration.
        uint256 id;
        uint256 amount;

        for (uint256 i = 0; i < ids.length; ) {
            id = ids[i];
            amount = amounts[i];

            balanceOf[from][id] -= amount;
            balanceOf[to][id] += amount;

            // An array can't have a total length
            // larger than the max uint256 value.
            unchecked {
                ++i;
            }
        }

        emit TransferBatch(msg.sender, from, to, ids, amounts);

        require(
            to.code.length == 0
                ? to != address(0)
                : ERC1155TokenReceiver(to).onERC1155BatchReceived(msg.sender, from, ids, amounts, data) ==
                    ERC1155TokenReceiver.onERC1155BatchReceived.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    function balanceOfBatch(address[] calldata owners, uint256[] calldata ids)
        public
        view
        virtual
        returns (uint256[] memory balances)
    {
        require(owners.length == ids.length, "LENGTH_MISMATCH");

        balances = new uint256[](owners.length);

        // Unchecked because the only math done is incrementing
        // the array index counter which cannot possibly overflow.
        unchecked {
            for (uint256 i = 0; i < owners.length; ++i) {
                balances[i] = balanceOf[owners[i]][ids[i]];
            }
        }
    }

    /*//////////////////////////////////////////////////////////////
                              ERC165 LOGIC
    //////////////////////////////////////////////////////////////*/

    function supportsInterface(bytes4 interfaceId) public view virtual returns (bool) {
        return
            interfaceId == 0x01ffc9a7 || // ERC165 Interface ID for ERC165
            interfaceId == 0xd9b67a26 || // ERC165 Interface ID for ERC1155
            interfaceId == 0x0e89341c; // ERC165 Interface ID for ERC1155MetadataURI
    }

    /*//////////////////////////////////////////////////////////////
                        INTERNAL MINT/BURN LOGIC
    //////////////////////////////////////////////////////////////*/

    function _mint(
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) internal virtual {
        balanceOf[to][id] += amount;

        emit TransferSingle(msg.sender, address(0), to, id, amount);

        require(
            to.code.length == 0
                ? to != address(0)
                : ERC1155TokenReceiver(to).onERC1155Received(msg.sender, address(0), id, amount, data) ==
                    ERC1155TokenReceiver.onERC1155Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    function _batchMint(
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) internal virtual {
        uint256 idsLength = ids.length; // Saves MLOADs.

        require(idsLength == amounts.length, "LENGTH_MISMATCH");

        for (uint256 i = 0; i < idsLength; ) {
            balanceOf[to][ids[i]] += amounts[i];

            // An array can't have a total length
            // larger than the max uint256 value.
            unchecked {
                ++i;
            }
        }

        emit TransferBatch(msg.sender, address(0), to, ids, amounts);

        require(
            to.code.length == 0
                ? to != address(0)
                : ERC1155TokenReceiver(to).onERC1155BatchReceived(msg.sender, address(0), ids, amounts, data) ==
                    ERC1155TokenReceiver.onERC1155BatchReceived.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    function _batchBurn(
        address from,
        uint256[] memory ids,
        uint256[] memory amounts
    ) internal virtual {
        uint256 idsLength = ids.length; // Saves MLOADs.

        require(idsLength == amounts.length, "LENGTH_MISMATCH");

        for (uint256 i = 0; i < idsLength; ) {
            balanceOf[from][ids[i]] -= amounts[i];

            // An array can't have a total length
            // larger than the max uint256 value.
            unchecked {
                ++i;
            }
        }

        emit TransferBatch(msg.sender, from, address(0), ids, amounts);
    }

    function _burn(
        address from,
        uint256 id,
        uint256 amount
    ) internal virtual {
        balanceOf[from][id] -= amount;

        emit TransferSingle(msg.sender, from, address(0), id, amount);
    }
}

/// @notice A generic interface for a contract which properly accepts ERC1155 tokens.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC1155.sol)
abstract contract ERC1155TokenReceiver {
    function onERC1155Received(
        address,
        address,
        uint256,
        uint256,
        bytes calldata
    ) external virtual returns (bytes4) {
        return ERC1155TokenReceiver.onERC1155Received.selector;
    }

    function onERC1155BatchReceived(
        address,
        address,
        uint256[] calldata,
        uint256[] calldata,
        bytes calldata
    ) external virtual returns (bytes4) {
        return ERC1155TokenReceiver.onERC1155BatchReceived.selector;
    }
}

/// @dev Name of the Rae token contract
string constant NAME = "Rae";

/// @dev Version number of the Rae token contract
string constant VERSION = "1";

/// @dev The EIP-712 typehash for the contract's domain
bytes32 constant DOMAIN_TYPEHASH = keccak256(
    "EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"
);

/// @dev The EIP-712 typehash for the permit struct used by the contract
bytes32 constant PERMIT_TYPEHASH = keccak256(
    "Permit(address owner,address operator,uint256 tokenId,bool approved,uint256 nonce,uint256 deadline)"
);

/// @dev The EIP-712 typehash for the permit all struct used by the contract
bytes32 constant PERMIT_ALL_TYPEHASH = keccak256(
    "PermitAll(address owner,address operator,bool approved,uint256 nonce,uint256 deadline)"
);

/// @title PermitBase
/// @author Tessera
/// @notice Utility contract for computing permit signature approvals for Rae tokens
abstract contract PermitBase {
    /// @notice Mapping of token owner to nonce value
    mapping(address => uint256) public nonces;

    /// @dev Computes hash of permit struct
    /// @param _owner Address of the owner of the token type
    /// @param _operator Address of the spender of the token type
    /// @param _id ID of the token type
    /// @param _approved Approval status for the token type
    /// @param _deadline Expiration of the signature
    function _computePermitStructHash(
        address _owner,
        address _operator,
        uint256 _id,
        bool _approved,
        uint256 _deadline
    ) internal returns (bytes32) {
        return
            keccak256(
                abi.encode(
                    PERMIT_TYPEHASH,
                    _owner,
                    _operator,
                    _id,
                    _approved,
                    nonces[_owner]++,
                    _deadline
                )
            );
    }

    /// @dev Computes hash of permit all struct
    /// @param _owner Address of the owner of the token type
    /// @param _operator Address of the spender of the token type
    /// @param _approved Approval status for the token type
    /// @param _deadline Expiration of the signature
    function _computePermitAllStructHash(
        address _owner,
        address _operator,
        bool _approved,
        uint256 _deadline
    ) internal returns (bytes32) {
        return
            keccak256(
                abi.encode(
                    PERMIT_ALL_TYPEHASH,
                    _owner,
                    _operator,
                    _approved,
                    nonces[_owner]++,
                    _deadline
                )
            );
    }

    /// @dev Computes domain separator to prevent signature collisions
    /// @return Hash of the contract-specific fields
    function _computeDomainSeparator() internal view returns (bytes32) {
        return
            keccak256(
                abi.encode(
                    DOMAIN_TYPEHASH,
                    keccak256(bytes(NAME)),
                    keccak256(bytes(VERSION)),
                    block.chainid,
                    address(this)
                )
            );
    }

    /// @dev Computes digest of domain separator and struct hash
    /// @param _domainSeparator Hash of contract-specific fields
    /// @param _structHash Hash of signature fields struct
    /// @return Hash of the signature digest
    function _computeDigest(bytes32 _domainSeparator, bytes32 _structHash)
        internal
        pure
        returns (bytes32)
    {
        return keccak256(abi.encode("\x19\x01", _domainSeparator, _structHash));
    }
}

