// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (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:
 *
 * ```
 * 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}:
 *
 * ```
 * 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.
 */
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());
        }
    }
}

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

pragma solidity ^0.8.1;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    function _revert(bytes memory returndata, string memory errorMessage) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert(errorMessage);
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.1) (utils/Checkpoints.sol)
// This file was procedurally generated from scripts/generate/templates/Checkpoints.js.

pragma solidity ^0.8.0;

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

/**
 * @dev This library defines the `History` struct, for checkpointing values as they change at different points in
 * time, and later looking up past values by block number. See {Votes} as an example.
 *
 * To create a history of checkpoints define a variable type `Checkpoints.History` in your contract, and store a new
 * checkpoint for the current transaction block using the {push} function.
 *
 * _Available since v4.5._
 */
library Checkpoints {
    struct History {
        Checkpoint[] _checkpoints;
    }

    struct Checkpoint {
        uint32 _blockNumber;
        uint224 _value;
    }

    /**
     * @dev Returns the value at a given block number. If a checkpoint is not available at that block, the closest one
     * before it is returned, or zero otherwise. Because the number returned corresponds to that at the end of the
     * block, the requested block number must be in the past, excluding the current block.
     */
    function getAtBlock(History storage self, uint256 blockNumber) internal view returns (uint256) {
        require(blockNumber < block.number, "Checkpoints: block not yet mined");
        uint32 key = SafeCast.toUint32(blockNumber);

        uint256 len = self._checkpoints.length;
        uint256 pos = _upperBinaryLookup(self._checkpoints, key, 0, len);
        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns the value at a given block number. If a checkpoint is not available at that block, the closest one
     * before it is returned, or zero otherwise. Similar to {upperLookup} but optimized for the case when the searched
     * checkpoint is probably "recent", defined as being among the last sqrt(N) checkpoints where N is the number of
     * checkpoints.
     */
    function getAtProbablyRecentBlock(History storage self, uint256 blockNumber) internal view returns (uint256) {
        require(blockNumber < block.number, "Checkpoints: block not yet mined");
        uint32 key = SafeCast.toUint32(blockNumber);

        uint256 len = self._checkpoints.length;

        uint256 low = 0;
        uint256 high = len;

        if (len > 5) {
            uint256 mid = len - Math.sqrt(len);
            if (key < _unsafeAccess(self._checkpoints, mid)._blockNumber) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }

        uint256 pos = _upperBinaryLookup(self._checkpoints, key, low, high);

        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Pushes a value onto a History so that it is stored as the checkpoint for the current block.
     *
     * Returns previous value and new value.
     */
    function push(History storage self, uint256 value) internal returns (uint256, uint256) {
        return _insert(self._checkpoints, SafeCast.toUint32(block.number), SafeCast.toUint224(value));
    }

    /**
     * @dev Pushes a value onto a History, by updating the latest value using binary operation `op`. The new value will
     * be set to `op(latest, delta)`.
     *
     * Returns previous value and new value.
     */
    function push(
        History storage self,
        function(uint256, uint256) view returns (uint256) op,
        uint256 delta
    ) internal returns (uint256, uint256) {
        return push(self, op(latest(self), delta));
    }

    /**
     * @dev Returns the value in the most recent checkpoint, or zero if there are no checkpoints.
     */
    function latest(History storage self) internal view returns (uint224) {
        uint256 pos = self._checkpoints.length;
        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns whether there is a checkpoint in the structure (i.e. it is not empty), and if so the key and value
     * in the most recent checkpoint.
     */
    function latestCheckpoint(History storage self)
        internal
        view
        returns (
            bool exists,
            uint32 _blockNumber,
            uint224 _value
        )
    {
        uint256 pos = self._checkpoints.length;
        if (pos == 0) {
            return (false, 0, 0);
        } else {
            Checkpoint memory ckpt = _unsafeAccess(self._checkpoints, pos - 1);
            return (true, ckpt._blockNumber, ckpt._value);
        }
    }

    /**
     * @dev Returns the number of checkpoint.
     */
    function length(History storage self) internal view returns (uint256) {
        return self._checkpoints.length;
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into an ordered list of checkpoints, either by inserting a new checkpoint,
     * or by updating the last one.
     */
    function _insert(
        Checkpoint[] storage self,
        uint32 key,
        uint224 value
    ) private returns (uint224, uint224) {
        uint256 pos = self.length;

        if (pos > 0) {
            // Copying to memory is important here.
            Checkpoint memory last = _unsafeAccess(self, pos - 1);

            // Checkpoints keys must be increasing.
            require(last._blockNumber <= key, "Checkpoint: invalid key");

            // Update or push new checkpoint
            if (last._blockNumber == key) {
                _unsafeAccess(self, pos - 1)._value = value;
            } else {
                self.push(Checkpoint({_blockNumber: key, _value: value}));
            }
            return (last._value, value);
        } else {
            self.push(Checkpoint({_blockNumber: key, _value: value}));
            return (0, value);
        }
    }

    /**
     * @dev Return the index of the oldest checkpoint whose key is greater than the search key, or `high` if there is none.
     * `low` and `high` define a section where to do the search, with inclusive `low` and exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _upperBinaryLookup(
        Checkpoint[] storage self,
        uint32 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._blockNumber > key) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return high;
    }

    /**
     * @dev Return the index of the oldest checkpoint whose key is greater or equal than the search key, or `high` if there is none.
     * `low` and `high` define a section where to do the search, with inclusive `low` and exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _lowerBinaryLookup(
        Checkpoint[] storage self,
        uint32 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._blockNumber < key) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return high;
    }

    /**
     * @dev Access an element of the array without performing bounds check. The position is assumed to be within bounds.
     */
    function _unsafeAccess(Checkpoint[] storage self, uint256 pos) private pure returns (Checkpoint storage result) {
        assembly {
            mstore(0, self.slot)
            result.slot := add(keccak256(0, 0x20), pos)
        }
    }

    struct Trace224 {
        Checkpoint224[] _checkpoints;
    }

    struct Checkpoint224 {
        uint32 _key;
        uint224 _value;
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into a Trace224 so that it is stored as the checkpoint.
     *
     * Returns previous value and new value.
     */
    function push(
        Trace224 storage self,
        uint32 key,
        uint224 value
    ) internal returns (uint224, uint224) {
        return _insert(self._checkpoints, key, value);
    }

    /**
     * @dev Returns the value in the oldest checkpoint with key greater or equal than the search key, or zero if there is none.
     */
    function lowerLookup(Trace224 storage self, uint32 key) internal view returns (uint224) {
        uint256 len = self._checkpoints.length;
        uint256 pos = _lowerBinaryLookup(self._checkpoints, key, 0, len);
        return pos == len ? 0 : _unsafeAccess(self._checkpoints, pos)._value;
    }

    /**
     * @dev Returns the value in the most recent checkpoint with key lower or equal than the search key.
     */
    function upperLookup(Trace224 storage self, uint32 key) internal view returns (uint224) {
        uint256 len = self._checkpoints.length;
        uint256 pos = _upperBinaryLookup(self._checkpoints, key, 0, len);
        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns the value in the most recent checkpoint, or zero if there are no checkpoints.
     */
    function latest(Trace224 storage self) internal view returns (uint224) {
        uint256 pos = self._checkpoints.length;
        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns whether there is a checkpoint in the structure (i.e. it is not empty), and if so the key and value
     * in the most recent checkpoint.
     */
    function latestCheckpoint(Trace224 storage self)
        internal
        view
        returns (
            bool exists,
            uint32 _key,
            uint224 _value
        )
    {
        uint256 pos = self._checkpoints.length;
        if (pos == 0) {
            return (false, 0, 0);
        } else {
            Checkpoint224 memory ckpt = _unsafeAccess(self._checkpoints, pos - 1);
            return (true, ckpt._key, ckpt._value);
        }
    }

    /**
     * @dev Returns the number of checkpoint.
     */
    function length(Trace224 storage self) internal view returns (uint256) {
        return self._checkpoints.length;
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into an ordered list of checkpoints, either by inserting a new checkpoint,
     * or by updating the last one.
     */
    function _insert(
        Checkpoint224[] storage self,
        uint32 key,
        uint224 value
    ) private returns (uint224, uint224) {
        uint256 pos = self.length;

        if (pos > 0) {
            // Copying to memory is important here.
            Checkpoint224 memory last = _unsafeAccess(self, pos - 1);

            // Checkpoints keys must be increasing.
            require(last._key <= key, "Checkpoint: invalid key");

            // Update or push new checkpoint
            if (last._key == key) {
                _unsafeAccess(self, pos - 1)._value = value;
            } else {
                self.push(Checkpoint224({_key: key, _value: value}));
            }
            return (last._value, value);
        } else {
            self.push(Checkpoint224({_key: key, _value: value}));
            return (0, value);
        }
    }

    /**
     * @dev Return the index of the oldest checkpoint whose key is greater than the search key, or `high` if there is none.
     * `low` and `high` define a section where to do the search, with inclusive `low` and exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _upperBinaryLookup(
        Checkpoint224[] storage self,
        uint32 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._key > key) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return high;
    }

    /**
     * @dev Return the index of the oldest checkpoint whose key is greater or equal than the search key, or `high` if there is none.
     * `low` and `high` define a section where to do the search, with inclusive `low` and exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _lowerBinaryLookup(
        Checkpoint224[] storage self,
        uint32 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._key < key) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return high;
    }

    /**
     * @dev Access an element of the array without performing bounds check. The position is assumed to be within bounds.
     */
    function _unsafeAccess(Checkpoint224[] storage self, uint256 pos)
        private
        pure
        returns (Checkpoint224 storage result)
    {
        assembly {
            mstore(0, self.slot)
            result.slot := add(keccak256(0, 0x20), pos)
        }
    }

    struct Trace160 {
        Checkpoint160[] _checkpoints;
    }

    struct Checkpoint160 {
        uint96 _key;
        uint160 _value;
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into a Trace160 so that it is stored as the checkpoint.
     *
     * Returns previous value and new value.
     */
    function push(
        Trace160 storage self,
        uint96 key,
        uint160 value
    ) internal returns (uint160, uint160) {
        return _insert(self._checkpoints, key, value);
    }

    /**
     * @dev Returns the value in the oldest checkpoint with key greater or equal than the search key, or zero if there is none.
     */
    function lowerLookup(Trace160 storage self, uint96 key) internal view returns (uint160) {
        uint256 len = self._checkpoints.length;
        uint256 pos = _lowerBinaryLookup(self._checkpoints, key, 0, len);
        return pos == len ? 0 : _unsafeAccess(self._checkpoints, pos)._value;
    }

    /**
     * @dev Returns the value in the most recent checkpoint with key lower or equal than the search key.
     */
    function upperLookup(Trace160 storage self, uint96 key) internal view returns (uint160) {
        uint256 len = self._checkpoints.length;
        uint256 pos = _upperBinaryLookup(self._checkpoints, key, 0, len);
        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns the value in the most recent checkpoint, or zero if there are no checkpoints.
     */
    function latest(Trace160 storage self) internal view returns (uint160) {
        uint256 pos = self._checkpoints.length;
        return pos == 0 ? 0 : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns whether there is a checkpoint in the structure (i.e. it is not empty), and if so the key and value
     * in the most recent checkpoint.
     */
    function latestCheckpoint(Trace160 storage self)
        internal
        view
        returns (
            bool exists,
            uint96 _key,
            uint160 _value
        )
    {
        uint256 pos = self._checkpoints.length;
        if (pos == 0) {
            return (false, 0, 0);
        } else {
            Checkpoint160 memory ckpt = _unsafeAccess(self._checkpoints, pos - 1);
            return (true, ckpt._key, ckpt._value);
        }
    }

    /**
     * @dev Returns the number of checkpoint.
     */
    function length(Trace160 storage self) internal view returns (uint256) {
        return self._checkpoints.length;
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into an ordered list of checkpoints, either by inserting a new checkpoint,
     * or by updating the last one.
     */
    function _insert(
        Checkpoint160[] storage self,
        uint96 key,
        uint160 value
    ) private returns (uint160, uint160) {
        uint256 pos = self.length;

        if (pos > 0) {
            // Copying to memory is important here.
            Checkpoint160 memory last = _unsafeAccess(self, pos - 1);

            // Checkpoints keys must be increasing.
            require(last._key <= key, "Checkpoint: invalid key");

            // Update or push new checkpoint
            if (last._key == key) {
                _unsafeAccess(self, pos - 1)._value = value;
            } else {
                self.push(Checkpoint160({_key: key, _value: value}));
            }
            return (last._value, value);
        } else {
            self.push(Checkpoint160({_key: key, _value: value}));
            return (0, value);
        }
    }

    /**
     * @dev Return the index of the oldest checkpoint whose key is greater than the search key, or `high` if there is none.
     * `low` and `high` define a section where to do the search, with inclusive `low` and exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _upperBinaryLookup(
        Checkpoint160[] storage self,
        uint96 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._key > key) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return high;
    }

