// File: @openzeppelin/contracts/access/AccessControl.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (access/AccessControl.sol)

pragma solidity ^0.8.0;

import "./IAccessControl.sol";
import "../utils/Context.sol";
import "../utils/Strings.sol";
import "../utils/introspection/ERC165.sol";

/**
 * @dev Contract module that allows children to implement role-based access
 * control mechanisms. This is a lightweight version that doesn't allow enumerating role
 * members except through off-chain means by accessing the contract event logs. Some
 * applications may benefit from on-chain enumerability, for those cases see
 * {AccessControlEnumerable}.
 *
 * Roles are referred to by their `bytes32` identifier. These should be exposed
 * in the external API and be unique. The best way to achieve this is by
 * using `public constant` hash digests:
 *
 * ```solidity
 * bytes32 public constant MY_ROLE = keccak256("MY_ROLE");
 * ```
 *
 * Roles can be used to represent a set of permissions. To restrict access to a
 * function call, use {hasRole}:
 *
 * ```solidity
 * function foo() public {
 *     require(hasRole(MY_ROLE, msg.sender));
 *     ...
 * }
 * ```
 *
 * Roles can be granted and revoked dynamically via the {grantRole} and
 * {revokeRole} functions. Each role has an associated admin role, and only
 * accounts that have a role's admin role can call {grantRole} and {revokeRole}.
 *
 * By default, the admin role for all roles is `DEFAULT_ADMIN_ROLE`, which means
 * that only accounts with this role will be able to grant or revoke other
 * roles. More complex role relationships can be created by using
 * {_setRoleAdmin}.
 *
 * WARNING: The `DEFAULT_ADMIN_ROLE` is also its own admin: it has permission to
 * grant and revoke this role. Extra precautions should be taken to secure
 * accounts that have been granted it. We recommend using {AccessControlDefaultAdminRules}
 * to enforce additional security measures for this role.
 */
abstract contract AccessControl is Context, IAccessControl, ERC165 {
    struct RoleData {
        mapping(address => bool) members;
        bytes32 adminRole;
    }

    mapping(bytes32 => RoleData) private _roles;

    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;

    /**
     * @dev Modifier that checks that an account has a specific role. Reverts
     * with a standardized message including the required role.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     *
     * _Available since v4.1._
     */
    modifier onlyRole(bytes32 role) {
        _checkRole(role);
        _;
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IAccessControl).interfaceId || super.supportsInterface(interfaceId);
    }

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) public view virtual override returns (bool) {
        return _roles[role].members[account];
    }

    /**
     * @dev Revert with a standard message if `_msgSender()` is missing `role`.
     * Overriding this function changes the behavior of the {onlyRole} modifier.
     *
     * Format of the revert message is described in {_checkRole}.
     *
     * _Available since v4.6._
     */
    function _checkRole(bytes32 role) internal view virtual {
        _checkRole(role, _msgSender());
    }

    /**
     * @dev Revert with a standard message if `account` is missing `role`.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     */
    function _checkRole(bytes32 role, address account) internal view virtual {
        if (!hasRole(role, account)) {
            revert(
                string(
                    abi.encodePacked(
                        "AccessControl: account ",
                        Strings.toHexString(account),
                        " is missing role ",
                        Strings.toHexString(uint256(role), 32)
                    )
                )
            );
        }
    }

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) public view virtual override returns (bytes32) {
        return _roles[role].adminRole;
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     *
     * May emit a {RoleGranted} event.
     */
    function grantRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _grantRole(role, account);
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     *
     * May emit a {RoleRevoked} event.
     */
    function revokeRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _revokeRole(role, account);
    }

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been revoked `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     *
     * May emit a {RoleRevoked} event.
     */
    function renounceRole(bytes32 role, address account) public virtual override {
        require(account == _msgSender(), "AccessControl: can only renounce roles for self");

        _revokeRole(role, account);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event. Note that unlike {grantRole}, this function doesn't perform any
     * checks on the calling account.
     *
     * May emit a {RoleGranted} event.
     *
     * [WARNING]
     * ====
     * This function should only be called from the constructor when setting
     * up the initial roles for the system.
     *
     * Using this function in any other way is effectively circumventing the admin
     * system imposed by {AccessControl}.
     * ====
     *
     * NOTE: This function is deprecated in favor of {_grantRole}.
     */
    function _setupRole(bytes32 role, address account) internal virtual {
        _grantRole(role, account);
    }

    /**
     * @dev Sets `adminRole` as ``role``'s admin role.
     *
     * Emits a {RoleAdminChanged} event.
     */
    function _setRoleAdmin(bytes32 role, bytes32 adminRole) internal virtual {
        bytes32 previousAdminRole = getRoleAdmin(role);
        _roles[role].adminRole = adminRole;
        emit RoleAdminChanged(role, previousAdminRole, adminRole);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleGranted} event.
     */
    function _grantRole(bytes32 role, address account) internal virtual {
        if (!hasRole(role, account)) {
            _roles[role].members[account] = true;
            emit RoleGranted(role, account, _msgSender());
        }
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleRevoked} event.
     */
    function _revokeRole(bytes32 role, address account) internal virtual {
        if (hasRole(role, account)) {
            _roles[role].members[account] = false;
            emit RoleRevoked(role, account, _msgSender());
        }
    }
}

// File: @openzeppelin/contracts/access/IAccessControl.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (access/IAccessControl.sol)

pragma solidity ^0.8.0;

/**
 * @dev External interface of AccessControl declared to support ERC165 detection.
 */
interface IAccessControl {
    /**
     * @dev Emitted when `newAdminRole` is set as ``role``'s admin role, replacing `previousAdminRole`
     *
     * `DEFAULT_ADMIN_ROLE` is the starting admin for all roles, despite
     * {RoleAdminChanged} not being emitted signaling this.
     *
     * _Available since v3.1._
     */
    event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);

    /**
     * @dev Emitted when `account` is granted `role`.
     *
     * `sender` is the account that originated the contract call, an admin role
     * bearer except when using {AccessControl-_setupRole}.
     */
    event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Emitted when `account` is revoked `role`.
     *
     * `sender` is the account that originated the contract call:
     *   - if using `revokeRole`, it is the admin role bearer
     *   - if using `renounceRole`, it is the role bearer (i.e. `account`)
     */
    event RoleRevoked(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) external view returns (bool);

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {AccessControl-_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) external view returns (bytes32);

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been granted `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     */
    function renounceRole(bytes32 role, address account) external;
}

// File: @openzeppelin/contracts/utils/Context.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
}

// File: @openzeppelin/contracts/utils/Strings.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/Math.sol";
import "./math/SignedMath.sol";

/**
 * @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 `int256` to its ASCII `string` decimal representation.
     */
    function toString(int256 value) internal pure returns (string memory) {
        return string(abi.encodePacked(value < 0 ? "-" : "", toString(SignedMath.abs(value))));
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, 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 Returns true if the two strings are equal.
     */
    function equal(string memory a, string memory b) internal pure returns (bool) {
        return keccak256(bytes(a)) == keccak256(bytes(b));
    }
}

// File: @openzeppelin/contracts/utils/cryptography/ECDSA.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.0;

import "../Strings.sol";

/**
 * @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 message) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, "\x19Ethereum Signed Message:\n32")
            mstore(0x1c, hash)
            message := keccak256(0x00, 0x3c)
        }
    }