/// @dev Interface of ERC-1155 token contract for raes
interface IRae {
    /// @dev Emitted when caller is not required address
    error InvalidSender(address _required, address _provided);
    /// @dev Emitted when owner signature is invalid
    error InvalidSignature(address _signer, address _owner);
    /// @dev Emitted when deadline for signature has passed
    error SignatureExpired(uint256 _timestamp, uint256 _deadline);
    /// @dev Emitted when royalty is set to value greater than 100%
    error InvalidRoyalty(uint256 _percentage);
    /// @dev Emitted when new controller is zero address
    error ZeroAddress();

    /// @dev Event log for updating the Controller of the token contract
    /// @param _newController Address of the controller
    event ControllerTransferred(address indexed _newController);
    /// @dev Event log for updating the metadata contract for a token type
    /// @param _metadata Address of the metadata contract that URI data is stored on
    /// @param _id ID of the token type
    event SetMetadata(address indexed _metadata, uint256 _id);
    /// @dev Event log for updating the royalty of a token type
    /// @param _receiver Address of the receiver of secondary sale royalties
    /// @param _id ID of the token type
    /// @param _percentage Royalty percent on secondary sales
    event SetRoyalty(address indexed _receiver, uint256 indexed _id, uint256 _percentage);
    /// @dev Event log for approving a spender of a token type
    /// @param _owner Address of the owner of the token type
    /// @param _operator Address of the spender of the token type
    /// @param _id ID of the token type
    /// @param _approved Approval status for the token type
    event SingleApproval(
        address indexed _owner,
        address indexed _operator,
        uint256 indexed _id,
        bool _approved
    );
    /// @notice Event log for Minting Raes of ID to account _to
    /// @param _to Address to mint rae tokens to
    /// @param _id Token ID to mint
    /// @param _amount Number of tokens to mint
    event MintRaes(address indexed _to, uint256 indexed _id, uint256 _amount);

    /// @notice Event log for Burning raes of ID from account _from
    /// @param _from Address to burn rae tokens from
    /// @param _id Token ID to burn
    /// @param _amount Number of tokens to burn
    event BurnRaes(address indexed _from, uint256 indexed _id, uint256 _amount);

    function INITIAL_CONTROLLER() external pure returns (address);

    function VAULT_REGISTRY() external pure returns (address);

    function burn(
        address _from,
        uint256 _id,
        uint256 _amount
    ) external;

    function contractURI() external view returns (string memory);

    function controller() external view returns (address controllerAddress);

    function isApproved(
        address,
        address,
        uint256
    ) external view returns (bool);

    function metadataDelegate() external view returns (address);

    function mint(
        address _to,
        uint256 _id,
        uint256 _amount,
        bytes memory _data
    ) external;

    function permit(
        address _owner,
        address _operator,
        uint256 _id,
        bool _approved,
        uint256 _deadline,
        uint8 _v,
        bytes32 _r,
        bytes32 _s
    ) external;

    function permitAll(
        address _owner,
        address _operator,
        bool _approved,
        uint256 _deadline,
        uint8 _v,
        bytes32 _r,
        bytes32 _s
    ) external;

    function royaltyInfo(uint256 _id, uint256 _salePrice)
        external
        view
        returns (address receiver, uint256 royaltyAmount);

    function safeTransferFrom(
        address _from,
        address _to,
        uint256 _id,
        uint256 _amount,
        bytes memory _data
    ) external;

    function setApprovalFor(
        address _operator,
        uint256 _id,
        bool _approved
    ) external;

    function setMetadataDelegate(address _metadata) external;

    function setRoyalties(
        uint256 _id,
        address _receiver,
        uint256 _percentage
    ) external;

    function totalSupply(uint256) external view returns (uint256);

    function transferController(address _newController) external;

    function uri(uint256 _id) external view returns (string memory);
}

/// @dev Interface for NFT Receiver contract
interface INFTReceiver {
    function onERC721Received(
        address,
        address,
        uint256,
        bytes calldata
    ) external returns (bytes4);

    function onERC1155Received(
        address,
        address,
        uint256,
        uint256,
        bytes calldata
    ) external returns (bytes4);

    function onERC1155BatchReceived(
        address,
        address,
        uint256[] calldata,
        uint256[] calldata,
        bytes calldata
    ) external returns (bytes4);
}

interface IMetadataDelegate {
    function tokenURI(uint256 tokenId) external view returns (string memory);

    function contractURI() external view returns (string memory);
}

/// @title Rae
/// @author Tessera
/// @notice An ERC-1155 implementation for Raes
contract Rae is Clone, ERC1155, IRae, PermitBase {
    /// @notice Address of interface identifier for royalty standard
    bytes4 private constant _INTERFACE_ID_ERC2981 = 0x2a55205a;
    /// @notice Address that can deploy new vaults and manage metadata for this collection
    address internal _controller;
    /// @notice contract address for the metadata delegate
    address public metadataDelegate;
    /// @notice Mapping of token owner to token operator to token ID type to approval status
    mapping(address => mapping(address => mapping(uint256 => bool))) public isApproved;
    /// @notice Mapping of token ID type to total supply of tokens
    mapping(uint256 => uint256) public totalSupply;
    /// @notice Mapping of token ID type to royalty beneficiary
    mapping(uint256 => address) private royaltyAddress;
    /// @notice Mapping of token ID type to royalty percentage
    mapping(uint256 => uint256) private royaltyPercent;

    /// @notice Modifier for restricting function calls to the controller account
    modifier onlyController() {
        address controller_ = controller();
        if (msg.sender != controller_) revert InvalidSender(controller_, msg.sender);
        _;
    }

    /// @notice Modifier for restricting function calls to the VaultRegistry
    modifier onlyRegistry() {
        address vaultRegistry = VAULT_REGISTRY();
        if (msg.sender != vaultRegistry) revert InvalidSender(vaultRegistry, msg.sender);
        _;
    }

    /// @notice Burns raes for an ID
    /// @param _from Address to burn rae tokens from
    /// @param _id Token ID to burn
    /// @param _amount Number of tokens to burn
    function burn(
        address _from,
        uint256 _id,
        uint256 _amount
    ) external onlyRegistry {
        totalSupply[_id] -= _amount;
        _burn(_from, _id, _amount);
        emit BurnRaes(_from, _id, _amount);
    }

    /// @notice Mints new raes for an ID
    /// @param _to Address to mint rae tokens to
    /// @param _id Token ID to mint
    /// @param _amount Number of tokens to mint
    /// @param _data Extra calldata to include in the mint
    function mint(
        address _to,
        uint256 _id,
        uint256 _amount,
        bytes memory _data
    ) external onlyRegistry {
        totalSupply[_id] += _amount;
        emit MintRaes(_to, _id, _amount);

        _mint(_to, _id, _amount, _data);
    }

    /// @notice Permit function that approves an operator for token type with a valid signature
    /// @param _owner Address of the owner of the token type
    /// @param _operator Address of the spender of the token type
    /// @param _id ID of the token type
    /// @param _approved Approval status for the token type
    /// @param _deadline Expiration of the signature
    /// @param _v The recovery ID (129th byte and chain ID) of the signature used to recover the signer
    /// @param _r The first 64 bytes of the signature
    /// @param _s Bytes 64-128 of the signature
    function permit(
        address _owner,
        address _operator,
        uint256 _id,
        bool _approved,
        uint256 _deadline,
        uint8 _v,
        bytes32 _r,
        bytes32 _s
    ) external {
        if (block.timestamp > _deadline) revert SignatureExpired(block.timestamp, _deadline);