    /**
     * @dev Return the index of the oldest checkpoint whose key is greater or equal than the search key, or `high` if there is none.
     * `low` and `high` define a section where to do the search, with inclusive `low` and exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _lowerBinaryLookup(
        Checkpoint160[] storage self,
        uint96 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._key < key) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return high;
    }

    /**
     * @dev Access an element of the array without performing bounds check. The position is assumed to be within bounds.
     */
    function _unsafeAccess(Checkpoint160[] storage self, uint256 pos)
        private
        pure
        returns (Checkpoint160 storage result)
    {
        assembly {
            mstore(0, self.slot)
            result.slot := add(keccak256(0, 0x20), pos)
        }
    }
}

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

pragma solidity ^0.8.0;

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (utils/structs/DoubleEndedQueue.sol)
pragma solidity ^0.8.4;

import "../math/SafeCast.sol";

/**
 * @dev A sequence of items with the ability to efficiently push and pop items (i.e. insert and remove) on both ends of
 * the sequence (called front and back). Among other access patterns, it can be used to implement efficient LIFO and
 * FIFO queues. Storage use is optimized, and all operations are O(1) constant time. This includes {clear}, given that
 * the existing queue contents are left in storage.
 *
 * The struct is called `Bytes32Deque`. Other types can be cast to and from `bytes32`. This data structure can only be
 * used in storage, and not in memory.
 * ```
 * DoubleEndedQueue.Bytes32Deque queue;
 * ```
 *
 * _Available since v4.6._
 */
library DoubleEndedQueue {
    /**
     * @dev An operation (e.g. {front}) couldn't be completed due to the queue being empty.
     */
    error Empty();

    /**
     * @dev An operation (e.g. {at}) couldn't be completed due to an index being out of bounds.
     */
    error OutOfBounds();

    /**
     * @dev Indices are signed integers because the queue can grow in any direction. They are 128 bits so begin and end
     * are packed in a single storage slot for efficient access. Since the items are added one at a time we can safely
     * assume that these 128-bit indices will not overflow, and use unchecked arithmetic.
     *
     * Struct members have an underscore prefix indicating that they are "private" and should not be read or written to
     * directly. Use the functions provided below instead. Modifying the struct manually may violate assumptions and
     * lead to unexpected behavior.
     *
     * Indices are in the range [begin, end) which means the first item is at data[begin] and the last item is at
     * data[end - 1].
     */
    struct Bytes32Deque {
        int128 _begin;
        int128 _end;
        mapping(int128 => bytes32) _data;
    }

    /**
     * @dev Inserts an item at the end of the queue.
     */
    function pushBack(Bytes32Deque storage deque, bytes32 value) internal {
        int128 backIndex = deque._end;
        deque._data[backIndex] = value;
        unchecked {
            deque._end = backIndex + 1;
        }
    }

    /**
     * @dev Removes the item at the end of the queue and returns it.
     *
     * Reverts with `Empty` if the queue is empty.
     */
    function popBack(Bytes32Deque storage deque) internal returns (bytes32 value) {
        if (empty(deque)) revert Empty();
        int128 backIndex;
        unchecked {
            backIndex = deque._end - 1;
        }
        value = deque._data[backIndex];
        delete deque._data[backIndex];
        deque._end = backIndex;
    }

    /**
     * @dev Inserts an item at the beginning of the queue.
     */
    function pushFront(Bytes32Deque storage deque, bytes32 value) internal {
        int128 frontIndex;
        unchecked {
            frontIndex = deque._begin - 1;
        }
        deque._data[frontIndex] = value;
        deque._begin = frontIndex;
    }

    /**
     * @dev Removes the item at the beginning of the queue and returns it.
     *
     * Reverts with `Empty` if the queue is empty.
     */
    function popFront(Bytes32Deque storage deque) internal returns (bytes32 value) {
        if (empty(deque)) revert Empty();
        int128 frontIndex = deque._begin;
        value = deque._data[frontIndex];
        delete deque._data[frontIndex];
        unchecked {
            deque._begin = frontIndex + 1;
        }
    }

    /**
     * @dev Returns the item at the beginning of the queue.
     *
     * Reverts with `Empty` if the queue is empty.
     */
    function front(Bytes32Deque storage deque) internal view returns (bytes32 value) {
        if (empty(deque)) revert Empty();
        int128 frontIndex = deque._begin;
        return deque._data[frontIndex];
    }

    /**
     * @dev Returns the item at the end of the queue.
     *
     * Reverts with `Empty` if the queue is empty.
     */
    function back(Bytes32Deque storage deque) internal view returns (bytes32 value) {
        if (empty(deque)) revert Empty();
        int128 backIndex;
        unchecked {
            backIndex = deque._end - 1;
        }
        return deque._data[backIndex];
    }

    /**
     * @dev Return the item at a position in the queue given by `index`, with the first item at 0 and last item at
     * `length(deque) - 1`.
     *
     * Reverts with `OutOfBounds` if the index is out of bounds.
     */
    function at(Bytes32Deque storage deque, uint256 index) internal view returns (bytes32 value) {
        // int256(deque._begin) is a safe upcast
        int128 idx = SafeCast.toInt128(int256(deque._begin) + SafeCast.toInt256(index));
        if (idx >= deque._end) revert OutOfBounds();
        return deque._data[idx];
    }

    /**
     * @dev Resets the queue back to being empty.
     *
     * NOTE: The current items are left behind in storage. This does not affect the functioning of the queue, but misses
     * out on potential gas refunds.
     */
    function clear(Bytes32Deque storage deque) internal {
        deque._begin = 0;
        deque._end = 0;
    }

    /**
     * @dev Returns the number of items in the queue.
     */
    function length(Bytes32Deque storage deque) internal view returns (uint256) {
        // The interface preserves the invariant that begin <= end so we assume this will not overflow.
        // We also assume there are at most int256.max items in the queue.
        unchecked {
            return uint256(int256(deque._end) - int256(deque._begin));
        }
    }

    /**
     * @dev Returns true if the queue is empty.
     */
    function empty(Bytes32Deque storage deque) internal view returns (bool) {
        return deque._end <= deque._begin;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (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) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n32", hash));
    }

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/EIP712.sol)

pragma solidity ^0.8.0;

import "./ECDSA.sol";

/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP 712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding specified in the EIP is very generic, and such a generic implementation in Solidity is not feasible,
 * thus this contract does not implement the encoding itself. Protocols need to implement the type-specific encoding
 * they need in their contracts using a combination of `abi.encode` and `keccak256`.
 *
 * This contract implements the EIP 712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
 * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
 * ({_hashTypedDataV4}).
 *
 * The implementation of the domain separator was designed to be as efficient as possible while still properly updating
 * the chain id to protect against replay attacks on an eventual fork of the chain.
 *
 * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
 * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].
 *
 * _Available since v3.4._
 */
abstract contract EIP712 {
    /* solhint-disable var-name-mixedcase */
    // Cache the domain separator as an immutable value, but also store the chain id that it corresponds to, in order to
    // invalidate the cached domain separator if the chain id changes.
    bytes32 private immutable _CACHED_DOMAIN_SEPARATOR;
    uint256 private immutable _CACHED_CHAIN_ID;
    address private immutable _CACHED_THIS;

    bytes32 private immutable _HASHED_NAME;
    bytes32 private immutable _HASHED_VERSION;
    bytes32 private immutable _TYPE_HASH;

    /* solhint-enable var-name-mixedcase */

    /**
     * @dev Initializes the domain separator and parameter caches.
     *
     * The meaning of `name` and `version` is specified in
     * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP 712]:
     *
     * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
     * - `version`: the current major version of the signing domain.
     *
     * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
     * contract upgrade].
     */
    constructor(string memory name, string memory version) {
        bytes32 hashedName = keccak256(bytes(name));
        bytes32 hashedVersion = keccak256(bytes(version));
        bytes32 typeHash = keccak256(
            "EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"
        );
        _HASHED_NAME = hashedName;
        _HASHED_VERSION = hashedVersion;
        _CACHED_CHAIN_ID = block.chainid;
        _CACHED_DOMAIN_SEPARATOR = _buildDomainSeparator(typeHash, hashedName, hashedVersion);
        _CACHED_THIS = address(this);
        _TYPE_HASH = typeHash;
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        if (address(this) == _CACHED_THIS && block.chainid == _CACHED_CHAIN_ID) {
            return _CACHED_DOMAIN_SEPARATOR;
        } else {
            return _buildDomainSeparator(_TYPE_HASH, _HASHED_NAME, _HASHED_VERSION);
        }
    }

    function _buildDomainSeparator(
        bytes32 typeHash,
        bytes32 nameHash,
        bytes32 versionHash
    ) private view returns (bytes32) {
        return keccak256(abi.encode(typeHash, nameHash, versionHash, block.chainid, address(this)));
    }

    /**
     * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
     * function returns the hash of the fully encoded EIP712 message for this domain.
     *
     * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:
     *
     * ```solidity
     * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
     *     keccak256("Mail(address to,string contents)"),
     *     mailTo,
     *     keccak256(bytes(mailContents))
     * )));
     * address signer = ECDSA.recover(digest, signature);
     * ```
     */
    function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) {
        return ECDSA.toTypedDataHash(_domainSeparatorV4(), structHash);
    }
}

// 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;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (governance/Governor.sol)

pragma solidity ^0.8.0;

import "../token/ERC721/IERC721Receiver.sol";
import "../token/ERC1155/IERC1155Receiver.sol";
import "../utils/cryptography/ECDSA.sol";
import "../utils/cryptography/EIP712.sol";
import "../utils/introspection/ERC165.sol";
import "../utils/math/SafeCast.sol";
import "../utils/structs/DoubleEndedQueue.sol";
import "../utils/Address.sol";
import "../utils/Context.sol";
import "../utils/Timers.sol";
import "./IGovernor.sol";

/**
 * @dev Core of the governance system, designed to be extended though various modules.
 *
 * This contract is abstract and requires several function to be implemented in various modules:
 *
 * - A counting module must implement {quorum}, {_quorumReached}, {_voteSucceeded} and {_countVote}
 * - A voting module must implement {_getVotes}
 * - Additionanly, the {votingPeriod} must also be implemented
 *
 * _Available since v4.3._
 */
abstract contract Governor is Context, ERC165, EIP712, IGovernor, IERC721Receiver, IERC1155Receiver {
    using DoubleEndedQueue for DoubleEndedQueue.Bytes32Deque;
    using SafeCast for uint256;
    using Timers for Timers.BlockNumber;

    bytes32 public constant BALLOT_TYPEHASH = keccak256("Ballot(uint256 proposalId,uint8 support)");
    bytes32 public constant EXTENDED_BALLOT_TYPEHASH =
        keccak256("ExtendedBallot(uint256 proposalId,uint8 support,string reason,bytes params)");

    struct ProposalCore {
        Timers.BlockNumber voteStart;
        Timers.BlockNumber voteEnd;
        bool executed;
        bool canceled;
    }

    string private _name;

    mapping(uint256 => ProposalCore) private _proposals;

    // This queue keeps track of the governor operating on itself. Calls to functions protected by the
    // {onlyGovernance} modifier needs to be whitelisted in this queue. Whitelisting is set in {_beforeExecute},
    // consumed by the {onlyGovernance} modifier and eventually reset in {_afterExecute}. This ensures that the
    // execution of {onlyGovernance} protected calls can only be achieved through successful proposals.
    DoubleEndedQueue.Bytes32Deque private _governanceCall;

    /**
     * @dev Restricts a function so it can only be executed through governance proposals. For example, governance
     * parameter setters in {GovernorSettings} are protected using this modifier.
     *
     * The governance executing address may be different from the Governor's own address, for example it could be a
     * timelock. This can be customized by modules by overriding {_executor}. The executor is only able to invoke these
     * functions during the execution of the governor's {execute} function, and not under any other circumstances. Thus,
     * for example, additional timelock proposers are not able to change governance parameters without going through the
     * governance protocol (since v4.6).
     */
    modifier onlyGovernance() {
        require(_msgSender() == _executor(), "Governor: onlyGovernance");
        if (_executor() != address(this)) {
            bytes32 msgDataHash = keccak256(_msgData());
            // loop until popping the expected operation - throw if deque is empty (operation not authorized)
            while (_governanceCall.popFront() != msgDataHash) {}
        }
        _;
    }

    /**
     * @dev Sets the value for {name} and {version}
     */
    constructor(string memory name_) EIP712(name_, version()) {
        _name = name_;
    }

    /**
     * @dev Function to receive ETH that will be handled by the governor (disabled if executor is a third party contract)
     */
    receive() external payable virtual {
        require(_executor() == address(this));
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override(IERC165, ERC165) returns (bool) {
        // In addition to the current interfaceId, also support previous version of the interfaceId that did not
        // include the castVoteWithReasonAndParams() function as standard
        return
            interfaceId ==
            (type(IGovernor).interfaceId ^
                this.castVoteWithReasonAndParams.selector ^
                this.castVoteWithReasonAndParamsBySig.selector ^
                this.getVotesWithParams.selector) ||
            interfaceId == type(IGovernor).interfaceId ||
            interfaceId == type(IERC1155Receiver).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IGovernor-name}.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev See {IGovernor-version}.
     */
    function version() public view virtual override returns (string memory) {
        return "1";
    }