    /**
     * @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 data) {
        /// @solidity memory-safe-assembly
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, "\x19\x01")
            mstore(add(ptr, 0x02), domainSeparator)
            mstore(add(ptr, 0x22), structHash)
            data := keccak256(ptr, 0x42)
        }
    }

    /**
     * @dev Returns an Ethereum Signed Data with intended validator, created from a
     * `validator` and `data` according to the version 0 of EIP-191.
     *
     * See {recover}.
     */
    function toDataWithIntendedValidatorHash(address validator, bytes memory data) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x00", validator, data));
    }
}

// File: @openzeppelin/contracts/utils/introspection/ERC165.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165.sol)

pragma solidity ^0.8.0;

import "./IERC165.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 *
 * Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
 */
abstract contract ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// File: @openzeppelin/contracts/utils/introspection/IERC165.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165 {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

// File: @openzeppelin/contracts/utils/math/Math.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library 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) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1, "Math: mulDiv overflow");

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10 ** 64) {
                value /= 10 ** 64;
                result += 64;
            }
            if (value >= 10 ** 32) {
                value /= 10 ** 32;
                result += 32;
            }
            if (value >= 10 ** 16) {
                value /= 10 ** 16;
                result += 16;
            }
            if (value >= 10 ** 8) {
                value /= 10 ** 8;
                result += 8;
            }
            if (value >= 10 ** 4) {
                value /= 10 ** 4;
                result += 4;
            }
            if (value >= 10 ** 2) {
                value /= 10 ** 2;
                result += 2;
            }
            if (value >= 10 ** 1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);
        }
    }
}

// File: @openzeppelin/contracts/utils/math/SignedMath.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }

    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}

// File: contracts/BlockHistory.sol



/// SPDX-License-Identifier: UNLICENSED
/// (c) Theori, Inc. 2022
/// All rights reserved

pragma solidity >=0.8.0;

import "@openzeppelin/contracts/access/AccessControl.sol";

import "./lib/CoreTypes.sol";
import "./lib/MerkleTree.sol";
import "./lib/AuxMerkleTree.sol";
import "./interfaces/IBlockHistory.sol";
import "./interfaces/IRecursiveVerifier.sol";

import {
    RecursiveProof,
    SignedRecursiveProof,
    getProofSigner,
    readHashWords
} from "./lib/Proofs.sol";

/**
 * @title BlockHistory
 * @author Theori, Inc.
 * @notice BlockHistory allows trustless and cheap verification of any
 *         historical block hash. Historical blocks are divided into chunks of
 *         fixed size, and each chunk's merkle root is stored on-chain. The
 *         merkle roots are validated on chain using aggregated SNARK proofs,
 *         enabling both trustlessness and scalability.
 *
 * @dev Each SNARK proof validates some contiguous block headers and has
 *      public inputs (parentHash, lastHash, merkleRoot). Here the merkleRoot
 *      is the merkleRoot of all block hashes contained in the proof, which may
 *      commit to many merkle roots which to commit on chain. If the last block
 *      is recent enough (<= 256 blocks old), the lastHash can be confirmed in
 *      the EVM, verifying that all blocks of the proof belong to this chain.
 *      Due to this, the historical blocks' merkle roots are imported in reverse
 *      order.
 */
contract BlockHistory is AccessControl, IBlockHistory {
    bytes32 public constant ADMIN_ROLE = keccak256("ADMIN_ROLE");
    bytes32 public constant QUERY_ROLE = keccak256("QUERY_ROLE");

    // depth of the merkle trees whose roots we store in storage
    uint256 private constant MERKLE_TREE_DEPTH = 13;
    uint256 private constant BLOCKS_PER_CHUNK = 1 << MERKLE_TREE_DEPTH;

    /// @dev address of the reliquary, immutable
    address public immutable reliquary;

    /// @dev the expected signer of the SNARK proofs - if 0, then no signatures
    address public signer;

    /// @dev maps numBlocks => SNARK verifier (with VK embedded), only assigned
    ///      to in the constructor
    mapping(uint256 => IRecursiveVerifier) public verifiers;

    /// @dev parent hash of oldest block in current merkle trees
    ///      (0 once backlog fully imported)
    bytes32 public parentHash;

    /// @dev the earliest merkle root that has been imported
    uint256 public earliestRoot;

    /// @dev hash of most recent block in merkle trees
    bytes32 public lastHash;

    /// @dev merkle roots of block chunks between parentHash and lastHash
    mapping(uint256 => bytes32) private merkleRoots;

    /// @dev ZK-Friendly merkle roots, used by auxiliary SNARKs
    mapping(uint256 => bytes32) private auxiliaryRoots;

    /// @dev whether auth checks should run on aux root queries
    bool private needsAuth;

    event ImportMerkleRoot(uint256 indexed index, bytes32 merkleRoot, bytes32 auxiliaryRoot);
    event NewSigner(address newSigner);

    enum ProofType {
        Merkle,
        SNARK
    }

    /// @dev A SNARK + Merkle proof used to prove validity of a block
    struct MerkleSNARKProof {
        uint256 numBlocks;
        uint256 endBlock;
        SignedRecursiveProof snark;
        bytes32[] merkleProof;
    }

    struct ProofInputs {
        bytes32 parent;
        bytes32 last;
        bytes32 merkleRoot;
        bytes32 auxiliaryRoot;
    }

    constructor(
        uint256[] memory sizes,
        IRecursiveVerifier[] memory _verifiers,
        address _reliquary
    ) AccessControl() {
        _setupRole(DEFAULT_ADMIN_ROLE, msg.sender);
        _setupRole(ADMIN_ROLE, msg.sender);
        _setupRole(QUERY_ROLE, msg.sender);

        reliquary = _reliquary;
        signer = msg.sender;

        require(sizes.length == _verifiers.length);
        for (uint256 i = 0; i < sizes.length; i++) {
            require(address(verifiers[sizes[i]]) == address(0));
            verifiers[sizes[i]] = _verifiers[i];
        }
    }

    /**
     * @notice Checks if a SNARK is valid and signed as expected.
     *         Signatures checks are disabled if stored signer == address(0)
     *         Properties proven by the SNARK:
     *         - (parent ... last) form a valid block chain of length numBlocks
     *         - root is the merkle root of all contained blocks
     *
     * @param proof the aggregated proof
     * @param numBlocks the number of blocks contained in the proof
     * @return the validity
     */
    function validSNARK(SignedRecursiveProof calldata proof, uint256 numBlocks)
        internal
        view
        returns (bool)
    {
        address expected = signer;
        if (expected != address(0) && getProofSigner(proof) != expected) {
            return false;
        }
        IRecursiveVerifier verifier = verifiers[numBlocks];
        require(address(verifier) != address(0), "invalid numBlocks");
        return verifier.verify(proof.inner);
    }

    /**
     * @notice Asserts that the provided SNARK proof is valid and contains
     *         the provied merkle roots.
     *
     * @param proof the aggregated proof
     * @param roots the block merkle roots
     * @param aux the auxiliary merkle roots
     * @return inputs the proof inputs
     */
    function assertValidSNARKWithRoots(
        SignedRecursiveProof calldata proof,
        bytes32[] calldata roots,
        bytes32[] calldata aux
    ) internal view returns (ProofInputs memory inputs) {
        require(roots.length & (roots.length - 1) == 0, "roots length must be a power of 2");
        require(roots.length == aux.length, "roots arrays must be same length");

