// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (access/AccessControl.sol)

pragma solidity ^0.8.20;

import {IAccessControl} from "./IAccessControl.sol";
import {Context} from "../utils/Context.sol";
import {ERC165} from "../utils/introspection/ERC165.sol";

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

    mapping(bytes32 role => RoleData) private _roles;

    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;

    /**
     * @dev Modifier that checks that an account has a specific role. Reverts
     * with an {AccessControlUnauthorizedAccount} error including the required role.
     */
    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 returns (bool) {
        return _roles[role].hasRole[account];
    }

    /**
     * @dev Reverts with an {AccessControlUnauthorizedAccount} error if `_msgSender()`
     * is missing `role`. Overriding this function changes the behavior of the {onlyRole} modifier.
     */
    function _checkRole(bytes32 role) internal view virtual {
        _checkRole(role, _msgSender());
    }

    /**
     * @dev Reverts with an {AccessControlUnauthorizedAccount} error if `account`
     * is missing `role`.
     */
    function _checkRole(bytes32 role, address account) internal view virtual {
        if (!hasRole(role, account)) {
            revert AccessControlUnauthorizedAccount(account, role);
        }
    }

    /**
     * @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 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 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 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 `callerConfirmation`.
     *
     * May emit a {RoleRevoked} event.
     */
    function renounceRole(bytes32 role, address callerConfirmation) public virtual {
        if (callerConfirmation != _msgSender()) {
            revert AccessControlBadConfirmation();
        }

        _revokeRole(role, callerConfirmation);
    }

    /**
     * @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 Attempts to grant `role` to `account` and returns a boolean indicating if `role` was granted.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleGranted} event.
     */
    function _grantRole(bytes32 role, address account) internal virtual returns (bool) {
        if (!hasRole(role, account)) {
            _roles[role].hasRole[account] = true;
            emit RoleGranted(role, account, _msgSender());
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Attempts to revoke `role` to `account` and returns a boolean indicating if `role` was revoked.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleRevoked} event.
     */
    function _revokeRole(bytes32 role, address account) internal virtual returns (bool) {
        if (hasRole(role, account)) {
            _roles[role].hasRole[account] = false;
            emit RoleRevoked(role, account, _msgSender());
            return true;
        } else {
            return false;
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/Address.sol)

pragma solidity ^0.8.20;

import {Errors} from "./Errors.sol";

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev There's no code at `target` (it is not a contract).
     */
    error AddressEmptyCode(address target);

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.8.20/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        if (address(this).balance < amount) {
            revert Errors.InsufficientBalance(address(this).balance, amount);
        }

        (bool success, ) = recipient.call{value: amount}("");
        if (!success) {
            revert Errors.FailedCall();
        }
    }

    /**
     * @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 or custom error, it is bubbled
     * up by this function (like regular Solidity function calls). However, if
     * the call reverted with no returned reason, this function reverts with a
     * {Errors.FailedCall} error.
     *
     * 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.
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0);
    }

    /**
     * @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`.
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        if (address(this).balance < value) {
            revert Errors.InsufficientBalance(address(this).balance, value);
        }
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

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

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

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and reverts if the target
     * was not a contract or bubbling up the revert reason (falling back to {Errors.FailedCall}) in case
     * of an unsuccessful call.
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata
    ) internal view returns (bytes memory) {
        if (!success) {
            _revert(returndata);
        } else {
            // only check if target is a contract if the call was successful and the return data is empty
            // otherwise we already know that it was a contract
            if (returndata.length == 0 && target.code.length == 0) {
                revert AddressEmptyCode(target);
            }
            return returndata;
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and reverts if it wasn't, either by bubbling the
     * revert reason or with a default {Errors.FailedCall} error.
     */
    function verifyCallResult(bool success, bytes memory returndata) internal pure returns (bytes memory) {
        if (!success) {
            _revert(returndata);
        } else {
            return returndata;
        }
    }

    /**
     * @dev Reverts with returndata if present. Otherwise reverts with {Errors.FailedCall}.
     */
    function _revert(bytes memory returndata) 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
            assembly ("memory-safe") {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert Errors.FailedCall();
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD2x18 } from "./ValueType.sol";

/// @notice Casts a UD2x18 number into SD59x18.
/// @dev There is no overflow check because UD2x18 ⊆ SD59x18.
function intoSD59x18(UD2x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(uint256(UD2x18.unwrap(x))));
}