    /**
     * @dev See {IGovernor-hashProposal}.
     *
     * The proposal id is produced by hashing the ABI encoded `targets` array, the `values` array, the `calldatas` array
     * and the descriptionHash (bytes32 which itself is the keccak256 hash of the description string). This proposal id
     * can be produced from the proposal data which is part of the {ProposalCreated} event. It can even be computed in
     * advance, before the proposal is submitted.
     *
     * Note that the chainId and the governor address are not part of the proposal id computation. Consequently, the
     * same proposal (with same operation and same description) will have the same id if submitted on multiple governors
     * across multiple networks. This also means that in order to execute the same operation twice (on the same
     * governor) the proposer will have to change the description in order to avoid proposal id conflicts.
     */
    function hashProposal(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 descriptionHash
    ) public pure virtual override returns (uint256) {
        return uint256(keccak256(abi.encode(targets, values, calldatas, descriptionHash)));
    }

    /**
     * @dev See {IGovernor-state}.
     */
    function state(uint256 proposalId) public view virtual override returns (ProposalState) {
        ProposalCore storage proposal = _proposals[proposalId];

        if (proposal.executed) {
            return ProposalState.Executed;
        }

        if (proposal.canceled) {
            return ProposalState.Canceled;
        }

        uint256 snapshot = proposalSnapshot(proposalId);

        if (snapshot == 0) {
            revert("Governor: unknown proposal id");
        }

        if (snapshot >= block.number) {
            return ProposalState.Pending;
        }

        uint256 deadline = proposalDeadline(proposalId);

        if (deadline >= block.number) {
            return ProposalState.Active;
        }

        if (_quorumReached(proposalId) && _voteSucceeded(proposalId)) {
            return ProposalState.Succeeded;
        } else {
            return ProposalState.Defeated;
        }
    }

    /**
     * @dev See {IGovernor-proposalSnapshot}.
     */
    function proposalSnapshot(uint256 proposalId) public view virtual override returns (uint256) {
        return _proposals[proposalId].voteStart.getDeadline();
    }

    /**
     * @dev See {IGovernor-proposalDeadline}.
     */
    function proposalDeadline(uint256 proposalId) public view virtual override returns (uint256) {
        return _proposals[proposalId].voteEnd.getDeadline();
    }

    /**
     * @dev Part of the Governor Bravo's interface: _"The number of votes required in order for a voter to become a proposer"_.
     */
    function proposalThreshold() public view virtual returns (uint256) {
        return 0;
    }

    /**
     * @dev Amount of votes already cast passes the threshold limit.
     */
    function _quorumReached(uint256 proposalId) internal view virtual returns (bool);

    /**
     * @dev Is the proposal successful or not.
     */
    function _voteSucceeded(uint256 proposalId) internal view virtual returns (bool);

    /**
     * @dev Get the voting weight of `account` at a specific `blockNumber`, for a vote as described by `params`.
     */
    function _getVotes(
        address account,
        uint256 blockNumber,
        bytes memory params
    ) internal view virtual returns (uint256);

    /**
     * @dev Register a vote for `proposalId` by `account` with a given `support`, voting `weight` and voting `params`.
     *
     * Note: Support is generic and can represent various things depending on the voting system used.
     */
    function _countVote(
        uint256 proposalId,
        address account,
        uint8 support,
        uint256 weight,
        bytes memory params
    ) internal virtual;

    /**
     * @dev Default additional encoded parameters used by castVote methods that don't include them
     *
     * Note: Should be overridden by specific implementations to use an appropriate value, the
     * meaning of the additional params, in the context of that implementation
     */
    function _defaultParams() internal view virtual returns (bytes memory) {
        return "";
    }

    /**
     * @dev See {IGovernor-propose}.
     */
    function propose(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        string memory description
    ) public virtual override returns (uint256) {
        require(
            getVotes(_msgSender(), block.number - 1) >= proposalThreshold(),
            "Governor: proposer votes below proposal threshold"
        );

        uint256 proposalId = hashProposal(targets, values, calldatas, keccak256(bytes(description)));

        require(targets.length == values.length, "Governor: invalid proposal length");
        require(targets.length == calldatas.length, "Governor: invalid proposal length");
        require(targets.length > 0, "Governor: empty proposal");

        ProposalCore storage proposal = _proposals[proposalId];
        require(proposal.voteStart.isUnset(), "Governor: proposal already exists");

        uint64 snapshot = block.number.toUint64() + votingDelay().toUint64();
        uint64 deadline = snapshot + votingPeriod().toUint64();

        proposal.voteStart.setDeadline(snapshot);
        proposal.voteEnd.setDeadline(deadline);

        emit ProposalCreated(
            proposalId,
            _msgSender(),
            targets,
            values,
            new string[](targets.length),
            calldatas,
            snapshot,
            deadline,
            description
        );

        return proposalId;
    }

    /**
     * @dev See {IGovernor-execute}.
     */
    function execute(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 descriptionHash
    ) public payable virtual override returns (uint256) {
        uint256 proposalId = hashProposal(targets, values, calldatas, descriptionHash);

        ProposalState status = state(proposalId);
        require(
            status == ProposalState.Succeeded || status == ProposalState.Queued,
            "Governor: proposal not successful"
        );
        _proposals[proposalId].executed = true;

        emit ProposalExecuted(proposalId);

        _beforeExecute(proposalId, targets, values, calldatas, descriptionHash);
        _execute(proposalId, targets, values, calldatas, descriptionHash);
        _afterExecute(proposalId, targets, values, calldatas, descriptionHash);

        return proposalId;
    }

    /**
     * @dev Internal execution mechanism. Can be overridden to implement different execution mechanism
     */
    function _execute(
        uint256, /* proposalId */
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 /*descriptionHash*/
    ) internal virtual {
        string memory errorMessage = "Governor: call reverted without message";
        for (uint256 i = 0; i < targets.length; ++i) {
            (bool success, bytes memory returndata) = targets[i].call{value: values[i]}(calldatas[i]);
            Address.verifyCallResult(success, returndata, errorMessage);
        }
    }

    /**
     * @dev Hook before execution is triggered.
     */
    function _beforeExecute(
        uint256, /* proposalId */
        address[] memory targets,
        uint256[] memory, /* values */
        bytes[] memory calldatas,
        bytes32 /*descriptionHash*/
    ) internal virtual {
        if (_executor() != address(this)) {
            for (uint256 i = 0; i < targets.length; ++i) {
                if (targets[i] == address(this)) {
                    _governanceCall.pushBack(keccak256(calldatas[i]));
                }
            }
        }
    }

    /**
     * @dev Hook after execution is triggered.
     */
    function _afterExecute(
        uint256, /* proposalId */
        address[] memory, /* targets */
        uint256[] memory, /* values */
        bytes[] memory, /* calldatas */
        bytes32 /*descriptionHash*/
    ) internal virtual {
        if (_executor() != address(this)) {
            if (!_governanceCall.empty()) {
                _governanceCall.clear();
            }
        }
    }

    /**
     * @dev Internal cancel mechanism: locks up the proposal timer, preventing it from being re-submitted. Marks it as
     * canceled to allow distinguishing it from executed proposals.
     *
     * Emits a {IGovernor-ProposalCanceled} event.
     */
    function _cancel(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 descriptionHash
    ) internal virtual returns (uint256) {
        uint256 proposalId = hashProposal(targets, values, calldatas, descriptionHash);
        ProposalState status = state(proposalId);

        require(
            status != ProposalState.Canceled && status != ProposalState.Expired && status != ProposalState.Executed,
            "Governor: proposal not active"
        );
        _proposals[proposalId].canceled = true;

        emit ProposalCanceled(proposalId);

        return proposalId;
    }

    /**
     * @dev See {IGovernor-getVotes}.
     */
    function getVotes(address account, uint256 blockNumber) public view virtual override returns (uint256) {
        return _getVotes(account, blockNumber, _defaultParams());
    }

    /**
     * @dev See {IGovernor-getVotesWithParams}.
     */
    function getVotesWithParams(
        address account,
        uint256 blockNumber,
        bytes memory params
    ) public view virtual override returns (uint256) {
        return _getVotes(account, blockNumber, params);
    }

    /**
     * @dev See {IGovernor-castVote}.
     */
    function castVote(uint256 proposalId, uint8 support) public virtual override returns (uint256) {
        address voter = _msgSender();
        return _castVote(proposalId, voter, support, "");
    }

    /**
     * @dev See {IGovernor-castVoteWithReason}.
     */
    function castVoteWithReason(
        uint256 proposalId,
        uint8 support,
        string calldata reason
    ) public virtual override returns (uint256) {
        address voter = _msgSender();
        return _castVote(proposalId, voter, support, reason);
    }

    /**
     * @dev See {IGovernor-castVoteWithReasonAndParams}.
     */
    function castVoteWithReasonAndParams(
        uint256 proposalId,
        uint8 support,
        string calldata reason,
        bytes memory params
    ) public virtual override returns (uint256) {
        address voter = _msgSender();
        return _castVote(proposalId, voter, support, reason, params);
    }

    /**
     * @dev See {IGovernor-castVoteBySig}.
     */
    function castVoteBySig(
        uint256 proposalId,
        uint8 support,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual override returns (uint256) {
        address voter = ECDSA.recover(
            _hashTypedDataV4(keccak256(abi.encode(BALLOT_TYPEHASH, proposalId, support))),
            v,
            r,
            s
        );
        return _castVote(proposalId, voter, support, "");
    }

    /**
     * @dev See {IGovernor-castVoteWithReasonAndParamsBySig}.
     */
    function castVoteWithReasonAndParamsBySig(
        uint256 proposalId,
        uint8 support,
        string calldata reason,
        bytes memory params,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual override returns (uint256) {
        address voter = ECDSA.recover(
            _hashTypedDataV4(
                keccak256(
                    abi.encode(
                        EXTENDED_BALLOT_TYPEHASH,
                        proposalId,
                        support,
                        keccak256(bytes(reason)),
                        keccak256(params)
                    )
                )
            ),
            v,
            r,
            s
        );

        return _castVote(proposalId, voter, support, reason, params);
    }

    /**
     * @dev Internal vote casting mechanism: Check that the vote is pending, that it has not been cast yet, retrieve
     * voting weight using {IGovernor-getVotes} and call the {_countVote} internal function. Uses the _defaultParams().
     *
     * Emits a {IGovernor-VoteCast} event.
     */
    function _castVote(
        uint256 proposalId,
        address account,
        uint8 support,
        string memory reason
    ) internal virtual returns (uint256) {
        return _castVote(proposalId, account, support, reason, _defaultParams());
    }

    /**
     * @dev Internal vote casting mechanism: Check that the vote is pending, that it has not been cast yet, retrieve
     * voting weight using {IGovernor-getVotes} and call the {_countVote} internal function.
     *
     * Emits a {IGovernor-VoteCast} event.
     */
    function _castVote(
        uint256 proposalId,
        address account,
        uint8 support,
        string memory reason,
        bytes memory params
    ) internal virtual returns (uint256) {
        ProposalCore storage proposal = _proposals[proposalId];
        require(state(proposalId) == ProposalState.Active, "Governor: vote not currently active");

        uint256 weight = _getVotes(account, proposal.voteStart.getDeadline(), params);
        _countVote(proposalId, account, support, weight, params);

        if (params.length == 0) {
            emit VoteCast(account, proposalId, support, weight, reason);
        } else {
            emit VoteCastWithParams(account, proposalId, support, weight, reason, params);
        }

        return weight;
    }

    /**
     * @dev Relays a transaction or function call to an arbitrary target. In cases where the governance executor
     * is some contract other than the governor itself, like when using a timelock, this function can be invoked
     * in a governance proposal to recover tokens or Ether that was sent to the governor contract by mistake.
     * Note that if the executor is simply the governor itself, use of `relay` is redundant.
     */
    function relay(
        address target,
        uint256 value,
        bytes calldata data
    ) external payable virtual onlyGovernance {
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        Address.verifyCallResult(success, returndata, "Governor: relay reverted without message");
    }

    /**
     * @dev Address through which the governor executes action. Will be overloaded by module that execute actions
     * through another contract such as a timelock.
     */
    function _executor() internal view virtual returns (address) {
        return address(this);
    }

    /**
     * @dev See {IERC721Receiver-onERC721Received}.
     */
    function onERC721Received(
        address,
        address,
        uint256,
        bytes memory
    ) public virtual override returns (bytes4) {
        return this.onERC721Received.selector;
    }

    /**
     * @dev See {IERC1155Receiver-onERC1155Received}.
     */
    function onERC1155Received(
        address,
        address,
        uint256,
        uint256,
        bytes memory
    ) public virtual override returns (bytes4) {
        return this.onERC1155Received.selector;
    }