        // extract the inputs from the proof
        inputs = parseProofInputs(proof);

        // ensure the merkle roots are valid
        require(inputs.merkleRoot == MerkleTree.computeRoot(roots), "invalid block roots");

        // ensure the auxiliary merkle roots are valid
        require(inputs.auxiliaryRoot == AuxMerkleTree.computeRoot(aux), "invalid aux roots");

        // assert the SNARK proof is valid
        require(validSNARK(proof, BLOCKS_PER_CHUNK * roots.length), "invalid SNARK");
    }

    /**
     * @notice Checks if the given block number/hash connects to the current
     *         block using a SNARK.
     *
     * @param num the block number to check
     * @param hash the block hash to check
     * @param encodedProof the encoded MerkleSNARKProof
     * @return the validity
     */
    function validBlockHashWithSNARK(
        bytes32 hash,
        uint256 num,
        bytes calldata encodedProof
    ) internal view returns (bool) {
        MerkleSNARKProof calldata proof = parseMerkleSNARKProof(encodedProof);

        ProofInputs memory inputs = parseProofInputs(proof.snark);

        // check that the proof ends with a current block
        if (!validCurrentBlock(inputs.last, proof.endBlock)) {
            return false;
        }

        if (!validSNARK(proof.snark, proof.numBlocks)) {
            return false;
        }

        // compute the first block number in the proof
        uint256 startBlock = proof.endBlock + 1 - proof.numBlocks;

        // check if the target block is the parent of the proven blocks
        if (num == startBlock - 1 && hash == inputs.parent) {
            // merkle proof not needed in this case
            return true;
        }

        // check if the target block is in the proven merkle root
        uint256 index = num - startBlock;
        return MerkleTree.validProof(inputs.merkleRoot, index, hash, proof.merkleProof);
    }

    /**
     * @notice Checks if the given block number + hash exists in a commited
     *         merkle tree.
     *
     * @param num the block number to check
     * @param hash the block hash to check
     * @param encodedProof the encoded merkle proof
     * @return the validity
     */
    function validBlockHashWithMerkle(
        bytes32 hash,
        uint256 num,
        bytes calldata encodedProof
    ) internal view returns (bool) {
        bytes32 merkleRoot = merkleRoots[num / BLOCKS_PER_CHUNK];
        if (merkleRoot == 0) {
            return false;
        }
        bytes32[] calldata proofHashes = parseMerkleProof(encodedProof);
        if (proofHashes.length != MERKLE_TREE_DEPTH) {
            return false;
        }
        return MerkleTree.validProof(merkleRoot, num % BLOCKS_PER_CHUNK, hash, proofHashes);
    }

    /**
     * @notice Checks if the block is a current block (defined as being
     *         accessible in the EVM, i.e. <= 256 blocks old) and that the hash
     *         is correct.
     *
     * @param hash the alleged block hash
     * @param num the block number
     * @return the validity
     */
    function validCurrentBlock(bytes32 hash, uint256 num) internal view returns (bool) {
        // the block hash must be accessible in the EVM and match
        return (block.number - num <= 256) && (blockhash(num) == hash);
    }

    /**
     * @notice Stores the merkle roots starting at the index
     *
     * @param index the index for the first merkle root
     * @param roots the merkle roots of the block hashes
     * @param aux the auxiliary merkle roots of the block hashes
     */
    function storeMerkleRoots(
        uint256 index,
        bytes32[] calldata roots,
        bytes32[] calldata aux
    ) internal {
        for (uint256 i = 0; i < roots.length; i++) {
            uint256 idx = index + i;
            merkleRoots[idx] = roots[i];
            auxiliaryRoots[idx] = aux[i];
            emit ImportMerkleRoot(idx, roots[i], aux[i]);
        }
    }

    /**
     * @notice Imports new chunks of blocks before the current parentHash
     *
     * @param proof the aggregated proof for these chunks
     * @param roots the merkle roots for the block hashes
     * @param aux the auxiliary roots for the block hashes
     */
    function importParent(
        SignedRecursiveProof calldata proof,
        bytes32[] calldata roots,
        bytes32[] calldata aux
    ) external {
        require(parentHash != 0 && earliestRoot != 0, "import not started or already completed");

        ProofInputs memory inputs = assertValidSNARKWithRoots(proof, roots, aux);

        // assert the last hash in the proof is our current parent hash
        require(parentHash == inputs.last, "proof doesn't connect with parentHash");

        // store the merkle roots
        uint256 index = earliestRoot - roots.length;
        storeMerkleRoots(index, roots, aux);

        // store the new parentHash and earliestRoot
        parentHash = inputs.parent;
        earliestRoot = index;
    }

    /**
     * @notice Imports new chunks of blocks after the current lastHash
     *
     * @param endBlock the last block number in the chunks
     * @param proof the aggregated proof for these chunks
     * @param roots the merkle roots for the block hashes
     * @param connectProof an optional SNARK proof connecting the proof to
     *                     a current block
     */
    function importLast(
        uint256 endBlock,
        SignedRecursiveProof calldata proof,
        bytes32[] calldata roots,
        bytes32[] calldata aux,
        bytes calldata connectProof
    ) external {
        require((endBlock + 1) % BLOCKS_PER_CHUNK == 0, "endBlock must end at a chunk boundary");

        ProofInputs memory inputs = assertValidSNARKWithRoots(proof, roots, aux);

        if (!validCurrentBlock(inputs.last, endBlock)) {
            // if the proof doesn't connect our lastHash with a current block,
            // then the connectProof must fill the gap
            require(
                validBlockHashWithSNARK(inputs.last, endBlock, connectProof),
                "connectProof invalid"
            );
        }

        uint256 index = (endBlock + 1) / BLOCKS_PER_CHUNK - roots.length;
        if (lastHash == 0) {
            // if we're importing for the first time, set parentHash and earliestRoot
            require(parentHash == 0);
            parentHash = inputs.parent;
            earliestRoot = index;
        } else {
            require(inputs.parent == lastHash, "proof doesn't connect with lastHash");
        }

        // store the new lastHash
        lastHash = inputs.last;

        // store the merkle roots
        storeMerkleRoots(index, roots, aux);
    }

    /**
     * @notice Checks if a block hash is valid. A proof is required unless the
     *         block is current (accesible in the EVM). If the target block has
     *         no commited merkle root, the proof must contain a SNARK proof.
     *
     * @param hash the hash to check
     * @param num the block number for the alleged hash
     * @param proof the merkle witness or SNARK proof (if needed)
     * @return the validity
     */
    function _validBlockHash(
        bytes32 hash,
        uint256 num,
        bytes calldata proof
    ) internal view returns (bool) {
        if (validCurrentBlock(hash, num)) {
            return true;
        }

        ProofType typ;
        (typ, proof) = parseProofType(proof);
        if (typ == ProofType.Merkle) {
            return validBlockHashWithMerkle(hash, num, proof);
        } else if (typ == ProofType.SNARK) {
            return validBlockHashWithSNARK(hash, num, proof);
        } else {
            revert("invalid proof type");
        }
    }