/// @notice Casts a UD2x18 number into UD60x18.
/// @dev There is no overflow check because UD2x18 ⊆ UD60x18.
function intoUD60x18(UD2x18 x) pure returns (UD60x18 result) {
    result = UD60x18.wrap(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint128.
/// @dev There is no overflow check because UD2x18 ⊆ uint128.
function intoUint128(UD2x18 x) pure returns (uint128 result) {
    result = uint128(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint256.
/// @dev There is no overflow check because UD2x18 ⊆ uint256.
function intoUint256(UD2x18 x) pure returns (uint256 result) {
    result = uint256(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint40.
/// @dev Requirements:
/// - x ≤ MAX_UINT40
function intoUint40(UD2x18 x) pure returns (uint40 result) {
    uint64 xUint = UD2x18.unwrap(x);
    if (xUint > uint64(Common.MAX_UINT40)) {
        revert Errors.PRBMath_UD2x18_IntoUint40_Overflow(x);
    }
    result = uint40(xUint);
}

/// @notice Alias for {wrap}.
function ud2x18(uint64 x) pure returns (UD2x18 result) {
    result = UD2x18.wrap(x);
}

/// @notice Unwrap a UD2x18 number into uint64.
function unwrap(UD2x18 x) pure returns (uint64 result) {
    result = UD2x18.unwrap(x);
}

/// @notice Wraps a uint64 number into UD2x18.
function wrap(uint64 x) pure returns (UD2x18 result) {
    result = UD2x18.wrap(x);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/structs/Checkpoints.sol)
// This file was procedurally generated from scripts/generate/templates/Checkpoints.js.

pragma solidity ^0.8.20;

import {Math} from "../math/Math.sol";

/**
 * @dev This library defines the `Trace*` 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.Trace*` in your contract, and store a new
 * checkpoint for the current transaction block using the {push} function.
 */
library Checkpoints {
    /**
     * @dev A value was attempted to be inserted on a past checkpoint.
     */
    error CheckpointUnorderedInsertion();

    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.
     *
     * IMPORTANT: Never accept `key` as a user input, since an arbitrary `type(uint32).max` key set will disable the
     * library.
     */
    function push(
        Trace224 storage self,
        uint32 key,
        uint224 value
    ) internal returns (uint224 oldValue, uint224 newValue) {
        return _insert(self._checkpoints, key, value);
    }

    /**
     * @dev Returns the value in the first (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 last (most recent) checkpoint with key lower or equal than the search key, or zero
     * if there is none.
     */
    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 last (most recent) checkpoint with key lower or equal than the search key, or zero
     * if there is none.
     *
     * NOTE: This is a variant of {upperLookup} that is optimised to find "recent" checkpoint (checkpoints with high
     * keys).
     */
    function upperLookupRecent(Trace224 storage self, uint32 key) internal view returns (uint224) {
        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)._key) {
                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 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 storage 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 Returns checkpoint at given position.
     */
    function at(Trace224 storage self, uint32 pos) internal view returns (Checkpoint224 memory) {
        return self._checkpoints[pos];
    }

    /**
     * @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 oldValue, uint224 newValue) {
        uint256 pos = self.length;

        if (pos > 0) {
            Checkpoint224 storage last = _unsafeAccess(self, pos - 1);
            uint32 lastKey = last._key;
            uint224 lastValue = last._value;

            // Checkpoint keys must be non-decreasing.
            if (lastKey > key) {
                revert CheckpointUnorderedInsertion();
            }

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

    /**
     * @dev Return the index of the first (oldest) checkpoint with key strictly bigger 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 first (oldest) checkpoint with key 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 Trace208 {
        Checkpoint208[] _checkpoints;
    }

    struct Checkpoint208 {
        uint48 _key;
        uint208 _value;
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into a Trace208 so that it is stored as the checkpoint.
     *
     * Returns previous value and new value.
     *
     * IMPORTANT: Never accept `key` as a user input, since an arbitrary `type(uint48).max` key set will disable the
     * library.
     */
    function push(
        Trace208 storage self,
        uint48 key,
        uint208 value
    ) internal returns (uint208 oldValue, uint208 newValue) {
        return _insert(self._checkpoints, key, value);
    }