    /**
     * @dev See {IERC1155Receiver-onERC1155BatchReceived}.
     */
    function onERC1155BatchReceived(
        address,
        address,
        uint256[] memory,
        uint256[] memory,
        bytes memory
    ) public virtual override returns (bytes4) {
        return this.onERC1155BatchReceived.selector;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.3) (governance/compatibility/GovernorCompatibilityBravo.sol)

pragma solidity ^0.8.0;

import "../../utils/math/SafeCast.sol";
import "../extensions/IGovernorTimelock.sol";
import "../Governor.sol";
import "./IGovernorCompatibilityBravo.sol";

/**
 * @dev Compatibility layer that implements GovernorBravo compatibility on to of {Governor}.
 *
 * This compatibility layer includes a voting system and requires a {IGovernorTimelock} compatible module to be added
 * through inheritance. It does not include token bindings, not does it include any variable upgrade patterns.
 *
 * NOTE: When using this module, you may need to enable the Solidity optimizer to avoid hitting the contract size limit.
 *
 * _Available since v4.3._
 */
abstract contract GovernorCompatibilityBravo is IGovernorTimelock, IGovernorCompatibilityBravo, Governor {
    enum VoteType {
        Against,
        For,
        Abstain
    }

    struct ProposalDetails {
        address proposer;
        address[] targets;
        uint256[] values;
        string[] signatures;
        bytes[] calldatas;
        uint256 forVotes;
        uint256 againstVotes;
        uint256 abstainVotes;
        mapping(address => Receipt) receipts;
        bytes32 descriptionHash;
    }

    mapping(uint256 => ProposalDetails) private _proposalDetails;

    // solhint-disable-next-line func-name-mixedcase
    function COUNTING_MODE() public pure virtual override returns (string memory) {
        return "support=bravo&quorum=bravo";
    }

    // ============================================== Proposal lifecycle ==============================================
    /**
     * @dev See {IGovernor-propose}.
     */
    function propose(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        string memory description
    ) public virtual override(IGovernor, Governor) returns (uint256) {
        _storeProposal(_msgSender(), targets, values, new string[](calldatas.length), calldatas, description);
        return super.propose(targets, values, calldatas, description);
    }

    /**
     * @dev See {IGovernorCompatibilityBravo-propose}.
     */
    function propose(
        address[] memory targets,
        uint256[] memory values,
        string[] memory signatures,
        bytes[] memory calldatas,
        string memory description
    ) public virtual override returns (uint256) {
        require(signatures.length == calldatas.length, "GovernorBravo: invalid signatures length");
        // Stores the full proposal and fallback to the public (possibly overridden) propose. The fallback is done
        // after the full proposal is stored, so the store operation included in the fallback will be skipped. Here we
        // call `propose` and not `super.propose` to make sure if a child contract override `propose`, whatever code
        // is added their is also executed when calling this alternative interface.
        _storeProposal(_msgSender(), targets, values, signatures, calldatas, description);
        return propose(targets, values, _encodeCalldata(signatures, calldatas), description);
    }

    /**
     * @dev See {IGovernorCompatibilityBravo-queue}.
     */
    function queue(uint256 proposalId) public virtual override {
        ProposalDetails storage details = _proposalDetails[proposalId];
        queue(
            details.targets,
            details.values,
            _encodeCalldata(details.signatures, details.calldatas),
            details.descriptionHash
        );
    }

    /**
     * @dev See {IGovernorCompatibilityBravo-execute}.
     */
    function execute(uint256 proposalId) public payable virtual override {
        ProposalDetails storage details = _proposalDetails[proposalId];
        execute(
            details.targets,
            details.values,
            _encodeCalldata(details.signatures, details.calldatas),
            details.descriptionHash
        );
    }

    function cancel(uint256 proposalId) public virtual override {
        ProposalDetails storage details = _proposalDetails[proposalId];

        require(
            _msgSender() == details.proposer || getVotes(details.proposer, block.number - 1) < proposalThreshold(),
            "GovernorBravo: proposer above threshold"
        );

        _cancel(
            details.targets,
            details.values,
            _encodeCalldata(details.signatures, details.calldatas),
            details.descriptionHash
        );
    }

    /**
     * @dev Encodes calldatas with optional function signature.
     */
    function _encodeCalldata(string[] memory signatures, bytes[] memory calldatas)
        private
        pure
        returns (bytes[] memory)
    {
        bytes[] memory fullcalldatas = new bytes[](calldatas.length);
        for (uint256 i = 0; i < fullcalldatas.length; ++i) {
            fullcalldatas[i] = bytes(signatures[i]).length == 0
                ? calldatas[i]
                : abi.encodePacked(bytes4(keccak256(bytes(signatures[i]))), calldatas[i]);
        }

        return fullcalldatas;
    }

    /**
     * @dev Store proposal metadata for later lookup
     */
    function _storeProposal(
        address proposer,
        address[] memory targets,
        uint256[] memory values,
        string[] memory signatures,
        bytes[] memory calldatas,
        string memory description
    ) private {
        bytes32 descriptionHash = keccak256(bytes(description));
        uint256 proposalId = hashProposal(targets, values, _encodeCalldata(signatures, calldatas), descriptionHash);

        ProposalDetails storage details = _proposalDetails[proposalId];
        if (details.descriptionHash == bytes32(0)) {
            details.proposer = proposer;
            details.targets = targets;
            details.values = values;
            details.signatures = signatures;
            details.calldatas = calldatas;
            details.descriptionHash = descriptionHash;
        }
    }

    // ==================================================== Views =====================================================
    /**
     * @dev See {IGovernorCompatibilityBravo-proposals}.
     */
    function proposals(uint256 proposalId)
        public
        view
        virtual
        override
        returns (
            uint256 id,
            address proposer,
            uint256 eta,
            uint256 startBlock,
            uint256 endBlock,
            uint256 forVotes,
            uint256 againstVotes,
            uint256 abstainVotes,
            bool canceled,
            bool executed
        )
    {
        id = proposalId;
        eta = proposalEta(proposalId);
        startBlock = proposalSnapshot(proposalId);
        endBlock = proposalDeadline(proposalId);

        ProposalDetails storage details = _proposalDetails[proposalId];
        proposer = details.proposer;
        forVotes = details.forVotes;
        againstVotes = details.againstVotes;
        abstainVotes = details.abstainVotes;

        ProposalState status = state(proposalId);
        canceled = status == ProposalState.Canceled;
        executed = status == ProposalState.Executed;
    }

    /**
     * @dev See {IGovernorCompatibilityBravo-getActions}.
     */
    function getActions(uint256 proposalId)
        public
        view
        virtual
        override
        returns (
            address[] memory targets,
            uint256[] memory values,
            string[] memory signatures,
            bytes[] memory calldatas
        )
    {
        ProposalDetails storage details = _proposalDetails[proposalId];
        return (details.targets, details.values, details.signatures, details.calldatas);
    }

    /**
     * @dev See {IGovernorCompatibilityBravo-getReceipt}.
     */
    function getReceipt(uint256 proposalId, address voter) public view virtual override returns (Receipt memory) {
        return _proposalDetails[proposalId].receipts[voter];
    }

    /**
     * @dev See {IGovernorCompatibilityBravo-quorumVotes}.
     */
    function quorumVotes() public view virtual override returns (uint256) {
        return quorum(block.number - 1);
    }

    // ==================================================== Voting ====================================================
    /**
     * @dev See {IGovernor-hasVoted}.
     */
    function hasVoted(uint256 proposalId, address account) public view virtual override returns (bool) {
        return _proposalDetails[proposalId].receipts[account].hasVoted;
    }

    /**
     * @dev See {Governor-_quorumReached}. In this module, only forVotes count toward the quorum.
     */
    function _quorumReached(uint256 proposalId) internal view virtual override returns (bool) {
        ProposalDetails storage details = _proposalDetails[proposalId];
        return quorum(proposalSnapshot(proposalId)) <= details.forVotes;
    }

    /**
     * @dev See {Governor-_voteSucceeded}. In this module, the forVotes must be scritly over the againstVotes.
     */
    function _voteSucceeded(uint256 proposalId) internal view virtual override returns (bool) {
        ProposalDetails storage details = _proposalDetails[proposalId];
        return details.forVotes > details.againstVotes;
    }

    /**
     * @dev See {Governor-_countVote}. In this module, the support follows Governor Bravo.
     */
    function _countVote(
        uint256 proposalId,
        address account,
        uint8 support,
        uint256 weight,
        bytes memory // params
    ) internal virtual override {
        ProposalDetails storage details = _proposalDetails[proposalId];
        Receipt storage receipt = details.receipts[account];

        require(!receipt.hasVoted, "GovernorCompatibilityBravo: vote already cast");
        receipt.hasVoted = true;
        receipt.support = support;
        receipt.votes = SafeCast.toUint96(weight);

        if (support == uint8(VoteType.Against)) {
            details.againstVotes += weight;
        } else if (support == uint8(VoteType.For)) {
            details.forVotes += weight;
        } else if (support == uint8(VoteType.Abstain)) {
            details.abstainVotes += weight;
        } else {
            revert("GovernorCompatibilityBravo: invalid vote type");
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.20;

import {IERC165} from "@openzeppelin/contracts/utils/introspection/IERC165.sol";
import {Governor, IGovernor} from "@openzeppelin/contracts/governance/Governor.sol";
import {GovernorSettings} from "@openzeppelin/contracts/governance/extensions/GovernorSettings.sol";
import {GovernorCompatibilityBravo} from "@openzeppelin/contracts/governance/compatibility/GovernorCompatibilityBravo.sol";
import {GovernorVotes, IVotes} from "@openzeppelin/contracts/governance/extensions/GovernorVotes.sol";
import {GovernorVotesQuorumFraction} from "@openzeppelin/contracts/governance/extensions/GovernorVotesQuorumFraction.sol";
import {GovernorTimelockControl, TimelockController} from "@openzeppelin/contracts/governance/extensions/GovernorTimelockControl.sol";

/// @title Governor OLAS - Smart contract for Autonolas governance
/// @author Aleksandr Kuperman - <aleksandr.kuperman@valory.xyz>
/// @dev The OpenZeppelin functions are used as is, version 4.8.3.
contract GovernorOLAS is Governor, GovernorSettings, GovernorCompatibilityBravo, GovernorVotes, GovernorVotesQuorumFraction, GovernorTimelockControl {
    constructor(
        IVotes governanceToken,
        TimelockController timelock,
        uint256 initialVotingDelay,
        uint256 initialVotingPeriod,
        uint256 initialProposalThreshold,
        uint256 quorumFraction
    )
        Governor("Governor OLAS")
        GovernorSettings(initialVotingDelay, initialVotingPeriod, initialProposalThreshold)
        GovernorVotes(governanceToken)
        GovernorVotesQuorumFraction(quorumFraction)
        GovernorTimelockControl(timelock)
    {}

    /// @dev Current state of a proposal, following Compound’s convention.
    /// @param proposalId Proposal Id.
    function state(uint256 proposalId) public view override(IGovernor, Governor, GovernorTimelockControl)
        returns (ProposalState)
    {
        return super.state(proposalId);
    }

    /// @dev Create a new proposal to change the protocol / contract parameters.
    /// @param targets The ordered list of target addresses for calls to be made during proposal execution.
    /// @param values The ordered list of values to be passed to the calls made during proposal execution.
    /// @param calldatas The ordered list of data to be passed to each individual function call during proposal execution.
    /// @param description A human readable description of the proposal and the changes it will enact.
    /// @return The Id of the newly created proposal.
    function propose(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        string memory description
    ) public override(IGovernor, Governor, GovernorCompatibilityBravo) returns (uint256)
    {
        return super.propose(targets, values, calldatas, description);
    }

    /// @dev Gets the voting power for the proposal threshold.
    /// @return The voting power required in order for a voter to become a proposer.
    function proposalThreshold() public view override(Governor, GovernorSettings) returns (uint256)
    {
        return super.proposalThreshold();
    }

    /// @dev Executes a proposal.
    /// @param proposalId Proposal Id.
    /// @param targets The ordered list of target addresses.
    /// @param values The ordered list of values.
    /// @param calldatas The ordered list of data to be passed to each individual function call.
    /// @param descriptionHash Hashed description of the proposal.
    function _execute(
        uint256 proposalId,
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 descriptionHash
    ) internal override(Governor, GovernorTimelockControl)
    {
        super._execute(proposalId, targets, values, calldatas, descriptionHash);
    }

    /// @dev Cancels a proposal.
    /// @param targets The ordered list of target addresses.
    /// @param values The ordered list of values.
    /// @param calldatas The ordered list of data to be passed to each individual function call.
    /// @param descriptionHash Hashed description of the proposal.
    /// @return The Id of the newly created proposal.
    function _cancel(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 descriptionHash
    ) internal override(Governor, GovernorTimelockControl) returns (uint256)
    {
        return super._cancel(targets, values, calldatas, descriptionHash);
    }

    /// @dev Gets the executor address.
    /// @return Executor address.
    function _executor() internal view override(Governor, GovernorTimelockControl) returns (address)
    {
        return super._executor();
    }

    /// @dev Gets information about the interface support.
    /// @param interfaceId A specified interface Id.
    /// @return True if this contract implements the interface defined by interfaceId.
    function supportsInterface(bytes4 interfaceId) public view override(IERC165, Governor, GovernorTimelockControl)
        returns (bool)
    {
        return super.supportsInterface(interfaceId);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (governance/extensions/GovernorSettings.sol)

pragma solidity ^0.8.0;

import "../Governor.sol";