    /**
     * @notice Checks if a block hash is correct. A proof is required unless the
     *         block is current (accesible in the EVM). If the target block has
     *         no commited merkle root, the proof must contain a SNARK proof.
     *         Reverts if block hash or proof is invalid.
     *
     * @param hash the hash to check
     * @param num the block number for the alleged hash
     * @param proof the merkle witness or SNARK proof (if needed)
     */
    function validBlockHash(
        bytes32 hash,
        uint256 num,
        bytes calldata proof
    ) external view returns (bool) {
        require(msg.sender == reliquary || hasRole(QUERY_ROLE, msg.sender));
        require(num < block.number);
        return _validBlockHash(hash, num, proof);
    }

    /**
     * @notice Queries an auxRoot
     *
     * @dev only authorized addresses can call this
     * @param idx the index of the root to query
     */
    function auxRoots(uint256 idx) external view returns (bytes32 root) {
        if (needsAuth) {
            _checkRole(QUERY_ROLE);
        }
        root = auxiliaryRoots[idx];
    }

    /**
     * @notice sets the needsAuth flag which controls auxRoot query auth checks
     *
     * @dev only the owner can call this
     * @param _needsAuth the new value
     */
    function setNeedsAuth(bool _needsAuth) external onlyRole(ADMIN_ROLE) {
        needsAuth = _needsAuth;
    }

    /**
     * @notice Parses a proof type and proof from the encoded proof
     *
     * @param proof the encoded proof
     * @return typ the proof type (SNARK or Merkle)
     * @return proof the remaining encoded proof
     */
    function parseProofType(bytes calldata encodedProof)
        internal
        pure
        returns (ProofType typ, bytes calldata proof)
    {
        require(encodedProof.length > 0, "cannot parse proof type");
        typ = ProofType(uint8(encodedProof[0]));
        proof = encodedProof[1:];
    }

    /**
     * @notice Parses a MerkleSNARKProof from calldata bytes
     *
     * @param proof the encoded proof
     * @return result a MerkleSNARKProof
     */
    function parseMerkleSNARKProof(bytes calldata proof)
        internal
        pure
        returns (MerkleSNARKProof calldata result)
    {
        // solidity doesn't support getting calldata outputs from abi.decode
        // but we can decode it; calldata structs are just offsets
        assembly {
            result := proof.offset
        }
    }

    /**
     * @notice Parses a merkle inclusion proof from the bytes
     *
     * @param proof the encoded merkle inclusion proof
     * @return result the array of proof hashes
     */
    function parseMerkleProof(bytes calldata proof)
        internal
        pure
        returns (bytes32[] calldata result)
    {
        require(proof.length % 32 == 0);
        require(proof.length >= 32);

        // solidity doesn't support getting calldata outputs from abi.decode
        // but we can decode it; calldata arrays are just (offset,length)
        assembly {
            result.offset := add(proof.offset, 0x20)
            result.length := calldataload(proof.offset)
        }
    }

    /**
     * @notice Parses the proof inputs for block history snark proofs
     *
     * @param proof the snark proof
     * @return result the parsed proof inputs
     */
    function parseProofInputs(SignedRecursiveProof calldata proof)
        internal
        pure
        returns (ProofInputs memory result)
    {
        uint256[] calldata inputs = proof.inner.inputs;
        require(inputs.length == 13);
        result = ProofInputs(
            readHashWords(inputs[0:4]),
            readHashWords(inputs[4:8]),
            readHashWords(inputs[8:12]),
            bytes32(inputs[12])
        );
    }

    /**
     * @notice sets the expected signer of the SNARK proofs, only callable by
     *         the contract owner
     *
     * @param _signer the new signer; if 0, disables signature checks
     */
    function setSigner(address _signer) external onlyRole(ADMIN_ROLE) {
        require(signer != _signer);
        signer = _signer;
        emit NewSigner(_signer);
    }
}

// File: contracts/interfaces/IBlockHistory.sol



/// SPDX-License-Identifier: UNLICENSED
/// (c) Theori, Inc. 2022
/// All rights reserved

pragma solidity >=0.8.0;

/**
 * @title Block history provider
 * @author Theori, Inc.
 * @notice IBlockHistory provides a way to verify a blockhash
 */

interface IBlockHistory {
    /**
     * @notice Determine if the given hash corresponds to the given block
     * @param hash the hash if the block in question
     * @param num the number of the block in question
     * @param proof any witness data required to prove the block hash is
     *        correct (such as a Merkle or SNARK proof)
     * @return boolean indicating if the block hash can be verified correct
     */
    function validBlockHash(
        bytes32 hash,
        uint256 num,
        bytes calldata proof
    ) external view returns (bool);
}

// File: contracts/interfaces/IRecursiveVerifier.sol



/// SPDX-License-Identifier: UNLICENSED
/// (c) Theori, Inc. 2022
/// All rights reserved

pragma solidity >=0.8.0;

import {RecursiveProof} from "../lib/Proofs.sol";

/**
 * @title Verifier of zk-SNARK proofs
 * @author Theori, Inc.
 * @notice Provider of validity checking of zk-SNARKs
 */
interface IRecursiveVerifier {
    /**
     * @notice Checks the validity of SNARK data
     * @param proof the proof to verify
     * @return the validity of the proof
     */
    function verify(RecursiveProof calldata proof) external view returns (bool);
}

// File: contracts/lib/AnemoiJive.sol



/// SPDX-License-Identifier: UNLICENSED
/// (c) Theori, Inc. 2022
/// All rights reserved

pragma solidity >=0.8.0;

/**
 * @title AnemoiJive
 * @author Theori, Inc.
 * @notice Implementation of the Anemoi hash function and Jive mode of operation
 */
library AnemoiJive {
    uint256 constant beta = 5;
    uint256 constant alpha_inv =
        17510594297471420177797124596205820070838691520332827474958563349260646796493;
    uint256 constant q =
        21888242871839275222246405745257275088548364400416034343698204186575808495617;
    uint256 constant delta =
        8755297148735710088898562298102910035419345760166413737479281674630323398247;