    /**
     * @dev Returns the value in the first (oldest) checkpoint with key greater or equal than the search key, or zero if
     * there is none.
     */
    function lowerLookup(Trace208 storage self, uint48 key) internal view returns (uint208) {
        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 last (most recent) checkpoint with key lower or equal than the search key, or zero
     * if there is none.
     */
    function upperLookup(Trace208 storage self, uint48 key) internal view returns (uint208) {
        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 last (most recent) checkpoint with key lower or equal than the search key, or zero
     * if there is none.
     *
     * NOTE: This is a variant of {upperLookup} that is optimised to find "recent" checkpoint (checkpoints with high
     * keys).
     */
    function upperLookupRecent(Trace208 storage self, uint48 key) internal view returns (uint208) {
        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)._key) {
                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 Returns the value in the most recent checkpoint, or zero if there are no checkpoints.
     */
    function latest(Trace208 storage self) internal view returns (uint208) {
        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(Trace208 storage self) internal view returns (bool exists, uint48 _key, uint208 _value) {
        uint256 pos = self._checkpoints.length;
        if (pos == 0) {
            return (false, 0, 0);
        } else {
            Checkpoint208 storage ckpt = _unsafeAccess(self._checkpoints, pos - 1);
            return (true, ckpt._key, ckpt._value);
        }
    }

    /**
     * @dev Returns the number of checkpoint.
     */
    function length(Trace208 storage self) internal view returns (uint256) {
        return self._checkpoints.length;
    }

    /**
     * @dev Returns checkpoint at given position.
     */
    function at(Trace208 storage self, uint32 pos) internal view returns (Checkpoint208 memory) {
        return self._checkpoints[pos];
    }

    /**
     * @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(
        Checkpoint208[] storage self,
        uint48 key,
        uint208 value
    ) private returns (uint208 oldValue, uint208 newValue) {
        uint256 pos = self.length;

        if (pos > 0) {
            Checkpoint208 storage last = _unsafeAccess(self, pos - 1);
            uint48 lastKey = last._key;
            uint208 lastValue = last._value;

            // Checkpoint keys must be non-decreasing.
            if (lastKey > key) {
                revert CheckpointUnorderedInsertion();
            }

            // Update or push new checkpoint
            if (lastKey == key) {
                last._value = value;
            } else {
                self.push(Checkpoint208({_key: key, _value: value}));
            }
            return (lastValue, value);
        } else {
            self.push(Checkpoint208({_key: key, _value: value}));
            return (0, value);
        }
    }

    /**
     * @dev Return the index of the first (oldest) checkpoint with key strictly bigger 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(
        Checkpoint208[] storage self,
        uint48 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 first (oldest) checkpoint with key 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(
        Checkpoint208[] storage self,
        uint48 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(
        Checkpoint208[] storage self,
        uint256 pos
    ) private pure returns (Checkpoint208 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.
     *
     * IMPORTANT: Never accept `key` as a user input, since an arbitrary `type(uint96).max` key set will disable the
     * library.
     */
    function push(
        Trace160 storage self,
        uint96 key,
        uint160 value
    ) internal returns (uint160 oldValue, uint160 newValue) {
        return _insert(self._checkpoints, key, value);
    }

    /**
     * @dev Returns the value in the first (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 last (most recent) checkpoint with key lower or equal than the search key, or zero
     * if there is none.
     */
    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 last (most recent) checkpoint with key lower or equal than the search key, or zero
     * if there is none.
     *
     * NOTE: This is a variant of {upperLookup} that is optimised to find "recent" checkpoint (checkpoints with high
     * keys).
     */
    function upperLookupRecent(Trace160 storage self, uint96 key) internal view returns (uint160) {
        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)._key) {
                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 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 storage 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 Returns checkpoint at given position.
     */
    function at(Trace160 storage self, uint32 pos) internal view returns (Checkpoint160 memory) {
        return self._checkpoints[pos];
    }

    /**
     * @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 oldValue, uint160 newValue) {
        uint256 pos = self.length;

        if (pos > 0) {
            Checkpoint160 storage last = _unsafeAccess(self, pos - 1);
            uint96 lastKey = last._key;
            uint160 lastValue = last._value;

            // Checkpoint keys must be non-decreasing.
            if (lastKey > key) {
                revert CheckpointUnorderedInsertion();
            }

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

    /**
     * @dev Return the index of the first (oldest) checkpoint with key strictly bigger 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 first (oldest) checkpoint with key 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
pragma solidity >=0.8.19;

// Common.sol
//
// Common mathematical functions used in both SD59x18 and UD60x18. Note that these global functions do not
// always operate with SD59x18 and UD60x18 numbers.