/**
 * @dev Extension of {Governor} for settings updatable through governance.
 *
 * _Available since v4.4._
 */
abstract contract GovernorSettings is Governor {
    uint256 private _votingDelay;
    uint256 private _votingPeriod;
    uint256 private _proposalThreshold;

    event VotingDelaySet(uint256 oldVotingDelay, uint256 newVotingDelay);
    event VotingPeriodSet(uint256 oldVotingPeriod, uint256 newVotingPeriod);
    event ProposalThresholdSet(uint256 oldProposalThreshold, uint256 newProposalThreshold);

    /**
     * @dev Initialize the governance parameters.
     */
    constructor(
        uint256 initialVotingDelay,
        uint256 initialVotingPeriod,
        uint256 initialProposalThreshold
    ) {
        _setVotingDelay(initialVotingDelay);
        _setVotingPeriod(initialVotingPeriod);
        _setProposalThreshold(initialProposalThreshold);
    }

    /**
     * @dev See {IGovernor-votingDelay}.
     */
    function votingDelay() public view virtual override returns (uint256) {
        return _votingDelay;
    }

    /**
     * @dev See {IGovernor-votingPeriod}.
     */
    function votingPeriod() public view virtual override returns (uint256) {
        return _votingPeriod;
    }

    /**
     * @dev See {Governor-proposalThreshold}.
     */
    function proposalThreshold() public view virtual override returns (uint256) {
        return _proposalThreshold;
    }

    /**
     * @dev Update the voting delay. This operation can only be performed through a governance proposal.
     *
     * Emits a {VotingDelaySet} event.
     */
    function setVotingDelay(uint256 newVotingDelay) public virtual onlyGovernance {
        _setVotingDelay(newVotingDelay);
    }

    /**
     * @dev Update the voting period. This operation can only be performed through a governance proposal.
     *
     * Emits a {VotingPeriodSet} event.
     */
    function setVotingPeriod(uint256 newVotingPeriod) public virtual onlyGovernance {
        _setVotingPeriod(newVotingPeriod);
    }

    /**
     * @dev Update the proposal threshold. This operation can only be performed through a governance proposal.
     *
     * Emits a {ProposalThresholdSet} event.
     */
    function setProposalThreshold(uint256 newProposalThreshold) public virtual onlyGovernance {
        _setProposalThreshold(newProposalThreshold);
    }

    /**
     * @dev Internal setter for the voting delay.
     *
     * Emits a {VotingDelaySet} event.
     */
    function _setVotingDelay(uint256 newVotingDelay) internal virtual {
        emit VotingDelaySet(_votingDelay, newVotingDelay);
        _votingDelay = newVotingDelay;
    }

    /**
     * @dev Internal setter for the voting period.
     *
     * Emits a {VotingPeriodSet} event.
     */
    function _setVotingPeriod(uint256 newVotingPeriod) internal virtual {
        // voting period must be at least one block long
        require(newVotingPeriod > 0, "GovernorSettings: voting period too low");
        emit VotingPeriodSet(_votingPeriod, newVotingPeriod);
        _votingPeriod = newVotingPeriod;
    }

    /**
     * @dev Internal setter for the proposal threshold.
     *
     * Emits a {ProposalThresholdSet} event.
     */
    function _setProposalThreshold(uint256 newProposalThreshold) internal virtual {
        emit ProposalThresholdSet(_proposalThreshold, newProposalThreshold);
        _proposalThreshold = newProposalThreshold;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (governance/extensions/GovernorTimelockControl.sol)

pragma solidity ^0.8.0;

import "./IGovernorTimelock.sol";
import "../Governor.sol";
import "../TimelockController.sol";

/**
 * @dev Extension of {Governor} that binds the execution process to an instance of {TimelockController}. This adds a
 * delay, enforced by the {TimelockController} to all successful proposal (in addition to the voting duration). The
 * {Governor} needs the proposer (and ideally the executor) roles for the {Governor} to work properly.
 *
 * Using this model means the proposal will be operated by the {TimelockController} and not by the {Governor}. Thus,
 * the assets and permissions must be attached to the {TimelockController}. Any asset sent to the {Governor} will be
 * inaccessible.
 *
 * WARNING: Setting up the TimelockController to have additional proposers besides the governor is very risky, as it
 * grants them powers that they must be trusted or known not to use: 1) {onlyGovernance} functions like {relay} are
 * available to them through the timelock, and 2) approved governance proposals can be blocked by them, effectively
 * executing a Denial of Service attack. This risk will be mitigated in a future release.
 *
 * _Available since v4.3._
 */
abstract contract GovernorTimelockControl is IGovernorTimelock, Governor {
    TimelockController private _timelock;
    mapping(uint256 => bytes32) private _timelockIds;

    /**
     * @dev Emitted when the timelock controller used for proposal execution is modified.
     */
    event TimelockChange(address oldTimelock, address newTimelock);

    /**
     * @dev Set the timelock.
     */
    constructor(TimelockController timelockAddress) {
        _updateTimelock(timelockAddress);
    }

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

    /**
     * @dev Overridden version of the {Governor-state} function with added support for the `Queued` status.
     */
    function state(uint256 proposalId) public view virtual override(IGovernor, Governor) returns (ProposalState) {
        ProposalState status = super.state(proposalId);

        if (status != ProposalState.Succeeded) {
            return status;
        }

        // core tracks execution, so we just have to check if successful proposal have been queued.
        bytes32 queueid = _timelockIds[proposalId];
        if (queueid == bytes32(0)) {
            return status;
        } else if (_timelock.isOperationDone(queueid)) {
            return ProposalState.Executed;
        } else if (_timelock.isOperationPending(queueid)) {
            return ProposalState.Queued;
        } else {
            return ProposalState.Canceled;
        }
    }

    /**
     * @dev Public accessor to check the address of the timelock
     */
    function timelock() public view virtual override returns (address) {
        return address(_timelock);
    }

    /**
     * @dev Public accessor to check the eta of a queued proposal
     */
    function proposalEta(uint256 proposalId) public view virtual override returns (uint256) {
        uint256 eta = _timelock.getTimestamp(_timelockIds[proposalId]);
        return eta == 1 ? 0 : eta; // _DONE_TIMESTAMP (1) should be replaced with a 0 value
    }

    /**
     * @dev Function to queue a proposal to the timelock.
     */
    function queue(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 descriptionHash
    ) public virtual override returns (uint256) {
        uint256 proposalId = hashProposal(targets, values, calldatas, descriptionHash);

        require(state(proposalId) == ProposalState.Succeeded, "Governor: proposal not successful");

        uint256 delay = _timelock.getMinDelay();
        _timelockIds[proposalId] = _timelock.hashOperationBatch(targets, values, calldatas, 0, descriptionHash);
        _timelock.scheduleBatch(targets, values, calldatas, 0, descriptionHash, delay);

        emit ProposalQueued(proposalId, block.timestamp + delay);

        return proposalId;
    }

    /**
     * @dev Overridden execute function that run the already queued proposal through the timelock.
     */
    function _execute(
        uint256, /* proposalId */
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 descriptionHash
    ) internal virtual override {
        _timelock.executeBatch{value: msg.value}(targets, values, calldatas, 0, descriptionHash);
    }

    /**
     * @dev Overridden version of the {Governor-_cancel} function to cancel the timelocked proposal if it as already
     * been queued.
     */
    // This function can reenter through the external call to the timelock, but we assume the timelock is trusted and
    // well behaved (according to TimelockController) and this will not happen.
    // slither-disable-next-line reentrancy-no-eth
    function _cancel(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 descriptionHash
    ) internal virtual override returns (uint256) {
        uint256 proposalId = super._cancel(targets, values, calldatas, descriptionHash);

        if (_timelockIds[proposalId] != 0) {
            _timelock.cancel(_timelockIds[proposalId]);
            delete _timelockIds[proposalId];
        }

        return proposalId;
    }

    /**
     * @dev Address through which the governor executes action. In this case, the timelock.
     */
    function _executor() internal view virtual override returns (address) {
        return address(_timelock);
    }

    /**
     * @dev Public endpoint to update the underlying timelock instance. Restricted to the timelock itself, so updates
     * must be proposed, scheduled, and executed through governance proposals.
     *
     * CAUTION: It is not recommended to change the timelock while there are other queued governance proposals.
     */
    function updateTimelock(TimelockController newTimelock) external virtual onlyGovernance {
        _updateTimelock(newTimelock);
    }

    function _updateTimelock(TimelockController newTimelock) private {
        emit TimelockChange(address(_timelock), address(newTimelock));
        _timelock = newTimelock;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (governance/extensions/GovernorVotes.sol)

pragma solidity ^0.8.0;

import "../Governor.sol";
import "../utils/IVotes.sol";

/**
 * @dev Extension of {Governor} for voting weight extraction from an {ERC20Votes} token, or since v4.5 an {ERC721Votes} token.
 *
 * _Available since v4.3._
 */
abstract contract GovernorVotes is Governor {
    IVotes public immutable token;

    constructor(IVotes tokenAddress) {
        token = tokenAddress;
    }

    /**
     * Read the voting weight from the token's built in snapshot mechanism (see {Governor-_getVotes}).
     */
    function _getVotes(
        address account,
        uint256 blockNumber,
        bytes memory /*params*/
    ) internal view virtual override returns (uint256) {
        return token.getPastVotes(account, blockNumber);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (governance/extensions/GovernorVotesQuorumFraction.sol)

pragma solidity ^0.8.0;

import "./GovernorVotes.sol";
import "../../utils/Checkpoints.sol";
import "../../utils/math/SafeCast.sol";

/**
 * @dev Extension of {Governor} for voting weight extraction from an {ERC20Votes} token and a quorum expressed as a
 * fraction of the total supply.
 *
 * _Available since v4.3._
 */
abstract contract GovernorVotesQuorumFraction is GovernorVotes {
    using Checkpoints for Checkpoints.History;

    uint256 private _quorumNumerator; // DEPRECATED
    Checkpoints.History private _quorumNumeratorHistory;

    event QuorumNumeratorUpdated(uint256 oldQuorumNumerator, uint256 newQuorumNumerator);

    /**
     * @dev Initialize quorum as a fraction of the token's total supply.
     *
     * The fraction is specified as `numerator / denominator`. By default the denominator is 100, so quorum is
     * specified as a percent: a numerator of 10 corresponds to quorum being 10% of total supply. The denominator can be
     * customized by overriding {quorumDenominator}.
     */
    constructor(uint256 quorumNumeratorValue) {
        _updateQuorumNumerator(quorumNumeratorValue);
    }

    /**
     * @dev Returns the current quorum numerator. See {quorumDenominator}.
     */
    function quorumNumerator() public view virtual returns (uint256) {
        return _quorumNumeratorHistory._checkpoints.length == 0 ? _quorumNumerator : _quorumNumeratorHistory.latest();
    }

    /**
     * @dev Returns the quorum numerator at a specific block number. See {quorumDenominator}.
     */
    function quorumNumerator(uint256 blockNumber) public view virtual returns (uint256) {
        // If history is empty, fallback to old storage
        uint256 length = _quorumNumeratorHistory._checkpoints.length;
        if (length == 0) {
            return _quorumNumerator;
        }

        // Optimistic search, check the latest checkpoint
        Checkpoints.Checkpoint memory latest = _quorumNumeratorHistory._checkpoints[length - 1];
        if (latest._blockNumber <= blockNumber) {
            return latest._value;
        }

        // Otherwise, do the binary search
        return _quorumNumeratorHistory.getAtBlock(blockNumber);
    }

    /**
     * @dev Returns the quorum denominator. Defaults to 100, but may be overridden.
     */
    function quorumDenominator() public view virtual returns (uint256) {
        return 100;
    }

    /**
     * @dev Returns the quorum for a block number, in terms of number of votes: `supply * numerator / denominator`.
     */
    function quorum(uint256 blockNumber) public view virtual override returns (uint256) {
        return (token.getPastTotalSupply(blockNumber) * quorumNumerator(blockNumber)) / quorumDenominator();
    }

    /**
     * @dev Changes the quorum numerator.
     *
     * Emits a {QuorumNumeratorUpdated} event.
     *
     * Requirements:
     *
     * - Must be called through a governance proposal.
     * - New numerator must be smaller or equal to the denominator.
     */
    function updateQuorumNumerator(uint256 newQuorumNumerator) external virtual onlyGovernance {
        _updateQuorumNumerator(newQuorumNumerator);
    }

    /**
     * @dev Changes the quorum numerator.
     *
     * Emits a {QuorumNumeratorUpdated} event.
     *
     * Requirements:
     *
     * - New numerator must be smaller or equal to the denominator.
     */
    function _updateQuorumNumerator(uint256 newQuorumNumerator) internal virtual {
        require(
            newQuorumNumerator <= quorumDenominator(),
            "GovernorVotesQuorumFraction: quorumNumerator over quorumDenominator"
        );

        uint256 oldQuorumNumerator = quorumNumerator();