    function CD(uint256 round) internal pure returns (uint256, uint256) {
        if (round == 0)
            return (
                37,
                8755297148735710088898562298102910035419345760166413737479281674630323398284
            );
        if (round == 1)
            return (
                13352247125433170118601974521234241686699252132838635793584252509352796067497,
                5240474505904316858775051800099222288270827863409873986701694203345984265770
            );
        if (round == 2)
            return (
                8959866518978803666083663798535154543742217570455117599799616562379347639707,
                9012679925958717565787111885188464538194947839997341443807348023221726055342
            );
        if (round == 3)
            return (
                3222831896788299315979047232033900743869692917288857580060845801753443388885,
                21855834035835287540286238525800162342051591799629360593177152465113152235615
            );
        if (round == 4)
            return (
                11437915391085696126542499325791687418764799800375359697173212755436799377493,
                11227229470941648605622822052481187204980748641142847464327016901091886692935
            );
        if (round == 5)
            return (
                14725846076402186085242174266911981167870784841637418717042290211288365715997,
                8277823808153992786803029269162651355418392229624501612473854822154276610437
            );
        if (round == 6)
            return (
                3625896738440557179745980526949999799504652863693655156640745358188128872126,
                20904607884889140694334069064199005451741168419308859136555043894134683701950
            );
        if (round == 7)
            return (
                463291105983501380924034618222275689104775247665779333141206049632645736639,
                1902748146936068574869616392736208205391158973416079524055965306829204527070
            );
        if (round == 8)
            return (
                17443852951621246980363565040958781632244400021738903729528591709655537559937,
                14452570815461138929654743535323908350592751448372202277464697056225242868484
            );
        if (round == 9)
            return (
                10761214205488034344706216213805155745482379858424137060372633423069634639664,
                10548134661912479705005015677785100436776982856523954428067830720054853946467
            );
        if (round == 10)
            return (
                1555059412520168878870894914371762771431462665764010129192912372490340449901,
                17068729307795998980462158858164249718900656779672000551618940554342475266265
            );
        if (round == 11)
            return (
                7985258549919592662769781896447490440621354347569971700598437766156081995625,
                16199718037005378969178070485166950928725365516399196926532630556982133691321
            );
        if (round == 12)
            return (
                9570976950823929161626934660575939683401710897903342799921775980893943353035,
                19148564379197615165212957504107910110246052442686857059768087896511716255278
            );
        if (round == 13)
            return (
                17962366505931708682321542383646032762931774796150042922562707170594807376009,
                5497141763311860520411283868772341077137612389285480008601414949457218086902
            );
        if (round == 14)
            return (
                12386136552538719544323156650508108618627836659179619225468319506857645902649,
                18379046272821041930426853913114663808750865563081998867954732461233335541378
            );
        if (round == 15)
            return (
                21184636178578575123799189548464293431630680704815247777768147599366857217074,
                7696001730141875853127759241422464241772355903155684178131833937483164915734
            );
        if (round == 16)
            return (
                3021529450787050964585040537124323203563336821758666690160233275817988779052,
                963844642109550260189938374814031216012862679737123536423540607519656220143
            );
        if (round == 17)
            return (
                7005374570978576078843482270548485551486006385990713926354381743200520456088,
                12412434690468911461310698766576920805270445399824272791985598210955534611003
            );
        if (round == 18)
            return (
                3870834761329466217812893622834770840278912371521351591476987639109753753261,
                6971318955459107915662273112161635903624047034354567202210253298398705502050
            );
        revert();
    }

    function expmod(
        uint256 base,
        uint256 e,
        uint256 m
    ) internal view returns (uint256 o) {
        assembly {
            // define pointer
            let p := mload(0x40)
            // store data assembly-favouring ways
            mstore(p, 0x20) // Length of Base
            mstore(add(p, 0x20), 0x20) // Length of Exponent
            mstore(add(p, 0x40), 0x20) // Length of Modulus
            mstore(add(p, 0x60), base) // Base
            mstore(add(p, 0x80), e) // Exponent
            mstore(add(p, 0xa0), m) // Modulus
            if iszero(staticcall(sub(gas(), 2000), 0x05, p, 0xc0, p, 0x20)) {
                revert(0, 0)
            }
            // data
            o := mload(p)
        }
    }

    function sbox(uint256 x, uint256 y) internal view returns (uint256, uint256) {
        x = addmod(x, q - mulmod(beta, mulmod(y, y, q), q), q);
        y = addmod(y, q - expmod(x, alpha_inv, q), q);
        x = addmod(addmod(x, mulmod(beta, mulmod(y, y, q), q), q), delta, q);
        return (x, y);
    }

    function ll(uint256 x, uint256 y) internal pure returns (uint256 r0, uint256 r1) {
        r0 = addmod(x, mulmod(5, y, q), q);
        r1 = addmod(y, mulmod(5, r0, q), q);
    }

    function compress(uint256 x, uint256 y) internal view returns (uint256) {
        uint256 sum = addmod(x, y, q);
        uint256 c;
        uint256 d;
        for (uint256 r = 0; r < 19; r++) {
            (c, d) = CD(r);
            x = addmod(x, c, q);
            y = addmod(y, d, q);
            (x, y) = ll(x, y);
            (x, y) = sbox(x, y);
        }
        (x, y) = ll(x, y);
        return addmod(addmod(x, y, q), sum, q);
    }
}

// File: contracts/lib/AuxMerkleTree.sol



/// SPDX-License-Identifier: UNLICENSED
/// (c) Theori, Inc. 2022
/// All rights reserved

pragma solidity >=0.8.0;

import "./AnemoiJive.sol";

/**
 * @title Auxiliary Merkle Tree
 * @author Theori, Inc.
 * @notice Gas optimized arithmetic-friendly merkle tree code.
 * @dev uses Anemoi / Jive 2-to-1
 */
library AuxMerkleTree {
    /**
     * @notice computes a jive merkle root of the provided hashes, in place
     * @param temp the mutable array of hashes
     * @return root the merkle root hash
     */
    function computeRoot(bytes32[] memory temp) internal view returns (bytes32 root) {
        uint256 count = temp.length;
        while (count > 1) {
            unchecked {
                for (uint256 i = 0; i < count / 2; i++) {
                    uint256 x;
                    uint256 y;
                    assembly {
                        let ptr := add(temp, add(0x20, mul(0x40, i)))
                        x := mload(ptr)
                        ptr := add(ptr, 0x20)
                        y := mload(ptr)
                    }
                    x = AnemoiJive.compress(x, y);
                    assembly {
                        mstore(add(temp, add(0x20, mul(0x20, i))), x)
                    }
                }
                count >>= 1;
            }
        }
        return temp[0];
    }
}

// File: contracts/lib/BytesCalldata.sol



/// SPDX-License-Identifier: UNLICENSED
/// (c) Theori, Inc. 2022
/// All rights reserved

pragma solidity >=0.8.13;

// custom bytes calldata pointer storing (length | offset) in one word,
// also allows calldata pointers to be stored in memory
type BytesCalldata is uint256;

using BytesCalldataOps for BytesCalldata global;

// can't introduce global using .. for non UDTs
// each consumer should add the following line:
using BytesCalldataOps for bytes;

/**
 * @author Theori, Inc
 * @title BytesCalldataOps
 * @notice Common operations for bytes calldata, implemented for both the builtin
 *         type and our BytesCalldata type. These operations are heavily optimized
 *         and omit safety checks, so this library should only be used when memory
 *         safety is not a security issue.
 */
library BytesCalldataOps {
    function length(BytesCalldata bc) internal pure returns (uint256 result) {
        assembly {
            result := shr(128, shl(128, bc))
        }
    }

    function offset(BytesCalldata bc) internal pure returns (uint256 result) {
        assembly {
            result := shr(128, bc)
        }
    }

    function convert(BytesCalldata bc) internal pure returns (bytes calldata value) {
        assembly {
            value.offset := shr(128, bc)
            value.length := shr(128, shl(128, bc))
        }
    }

    function convert(bytes calldata inp) internal pure returns (BytesCalldata bc) {
        assembly {
            bc := or(shl(128, inp.offset), inp.length)
        }
    }

    function slice(
        BytesCalldata bc,
        uint256 start,
        uint256 len
    ) internal pure returns (BytesCalldata result) {
        assembly {
            result := shl(128, add(shr(128, bc), start)) // add to the offset and clear the length
            result := or(result, len) // set the new length
        }
    }

    function slice(
        bytes calldata value,
        uint256 start,
        uint256 len
    ) internal pure returns (bytes calldata result) {
        assembly {
            result.offset := add(value.offset, start)
            result.length := len
        }
    }