        // cannot realistically overflow on human timescales
        unchecked {
            bytes32 structHash = _computePermitStructHash(
                _owner,
                _operator,
                _id,
                _approved,
                _deadline
            );

            bytes32 digest = _computeDigest(_computeDomainSeparator(), structHash);

            address signer = ECDSA.recover(digest, _v, _r, _s);

            if (signer == address(0) || signer != _owner) revert InvalidSignature(signer, _owner);
        }

        isApproved[_owner][_operator][_id] = _approved;

        emit SingleApproval(_owner, _operator, _id, _approved);
    }

    /// @notice Permit function that approves an operator for all token types with a valid signature
    /// @param _owner Address of the owner of the token type
    /// @param _operator Address of the spender of the token type
    /// @param _approved Approval status for the token type
    /// @param _deadline Expiration of the signature
    /// @param _v The recovery ID (129th byte and chain ID) of the signature used to recover the signer
    /// @param _r The first 64 bytes of the signature
    /// @param _s Bytes 64-128 of the signature
    function permitAll(
        address _owner,
        address _operator,
        bool _approved,
        uint256 _deadline,
        uint8 _v,
        bytes32 _r,
        bytes32 _s
    ) external {
        if (block.timestamp > _deadline) revert SignatureExpired(block.timestamp, _deadline);

        // cannot realistically overflow on human timescales
        unchecked {
            bytes32 structHash = _computePermitAllStructHash(
                _owner,
                _operator,
                _approved,
                _deadline
            );

            bytes32 digest = _computeDigest(_computeDomainSeparator(), structHash);

            address signer = ECDSA.recover(digest, _v, _r, _s);

            if (signer == address(0) || signer != _owner) revert InvalidSignature(signer, _owner);
        }

        isApprovedForAll[_owner][_operator] = _approved;

        emit ApprovalForAll(_owner, _operator, _approved);
    }

    /// @notice Scoped approvals allow us to eliminate some of the risks associated with setting the approval for an entire collection
    /// @param _operator Address of spender account
    /// @param _id ID of the token type
    /// @param _approved Approval status for operator(spender) account
    function setApprovalFor(
        address _operator,
        uint256 _id,
        bool _approved
    ) external {
        isApproved[msg.sender][_operator][_id] = _approved;

        emit SingleApproval(msg.sender, _operator, _id, _approved);
    }

    /// @notice Sets the token metadata contract
    /// @param _metadata Address for metadata contract
    function setMetadataDelegate(address _metadata) external onlyController {
        metadataDelegate = _metadata;
    }

    /// @notice Sets the token royalties
    /// @param _id Token ID royalties are being updated for
    /// @param _receiver Address to receive royalties
    /// @param _percentage Percentage of royalties on secondary sales (2 decimals of precision)
    function setRoyalties(
        uint256 _id,
        address _receiver,
        uint256 _percentage
    ) external onlyController {
        if (_percentage > 10000) revert InvalidRoyalty(_percentage);
        royaltyAddress[_id] = _receiver;
        royaltyPercent[_id] = _percentage;
        emit SetRoyalty(_receiver, _id, _percentage);
    }

    /// @notice Updates the controller address for the Rae token contract
    /// @param _newController Address of new controlling entity
    function transferController(address _newController) external onlyController {
        if (_newController == address(0)) revert ZeroAddress();
        _controller = _newController;
        emit ControllerTransferred(_newController);
    }

    function contractURI() external view returns (string memory) {
        return IMetadataDelegate(metadataDelegate).contractURI();
    }

    /// @notice Sets the token royalties
    /// @param _id Token ID royalties are being updated for
    /// @param _salePrice Sale price to calculate the royalty for
    function royaltyInfo(uint256 _id, uint256 _salePrice)
        external
        view
        returns (address receiver, uint256 royaltyAmount)
    {
        receiver = royaltyAddress[_id];
        royaltyAmount = (_salePrice * royaltyPercent[_id]) / 10000;
    }

    /// @notice ERC165 implementation
    /// @param interfaceId ERC165 Interface ID
    function supportsInterface(bytes4 interfaceId) public view override returns (bool) {
        return interfaceId == _INTERFACE_ID_ERC2981 || super.supportsInterface(interfaceId); // ERC165 Interface ID for ERC2981
    }

    /// @notice Transfer an amount of a token type between two accounts
    /// @param _from Source address for an amount of tokens
    /// @param _to Destination address for an amount of tokens
    /// @param _id ID of the token type
    /// @param _amount The amount of tokens being transferred
    /// @param _data Additional calldata
    function safeTransferFrom(
        address _from,
        address _to,
        uint256 _id,
        uint256 _amount,
        bytes memory _data
    ) public override(ERC1155, IRae) {
        require(
            msg.sender == _from ||
                isApprovedForAll[_from][msg.sender] ||
                isApproved[_from][msg.sender][_id],
            "NOT_AUTHORIZED"
        );

        balanceOf[_from][_id] -= _amount;
        balanceOf[_to][_id] += _amount;

        emit TransferSingle(msg.sender, _from, _to, _id, _amount);

        require(
            _to.code.length == 0
                ? _to != address(0)
                : INFTReceiver(_to).onERC1155Received(msg.sender, _from, _id, _amount, _data) ==
                    INFTReceiver.onERC1155Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    /// @notice Getter for URI of a token type
    /// @param _id ID of the token type
    function uri(uint256 _id) public view override(ERC1155, IRae) returns (string memory) {
        return IMetadataDelegate(metadataDelegate).tokenURI(_id);
    }

    /// @notice Getter for controller account
    function controller() public view returns (address controllerAddress) {
        _controller == address(0)
            ? controllerAddress = INITIAL_CONTROLLER()
            : controllerAddress = _controller;
    }

    /// @notice Getter for initial controller account immutable argument stored in calldata
    function INITIAL_CONTROLLER() public pure returns (address) {
        return _getArgAddress(0);
    }

    /// @notice VaultRegistry address that is allowed to call mint() and burn()
    function VAULT_REGISTRY() public pure returns (address) {
        return _getArgAddress(20);
    }
}

/// @dev Initialization call information
struct InitInfo {
    // Address of target contract
    address target;
    // Initialization data
    bytes data;
    // Merkle proof for call
    bytes32[] proof;
}

/// @dev Interface for Vault proxy contract
interface IVault {
    /// @dev Emitted when execution reverted with no reason
    error ExecutionReverted();
    /// @dev Emitted when the caller is not the owner
    error NotAuthorized(address _caller, address _target, bytes4 _selector);
    /// @dev Emitted when the caller is not the owner
    error NotOwner(address _owner, address _caller);
    /// @dev Emitted when the caller is not the factory
    error NotFactory(address _factory, address _caller);
    /// @dev Emitted when passing an EOA or an undeployed contract as the target
    error TargetInvalid(address _target);

    /// @dev Event log for executing transactions
    /// @param _target Address of target contract
    /// @param _data Transaction data being executed
    /// @param _response Return data of delegatecall
    event Execute(address indexed _target, bytes _data, bytes _response);

    function execute(
        address _target,
        bytes memory _data,
        bytes32[] memory _proof
    ) external payable returns (bool success, bytes memory response);

    function MERKLE_ROOT() external view returns (bytes32);

    function OWNER() external view returns (address);

    function FACTORY() external view returns (address);
}

/// @dev Vault permissions
struct Permission {
    // Address of module contract
    address module;
    // Address of target contract
    address target;
    // Function selector from target contract
    bytes4 selector;
}

/// @dev Vault information
struct VaultInfo {
    // Address of Rae token contract
    address token;
    // ID of the token type
    uint256 id;
}

/// @dev Interface for VaultRegistry contract
interface IVaultRegistry {
    /// @dev Emitted when the caller is not the controller
    error InvalidController(address _controller, address _sender);
    /// @dev Emitted when the caller is not a registered vault
    error UnregisteredVault(address _sender);