        // Make sure we keep track of the original numerator in contracts upgraded from a version without checkpoints.
        if (oldQuorumNumerator != 0 && _quorumNumeratorHistory._checkpoints.length == 0) {
            _quorumNumeratorHistory._checkpoints.push(
                Checkpoints.Checkpoint({_blockNumber: 0, _value: SafeCast.toUint224(oldQuorumNumerator)})
            );
        }

        // Set new quorum for future proposals
        _quorumNumeratorHistory.push(newQuorumNumerator);

        emit QuorumNumeratorUpdated(oldQuorumNumerator, newQuorumNumerator);
    }
}

// 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;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (token/ERC1155/IERC1155Receiver.sol)

pragma solidity ^0.8.0;

import "../../utils/introspection/IERC165.sol";

/**
 * @dev _Available since v3.1._
 */
interface IERC1155Receiver is IERC165 {
    /**
     * @dev Handles the receipt of a single ERC1155 token type. This function is
     * called at the end of a `safeTransferFrom` after the balance has been updated.
     *
     * NOTE: To accept the transfer, this must return
     * `bytes4(keccak256("onERC1155Received(address,address,uint256,uint256,bytes)"))`
     * (i.e. 0xf23a6e61, or its own function selector).
     *
     * @param operator The address which initiated the transfer (i.e. msg.sender)
     * @param from The address which previously owned the token
     * @param id The ID of the token being transferred
     * @param value The amount of tokens being transferred
     * @param data Additional data with no specified format
     * @return `bytes4(keccak256("onERC1155Received(address,address,uint256,uint256,bytes)"))` if transfer is allowed
     */
    function onERC1155Received(
        address operator,
        address from,
        uint256 id,
        uint256 value,
        bytes calldata data
    ) external returns (bytes4);

    /**
     * @dev Handles the receipt of a multiple ERC1155 token types. This function
     * is called at the end of a `safeBatchTransferFrom` after the balances have
     * been updated.
     *
     * NOTE: To accept the transfer(s), this must return
     * `bytes4(keccak256("onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)"))`
     * (i.e. 0xbc197c81, or its own function selector).
     *
     * @param operator The address which initiated the batch transfer (i.e. msg.sender)
     * @param from The address which previously owned the token
     * @param ids An array containing ids of each token being transferred (order and length must match values array)
     * @param values An array containing amounts of each token being transferred (order and length must match ids array)
     * @param data Additional data with no specified format
     * @return `bytes4(keccak256("onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)"))` if transfer is allowed
     */
    function onERC1155BatchReceived(
        address operator,
        address from,
        uint256[] calldata ids,
        uint256[] calldata values,
        bytes calldata data
    ) external returns (bytes4);
}

// 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);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC721/IERC721Receiver.sol)

pragma solidity ^0.8.0;

/**
 * @title ERC721 token receiver interface
 * @dev Interface for any contract that wants to support safeTransfers
 * from ERC721 asset contracts.
 */
interface IERC721Receiver {
    /**
     * @dev Whenever an {IERC721} `tokenId` token is transferred to this contract via {IERC721-safeTransferFrom}
     * by `operator` from `from`, this function is called.
     *
     * It must return its Solidity selector to confirm the token transfer.
     * If any other value is returned or the interface is not implemented by the recipient, the transfer will be reverted.
     *
     * The selector can be obtained in Solidity with `IERC721Receiver.onERC721Received.selector`.
     */
    function onERC721Received(
        address operator,
        address from,
        uint256 tokenId,
        bytes calldata data
    ) external returns (bytes4);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (governance/IGovernor.sol)

pragma solidity ^0.8.0;

import "../utils/introspection/ERC165.sol";

/**
 * @dev Interface of the {Governor} core.
 *
 * _Available since v4.3._
 */
abstract contract IGovernor is IERC165 {
    enum ProposalState {
        Pending,
        Active,
        Canceled,
        Defeated,
        Succeeded,
        Queued,
        Expired,
        Executed
    }

    /**
     * @dev Emitted when a proposal is created.
     */
    event ProposalCreated(
        uint256 proposalId,
        address proposer,
        address[] targets,
        uint256[] values,
        string[] signatures,
        bytes[] calldatas,
        uint256 startBlock,
        uint256 endBlock,
        string description
    );

    /**
     * @dev Emitted when a proposal is canceled.
     */
    event ProposalCanceled(uint256 proposalId);

    /**
     * @dev Emitted when a proposal is executed.
     */
    event ProposalExecuted(uint256 proposalId);

    /**
     * @dev Emitted when a vote is cast without params.
     *
     * Note: `support` values should be seen as buckets. Their interpretation depends on the voting module used.
     */
    event VoteCast(address indexed voter, uint256 proposalId, uint8 support, uint256 weight, string reason);

    /**
     * @dev Emitted when a vote is cast with params.
     *
     * Note: `support` values should be seen as buckets. Their interpretation depends on the voting module used.
     * `params` are additional encoded parameters. Their intepepretation also depends on the voting module used.
     */
    event VoteCastWithParams(
        address indexed voter,
        uint256 proposalId,
        uint8 support,
        uint256 weight,
        string reason,
        bytes params
    );

    /**
     * @notice module:core
     * @dev Name of the governor instance (used in building the ERC712 domain separator).
     */
    function name() public view virtual returns (string memory);

    /**
     * @notice module:core
     * @dev Version of the governor instance (used in building the ERC712 domain separator). Default: "1"
     */
    function version() public view virtual returns (string memory);

    /**
     * @notice module:voting
     * @dev A description of the possible `support` values for {castVote} and the way these votes are counted, meant to
     * be consumed by UIs to show correct vote options and interpret the results. The string is a URL-encoded sequence of
     * key-value pairs that each describe one aspect, for example `support=bravo&quorum=for,abstain`.
     *
     * There are 2 standard keys: `support` and `quorum`.
     *
     * - `support=bravo` refers to the vote options 0 = Against, 1 = For, 2 = Abstain, as in `GovernorBravo`.
     * - `quorum=bravo` means that only For votes are counted towards quorum.
     * - `quorum=for,abstain` means that both For and Abstain votes are counted towards quorum.
     *
     * If a counting module makes use of encoded `params`, it should  include this under a `params` key with a unique
     * name that describes the behavior. For example:
     *
     * - `params=fractional` might refer to a scheme where votes are divided fractionally between for/against/abstain.
     * - `params=erc721` might refer to a scheme where specific NFTs are delegated to vote.
     *
     * NOTE: The string can be decoded by the standard
     * https://developer.mozilla.org/en-US/docs/Web/API/URLSearchParams[`URLSearchParams`]
     * JavaScript class.
     */
    // solhint-disable-next-line func-name-mixedcase
    function COUNTING_MODE() public pure virtual returns (string memory);

    /**
     * @notice module:core
     * @dev Hashing function used to (re)build the proposal id from the proposal details..
     */
    function hashProposal(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 descriptionHash
    ) public pure virtual returns (uint256);

    /**
     * @notice module:core
     * @dev Current state of a proposal, following Compound's convention
     */
    function state(uint256 proposalId) public view virtual returns (ProposalState);

    /**
     * @notice module:core
     * @dev Block number used to retrieve user's votes and quorum. As per Compound's Comp and OpenZeppelin's
     * ERC20Votes, the snapshot is performed at the end of this block. Hence, voting for this proposal starts at the
     * beginning of the following block.
     */
    function proposalSnapshot(uint256 proposalId) public view virtual returns (uint256);

    /**
     * @notice module:core
     * @dev Block number at which votes close. Votes close at the end of this block, so it is possible to cast a vote
     * during this block.
     */
    function proposalDeadline(uint256 proposalId) public view virtual returns (uint256);

    /**
     * @notice module:user-config
     * @dev Delay, in number of block, between the proposal is created and the vote starts. This can be increassed to
     * leave time for users to buy voting power, or delegate it, before the voting of a proposal starts.
     */
    function votingDelay() public view virtual returns (uint256);

    /**
     * @notice module:user-config
     * @dev Delay, in number of blocks, between the vote start and vote ends.
     *
     * NOTE: The {votingDelay} can delay the start of the vote. This must be considered when setting the voting
     * duration compared to the voting delay.
     */
    function votingPeriod() public view virtual returns (uint256);

    /**
     * @notice module:user-config
     * @dev Minimum number of cast voted required for a proposal to be successful.
     *
     * Note: The `blockNumber` parameter corresponds to the snapshot used for counting vote. This allows to scale the
     * quorum depending on values such as the totalSupply of a token at this block (see {ERC20Votes}).
     */
    function quorum(uint256 blockNumber) public view virtual returns (uint256);

    /**
     * @notice module:reputation
     * @dev Voting power of an `account` at a specific `blockNumber`.
     *
     * Note: this can be implemented in a number of ways, for example by reading the delegated balance from one (or
     * multiple), {ERC20Votes} tokens.
     */
    function getVotes(address account, uint256 blockNumber) public view virtual returns (uint256);

    /**
     * @notice module:reputation
     * @dev Voting power of an `account` at a specific `blockNumber` given additional encoded parameters.
     */
    function getVotesWithParams(
        address account,
        uint256 blockNumber,
        bytes memory params
    ) public view virtual returns (uint256);

    /**
     * @notice module:voting
     * @dev Returns whether `account` has cast a vote on `proposalId`.
     */
    function hasVoted(uint256 proposalId, address account) public view virtual returns (bool);

    /**
     * @dev Create a new proposal. Vote start {IGovernor-votingDelay} blocks after the proposal is created and ends
     * {IGovernor-votingPeriod} blocks after the voting starts.
     *
     * Emits a {ProposalCreated} event.
     */
    function propose(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        string memory description
    ) public virtual returns (uint256 proposalId);

    /**
     * @dev Execute a successful proposal. This requires the quorum to be reached, the vote to be successful, and the
     * deadline to be reached.
     *
     * Emits a {ProposalExecuted} event.
     *
     * Note: some module can modify the requirements for execution, for example by adding an additional timelock.
     */
    function execute(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 descriptionHash
    ) public payable virtual returns (uint256 proposalId);

    /**
     * @dev Cast a vote
     *
     * Emits a {VoteCast} event.
     */
    function castVote(uint256 proposalId, uint8 support) public virtual returns (uint256 balance);

    /**
     * @dev Cast a vote with a reason
     *
     * Emits a {VoteCast} event.
     */
    function castVoteWithReason(
        uint256 proposalId,
        uint8 support,
        string calldata reason
    ) public virtual returns (uint256 balance);

    /**
     * @dev Cast a vote with a reason and additional encoded parameters
     *
     * Emits a {VoteCast} or {VoteCastWithParams} event depending on the length of params.
     */
    function castVoteWithReasonAndParams(
        uint256 proposalId,
        uint8 support,
        string calldata reason,
        bytes memory params
    ) public virtual returns (uint256 balance);

    /**
     * @dev Cast a vote using the user's cryptographic signature.
     *
     * Emits a {VoteCast} event.
     */
    function castVoteBySig(
        uint256 proposalId,
        uint8 support,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual returns (uint256 balance);

    /**
     * @dev Cast a vote with a reason and additional encoded parameters using the user's cryptographic signature.
     *
     * Emits a {VoteCast} or {VoteCastWithParams} event depending on the length of params.
     */
    function castVoteWithReasonAndParamsBySig(
        uint256 proposalId,
        uint8 support,
        string calldata reason,
        bytes memory params,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual returns (uint256 balance);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (governance/compatibility/IGovernorCompatibilityBravo.sol)

pragma solidity ^0.8.0;

import "../IGovernor.sol";

/**
 * @dev Interface extension that adds missing functions to the {Governor} core to provide `GovernorBravo` compatibility.
 *
 * _Available since v4.3._
 */
abstract contract IGovernorCompatibilityBravo is IGovernor {
    /**
     * @dev Proposal structure from Compound Governor Bravo. Not actually used by the compatibility layer, as
     * {{proposal}} returns a very different structure.
     */
    struct Proposal {
        uint256 id;
        address proposer;
        uint256 eta;
        address[] targets;
        uint256[] values;
        string[] signatures;
        bytes[] calldatas;
        uint256 startBlock;
        uint256 endBlock;
        uint256 forVotes;
        uint256 againstVotes;
        uint256 abstainVotes;
        bool canceled;
        bool executed;
        mapping(address => Receipt) receipts;
    }

    /**
     * @dev Receipt structure from Compound Governor Bravo
     */
    struct Receipt {
        bool hasVoted;
        uint8 support;
        uint96 votes;
    }

    /**
     * @dev Part of the Governor Bravo's interface.
     */
    function quorumVotes() public view virtual returns (uint256);

    /**
     * @dev Part of the Governor Bravo's interface: _"The official record of all proposals ever proposed"_.
     */
    function proposals(uint256)
        public
        view
        virtual
        returns (
            uint256 id,
            address proposer,
            uint256 eta,
            uint256 startBlock,
            uint256 endBlock,
            uint256 forVotes,
            uint256 againstVotes,
            uint256 abstainVotes,
            bool canceled,
            bool executed
        );