    function prefix(BytesCalldata bc, uint256 len) internal pure returns (BytesCalldata result) {
        assembly {
            result := shl(128, shr(128, bc)) // clear out the length
            result := or(result, len) // set it to the new length
        }
    }

    function prefix(bytes calldata value, uint256 len)
        internal
        pure
        returns (bytes calldata result)
    {
        assembly {
            result.offset := value.offset
            result.length := len
        }
    }

    function suffix(BytesCalldata bc, uint256 start) internal pure returns (BytesCalldata result) {
        assembly {
            result := add(bc, shl(128, start)) // add to the offset
            result := sub(result, start) // subtract from the length
        }
    }

    function suffix(bytes calldata value, uint256 start)
        internal
        pure
        returns (bytes calldata result)
    {
        assembly {
            result.offset := add(value.offset, start)
            result.length := sub(value.length, start)
        }
    }

    function split(BytesCalldata bc, uint256 start)
        internal
        pure
        returns (BytesCalldata, BytesCalldata)
    {
        return (prefix(bc, start), suffix(bc, start));
    }

    function split(bytes calldata value, uint256 start)
        internal
        pure
        returns (bytes calldata, bytes calldata)
    {
        return (prefix(value, start), suffix(value, start));
    }
}

// File: contracts/lib/CoreTypes.sol



/// SPDX-License-Identifier: UNLICENSED
/// (c) Theori, Inc. 2022
/// All rights reserved

pragma solidity >=0.8.0;

import "./BytesCalldata.sol";
import "./RLP.sol";

/**
 * @title CoreTypes
 * @author Theori, Inc.
 * @notice Data types and parsing functions for core types, including block headers
 *         and account data.
 */
library CoreTypes {
    using BytesCalldataOps for bytes;
    struct BlockHeaderData {
        bytes32 ParentHash;
        address Coinbase;
        bytes32 Root;
        bytes32 TxHash;
        bytes32 ReceiptHash;
        uint256 Number;
        uint256 GasLimit;
        uint256 GasUsed;
        uint256 Time;
        bytes32 MixHash;
        uint256 BaseFee;
        bytes32 WithdrawalsHash;
    }

    struct AccountData {
        uint256 Nonce;
        uint256 Balance;
        bytes32 StorageRoot;
        bytes32 CodeHash;
    }

    struct LogData {
        address Address;
        bytes32[] Topics;
        bytes Data;
    }

    struct WithdrawalData {
        uint256 Index;
        uint256 ValidatorIndex;
        address Address;
        uint256 AmountInGwei;
    }

    function parseHash(bytes calldata buf) internal pure returns (bytes32 result, uint256 offset) {
        uint256 value;
        (value, offset) = RLP.parseUint(buf);
        result = bytes32(value);
    }

    function parseAddress(bytes calldata buf)
        internal
        pure
        returns (address result, uint256 offset)
    {
        uint256 value;
        (value, offset) = RLP.parseUint(buf);
        result = address(uint160(value));
    }

    function parseBlockHeader(bytes calldata header)
        internal
        pure
        returns (BlockHeaderData memory data)
    {
        (uint256 listSize, uint256 offset) = RLP.parseList(header);
        header = header.slice(offset, listSize);

        (data.ParentHash, offset) = parseHash(header); // ParentHash
        header = header.suffix(offset);
        header = RLP.skip(header); // UncleHash
        (data.Coinbase, offset) = parseAddress(header); // Coinbase
        header = header.suffix(offset);
        (data.Root, offset) = parseHash(header); // Root
        header = header.suffix(offset);
        (data.TxHash, offset) = parseHash(header); // TxHash
        header = header.suffix(offset);
        (data.ReceiptHash, offset) = parseHash(header); // ReceiptHash
        header = header.suffix(offset);
        header = RLP.skip(header); // Bloom
        header = RLP.skip(header); // Difficulty
        (data.Number, offset) = RLP.parseUint(header); // Number
        header = header.suffix(offset);
        (data.GasLimit, offset) = RLP.parseUint(header); // GasLimit
        header = header.suffix(offset);
        (data.GasUsed, offset) = RLP.parseUint(header); // GasUsed
        header = header.suffix(offset);
        (data.Time, offset) = RLP.parseUint(header); // Time
        header = header.suffix(offset);
        header = RLP.skip(header); // Extra
        (data.MixHash, offset) = parseHash(header); // MixHash
        header = header.suffix(offset);
        header = RLP.skip(header); // Nonce

        if (header.length > 0) {
            (data.BaseFee, offset) = RLP.parseUint(header); // BaseFee
            header = header.suffix(offset);
        }

        if (header.length > 0) {
            (data.WithdrawalsHash, offset) = parseHash(header); // WithdrawalsHash
        }
    }

    function getBlockHeaderHashAndSize(bytes calldata header)
        internal
        pure
        returns (bytes32 blockHash, uint256 headerSize)
    {
        (uint256 listSize, uint256 offset) = RLP.parseList(header);
        unchecked {
            headerSize = offset + listSize;
        }
        blockHash = keccak256(header.prefix(headerSize));
    }

    function parseAccount(bytes calldata account) internal pure returns (AccountData memory data) {
        (, uint256 offset) = RLP.parseList(account);
        account = account.suffix(offset);

        (data.Nonce, offset) = RLP.parseUint(account); // Nonce
        account = account.suffix(offset);
        (data.Balance, offset) = RLP.parseUint(account); // Balance
        account = account.suffix(offset);
        (data.StorageRoot, offset) = parseHash(account); // StorageRoot
        account = account.suffix(offset);
        (data.CodeHash, offset) = parseHash(account); // CodeHash
        account = account.suffix(offset);
    }

    function parseLog(bytes calldata log) internal pure returns (LogData memory data) {
        (, uint256 offset) = RLP.parseList(log);
        log = log.suffix(offset);

        uint256 tmp;
        (tmp, offset) = RLP.parseUint(log); // Address
        data.Address = address(uint160(tmp));
        log = log.suffix(offset);

        (tmp, offset) = RLP.parseList(log); // Topics
        bytes calldata topics = log.slice(offset, tmp);
        log = log.suffix(offset + tmp);

        require(topics.length % 33 == 0);
        data.Topics = new bytes32[](tmp / 33);
        uint256 i = 0;
        while (topics.length > 0) {
            (data.Topics[i], offset) = parseHash(topics);
            topics = topics.suffix(offset);
            unchecked {
                i++;
            }
        }

        (data.Data, ) = RLP.splitBytes(log);
    }

    function extractLog(bytes calldata receiptValue, uint256 logIdx)
        internal
        pure
        returns (LogData memory)
    {
        // support EIP-2718: Currently all transaction types have the same
        // receipt RLP format, so we can just skip the receipt type byte
        if (receiptValue[0] < 0x80) {
            receiptValue = receiptValue.suffix(1);
        }

        (, uint256 offset) = RLP.parseList(receiptValue);
        receiptValue = receiptValue.suffix(offset);

        // pre EIP-658, receipts stored an intermediate state root in this field
        // post EIP-658, the field is a tx status (0 for failure, 1 for success)
        uint256 statusOrIntermediateRoot;
        (statusOrIntermediateRoot, offset) = RLP.parseUint(receiptValue);
        require(statusOrIntermediateRoot != 0, "tx did not succeed");
        receiptValue = receiptValue.suffix(offset);

        receiptValue = RLP.skip(receiptValue); // GasUsed
        receiptValue = RLP.skip(receiptValue); // LogsBloom

        uint256 length;
        (length, offset) = RLP.parseList(receiptValue); // Logs
        receiptValue = receiptValue.slice(offset, length);