/*//////////////////////////////////////////////////////////////////////////
                                CUSTOM ERRORS
//////////////////////////////////////////////////////////////////////////*/

/// @notice Thrown when the resultant value in {mulDiv} overflows uint256.
error PRBMath_MulDiv_Overflow(uint256 x, uint256 y, uint256 denominator);

/// @notice Thrown when the resultant value in {mulDiv18} overflows uint256.
error PRBMath_MulDiv18_Overflow(uint256 x, uint256 y);

/// @notice Thrown when one of the inputs passed to {mulDivSigned} is `type(int256).min`.
error PRBMath_MulDivSigned_InputTooSmall();

/// @notice Thrown when the resultant value in {mulDivSigned} overflows int256.
error PRBMath_MulDivSigned_Overflow(int256 x, int256 y);

/*//////////////////////////////////////////////////////////////////////////
                                    CONSTANTS
//////////////////////////////////////////////////////////////////////////*/

/// @dev The maximum value a uint128 number can have.
uint128 constant MAX_UINT128 = type(uint128).max;

/// @dev The maximum value a uint40 number can have.
uint40 constant MAX_UINT40 = type(uint40).max;

/// @dev The maximum value a uint64 number can have.
uint64 constant MAX_UINT64 = type(uint64).max;

/// @dev The unit number, which the decimal precision of the fixed-point types.
uint256 constant UNIT = 1e18;

/// @dev The unit number inverted mod 2^256.
uint256 constant UNIT_INVERSE = 78156646155174841979727994598816262306175212592076161876661_508869554232690281;

/// @dev The the largest power of two that divides the decimal value of `UNIT`. The logarithm of this value is the least significant
/// bit in the binary representation of `UNIT`.
uint256 constant UNIT_LPOTD = 262144;

/*//////////////////////////////////////////////////////////////////////////
                                    FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

/// @notice Calculates the binary exponent of x using the binary fraction method.
/// @dev Has to use 192.64-bit fixed-point numbers. See https://ethereum.stackexchange.com/a/96594/24693.
/// @param x The exponent as an unsigned 192.64-bit fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
/// @custom:smtchecker abstract-function-nondet
function exp2(uint256 x) pure returns (uint256 result) {
    unchecked {
        // Start from 0.5 in the 192.64-bit fixed-point format.
        result = 0x800000000000000000000000000000000000000000000000;

        // The following logic multiplies the result by $\sqrt{2^{-i}}$ when the bit at position i is 1. Key points:
        //
        // 1. Intermediate results will not overflow, as the starting point is 2^191 and all magic factors are under 2^65.
        // 2. The rationale for organizing the if statements into groups of 8 is gas savings. If the result of performing
        // a bitwise AND operation between x and any value in the array [0x80; 0x40; 0x20; 0x10; 0x08; 0x04; 0x02; 0x01] is 1,
        // we know that `x & 0xFF` is also 1.
        if (x & 0xFF00000000000000 > 0) {
            if (x & 0x8000000000000000 > 0) {
                result = (result * 0x16A09E667F3BCC909) >> 64;
            }
            if (x & 0x4000000000000000 > 0) {
                result = (result * 0x1306FE0A31B7152DF) >> 64;
            }
            if (x & 0x2000000000000000 > 0) {
                result = (result * 0x1172B83C7D517ADCE) >> 64;
            }
            if (x & 0x1000000000000000 > 0) {
                result = (result * 0x10B5586CF9890F62A) >> 64;
            }
            if (x & 0x800000000000000 > 0) {
                result = (result * 0x1059B0D31585743AE) >> 64;
            }
            if (x & 0x400000000000000 > 0) {
                result = (result * 0x102C9A3E778060EE7) >> 64;
            }
            if (x & 0x200000000000000 > 0) {
                result = (result * 0x10163DA9FB33356D8) >> 64;
            }
            if (x & 0x100000000000000 > 0) {
                result = (result * 0x100B1AFA5ABCBED61) >> 64;
            }
        }