    /**
     * @dev Part of the Governor Bravo's interface: _"Function used to propose a new proposal"_.
     */
    function propose(
        address[] memory targets,
        uint256[] memory values,
        string[] memory signatures,
        bytes[] memory calldatas,
        string memory description
    ) public virtual returns (uint256);

    /**
     * @dev Part of the Governor Bravo's interface: _"Queues a proposal of state succeeded"_.
     */
    function queue(uint256 proposalId) public virtual;

    /**
     * @dev Part of the Governor Bravo's interface: _"Executes a queued proposal if eta has passed"_.
     */
    function execute(uint256 proposalId) public payable virtual;

    /**
     * @dev Cancels a proposal only if sender is the proposer, or proposer delegates dropped below proposal threshold.
     */
    function cancel(uint256 proposalId) public virtual;

    /**
     * @dev Part of the Governor Bravo's interface: _"Gets actions of a proposal"_.
     */
    function getActions(uint256 proposalId)
        public
        view
        virtual
        returns (
            address[] memory targets,
            uint256[] memory values,
            string[] memory signatures,
            bytes[] memory calldatas
        );

    /**
     * @dev Part of the Governor Bravo's interface: _"Gets the receipt for a voter on a given proposal"_.
     */
    function getReceipt(uint256 proposalId, address voter) public view virtual returns (Receipt memory);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (governance/extensions/IGovernorTimelock.sol)

pragma solidity ^0.8.0;

import "../IGovernor.sol";

/**
 * @dev Extension of the {IGovernor} for timelock supporting modules.
 *
 * _Available since v4.3._
 */
abstract contract IGovernorTimelock is IGovernor {
    event ProposalQueued(uint256 proposalId, uint256 eta);

    function timelock() public view virtual returns (address);

    function proposalEta(uint256 proposalId) public view virtual returns (uint256);

    function queue(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 descriptionHash
    ) public virtual returns (uint256 proposalId);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (governance/utils/IVotes.sol)
pragma solidity ^0.8.0;

/**
 * @dev Common interface for {ERC20Votes}, {ERC721Votes}, and other {Votes}-enabled contracts.
 *
 * _Available since v4.5._
 */
interface IVotes {
    /**
     * @dev Emitted when an account changes their delegate.
     */
    event DelegateChanged(address indexed delegator, address indexed fromDelegate, address indexed toDelegate);

    /**
     * @dev Emitted when a token transfer or delegate change results in changes to a delegate's number of votes.
     */
    event DelegateVotesChanged(address indexed delegate, uint256 previousBalance, uint256 newBalance);

    /**
     * @dev Returns the current amount of votes that `account` has.
     */
    function getVotes(address account) external view returns (uint256);

    /**
     * @dev Returns the amount of votes that `account` had at the end of a past block (`blockNumber`).
     */
    function getPastVotes(address account, uint256 blockNumber) external view returns (uint256);

    /**
     * @dev Returns the total supply of votes available at the end of a past block (`blockNumber`).
     *
     * NOTE: This value is the sum of all available votes, which is not necessarily the sum of all delegated votes.
     * Votes that have not been delegated are still part of total supply, even though they would not participate in a
     * vote.
     */
    function getPastTotalSupply(uint256 blockNumber) external view returns (uint256);

    /**
     * @dev Returns the delegate that `account` has chosen.
     */
    function delegates(address account) external view returns (address);

    /**
     * @dev Delegates votes from the sender to `delegatee`.
     */
    function delegate(address delegatee) external;

    /**
     * @dev Delegates votes from signer to `delegatee`.
     */
    function delegateBySig(
        address delegatee,
        uint256 nonce,
        uint256 expiry,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (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) {
                return prod0 / denominator;
            }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result * 8) < value ? 1 : 0);
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SafeCast.sol)
// This file was procedurally generated from scripts/generate/templates/SafeCast.js.

pragma solidity ^0.8.0;

/**
 * @dev Wrappers over Solidity's uintXX/intXX casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such an operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 *
 * Can be combined with {SafeMath} and {SignedSafeMath} to extend it to smaller types, by performing
 * all math on `uint256` and `int256` and then downcasting.
 */
library SafeCast {
    /**
     * @dev Returns the downcasted uint248 from uint256, reverting on
     * overflow (when the input is greater than largest uint248).
     *
     * Counterpart to Solidity's `uint248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     *
     * _Available since v4.7._
     */
    function toUint248(uint256 value) internal pure returns (uint248) {
        require(value <= type(uint248).max, "SafeCast: value doesn't fit in 248 bits");
        return uint248(value);
    }

    /**
     * @dev Returns the downcasted uint240 from uint256, reverting on
     * overflow (when the input is greater than largest uint240).
     *
     * Counterpart to Solidity's `uint240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     *
     * _Available since v4.7._
     */
    function toUint240(uint256 value) internal pure returns (uint240) {
        require(value <= type(uint240).max, "SafeCast: value doesn't fit in 240 bits");
        return uint240(value);
    }

    /**
     * @dev Returns the downcasted uint232 from uint256, reverting on
     * overflow (when the input is greater than largest uint232).
     *
     * Counterpart to Solidity's `uint232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     *
     * _Available since v4.7._
     */
    function toUint232(uint256 value) internal pure returns (uint232) {
        require(value <= type(uint232).max, "SafeCast: value doesn't fit in 232 bits");
        return uint232(value);
    }

    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     *
     * _Available since v4.2._
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        require(value <= type(uint224).max, "SafeCast: value doesn't fit in 224 bits");
        return uint224(value);
    }

    /**
     * @dev Returns the downcasted uint216 from uint256, reverting on
     * overflow (when the input is greater than largest uint216).
     *
     * Counterpart to Solidity's `uint216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     *
     * _Available since v4.7._
     */
    function toUint216(uint256 value) internal pure returns (uint216) {
        require(value <= type(uint216).max, "SafeCast: value doesn't fit in 216 bits");
        return uint216(value);
    }

    /**
     * @dev Returns the downcasted uint208 from uint256, reverting on
     * overflow (when the input is greater than largest uint208).
     *
     * Counterpart to Solidity's `uint208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     *
     * _Available since v4.7._
     */
    function toUint208(uint256 value) internal pure returns (uint208) {
        require(value <= type(uint208).max, "SafeCast: value doesn't fit in 208 bits");
        return uint208(value);
    }

    /**
     * @dev Returns the downcasted uint200 from uint256, reverting on
     * overflow (when the input is greater than largest uint200).
     *
     * Counterpart to Solidity's `uint200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     *
     * _Available since v4.7._
     */
    function toUint200(uint256 value) internal pure returns (uint200) {
        require(value <= type(uint200).max, "SafeCast: value doesn't fit in 200 bits");
        return uint200(value);
    }

    /**
     * @dev Returns the downcasted uint192 from uint256, reverting on
     * overflow (when the input is greater than largest uint192).
     *
     * Counterpart to Solidity's `uint192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     *
     * _Available since v4.7._
     */
    function toUint192(uint256 value) internal pure returns (uint192) {
        require(value <= type(uint192).max, "SafeCast: value doesn't fit in 192 bits");
        return uint192(value);
    }

    /**
     * @dev Returns the downcasted uint184 from uint256, reverting on
     * overflow (when the input is greater than largest uint184).
     *
     * Counterpart to Solidity's `uint184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     *
     * _Available since v4.7._
     */
    function toUint184(uint256 value) internal pure returns (uint184) {
        require(value <= type(uint184).max, "SafeCast: value doesn't fit in 184 bits");
        return uint184(value);
    }

    /**
     * @dev Returns the downcasted uint176 from uint256, reverting on
     * overflow (when the input is greater than largest uint176).
     *
     * Counterpart to Solidity's `uint176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     *
     * _Available since v4.7._
     */
    function toUint176(uint256 value) internal pure returns (uint176) {
        require(value <= type(uint176).max, "SafeCast: value doesn't fit in 176 bits");
        return uint176(value);
    }

    /**
     * @dev Returns the downcasted uint168 from uint256, reverting on
     * overflow (when the input is greater than largest uint168).
     *
     * Counterpart to Solidity's `uint168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     *
     * _Available since v4.7._
     */
    function toUint168(uint256 value) internal pure returns (uint168) {
        require(value <= type(uint168).max, "SafeCast: value doesn't fit in 168 bits");
        return uint168(value);
    }

    /**
     * @dev Returns the downcasted uint160 from uint256, reverting on
     * overflow (when the input is greater than largest uint160).
     *
     * Counterpart to Solidity's `uint160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     *
     * _Available since v4.7._
     */
    function toUint160(uint256 value) internal pure returns (uint160) {
        require(value <= type(uint160).max, "SafeCast: value doesn't fit in 160 bits");
        return uint160(value);
    }

    /**
     * @dev Returns the downcasted uint152 from uint256, reverting on
     * overflow (when the input is greater than largest uint152).
     *
     * Counterpart to Solidity's `uint152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     *
     * _Available since v4.7._
     */
    function toUint152(uint256 value) internal pure returns (uint152) {
        require(value <= type(uint152).max, "SafeCast: value doesn't fit in 152 bits");
        return uint152(value);
    }

    /**
     * @dev Returns the downcasted uint144 from uint256, reverting on
     * overflow (when the input is greater than largest uint144).
     *
     * Counterpart to Solidity's `uint144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     *
     * _Available since v4.7._
     */
    function toUint144(uint256 value) internal pure returns (uint144) {
        require(value <= type(uint144).max, "SafeCast: value doesn't fit in 144 bits");
        return uint144(value);
    }

    /**
     * @dev Returns the downcasted uint136 from uint256, reverting on
     * overflow (when the input is greater than largest uint136).
     *
     * Counterpart to Solidity's `uint136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     *
     * _Available since v4.7._
     */
    function toUint136(uint256 value) internal pure returns (uint136) {
        require(value <= type(uint136).max, "SafeCast: value doesn't fit in 136 bits");
        return uint136(value);
    }

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     *
     * _Available since v2.5._
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        require(value <= type(uint128).max, "SafeCast: value doesn't fit in 128 bits");
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint120 from uint256, reverting on
     * overflow (when the input is greater than largest uint120).
     *
     * Counterpart to Solidity's `uint120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     *
     * _Available since v4.7._
     */
    function toUint120(uint256 value) internal pure returns (uint120) {
        require(value <= type(uint120).max, "SafeCast: value doesn't fit in 120 bits");
        return uint120(value);
    }

    /**
     * @dev Returns the downcasted uint112 from uint256, reverting on
     * overflow (when the input is greater than largest uint112).
     *
     * Counterpart to Solidity's `uint112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     *
     * _Available since v4.7._
     */
    function toUint112(uint256 value) internal pure returns (uint112) {
        require(value <= type(uint112).max, "SafeCast: value doesn't fit in 112 bits");
        return uint112(value);
    }

    /**
     * @dev Returns the downcasted uint104 from uint256, reverting on
     * overflow (when the input is greater than largest uint104).
     *
     * Counterpart to Solidity's `uint104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     *
     * _Available since v4.7._
     */
    function toUint104(uint256 value) internal pure returns (uint104) {
        require(value <= type(uint104).max, "SafeCast: value doesn't fit in 104 bits");
        return uint104(value);
    }

    /**
     * @dev Returns the downcasted uint96 from uint256, reverting on
     * overflow (when the input is greater than largest uint96).
     *
     * Counterpart to Solidity's `uint96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     *
     * _Available since v4.2._
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        require(value <= type(uint96).max, "SafeCast: value doesn't fit in 96 bits");
        return uint96(value);
    }

    /**
     * @dev Returns the downcasted uint88 from uint256, reverting on
     * overflow (when the input is greater than largest uint88).
     *
     * Counterpart to Solidity's `uint88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     *
     * _Available since v4.7._
     */
    function toUint88(uint256 value) internal pure returns (uint88) {
        require(value <= type(uint88).max, "SafeCast: value doesn't fit in 88 bits");
        return uint88(value);
    }

    /**
     * @dev Returns the downcasted uint80 from uint256, reverting on
     * overflow (when the input is greater than largest uint80).
     *
     * Counterpart to Solidity's `uint80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     *
     * _Available since v4.7._
     */
    function toUint80(uint256 value) internal pure returns (uint80) {
        require(value <= type(uint80).max, "SafeCast: value doesn't fit in 80 bits");
        return uint80(value);
    }

    /**
     * @dev Returns the downcasted uint72 from uint256, reverting on
     * overflow (when the input is greater than largest uint72).
     *
     * Counterpart to Solidity's `uint72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     *
     * _Available since v4.7._
     */
    function toUint72(uint256 value) internal pure returns (uint72) {
        require(value <= type(uint72).max, "SafeCast: value doesn't fit in 72 bits");
        return uint72(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     *
     * _Available since v2.5._
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        require(value <= type(uint64).max, "SafeCast: value doesn't fit in 64 bits");
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint56 from uint256, reverting on
     * overflow (when the input is greater than largest uint56).
     *
     * Counterpart to Solidity's `uint56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     *
     * _Available since v4.7._
     */
    function toUint56(uint256 value) internal pure returns (uint56) {
        require(value <= type(uint56).max, "SafeCast: value doesn't fit in 56 bits");
        return uint56(value);
    }