    /// @dev Event log for deploying vault
    /// @param _vault Address of the vault
    /// @param _token Address of the token
    /// @param _id Id of the token
    event VaultDeployed(address indexed _vault, address indexed _token, uint256 indexed _id);

    function createFor(
        bytes32 _merkleRoot,
        address _owner,
        InitInfo[] calldata _calls
    ) external returns (address vault);

    function createFor(bytes32 _merkleRoot, address _owner) external returns (address vault);

    function create(bytes32 _merkleRoot, InitInfo[] calldata _calls)
        external
        returns (address vault);

    function create(bytes32 _merkleRoot) external returns (address vault);

    function createCollectionFor(
        bytes32 _merkleRoot,
        address _controller,
        InitInfo[] calldata _calls
    ) external returns (address vault, address token);

    function createCollection(bytes32 _merkleRoot, InitInfo[] calldata _calls)
        external
        returns (address vault, address token);

    function createInCollection(
        bytes32 _merkleRoot,
        address _token,
        InitInfo[] calldata _calls
    ) external returns (address vault);

    function factory() external view returns (address);

    function rae() external view returns (address);

    function raeImplementation() external view returns (address);

    function burn(address _from, uint256 _value) external;

    function mint(address _to, uint256 _value) external;

    function nextId(address) external view returns (uint256);

    function totalSupply(address _vault) external view returns (uint256);

    function uri(address _vault) external view returns (string memory);

    function vaultToToken(address) external view returns (address token, uint256 id);
}

/// @title ClonesWithImmutableArgs
/// @author wighawag, zefram.eth
/// @notice Enables creating clone contracts with immutable args
library Create2ClonesWithImmutableArgs {
    error CreateFail();

    function cloneCreationCode(address implementation, bytes memory data)
        internal
        pure
        returns (uint256 ptr, uint256 creationSize)
    {
        // unchecked is safe because it is unrealistic for memory ptr or data length to exceed 256 bits
        unchecked {
            uint256 extraLength = data.length + 2; // +2 bytes for telling how much data there is appended to the call
            creationSize = 0x43 + extraLength;
            uint256 runSize = creationSize - 11;
            uint256 dataPtr;
            // solhint-disable-next-line no-inline-assembly
            assembly {
                ptr := mload(0x40)

                // -------------------------------------------------------------------------------------------------------------
                // CREATION (11 bytes)
                // -------------------------------------------------------------------------------------------------------------

                // 3d          | RETURNDATASIZE        | 0                       | –
                // 61 runtime  | PUSH2 runtime (r)     | r 0                     | –
                mstore(
                    ptr,
                    0x3d61000000000000000000000000000000000000000000000000000000000000
                )
                mstore(add(ptr, 0x02), shl(240, runSize)) // size of the contract running bytecode (16 bits)

                // creation size = 0b
                // 80          | DUP1                  | r r 0                   | –
                // 60 creation | PUSH1 creation (c)    | c r r 0                 | –
                // 3d          | RETURNDATASIZE        | 0 c r r 0               | –
                // 39          | CODECOPY              | r 0                     | [0-2d]: runtime code
                // 81          | DUP2                  | 0 c  0                  | [0-2d]: runtime code
                // f3          | RETURN                | 0                       | [0-2d]: runtime code
                mstore(
                    add(ptr, 0x04),
                    0x80600b3d3981f300000000000000000000000000000000000000000000000000
                )

                // -------------------------------------------------------------------------------------------------------------
                // RUNTIME
                // -------------------------------------------------------------------------------------------------------------

                // 36          | CALLDATASIZE          | cds                     | –
                // 3d          | RETURNDATASIZE        | 0 cds                   | –
                // 3d          | RETURNDATASIZE        | 0 0 cds                 | –
                // 37          | CALLDATACOPY          | –                       | [0, cds] = calldata
                // 61          | PUSH2 extra           | extra                   | [0, cds] = calldata
                mstore(
                    add(ptr, 0x0b),
                    0x363d3d3761000000000000000000000000000000000000000000000000000000
                )
                mstore(add(ptr, 0x10), shl(240, extraLength))

                // 60 0x38     | PUSH1 0x38            | 0x38 extra              | [0, cds] = calldata // 0x38 (56) is runtime size - data
                // 36          | CALLDATASIZE          | cds 0x38 extra          | [0, cds] = calldata
                // 39          | CODECOPY              | _                       | [0, cds] = calldata
                // 3d          | RETURNDATASIZE        | 0                       | [0, cds] = calldata
                // 3d          | RETURNDATASIZE        | 0 0                     | [0, cds] = calldata
                // 3d          | RETURNDATASIZE        | 0 0 0                   | [0, cds] = calldata
                // 36          | CALLDATASIZE          | cds 0 0 0               | [0, cds] = calldata
                // 61 extra    | PUSH2 extra           | extra cds 0 0 0         | [0, cds] = calldata
                mstore(
                    add(ptr, 0x12),
                    0x603836393d3d3d36610000000000000000000000000000000000000000000000
                )
                mstore(add(ptr, 0x1b), shl(240, extraLength))

                // 01          | ADD                   | cds+extra 0 0 0         | [0, cds] = calldata
                // 3d          | RETURNDATASIZE        | 0 cds 0 0 0             | [0, cds] = calldata
                // 73 addr     | PUSH20 0x123…         | addr 0 cds 0 0 0        | [0, cds] = calldata
                mstore(
                    add(ptr, 0x1d),
                    0x013d730000000000000000000000000000000000000000000000000000000000
                )
                mstore(add(ptr, 0x20), shl(0x60, implementation))

                // 5a          | GAS                   | gas addr 0 cds 0 0 0    | [0, cds] = calldata
                // f4          | DELEGATECALL          | success 0               | [0, cds] = calldata
                // 3d          | RETURNDATASIZE        | rds success 0           | [0, cds] = calldata
                // 82          | DUP3                  | 0 rds success 0         | [0, cds] = calldata
                // 80          | DUP1                  | 0 0 rds success 0       | [0, cds] = calldata
                // 3e          | RETURNDATACOPY        | success 0               | [0, rds] = return data (there might be some irrelevant leftovers in memory [rds, cds] when rds < cds)
                // 90          | SWAP1                 | 0 success               | [0, rds] = return data
                // 3d          | RETURNDATASIZE        | rds 0 success           | [0, rds] = return data
                // 91          | SWAP2                 | success 0 rds           | [0, rds] = return data
                // 60 0x36     | PUSH1 0x36            | 0x36 sucess 0 rds       | [0, rds] = return data
                // 57          | JUMPI                 | 0 rds                   | [0, rds] = return data
                // fd          | REVERT                | –                       | [0, rds] = return data
                // 5b          | JUMPDEST              | 0 rds                   | [0, rds] = return data
                // f3          | RETURN                | –                       | [0, rds] = return data

                mstore(
                    add(ptr, 0x34),
                    0x5af43d82803e903d91603657fd5bf30000000000000000000000000000000000
                )
            }

            // -------------------------------------------------------------------------------------------------------------
            // APPENDED DATA (Accessible from extcodecopy)
            // (but also send as appended data to the delegatecall)
            // -------------------------------------------------------------------------------------------------------------

            extraLength -= 2;
            uint256 counter = extraLength;
            uint256 copyPtr;
            assembly {
                copyPtr := add(ptr, 0x43)
            }
            // solhint-disable-next-line no-inline-assembly
            assembly {
                dataPtr := add(data, 32)
            }
            for (; counter >= 32; counter -= 32) {
                // solhint-disable-next-line no-inline-assembly
                assembly {
                    mstore(copyPtr, mload(dataPtr))
                }

                copyPtr += 32;
                dataPtr += 32;
            }
            uint256 mask = ~(256**(32 - counter) - 1);
            // solhint-disable-next-line no-inline-assembly
            assembly {
                mstore(copyPtr, and(mload(dataPtr), mask))
            }
            copyPtr += counter;
            // solhint-disable-next-line no-inline-assembly
            assembly {
                mstore(copyPtr, shl(240, extraLength))
            }
        }
    }