        // skip the earlier logs
        for (uint256 i = 0; i < logIdx; i++) {
            require(receiptValue.length > 0, "log index does not exist");
            receiptValue = RLP.skip(receiptValue);
        }

        return parseLog(receiptValue);
    }

    function parseWithdrawal(bytes calldata withdrawal)
        internal
        pure
        returns (WithdrawalData memory data)
    {
        (, uint256 offset) = RLP.parseList(withdrawal);
        withdrawal = withdrawal.suffix(offset);

        (data.Index, offset) = RLP.parseUint(withdrawal); // Index
        withdrawal = withdrawal.suffix(offset);
        (data.ValidatorIndex, offset) = RLP.parseUint(withdrawal); // ValidatorIndex
        withdrawal = withdrawal.suffix(offset);
        (data.Address, offset) = parseAddress(withdrawal); // Address
        withdrawal = withdrawal.suffix(offset);
        (data.AmountInGwei, offset) = RLP.parseUint(withdrawal); // Amount
    }
}

// File: contracts/lib/MerkleTree.sol



/// SPDX-License-Identifier: UNLICENSED
/// (c) Theori, Inc. 2022
/// All rights reserved

pragma solidity >=0.8.0;

/**
 * @title Merkle Tree
 * @author Theori, Inc.
 * @notice Gas optimized SHA256 Merkle tree code.
 */
library MerkleTree {
    /**
     * @notice computes a SHA256 merkle root of the provided hashes, in place
     * @param temp the mutable array of hashes
     * @return the merkle root hash
     */
    function computeRoot(bytes32[] memory temp) internal view returns (bytes32) {
        uint256 count = temp.length;
        assembly {
            // repeat until we arrive at one root hash
            for {

            } gt(count, 1) {

            } {
                let dataElementLocation := add(temp, 0x20)
                let hashElementLocation := add(temp, 0x20)
                for {
                    let i := 0
                } lt(i, count) {
                    i := add(i, 2)
                } {
                    if iszero(
                        staticcall(gas(), 0x2, hashElementLocation, 0x40, dataElementLocation, 0x20)
                    ) {
                        revert(0, 0)
                    }
                    dataElementLocation := add(dataElementLocation, 0x20)
                    hashElementLocation := add(hashElementLocation, 0x40)
                }
                count := shr(1, count)
            }
        }
        return temp[0];
    }

    /**
     * @notice check if a hash is in the merkle tree for rootHash
     * @param rootHash the merkle root
     * @param index the index of the node to check
     * @param hash the hash to check
     * @param proofHashes the proof, i.e. the sequence of siblings from the
     *        node to root
     */
    function validProof(
        bytes32 rootHash,
        uint256 index,
        bytes32 hash,
        bytes32[] memory proofHashes
    ) internal view returns (bool result) {
        assembly {
            let constructedHash := hash
            let length := mload(proofHashes)
            let start := add(proofHashes, 0x20)
            let end := add(start, mul(length, 0x20))
            for {
                let ptr := start
            } lt(ptr, end) {
                ptr := add(ptr, 0x20)
            } {
                let proofHash := mload(ptr)

                // use scratch space (0x0 - 0x40) for hash input
                switch and(index, 1)
                case 0 {
                    mstore(0x0, constructedHash)
                    mstore(0x20, proofHash)
                }
                case 1 {
                    mstore(0x0, proofHash)
                    mstore(0x20, constructedHash)
                }

                // compute sha256
                if iszero(staticcall(gas(), 0x2, 0x0, 0x40, 0x0, 0x20)) {
                    revert(0, 0)
                }
                constructedHash := mload(0x0)

                index := shr(1, index)
            }
            result := eq(constructedHash, rootHash)
        }
    }
}

// File: contracts/lib/Proofs.sol



/// SPDX-License-Identifier: UNLICENSED
/// (c) Theori, Inc. 2022
/// All rights reserved

/*
 * @author Theori, Inc.
 */

pragma solidity >=0.8.0;

import "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";

uint256 constant BASE_PROOF_SIZE = 34;
uint256 constant SUBPROOF_LIMBS_SIZE = 16;

struct RecursiveProof {
    uint256[BASE_PROOF_SIZE] base;
    uint256[SUBPROOF_LIMBS_SIZE] subproofLimbs;
    uint256[] inputs;
}

struct SignedRecursiveProof {
    RecursiveProof inner;
    bytes signature;
}

/**
 * @notice recover the signer of the proof
 * @param proof the SignedRecursiveProof
 * @return the address of the signer
 */
function getProofSigner(SignedRecursiveProof calldata proof) pure returns (address) {
    bytes32 msgHash = keccak256(
        abi.encodePacked("\x19Ethereum Signed Message:\n", "32", hashProof(proof.inner))
    );
    return ECDSA.recover(msgHash, proof.signature);
}

/**
 * @notice hash the contents of a RecursiveProof
 * @param proof the RecursiveProof
 * @return result a 32-byte digest of the proof
 */
function hashProof(RecursiveProof calldata proof) pure returns (bytes32 result) {
    uint256[] calldata inputs = proof.inputs;
    assembly {
        let ptr := mload(0x40)
        let contigLen := mul(0x20, add(BASE_PROOF_SIZE, SUBPROOF_LIMBS_SIZE))
        let inputsLen := mul(0x20, inputs.length)
        calldatacopy(ptr, proof, contigLen)
        calldatacopy(add(ptr, contigLen), inputs.offset, inputsLen)
        result := keccak256(ptr, add(contigLen, inputsLen))
    }
}

/**
 * @notice reverse the byte order of a uint256
 * @param input the input value
 * @return v the byte-order reversed value
 */
function byteReverse(uint256 input) pure returns (uint256 v) {
    v = input;

    uint256 MASK08 = 0xFF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00;
    uint256 MASK16 = 0xFFFF0000FFFF0000FFFF0000FFFF0000FFFF0000FFFF0000FFFF0000FFFF0000;
    uint256 MASK32 = 0xFFFFFFFF00000000FFFFFFFF00000000FFFFFFFF00000000FFFFFFFF00000000;
    uint256 MASK64 = 0xFFFFFFFFFFFFFFFF0000000000000000FFFFFFFFFFFFFFFF0000000000000000;

    // swap bytes
    v = ((v & MASK08) >> 8) | ((v & (~MASK08)) << 8);

    // swap 2-byte long pairs
    v = ((v & MASK16) >> 16) | ((v & (~MASK16)) << 16);

    // swap 4-byte long pairs
    v = ((v & MASK32) >> 32) | ((v & (~MASK32)) << 32);

    // swap 8-byte long pairs
    v = ((v & MASK64) >> 64) | ((v & (~MASK64)) << 64);

    // swap 16-byte long pairs
    v = (v >> 128) | (v << 128);
}

/**
 * @notice reads a 32-byte hash from its little-endian word-encoded form
 * @param words the hash words
 * @return the hash
 */
function readHashWords(uint256[] calldata words) pure returns (bytes32) {
    uint256 mask = 0xffffffffffffffff;
    uint256 result = (words[0] & mask);
    result |= (words[1] & mask) << 0x40;
    result |= (words[2] & mask) << 0x80;
    result |= (words[3] & mask) << 0xc0;
    return bytes32(byteReverse(result));
}