        if (x & 0xFF000000000000 > 0) {
            if (x & 0x80000000000000 > 0) {
                result = (result * 0x10058C86DA1C09EA2) >> 64;
            }
            if (x & 0x40000000000000 > 0) {
                result = (result * 0x1002C605E2E8CEC50) >> 64;
            }
            if (x & 0x20000000000000 > 0) {
                result = (result * 0x100162F3904051FA1) >> 64;
            }
            if (x & 0x10000000000000 > 0) {
                result = (result * 0x1000B175EFFDC76BA) >> 64;
            }
            if (x & 0x8000000000000 > 0) {
                result = (result * 0x100058BA01FB9F96D) >> 64;
            }
            if (x & 0x4000000000000 > 0) {
                result = (result * 0x10002C5CC37DA9492) >> 64;
            }
            if (x & 0x2000000000000 > 0) {
                result = (result * 0x1000162E525EE0547) >> 64;
            }
            if (x & 0x1000000000000 > 0) {
                result = (result * 0x10000B17255775C04) >> 64;
            }
        }

        if (x & 0xFF0000000000 > 0) {
            if (x & 0x800000000000 > 0) {
                result = (result * 0x1000058B91B5BC9AE) >> 64;
            }
            if (x & 0x400000000000 > 0) {
                result = (result * 0x100002C5C89D5EC6D) >> 64;
            }
            if (x & 0x200000000000 > 0) {
                result = (result * 0x10000162E43F4F831) >> 64;
            }
            if (x & 0x100000000000 > 0) {
                result = (result * 0x100000B1721BCFC9A) >> 64;
            }
            if (x & 0x80000000000 > 0) {
                result = (result * 0x10000058B90CF1E6E) >> 64;
            }
            if (x & 0x40000000000 > 0) {
                result = (result * 0x1000002C5C863B73F) >> 64;
            }
            if (x & 0x20000000000 > 0) {
                result = (result * 0x100000162E430E5A2) >> 64;
            }
            if (x & 0x10000000000 > 0) {
                result = (result * 0x1000000B172183551) >> 64;
            }
        }

        if (x & 0xFF00000000 > 0) {
            if (x & 0x8000000000 > 0) {
                result = (result * 0x100000058B90C0B49) >> 64;
            }
            if (x & 0x4000000000 > 0) {
                result = (result * 0x10000002C5C8601CC) >> 64;
            }
            if (x & 0x2000000000 > 0) {
                result = (result * 0x1000000162E42FFF0) >> 64;
            }
            if (x & 0x1000000000 > 0) {
                result = (result * 0x10000000B17217FBB) >> 64;
            }
            if (x & 0x800000000 > 0) {
                result = (result * 0x1000000058B90BFCE) >> 64;
            }
            if (x & 0x400000000 > 0) {
                result = (result * 0x100000002C5C85FE3) >> 64;
            }
            if (x & 0x200000000 > 0) {
                result = (result * 0x10000000162E42FF1) >> 64;
            }
            if (x & 0x100000000 > 0) {
                result = (result * 0x100000000B17217F8) >> 64;
            }
        }

        if (x & 0xFF000000 > 0) {
            if (x & 0x80000000 > 0) {
                result = (result * 0x10000000058B90BFC) >> 64;
            }
            if (x & 0x40000000 > 0) {
                result = (result * 0x1000000002C5C85FE) >> 64;
            }
            if (x & 0x20000000 > 0) {
                result = (result * 0x100000000162E42FF) >> 64;
            }
            if (x & 0x10000000 > 0) {
                result = (result * 0x1000000000B17217F) >> 64;
            }
            if (x & 0x8000000 > 0) {
                result = (result * 0x100000000058B90C0) >> 64;
            }
            if (x & 0x4000000 > 0) {
                result = (result * 0x10000000002C5C860) >> 64;
            }
            if (x & 0x2000000 > 0) {
                result = (result * 0x1000000000162E430) >> 64;
            }
            if (x & 0x1000000 > 0) {
                result = (result * 0x10000000000B17218) >> 64;
            }
        }

        if (x & 0xFF0000 > 0) {
            if (x & 0x800000 > 0) {
                result = (result * 0x1000000000058B90C) >> 64;
            }
            if (x & 0x400000 > 0) {
                result = (result * 0x100000000002C5C86) >> 64;
            }
            if (x & 0x200000 > 0) {
                result = (result * 0x10000000000162E43) >> 64;
            }
            if (x & 0x100000 > 0) {
                result = (result * 0x100000000000B1721) >> 64;
            }
            if (x & 0x80000 > 0) {
                result = (result * 0x10000000000058B91) >> 64;
            }
            if (x & 0x40000 > 0) {
                result = (result * 0x1000000000002C5C8) >> 64;
            }
            if (x & 0x20000 > 0) {
                result = (result * 0x100000000000162E4) >> 64;
            }
            if (x & 0x10000 > 0) {
                result = (result * 0x1000000000000B172) >> 64;
            }
        }