    /// @notice Creates a clone proxy of the implementation contract, with immutable args
    /// @dev data cannot exceed 65535 bytes, since 2 bytes are used to store the data length
    /// @param implementation The implementation contract to clone
    /// @param data Encoded immutable args
    /// @return instance The address of the created clone
    function clone(
        address implementation,
        bytes32 salt,
        bytes memory data
    ) internal returns (address payable instance) {
        (uint256 creationPtr, uint256 creationSize) = cloneCreationCode(
            implementation,
            data
        );

        // solhint-disable-next-line no-inline-assembly
        assembly {
            instance := create2(0, creationPtr, creationSize, salt)
        }

        // if the create failed, the instance address won't be set
        if (instance == address(0)) {
            revert CreateFail();
        }
    }
}

/// @dev Interface for VaultFactory contract
interface IVaultFactory {
    /// @dev Event log for deploying vault
    /// @param _origin Address of transaction origin
    /// @param _deployer Address of sender
    /// @param _owner Address of vault owner
    /// @param _seed Value of seed
    /// @param _salt Value of salt
    /// @param _vault Address of deployed vault
    event DeployVault(
        address indexed _origin,
        address indexed _deployer,
        address indexed _owner,
        bytes32 _seed,
        bytes32 _salt,
        address _vault,
        bytes32 _root
    );

    function deploy(bytes32 _merkleRoot) external returns (address payable vault);

    function deployFor(bytes32 _merkleRoot, address _owner)
        external
        returns (address payable vault);

    function getNextAddress(
        address _origin,
        address _owner,
        bytes32 _merkleRoot
    ) external view returns (address vault);

    function getNextSeed(address _deployer) external view returns (bytes32);

    function implementation() external view returns (address);
}

// OpenZeppelin Contracts (last updated v4.7.0) (utils/cryptography/MerkleProof.sol)

/**
 * @dev These functions deal with verification of Merkle Tree proofs.
 *
 * The proofs can be generated using the JavaScript library
 * https://github.com/miguelmota/merkletreejs[merkletreejs].
 * Note: the hashing algorithm should be keccak256 and pair sorting should be enabled.
 *
 * See `test/utils/cryptography/MerkleProof.test.js` for some examples.
 *
 * WARNING: You should avoid using leaf values that are 64 bytes long prior to
 * hashing, or use a hash function other than keccak256 for hashing leaves.
 * This is because the concatenation of a sorted pair of internal nodes in
 * the merkle tree could be reinterpreted as a leaf value.
 */
library MerkleProof {
    /**
     * @dev Returns true if a `leaf` can be proved to be a part of a Merkle tree
     * defined by `root`. For this, a `proof` must be provided, containing
     * sibling hashes on the branch from the leaf to the root of the tree. Each
     * pair of leaves and each pair of pre-images are assumed to be sorted.
     */
    function verify(
        bytes32[] memory proof,
        bytes32 root,
        bytes32 leaf
    ) internal pure returns (bool) {
        return processProof(proof, leaf) == root;
    }

    /**
     * @dev Calldata version of {verify}
     *
     * _Available since v4.7._
     */
    function verifyCalldata(
        bytes32[] calldata proof,
        bytes32 root,
        bytes32 leaf
    ) internal pure returns (bool) {
        return processProofCalldata(proof, leaf) == root;
    }

    /**
     * @dev Returns the rebuilt hash obtained by traversing a Merkle tree up
     * from `leaf` using `proof`. A `proof` is valid if and only if the rebuilt
     * hash matches the root of the tree. When processing the proof, the pairs
     * of leafs & pre-images are assumed to be sorted.
     *
     * _Available since v4.4._
     */
    function processProof(bytes32[] memory proof, bytes32 leaf) internal pure returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            computedHash = _hashPair(computedHash, proof[i]);
        }
        return computedHash;
    }

    /**
     * @dev Calldata version of {processProof}
     *
     * _Available since v4.7._
     */
    function processProofCalldata(bytes32[] calldata proof, bytes32 leaf) internal pure returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            computedHash = _hashPair(computedHash, proof[i]);
        }
        return computedHash;
    }

    /**
     * @dev Returns true if the `leaves` can be simultaneously proven to be a part of a merkle tree defined by
     * `root`, according to `proof` and `proofFlags` as described in {processMultiProof}.
     *
     * CAUTION: Not all merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * _Available since v4.7._
     */
    function multiProofVerify(
        bytes32[] memory proof,
        bool[] memory proofFlags,
        bytes32 root,
        bytes32[] memory leaves
    ) internal pure returns (bool) {
        return processMultiProof(proof, proofFlags, leaves) == root;
    }

    /**
     * @dev Calldata version of {multiProofVerify}
     *
     * CAUTION: Not all merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * _Available since v4.7._
     */
    function multiProofVerifyCalldata(
        bytes32[] calldata proof,
        bool[] calldata proofFlags,
        bytes32 root,
        bytes32[] memory leaves
    ) internal pure returns (bool) {
        return processMultiProofCalldata(proof, proofFlags, leaves) == root;
    }

    /**
     * @dev Returns the root of a tree reconstructed from `leaves` and sibling nodes in `proof`. The reconstruction
     * proceeds by incrementally reconstructing all inner nodes by combining a leaf/inner node with either another
     * leaf/inner node or a proof sibling node, depending on whether each `proofFlags` item is true or false
     * respectively.
     *
     * CAUTION: Not all merkle trees admit multiproofs. To use multiproofs, it is sufficient to ensure that: 1) the tree
     * is complete (but not necessarily perfect), 2) the leaves to be proven are in the opposite order they are in the
     * tree (i.e., as seen from right to left starting at the deepest layer and continuing at the next layer).
     *
     * _Available since v4.7._
     */
    function processMultiProof(
        bytes32[] memory proof,
        bool[] memory proofFlags,
        bytes32[] memory leaves
    ) internal pure returns (bytes32 merkleRoot) {
        // This function rebuild the root hash by traversing the tree up from the leaves. The root is rebuilt by
        // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the
        // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of
        // the merkle tree.
        uint256 leavesLen = leaves.length;
        uint256 totalHashes = proofFlags.length;

        // Check proof validity.
        require(leavesLen + proof.length - 1 == totalHashes, "MerkleProof: invalid multiproof");

        // The xxxPos values are "pointers" to the next value to consume in each array. All accesses are done using
        // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's "pop".
        bytes32[] memory hashes = new bytes32[](totalHashes);
        uint256 leafPos = 0;
        uint256 hashPos = 0;
        uint256 proofPos = 0;
        // At each step, we compute the next hash using two values:
        // - a value from the "main queue". If not all leaves have been consumed, we get the next leaf, otherwise we
        //   get the next hash.
        // - depending on the flag, either another value for the "main queue" (merging branches) or an element from the
        //   `proof` array.
        for (uint256 i = 0; i < totalHashes; i++) {
            bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];
            bytes32 b = proofFlags[i] ? leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++] : proof[proofPos++];
            hashes[i] = _hashPair(a, b);
        }

        if (totalHashes > 0) {
            return hashes[totalHashes - 1];
        } else if (leavesLen > 0) {
            return leaves[0];
        } else {
            return proof[0];
        }
    }

    /**
     * @dev Calldata version of {processMultiProof}.
     *
     * CAUTION: Not all merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * _Available since v4.7._
     */
    function processMultiProofCalldata(
        bytes32[] calldata proof,
        bool[] calldata proofFlags,
        bytes32[] memory leaves
    ) internal pure returns (bytes32 merkleRoot) {
        // This function rebuild the root hash by traversing the tree up from the leaves. The root is rebuilt by
        // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the
        // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of
        // the merkle tree.
        uint256 leavesLen = leaves.length;
        uint256 totalHashes = proofFlags.length;