    /**
     * @dev Returns the downcasted uint48 from uint256, reverting on
     * overflow (when the input is greater than largest uint48).
     *
     * Counterpart to Solidity's `uint48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     *
     * _Available since v4.7._
     */
    function toUint48(uint256 value) internal pure returns (uint48) {
        require(value <= type(uint48).max, "SafeCast: value doesn't fit in 48 bits");
        return uint48(value);
    }

    /**
     * @dev Returns the downcasted uint40 from uint256, reverting on
     * overflow (when the input is greater than largest uint40).
     *
     * Counterpart to Solidity's `uint40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     *
     * _Available since v4.7._
     */
    function toUint40(uint256 value) internal pure returns (uint40) {
        require(value <= type(uint40).max, "SafeCast: value doesn't fit in 40 bits");
        return uint40(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     *
     * _Available since v2.5._
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        require(value <= type(uint32).max, "SafeCast: value doesn't fit in 32 bits");
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint24 from uint256, reverting on
     * overflow (when the input is greater than largest uint24).
     *
     * Counterpart to Solidity's `uint24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     *
     * _Available since v4.7._
     */
    function toUint24(uint256 value) internal pure returns (uint24) {
        require(value <= type(uint24).max, "SafeCast: value doesn't fit in 24 bits");
        return uint24(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     *
     * _Available since v2.5._
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        require(value <= type(uint16).max, "SafeCast: value doesn't fit in 16 bits");
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     *
     * _Available since v2.5._
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        require(value <= type(uint8).max, "SafeCast: value doesn't fit in 8 bits");
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     *
     * _Available since v3.0._
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        require(value >= 0, "SafeCast: value must be positive");
        return uint256(value);
    }

    /**
     * @dev Returns the downcasted int248 from int256, reverting on
     * overflow (when the input is less than smallest int248 or
     * greater than largest int248).
     *
     * Counterpart to Solidity's `int248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     *
     * _Available since v4.7._
     */
    function toInt248(int256 value) internal pure returns (int248 downcasted) {
        downcasted = int248(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 248 bits");
    }

    /**
     * @dev Returns the downcasted int240 from int256, reverting on
     * overflow (when the input is less than smallest int240 or
     * greater than largest int240).
     *
     * Counterpart to Solidity's `int240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     *
     * _Available since v4.7._
     */
    function toInt240(int256 value) internal pure returns (int240 downcasted) {
        downcasted = int240(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 240 bits");
    }

    /**
     * @dev Returns the downcasted int232 from int256, reverting on
     * overflow (when the input is less than smallest int232 or
     * greater than largest int232).
     *
     * Counterpart to Solidity's `int232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     *
     * _Available since v4.7._
     */
    function toInt232(int256 value) internal pure returns (int232 downcasted) {
        downcasted = int232(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 232 bits");
    }

    /**
     * @dev Returns the downcasted int224 from int256, reverting on
     * overflow (when the input is less than smallest int224 or
     * greater than largest int224).
     *
     * Counterpart to Solidity's `int224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     *
     * _Available since v4.7._
     */
    function toInt224(int256 value) internal pure returns (int224 downcasted) {
        downcasted = int224(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 224 bits");
    }

    /**
     * @dev Returns the downcasted int216 from int256, reverting on
     * overflow (when the input is less than smallest int216 or
     * greater than largest int216).
     *
     * Counterpart to Solidity's `int216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     *
     * _Available since v4.7._
     */
    function toInt216(int256 value) internal pure returns (int216 downcasted) {
        downcasted = int216(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 216 bits");
    }

    /**
     * @dev Returns the downcasted int208 from int256, reverting on
     * overflow (when the input is less than smallest int208 or
     * greater than largest int208).
     *
     * Counterpart to Solidity's `int208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     *
     * _Available since v4.7._
     */
    function toInt208(int256 value) internal pure returns (int208 downcasted) {
        downcasted = int208(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 208 bits");
    }

    /**
     * @dev Returns the downcasted int200 from int256, reverting on
     * overflow (when the input is less than smallest int200 or
     * greater than largest int200).
     *
     * Counterpart to Solidity's `int200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     *
     * _Available since v4.7._
     */
    function toInt200(int256 value) internal pure returns (int200 downcasted) {
        downcasted = int200(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 200 bits");
    }

    /**
     * @dev Returns the downcasted int192 from int256, reverting on
     * overflow (when the input is less than smallest int192 or
     * greater than largest int192).
     *
     * Counterpart to Solidity's `int192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     *
     * _Available since v4.7._
     */
    function toInt192(int256 value) internal pure returns (int192 downcasted) {
        downcasted = int192(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 192 bits");
    }

    /**
     * @dev Returns the downcasted int184 from int256, reverting on
     * overflow (when the input is less than smallest int184 or
     * greater than largest int184).
     *
     * Counterpart to Solidity's `int184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     *
     * _Available since v4.7._
     */
    function toInt184(int256 value) internal pure returns (int184 downcasted) {
        downcasted = int184(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 184 bits");
    }

    /**
     * @dev Returns the downcasted int176 from int256, reverting on
     * overflow (when the input is less than smallest int176 or
     * greater than largest int176).
     *
     * Counterpart to Solidity's `int176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     *
     * _Available since v4.7._
     */
    function toInt176(int256 value) internal pure returns (int176 downcasted) {
        downcasted = int176(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 176 bits");
    }

    /**
     * @dev Returns the downcasted int168 from int256, reverting on
     * overflow (when the input is less than smallest int168 or
     * greater than largest int168).
     *
     * Counterpart to Solidity's `int168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     *
     * _Available since v4.7._
     */
    function toInt168(int256 value) internal pure returns (int168 downcasted) {
        downcasted = int168(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 168 bits");
    }

    /**
     * @dev Returns the downcasted int160 from int256, reverting on
     * overflow (when the input is less than smallest int160 or
     * greater than largest int160).
     *
     * Counterpart to Solidity's `int160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     *
     * _Available since v4.7._
     */
    function toInt160(int256 value) internal pure returns (int160 downcasted) {
        downcasted = int160(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 160 bits");
    }

    /**
     * @dev Returns the downcasted int152 from int256, reverting on
     * overflow (when the input is less than smallest int152 or
     * greater than largest int152).
     *
     * Counterpart to Solidity's `int152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     *
     * _Available since v4.7._
     */
    function toInt152(int256 value) internal pure returns (int152 downcasted) {
        downcasted = int152(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 152 bits");
    }

    /**
     * @dev Returns the downcasted int144 from int256, reverting on
     * overflow (when the input is less than smallest int144 or
     * greater than largest int144).
     *
     * Counterpart to Solidity's `int144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     *
     * _Available since v4.7._
     */
    function toInt144(int256 value) internal pure returns (int144 downcasted) {
        downcasted = int144(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 144 bits");
    }

    /**
     * @dev Returns the downcasted int136 from int256, reverting on
     * overflow (when the input is less than smallest int136 or
     * greater than largest int136).
     *
     * Counterpart to Solidity's `int136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     *
     * _Available since v4.7._
     */
    function toInt136(int256 value) internal pure returns (int136 downcasted) {
        downcasted = int136(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 136 bits");
    }

    /**
     * @dev Returns the downcasted int128 from int256, reverting on
     * overflow (when the input is less than smallest int128 or
     * greater than largest int128).
     *
     * Counterpart to Solidity's `int128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     *
     * _Available since v3.1._
     */
    function toInt128(int256 value) internal pure returns (int128 downcasted) {
        downcasted = int128(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 128 bits");
    }

    /**
     * @dev Returns the downcasted int120 from int256, reverting on
     * overflow (when the input is less than smallest int120 or
     * greater than largest int120).
     *
     * Counterpart to Solidity's `int120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     *
     * _Available since v4.7._
     */
    function toInt120(int256 value) internal pure returns (int120 downcasted) {
        downcasted = int120(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 120 bits");
    }

    /**
     * @dev Returns the downcasted int112 from int256, reverting on
     * overflow (when the input is less than smallest int112 or
     * greater than largest int112).
     *
     * Counterpart to Solidity's `int112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     *
     * _Available since v4.7._
     */
    function toInt112(int256 value) internal pure returns (int112 downcasted) {
        downcasted = int112(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 112 bits");
    }

    /**
     * @dev Returns the downcasted int104 from int256, reverting on
     * overflow (when the input is less than smallest int104 or
     * greater than largest int104).
     *
     * Counterpart to Solidity's `int104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     *
     * _Available since v4.7._
     */
    function toInt104(int256 value) internal pure returns (int104 downcasted) {
        downcasted = int104(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 104 bits");
    }

    /**
     * @dev Returns the downcasted int96 from int256, reverting on
     * overflow (when the input is less than smallest int96 or
     * greater than largest int96).
     *
     * Counterpart to Solidity's `int96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     *
     * _Available since v4.7._
     */
    function toInt96(int256 value) internal pure returns (int96 downcasted) {
        downcasted = int96(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 96 bits");
    }

    /**
     * @dev Returns the downcasted int88 from int256, reverting on
     * overflow (when the input is less than smallest int88 or
     * greater than largest int88).
     *
     * Counterpart to Solidity's `int88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     *
     * _Available since v4.7._
     */
    function toInt88(int256 value) internal pure returns (int88 downcasted) {
        downcasted = int88(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 88 bits");
    }

    /**
     * @dev Returns the downcasted int80 from int256, reverting on
     * overflow (when the input is less than smallest int80 or
     * greater than largest int80).
     *
     * Counterpart to Solidity's `int80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     *
     * _Available since v4.7._
     */
    function toInt80(int256 value) internal pure returns (int80 downcasted) {
        downcasted = int80(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 80 bits");
    }

    /**
     * @dev Returns the downcasted int72 from int256, reverting on
     * overflow (when the input is less than smallest int72 or
     * greater than largest int72).
     *
     * Counterpart to Solidity's `int72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     *
     * _Available since v4.7._
     */
    function toInt72(int256 value) internal pure returns (int72 downcasted) {
        downcasted = int72(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 72 bits");
    }

    /**
     * @dev Returns the downcasted int64 from int256, reverting on
     * overflow (when the input is less than smallest int64 or
     * greater than largest int64).
     *
     * Counterpart to Solidity's `int64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     *
     * _Available since v3.1._
     */
    function toInt64(int256 value) internal pure returns (int64 downcasted) {
        downcasted = int64(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 64 bits");
    }

    /**
     * @dev Returns the downcasted int56 from int256, reverting on
     * overflow (when the input is less than smallest int56 or
     * greater than largest int56).
     *
     * Counterpart to Solidity's `int56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     *
     * _Available since v4.7._
     */
    function toInt56(int256 value) internal pure returns (int56 downcasted) {
        downcasted = int56(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 56 bits");
    }

    /**
     * @dev Returns the downcasted int48 from int256, reverting on
     * overflow (when the input is less than smallest int48 or
     * greater than largest int48).
     *
     * Counterpart to Solidity's `int48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     *
     * _Available since v4.7._
     */
    function toInt48(int256 value) internal pure returns (int48 downcasted) {
        downcasted = int48(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 48 bits");
    }

    /**
     * @dev Returns the downcasted int40 from int256, reverting on
     * overflow (when the input is less than smallest int40 or
     * greater than largest int40).
     *
     * Counterpart to Solidity's `int40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     *
     * _Available since v4.7._
     */
    function toInt40(int256 value) internal pure returns (int40 downcasted) {
        downcasted = int40(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 40 bits");
    }

    /**
     * @dev Returns the downcasted int32 from int256, reverting on
     * overflow (when the input is less than smallest int32 or
     * greater than largest int32).
     *
     * Counterpart to Solidity's `int32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     *
     * _Available since v3.1._
     */
    function toInt32(int256 value) internal pure returns (int32 downcasted) {
        downcasted = int32(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 32 bits");
    }

    /**
     * @dev Returns the downcasted int24 from int256, reverting on
     * overflow (when the input is less than smallest int24 or
     * greater than largest int24).
     *
     * Counterpart to Solidity's `int24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     *
     * _Available since v4.7._
     */
    function toInt24(int256 value) internal pure returns (int24 downcasted) {
        downcasted = int24(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 24 bits");
    }

    /**
     * @dev Returns the downcasted int16 from int256, reverting on
     * overflow (when the input is less than smallest int16 or
     * greater than largest int16).
     *
     * Counterpart to Solidity's `int16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     *
     * _Available since v3.1._
     */
    function toInt16(int256 value) internal pure returns (int16 downcasted) {
        downcasted = int16(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 16 bits");
    }

    /**
     * @dev Returns the downcasted int8 from int256, reverting on
     * overflow (when the input is less than smallest int8 or
     * greater than largest int8).
     *
     * Counterpart to Solidity's `int8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     *
     * _Available since v3.1._
     */
    function toInt8(int256 value) internal pure returns (int8 downcasted) {
        downcasted = int8(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 8 bits");
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     *
     * _Available since v3.0._
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        require(value <= uint256(type(int256).max), "SafeCast: value doesn't fit in an int256");
        return int256(value);
    }
}