        if (x & 0xFF00 > 0) {
            if (x & 0x8000 > 0) {
                result = (result * 0x100000000000058B9) >> 64;
            }
            if (x & 0x4000 > 0) {
                result = (result * 0x10000000000002C5D) >> 64;
            }
            if (x & 0x2000 > 0) {
                result = (result * 0x1000000000000162E) >> 64;
            }
            if (x & 0x1000 > 0) {
                result = (result * 0x10000000000000B17) >> 64;
            }
            if (x & 0x800 > 0) {
                result = (result * 0x1000000000000058C) >> 64;
            }
            if (x & 0x400 > 0) {
                result = (result * 0x100000000000002C6) >> 64;
            }
            if (x & 0x200 > 0) {
                result = (result * 0x10000000000000163) >> 64;
            }
            if (x & 0x100 > 0) {
                result = (result * 0x100000000000000B1) >> 64;
            }
        }

        if (x & 0xFF > 0) {
            if (x & 0x80 > 0) {
                result = (result * 0x10000000000000059) >> 64;
            }
            if (x & 0x40 > 0) {
                result = (result * 0x1000000000000002C) >> 64;
            }
            if (x & 0x20 > 0) {
                result = (result * 0x10000000000000016) >> 64;
            }
            if (x & 0x10 > 0) {
                result = (result * 0x1000000000000000B) >> 64;
            }
            if (x & 0x8 > 0) {
                result = (result * 0x10000000000000006) >> 64;
            }
            if (x & 0x4 > 0) {
                result = (result * 0x10000000000000003) >> 64;
            }
            if (x & 0x2 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }
            if (x & 0x1 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }
        }

        // In the code snippet below, two operations are executed simultaneously:
        //
        // 1. The result is multiplied by $(2^n + 1)$, where $2^n$ represents the integer part, and the additional 1
        // accounts for the initial guess of 0.5. This is achieved by subtracting from 191 instead of 192.
        // 2. The result is then converted to an unsigned 60.18-decimal fixed-point format.
        //
        // The underlying logic is based on the relationship $2^{191-ip} = 2^{ip} / 2^{191}$, where $ip$ denotes the,
        // integer part, $2^n$.
        result *= UNIT;
        result >>= (191 - (x >> 64));
    }
}

/// @notice Finds the zero-based index of the first 1 in the binary representation of x.
///
/// @dev See the note on "msb" in this Wikipedia article: https://en.wikipedia.org/wiki/Find_first_set
///
/// Each step in this implementation is equivalent to this high-level code:
///
/// ```solidity
/// if (x >= 2 ** 128) {
///     x >>= 128;
///     result += 128;
/// }
/// ```
///
/// Where 128 is replaced with each respective power of two factor. See the full high-level implementation here:
/// https://gist.github.com/PaulRBerg/f932f8693f2733e30c4d479e8e980948
///
/// The Yul instructions used below are:
///
/// - "gt" is "greater than"
/// - "or" is the OR bitwise operator
/// - "shl" is "shift left"
/// - "shr" is "shift right"
///
/// @param x The uint256 number for which to find the index of the most significant bit.
/// @return result The index of the most significant bit as a uint256.
/// @custom:smtchecker abstract-function-nondet
function msb(uint256 x) pure returns (uint256 result) {
    // 2^128
    assembly ("memory-safe") {
        let factor := shl(7, gt(x, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^64
    assembly ("memory-safe") {
        let factor := shl(6, gt(x, 0xFFFFFFFFFFFFFFFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^32
    assembly ("memory-safe") {
        let factor := shl(5, gt(x, 0xFFFFFFFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^16
    assembly ("memory-safe") {
        let factor := shl(4, gt(x, 0xFFFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^8
    assembly ("memory-safe") {
        let factor := shl(3, gt(x, 0xFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^4
    assembly ("memory-safe") {
        let factor := shl(2, gt(x, 0xF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^2
    assembly ("memory-safe") {
        let factor := shl(1, gt(x, 0x3))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^1
    // No need to shift x any more.
    assembly ("memory-safe") {
        let factor := gt(x, 0x1)
        result := or(result, factor)
    }
}