        // Check proof validity.
        require(leavesLen + proof.length - 1 == totalHashes, "MerkleProof: invalid multiproof");

        // The xxxPos values are "pointers" to the next value to consume in each array. All accesses are done using
        // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's "pop".
        bytes32[] memory hashes = new bytes32[](totalHashes);
        uint256 leafPos = 0;
        uint256 hashPos = 0;
        uint256 proofPos = 0;
        // At each step, we compute the next hash using two values:
        // - a value from the "main queue". If not all leaves have been consumed, we get the next leaf, otherwise we
        //   get the next hash.
        // - depending on the flag, either another value for the "main queue" (merging branches) or an element from the
        //   `proof` array.
        for (uint256 i = 0; i < totalHashes; i++) {
            bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];
            bytes32 b = proofFlags[i] ? leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++] : proof[proofPos++];
            hashes[i] = _hashPair(a, b);
        }

        if (totalHashes > 0) {
            return hashes[totalHashes - 1];
        } else if (leavesLen > 0) {
            return leaves[0];
        } else {
            return proof[0];
        }
    }

    function _hashPair(bytes32 a, bytes32 b) private pure returns (bytes32) {
        return a < b ? _efficientHash(a, b) : _efficientHash(b, a);
    }

    function _efficientHash(bytes32 a, bytes32 b) private pure returns (bytes32 value) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, a)
            mstore(0x20, b)
            value := keccak256(0x00, 0x40)
        }
    }
}

/// @notice Modern, minimalist, and gas efficient ERC-721 implementation.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC721.sol)
abstract contract ERC721 {
    /*//////////////////////////////////////////////////////////////
                                 EVENTS
    //////////////////////////////////////////////////////////////*/

    event Transfer(address indexed from, address indexed to, uint256 indexed id);

    event Approval(address indexed owner, address indexed spender, uint256 indexed id);

    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    /*//////////////////////////////////////////////////////////////
                         METADATA STORAGE/LOGIC
    //////////////////////////////////////////////////////////////*/

    string public name;

    string public symbol;

    function tokenURI(uint256 id) public view virtual returns (string memory);

    /*//////////////////////////////////////////////////////////////
                      ERC721 BALANCE/OWNER STORAGE
    //////////////////////////////////////////////////////////////*/

    mapping(uint256 => address) internal _ownerOf;

    mapping(address => uint256) internal _balanceOf;

    function ownerOf(uint256 id) public view virtual returns (address owner) {
        require((owner = _ownerOf[id]) != address(0), "NOT_MINTED");
    }

    function balanceOf(address owner) public view virtual returns (uint256) {
        require(owner != address(0), "ZERO_ADDRESS");

        return _balanceOf[owner];
    }

    /*//////////////////////////////////////////////////////////////
                         ERC721 APPROVAL STORAGE
    //////////////////////////////////////////////////////////////*/

    mapping(uint256 => address) public getApproved;

    mapping(address => mapping(address => bool)) public isApprovedForAll;

    /*//////////////////////////////////////////////////////////////
                               CONSTRUCTOR
    //////////////////////////////////////////////////////////////*/

    constructor(string memory _name, string memory _symbol) {
        name = _name;
        symbol = _symbol;
    }

    /*//////////////////////////////////////////////////////////////
                              ERC721 LOGIC
    //////////////////////////////////////////////////////////////*/

    function approve(address spender, uint256 id) public virtual {
        address owner = _ownerOf[id];

        require(msg.sender == owner || isApprovedForAll[owner][msg.sender], "NOT_AUTHORIZED");

        getApproved[id] = spender;

        emit Approval(owner, spender, id);
    }

    function setApprovalForAll(address operator, bool approved) public virtual {
        isApprovedForAll[msg.sender][operator] = approved;

        emit ApprovalForAll(msg.sender, operator, approved);
    }

    function transferFrom(
        address from,
        address to,
        uint256 id
    ) public virtual {
        require(from == _ownerOf[id], "WRONG_FROM");

        require(to != address(0), "INVALID_RECIPIENT");

        require(
            msg.sender == from || isApprovedForAll[from][msg.sender] || msg.sender == getApproved[id],
            "NOT_AUTHORIZED"
        );

        // Underflow of the sender's balance is impossible because we check for
        // ownership above and the recipient's balance can't realistically overflow.
        unchecked {
            _balanceOf[from]--;

            _balanceOf[to]++;
        }

        _ownerOf[id] = to;

        delete getApproved[id];

        emit Transfer(from, to, id);
    }

    function safeTransferFrom(
        address from,
        address to,
        uint256 id
    ) public virtual {
        transferFrom(from, to, id);

        require(
            to.code.length == 0 ||
                ERC721TokenReceiver(to).onERC721Received(msg.sender, from, id, "") ==
                ERC721TokenReceiver.onERC721Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        bytes calldata data
    ) public virtual {
        transferFrom(from, to, id);

        require(
            to.code.length == 0 ||
                ERC721TokenReceiver(to).onERC721Received(msg.sender, from, id, data) ==
                ERC721TokenReceiver.onERC721Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    /*//////////////////////////////////////////////////////////////
                              ERC165 LOGIC
    //////////////////////////////////////////////////////////////*/

    function supportsInterface(bytes4 interfaceId) public view virtual returns (bool) {
        return
            interfaceId == 0x01ffc9a7 || // ERC165 Interface ID for ERC165
            interfaceId == 0x80ac58cd || // ERC165 Interface ID for ERC721
            interfaceId == 0x5b5e139f; // ERC165 Interface ID for ERC721Metadata
    }

    /*//////////////////////////////////////////////////////////////
                        INTERNAL MINT/BURN LOGIC
    //////////////////////////////////////////////////////////////*/

    function _mint(address to, uint256 id) internal virtual {
        require(to != address(0), "INVALID_RECIPIENT");

        require(_ownerOf[id] == address(0), "ALREADY_MINTED");

        // Counter overflow is incredibly unrealistic.
        unchecked {
            _balanceOf[to]++;
        }

        _ownerOf[id] = to;

        emit Transfer(address(0), to, id);
    }

    function _burn(uint256 id) internal virtual {
        address owner = _ownerOf[id];

        require(owner != address(0), "NOT_MINTED");

        // Ownership check above ensures no underflow.
        unchecked {
            _balanceOf[owner]--;
        }

        delete _ownerOf[id];

        delete getApproved[id];

        emit Transfer(owner, address(0), id);
    }

    /*//////////////////////////////////////////////////////////////
                        INTERNAL SAFE MINT LOGIC
    //////////////////////////////////////////////////////////////*/

    function _safeMint(address to, uint256 id) internal virtual {
        _mint(to, id);

        require(
            to.code.length == 0 ||
                ERC721TokenReceiver(to).onERC721Received(msg.sender, address(0), id, "") ==
                ERC721TokenReceiver.onERC721Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    function _safeMint(
        address to,
        uint256 id,
        bytes memory data
    ) internal virtual {
        _mint(to, id);

        require(
            to.code.length == 0 ||
                ERC721TokenReceiver(to).onERC721Received(msg.sender, address(0), id, data) ==
                ERC721TokenReceiver.onERC721Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }
}

/// @notice A generic interface for a contract which properly accepts ERC721 tokens.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC721.sol)
abstract contract ERC721TokenReceiver {
    function onERC721Received(
        address,
        address,
        uint256,
        bytes calldata
    ) external virtual returns (bytes4) {
        return ERC721TokenReceiver.onERC721Received.selector;
    }
}