// File: contracts/lib/RLP.sol



/// SPDX-License-Identifier: UNLICENSED
/// (c) Theori, Inc. 2022
/// All rights reserved

pragma solidity >=0.8.0;

/**
 * @title RLP
 * @author Theori, Inc.
 * @notice Gas optimized RLP parsing code. Note that some parsing logic is
 *         duplicated because helper functions are oddly expensive.
 */
library RLP {
    function parseUint(bytes calldata buf) internal pure returns (uint256 result, uint256 size) {
        assembly {
            // check that we have at least one byte of input
            if iszero(buf.length) {
                revert(0, 0)
            }
            let first32 := calldataload(buf.offset)
            let kind := shr(248, first32)

            // ensure it's a not a long string or list (> 0xB7)
            // also ensure it's not a short string longer than 32 bytes (> 0xA0)
            if gt(kind, 0xA0) {
                revert(0, 0)
            }

            switch lt(kind, 0x80)
            case true {
                // small single byte
                result := kind
                size := 1
            }
            case false {
                // short string
                size := sub(kind, 0x80)

                // ensure it's not reading out of bounds
                if lt(buf.length, size) {
                    revert(0, 0)
                }

                switch eq(size, 32)
                case true {
                    // if it's exactly 32 bytes, read it from calldata
                    result := calldataload(add(buf.offset, 1))
                }
                case false {
                    // if it's < 32 bytes, we've already read it from calldata
                    result := shr(shl(3, sub(32, size)), shl(8, first32))
                }
                size := add(size, 1)
            }
        }
    }

    function nextSize(bytes calldata buf) internal pure returns (uint256 size) {
        assembly {
            if iszero(buf.length) {
                revert(0, 0)
            }
            let first32 := calldataload(buf.offset)
            let kind := shr(248, first32)

            switch lt(kind, 0x80)
            case true {
                // small single byte
                size := 1
            }
            case false {
                switch lt(kind, 0xB8)
                case true {
                    // short string
                    size := add(1, sub(kind, 0x80))
                }
                case false {
                    switch lt(kind, 0xC0)
                    case true {
                        // long string
                        let lengthSize := sub(kind, 0xB7)

                        // ensure that we don't overflow
                        if gt(lengthSize, 31) {
                            revert(0, 0)
                        }

                        // ensure that we don't read out of bounds
                        if lt(buf.length, lengthSize) {
                            revert(0, 0)
                        }
                        size := shr(mul(8, sub(32, lengthSize)), shl(8, first32))
                        size := add(size, add(1, lengthSize))
                    }
                    case false {
                        switch lt(kind, 0xF8)
                        case true {
                            // short list
                            size := add(1, sub(kind, 0xC0))
                        }
                        case false {
                            let lengthSize := sub(kind, 0xF7)

                            // ensure that we don't overflow
                            if gt(lengthSize, 31) {
                                revert(0, 0)
                            }
                            // ensure that we don't read out of bounds
                            if lt(buf.length, lengthSize) {
                                revert(0, 0)
                            }
                            size := shr(mul(8, sub(32, lengthSize)), shl(8, first32))
                            size := add(size, add(1, lengthSize))
                        }
                    }
                }
            }
        }
    }

    function skip(bytes calldata buf) internal pure returns (bytes calldata) {
        uint256 size = RLP.nextSize(buf);
        assembly {
            buf.offset := add(buf.offset, size)
            buf.length := sub(buf.length, size)
        }
        return buf;
    }

    function parseList(bytes calldata buf)
        internal
        pure
        returns (uint256 listSize, uint256 offset)
    {
        assembly {
            // check that we have at least one byte of input
            if iszero(buf.length) {
                revert(0, 0)
            }
            let first32 := calldataload(buf.offset)
            let kind := shr(248, first32)

            // ensure it's a list
            if lt(kind, 0xC0) {
                revert(0, 0)
            }

            switch lt(kind, 0xF8)
            case true {
                // short list
                listSize := sub(kind, 0xC0)
                offset := 1
            }
            case false {
                // long list
                let lengthSize := sub(kind, 0xF7)

                // ensure that we don't overflow
                if gt(lengthSize, 31) {
                    revert(0, 0)
                }
                // ensure that we don't read out of bounds
                if lt(buf.length, lengthSize) {
                    revert(0, 0)
                }
                listSize := shr(mul(8, sub(32, lengthSize)), shl(8, first32))
                offset := add(lengthSize, 1)
            }
        }
    }

    function splitBytes(bytes calldata buf)
        internal
        pure
        returns (bytes calldata result, bytes calldata rest)
    {
        uint256 offset;
        uint256 size;
        assembly {
            // check that we have at least one byte of input
            if iszero(buf.length) {
                revert(0, 0)
            }
            let first32 := calldataload(buf.offset)
            let kind := shr(248, first32)

            // ensure it's a not list
            if gt(kind, 0xBF) {
                revert(0, 0)
            }

            switch lt(kind, 0x80)
            case true {
                // small single byte
                offset := 0
                size := 1
            }
            case false {
                switch lt(kind, 0xB8)
                case true {
                    // short string
                    offset := 1
                    size := sub(kind, 0x80)
                }
                case false {
                    // long string
                    let lengthSize := sub(kind, 0xB7)

                    // ensure that we don't overflow
                    if gt(lengthSize, 31) {
                        revert(0, 0)
                    }
                    // ensure we don't read out of bounds
                    if lt(buf.length, lengthSize) {
                        revert(0, 0)
                    }
                    size := shr(mul(8, sub(32, lengthSize)), shl(8, first32))
                    offset := add(lengthSize, 1)
                }
            }

            result.offset := add(buf.offset, offset)
            result.length := size

            let end := add(offset, size)
            rest.offset := add(buf.offset, end)
            rest.length := sub(buf.length, end)
        }
    }

    function encodeUint(uint256 value) internal pure returns (bytes memory) {
        // allocate our result bytes
        bytes memory result = new bytes(33);

        if (value == 0) {
            // store length = 1, value = 0x80
            assembly {
                mstore(add(result, 1), 0x180)
            }
            return result;
        }

        if (value < 128) {
            // store length = 1, value = value
            assembly {
                mstore(add(result, 1), or(0x100, value))
            }
            return result;
        }

        if (value > 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff) {
            // length 33, prefix 0xa0 followed by value
            assembly {
                mstore(add(result, 1), 0x21a0)
                mstore(add(result, 33), value)
            }
            return result;
        }

        if (value > 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff) {
            // length 32, prefix 0x9f followed by value
            assembly {
                mstore(add(result, 1), 0x209f)
                mstore(add(result, 33), shl(8, value))
            }
            return result;
        }

        assembly {
            let length := 1
            for {
                let min := 0x100
            } lt(sub(min, 1), value) {
                min := shl(8, min)
            } {
                length := add(length, 1)
            }

            let bytesLength := add(length, 1)

            // bytes length field
            let hi := shl(mul(bytesLength, 8), bytesLength)

            // rlp encoding of value
            let lo := or(shl(mul(length, 8), add(length, 0x80)), value)

            mstore(add(result, bytesLength), or(hi, lo))
        }
        return result;
    }
}