/// @notice Calculates x*y÷denominator with 512-bit precision.
///
/// @dev Credits to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
///
/// Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - The denominator must not be zero.
/// - The result must fit in uint256.
///
/// @param x The multiplicand as a uint256.
/// @param y The multiplier as a uint256.
/// @param denominator The divisor as a uint256.
/// @return result The result as a uint256.
/// @custom:smtchecker abstract-function-nondet
function mulDiv(uint256 x, uint256 y, uint256 denominator) pure returns (uint256 result) {
    // 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 ("memory-safe") {
        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) {
        unchecked {
            return prod0 / denominator;
        }
    }

    // Make sure the result is less than 2^256. Also prevents denominator == 0.
    if (prod1 >= denominator) {
        revert PRBMath_MulDiv_Overflow(x, y, denominator);
    }

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

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

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

    unchecked {
        // Calculate the largest power of two divisor of the denominator using the unary operator ~. This operation cannot overflow
        // because the denominator cannot be zero at this point in the function execution. The result is always >= 1.
        // For more detail, see https://cs.stackexchange.com/q/138556/92363.
        uint256 lpotdod = denominator & (~denominator + 1);
        uint256 flippedLpotdod;

        assembly ("memory-safe") {
            // Factor powers of two out of denominator.
            denominator := div(denominator, lpotdod)

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

            // Get the flipped value `2^256 / lpotdod`. If the `lpotdod` is zero, the flipped value is one.
            // `sub(0, lpotdod)` produces the two's complement version of `lpotdod`, which is equivalent to flipping all the bits.
            // However, `div` interprets this value as an unsigned value: https://ethereum.stackexchange.com/q/147168/24693
            flippedLpotdod := add(div(sub(0, lpotdod), lpotdod), 1)
        }

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

        // 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;
    }
}

/// @notice Calculates x*y÷1e18 with 512-bit precision.
///
/// @dev A variant of {mulDiv} with constant folding, i.e. in which the denominator is hard coded to 1e18.
///
/// Notes:
/// - The body is purposely left uncommented; to understand how this works, see the documentation in {mulDiv}.
/// - The result is rounded toward zero.
/// - We take as an axiom that the result cannot be `MAX_UINT256` when x and y solve the following system of equations:
///
/// $$
/// \begin{cases}
///     x * y = MAX\_UINT256 * UNIT \\
///     (x * y) \% UNIT \geq \frac{UNIT}{2}
/// \end{cases}
/// $$
///
/// Requirements:
/// - Refer to the requirements in {mulDiv}.
/// - The result must fit in uint256.
///
/// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.
/// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
/// @custom:smtchecker abstract-function-nondet
function mulDiv18(uint256 x, uint256 y) pure returns (uint256 result) {
    uint256 prod0;
    uint256 prod1;
    assembly ("memory-safe") {
        let mm := mulmod(x, y, not(0))
        prod0 := mul(x, y)
        prod1 := sub(sub(mm, prod0), lt(mm, prod0))
    }

    if (prod1 == 0) {
        unchecked {
            return prod0 / UNIT;
        }
    }

    if (prod1 >= UNIT) {
        revert PRBMath_MulDiv18_Overflow(x, y);
    }

    uint256 remainder;
    assembly ("memory-safe") {
        remainder := mulmod(x, y, UNIT)
        result :=
            mul(
                or(
                    div(sub(prod0, remainder), UNIT_LPOTD),
                    mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, UNIT_LPOTD), UNIT_LPOTD), 1))
                ),
                UNIT_INVERSE
            )
    }
}

/// @notice Calculates x*y÷denominator with 512-bit precision.
///
/// @dev This is an extension of {mulDiv} for signed numbers, which works by computing the signs and the absolute values separately.
///
/// Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - Refer to the requirements in {mulDiv}.
/// - None of the inputs can be `type(int256).min`.
/// - The result must fit in int256.
///
/// @param x The multiplicand as an int256.
/// @param y The multiplier as an int256.
/// @param denominator The divisor as an int256.
/// @return result The result as an int256.
/// @custom:smtchecker abstract-function-nondet
function mulDivSigned(int256 x, int256 y, int256 denominator) pure returns (int256 result) {
    if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {
        revert PRBMath_MulDivSigned_InputTooSmall();
    }