/// @title NFT Receiver
/// @author Tessera
/// @notice Plugin contract for handling receipts of non-fungible tokens
contract NFTReceiver is ERC721TokenReceiver, ERC1155TokenReceiver {
    /// @notice Handles the receipt of a single ERC721 token
    function onERC721Received(
        address,
        address,
        uint256,
        bytes calldata
    ) external virtual override returns (bytes4) {
        return ERC721TokenReceiver.onERC721Received.selector;
    }

    /// @notice Handles the receipt of a single ERC1155 token type
    function onERC1155Received(
        address,
        address,
        uint256,
        uint256,
        bytes calldata
    ) external virtual override returns (bytes4) {
        return ERC1155TokenReceiver.onERC1155Received.selector;
    }

    /// @notice Handles the receipt of multiple ERC1155 token types
    function onERC1155BatchReceived(
        address,
        address,
        uint256[] calldata,
        uint256[] calldata,
        bytes calldata
    ) external virtual override returns (bytes4) {
        return ERC1155TokenReceiver.onERC1155BatchReceived.selector;
    }
}

/// @title Vault
/// @author Tessera
/// @notice Proxy contract for storing Assets
contract Vault is Clone, IVault, NFTReceiver {
    address public immutable original;
    /// @dev Minimum reserve of gas units
    uint256 private constant MIN_GAS_RESERVE = 5_000;
    uint256 private constant MERKLE_ROOT_POSITION = 0;
    uint256 private constant OWNER_POSITION = 32;
    uint256 private constant FACTORY_POSITION = 52;

    constructor() {
        original = address(this);
    }

    /// @dev Callback for receiving Ether when the calldata is empty
    receive() external payable {}

    /// @dev Executed if none of the other functions match the function identifier
    fallback() external payable {}

    /// @notice Executes vault transactions through delegatecall
    /// @param _target Target address
    /// @param _data Transaction data
    /// @param _proof Merkle proof of permission hash
    /// @return success Result status of delegatecall
    /// @return response Return data of delegatecall
    function execute(
        address _target,
        bytes calldata _data,
        bytes32[] calldata _proof
    ) external payable returns (bool success, bytes memory response) {
        bytes4 selector;
        assembly {
            selector := calldataload(_data.offset)
        }

        // Generate leaf node by hashing module, target and function selector.
        bytes32 leaf = keccak256(abi.encode(msg.sender, _target, selector));
        // Check that the caller is either a module with permission to call or the owner.
        if (!MerkleProof.verify(_proof, MERKLE_ROOT(), leaf)) {
            if (msg.sender != FACTORY() && msg.sender != OWNER())
                revert NotAuthorized(msg.sender, _target, selector);
        }

        (success, response) = _execute(_target, _data);
    }

    /// @notice Getter for merkle root stored as an immutable argument
    function MERKLE_ROOT() public pure returns (bytes32) {
        return _getArgBytes32(MERKLE_ROOT_POSITION);
    }

    /// @notice Getter for owner of vault
    function OWNER() public pure returns (address) {
        return _getArgAddress(OWNER_POSITION);
    }

    /// @notice Getter for factory of vault
    function FACTORY() public pure returns (address) {
        return _getArgAddress(FACTORY_POSITION);
    }

    /// @notice Executes plugin transactions through delegatecall
    /// @param _target Target address
    /// @param _data Transaction data
    /// @return success Result status of delegatecall
    /// @return response Return data of delegatecall
    function _execute(address _target, bytes calldata _data)
        internal
        returns (bool success, bytes memory response)
    {
        require(original != address(this), "only delegate call");
        if (_target.code.length == 0) revert TargetInvalid(_target);
        // Reserve some gas to ensure that the function has enough to finish the execution
        uint256 stipend = gasleft() - MIN_GAS_RESERVE;

        // Delegate call to the target contract
        (success, response) = _target.delegatecall{gas: stipend}(_data);

        // Revert if execution was unsuccessful
        if (!success) {
            if (response.length == 0) revert ExecutionReverted();
            _revertedWithReason(response);
        }
    }

    /// @notice Reverts transaction with reason
    /// @param _response Unsucessful return response of the delegate call
    function _revertedWithReason(bytes memory _response) internal pure {
        assembly {
            let returndata_size := mload(_response)
            revert(add(32, _response), returndata_size)
        }
    }
}

/// @title Vault Factory
/// @author Tessera
/// @notice Factory contract for deploying Tessera vaults
contract VaultFactory is IVaultFactory {
    /// @dev Use clones library for address types
    using Create2ClonesWithImmutableArgs for address;
    /// @notice Address of Vault proxy contract
    address public implementation;
    /// @dev Internal mapping to track the next seed to be used by an EOA
    mapping(address => bytes32) internal nextSeeds;

    /// @notice Initializes implementation contract
    constructor() {
        implementation = address(new Vault());
    }

    /// @notice Deploys new vault for sender
    /// @param _merkleRoot Merkle root of deployed vault
    /// @return vault Address of deployed vault
    function deploy(bytes32 _merkleRoot) external returns (address payable vault) {
        vault = deployFor(_merkleRoot, msg.sender);
    }

    /// @notice Gets pre-computed address of vault deployed by given account
    /// @param _origin Address of vault originating account
    /// @param _owner Address of vault deployer
    /// @param _merkleRoot Merkle root of deployed vault
    /// @return vault Address of next vault
    function getNextAddress(
        address _origin,
        address _owner,
        bytes32 _merkleRoot
    ) external view returns (address vault) {
        bytes32 salt = keccak256(abi.encode(_origin, nextSeeds[_origin]));
        (uint256 creationPtr, uint256 creationSize) = implementation.cloneCreationCode(
            abi.encodePacked(_merkleRoot, _owner, address(this))
        );
        bytes32 creationHash;
        // solhint-disable-next-line no-inline-assembly
        assembly {
            creationHash := keccak256(creationPtr, creationSize)
        }
        bytes32 data = keccak256(abi.encodePacked(bytes1(0xff), address(this), salt, creationHash));
        vault = address(uint160(uint256(data)));
    }

    /// @notice Gets next seed value of given account
    /// @param _deployer Address of vault deployer
    /// @return Value of next seed
    function getNextSeed(address _deployer) external view returns (bytes32) {
        return nextSeeds[_deployer];
    }

    /// @notice Deploys new vault for given address
    /// @param _merkleRoot Merkle root of deployed vault
    /// @param _owner Address of vault owner
    /// @return vault Address of deployed vault
    function deployFor(bytes32 _merkleRoot, address _owner) public returns (address payable vault) {
        vault = _computeSalt(_merkleRoot, _owner);
    }

    /// @notice Deploys new vault for given address and executes calls
    /// @param _merkleRoot Merkle root of deployed vault
    /// @param _owner Address of vault owner
    /// @param _calls List of calls to execute upon deployment
    /// @return vault Address of deployed vault
    function deployFor(
        bytes32 _merkleRoot,
        address _owner,
        InitInfo[] calldata _calls
    ) public returns (address payable vault) {
        vault = _computeSalt(_merkleRoot, _owner);
        unchecked {
            for (uint256 i; i < _calls.length; ++i) {
                Vault(vault).execute(_calls[i].target, _calls[i].data, _calls[i].proof);
            }
        }
    }

    function _computeSalt(bytes32 _merkleRoot, address _owner)
        internal
        returns (address payable vault)
    {
        bytes32 seed = nextSeeds[tx.origin];

        // Prevent front-running the salt by hashing the concatenation of tx.origin and the user-provided seed.
        bytes32 salt = keccak256(abi.encode(tx.origin, seed));

        vault = _cloneVault(_merkleRoot, _owner, seed, salt);
    }

    function _cloneVault(
        bytes32 _merkleRoot,
        address _owner,
        bytes32 _seed,
        bytes32 _salt
    ) internal returns (address payable vault) {
        bytes memory data = abi.encodePacked(_merkleRoot, _owner, address(this));
        vault = implementation.clone(_salt, data);

        // Increment the seed.
        unchecked {
            nextSeeds[tx.origin] = bytes32(uint256(_seed) + 1);
        }

        /// Log the vault via en event.
        emit DeployVault(tx.origin, msg.sender, _owner, _seed, _salt, vault, _merkleRoot);
    }
}

/// @title Vault Registry
/// @author Tessera
/// @notice Registry contract for tracking all Rae vaults
contract VaultRegistry is IVaultRegistry {
    /// @dev Use clones library with address types
    using ClonesWithImmutableArgs for address;
    /// @notice Address of VaultFactory contract
    address public immutable factory;
    /// @notice Address of Rae token contract
    address public immutable rae;
    /// @notice Address of Implementation for Rae token contract
    address public immutable raeImplementation;
    /// @notice Mapping of collection address to next token ID type
    mapping(address => uint256) public nextId;
    /// @notice Mapping of vault address to vault information
    mapping(address => VaultInfo) public vaultToToken;

    /// @notice Initializes factory, implementation, and token contracts
    constructor() {
        factory = address(new VaultFactory());
        raeImplementation = address(new Rae());
        rae = raeImplementation.clone(abi.encodePacked(msg.sender, address(this)));
    }

    /// @notice Creates a new vault with permissions and initialization calls, and transfers ownership to a given owner
    /// @dev This should only be done in limited cases i.e. if you're okay with a trusted individual(s)
    /// having control over the vault. Ideally, execution would be locked behind a Multisig wallet.
    /// @param _merkleRoot Hash of merkle root for vault permissions
    /// @param _owner Address of the vault owner
    /// @param _calls List of initialization calls
    /// @return vault Address of Proxy contract
    function createFor(
        bytes32 _merkleRoot,
        address _owner,
        InitInfo[] calldata _calls
    ) public returns (address vault) {
        vault = _deployVault(_merkleRoot, _owner, rae, _calls);
    }

    /// @notice Creates a new vault with permissions
    /// @param _merkleRoot Hash of merkle root for vault permissions
    /// @return vault Address of Proxy contract
    function createFor(bytes32 _merkleRoot, address _owner) public returns (address vault) {
        vault = _deployVault(_merkleRoot, _owner, rae);
    }

    /// @notice Creates a new vault with permissions and initialization calls
    /// @param _merkleRoot Hash of merkle root for vault permissions
    /// @param _calls List of initialization calls
    /// @return vault Address of Proxy contract
    function create(bytes32 _merkleRoot, InitInfo[] calldata _calls)
        external
        returns (address vault)
    {
        vault = createFor(_merkleRoot, address(this), _calls);
    }

    /// @notice Creates a new vault with permissions and initialization calls
    /// @param _merkleRoot Hash of merkle root for vault permissions
    /// @return vault Address of Proxy contract
    function create(bytes32 _merkleRoot) external returns (address vault) {
        vault = createFor(_merkleRoot, address(this));
    }

    /// @notice Creates a new vault with permissions and initialization calls for a given controller
    /// @param _merkleRoot Hash of merkle root for vault permissions
    /// @param _controller Address of token controller
    /// @param _calls List of initialization calls
    /// @return vault Address of Proxy contract
    /// @return token Address of Rae contract
    function createCollectionFor(
        bytes32 _merkleRoot,
        address _controller,
        InitInfo[] calldata _calls
    ) public returns (address vault, address token) {
        token = raeImplementation.clone(abi.encodePacked(_controller, address(this)));
        vault = _deployVault(_merkleRoot, address(this), token, _calls);
    }

    /// @notice Creates a new vault with permissions and intialization calls for the message sender
    /// @param _merkleRoot Hash of merkle root for vault permissions
    /// @param _calls List of initialization calls
    /// @return vault Address of Proxy contract
    /// @return token Address of Rae contract
    function createCollection(bytes32 _merkleRoot, InitInfo[] calldata _calls)
        external
        returns (address vault, address token)
    {
        (vault, token) = createCollectionFor(_merkleRoot, msg.sender, _calls);
    }

    /// @notice Creates a new vault with permissions and initialization calls for an existing collection
    /// @param _merkleRoot Hash of merkle root for vault permissions
    /// @param _token Address of Rae contract
    /// @param _calls List of initialization calls
    /// @return vault Address of Proxy contract
    function createInCollection(
        bytes32 _merkleRoot,
        address _token,
        InitInfo[] calldata _calls
    ) external returns (address vault) {
        address controller = Rae(_token).controller();
        if (controller != msg.sender) revert InvalidController(controller, msg.sender);
        vault = _deployVault(_merkleRoot, address(this), _token, _calls);
    }

    /// @notice Burns vault tokens
    /// @param _from Source address
    /// @param _value Amount of tokens
    function burn(address _from, uint256 _value) external {
        VaultInfo memory info = vaultToToken[msg.sender];
        uint256 id = info.id;
        if (id == 0) revert UnregisteredVault(msg.sender);
        Rae(info.token).burn(_from, id, _value);
    }

    /// @notice Mints vault tokens
    /// @param _to Target address
    /// @param _value Amount of tokens
    function mint(address _to, uint256 _value) external {
        VaultInfo memory info = vaultToToken[msg.sender];
        uint256 id = info.id;
        if (id == 0) revert UnregisteredVault(msg.sender);
        Rae(info.token).mint(_to, id, _value, "");
    }

    /// @notice Gets the total supply for a token and ID associated with a vault
    /// @param _vault Address of the vault
    /// @return Total supply
    function totalSupply(address _vault) external view returns (uint256) {
        VaultInfo memory info = vaultToToken[_vault];
        return Rae(info.token).totalSupply(info.id);
    }

    /// @notice Gets the uri for a given token and ID associated with a vault
    /// @param _vault Address of the vault
    /// @return URI of token
    function uri(address _vault) external view returns (string memory) {
        VaultInfo memory info = vaultToToken[_vault];
        return Rae(info.token).uri(info.id);
    }

    /// @dev Deploys new vault for specified token and sets the merkle root
    /// @param _merkleRoot Hash of merkle root for vault permissions
    /// @param _token Address of Rae contract
    /// @return vault Address of Proxy contract
    function _deployVault(
        bytes32 _merkleRoot,
        address _owner,
        address _token
    ) internal returns (address vault) {
        vault = VaultFactory(factory).deployFor(_merkleRoot, _owner);
        vaultToToken[vault] = VaultInfo(_token, ++nextId[_token]);
        emit VaultDeployed(vault, _token, nextId[_token]);
    }

    /// @dev Deploys new vault for specified token and sets the merkle root
    /// @param _merkleRoot Hash of merkle root for vault permissions
    /// @param _token Address of Rae contract
    /// @param _calls List of initialization calls
    /// @return vault Address of Proxy contract
    function _deployVault(
        bytes32 _merkleRoot,
        address _owner,
        address _token,
        InitInfo[] calldata _calls
    ) internal returns (address vault) {
        // pre-compute the next vault's address in order to register it before initialization calls
        vault = VaultFactory(factory).getNextAddress(tx.origin, _owner, _merkleRoot);
        vaultToToken[vault] = VaultInfo(_token, ++nextId[_token]);
        VaultFactory(factory).deployFor(_merkleRoot, _owner, _calls);
        emit VaultDeployed(vault, _token, nextId[_token]);
    }
}

{
  "optimizer": {
    "enabled": true,
    "runs": 200
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
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}

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