    // Get hold of the absolute values of x, y and the denominator.
    uint256 xAbs;
    uint256 yAbs;
    uint256 dAbs;
    unchecked {
        xAbs = x < 0 ? uint256(-x) : uint256(x);
        yAbs = y < 0 ? uint256(-y) : uint256(y);
        dAbs = denominator < 0 ? uint256(-denominator) : uint256(denominator);
    }

    // Compute the absolute value of x*y÷denominator. The result must fit in int256.
    uint256 resultAbs = mulDiv(xAbs, yAbs, dAbs);
    if (resultAbs > uint256(type(int256).max)) {
        revert PRBMath_MulDivSigned_Overflow(x, y);
    }

    // Get the signs of x, y and the denominator.
    uint256 sx;
    uint256 sy;
    uint256 sd;
    assembly ("memory-safe") {
        // "sgt" is the "signed greater than" assembly instruction and "sub(0,1)" is -1 in two's complement.
        sx := sgt(x, sub(0, 1))
        sy := sgt(y, sub(0, 1))
        sd := sgt(denominator, sub(0, 1))
    }

    // XOR over sx, sy and sd. What this does is to check whether there are 1 or 3 negative signs in the inputs.
    // If there are, the result should be negative. Otherwise, it should be positive.
    unchecked {
        result = sx ^ sy ^ sd == 0 ? -int256(resultAbs) : int256(resultAbs);
    }
}

/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - If x is not a perfect square, the result is rounded down.
/// - Credits to OpenZeppelin for the explanations in comments below.
///
/// @param x The uint256 number for which to calculate the square root.
/// @return result The result as a uint256.
/// @custom:smtchecker abstract-function-nondet
function sqrt(uint256 x) pure returns (uint256 result) {
    if (x == 0) {
        return 0;
    }

    // For our first guess, we calculate the biggest power of 2 which is smaller than the square root of x.
    //
    // We know that the "msb" (most significant bit) of x is a power of 2 such that we have:
    //
    // $$
    // msb(x) <= x <= 2*msb(x)$
    // $$
    //
    // We write $msb(x)$ as $2^k$, and we get:
    //
    // $$
    // k = log_2(x)
    // $$
    //
    // Thus, we can write the initial inequality as:
    //
    // $$
    // 2^{log_2(x)} <= x <= 2*2^{log_2(x)+1} \\
    // sqrt(2^k) <= sqrt(x) < sqrt(2^{k+1}) \\
    // 2^{k/2} <= sqrt(x) < 2^{(k+1)/2} <= 2^{(k/2)+1}
    // $$
    //
    // Consequently, $2^{log_2(x) /2} is a good first approximation of sqrt(x) with at least one correct bit.
    uint256 xAux = uint256(x);
    result = 1;
    if (xAux >= 2 ** 128) {
        xAux >>= 128;
        result <<= 64;
    }
    if (xAux >= 2 ** 64) {
        xAux >>= 64;
        result <<= 32;
    }
    if (xAux >= 2 ** 32) {
        xAux >>= 32;
        result <<= 16;
    }
    if (xAux >= 2 ** 16) {
        xAux >>= 16;
        result <<= 8;
    }
    if (xAux >= 2 ** 8) {
        xAux >>= 8;
        result <<= 4;
    }
    if (xAux >= 2 ** 4) {
        xAux >>= 4;
        result <<= 2;
    }
    if (xAux >= 2 ** 2) {
        result <<= 1;
    }

    // At this point, `result` is an estimation with at least one bit of precision. We know the true value has at
    // most 128 bits, 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 + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;

        // If x is not a perfect square, round the result toward zero.
        uint256 roundedResult = x / result;
        if (result >= roundedResult) {
            result = roundedResult;
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { UD21x18 } from "./ValueType.sol";

/// @dev Euler's number as a UD21x18 number.
UD21x18 constant E = UD21x18.wrap(2_718281828459045235);

/// @dev The maximum value a UD21x18 number can have.
uint128 constant uMAX_UD21x18 = 340282366920938463463_374607431768211455;
UD21x18 constant MAX_UD21x18 = UD21x18.wrap(uMAX_UD21x18);

/// @dev PI as a UD21x18 number.
UD21x18 constant PI = UD21x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of UD21x18.
uint256 constant uUNIT = 1e18;
UD21x18 constant UNIT = UD21x18.wrap(1e18);

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.1) (utils/Context.sol)

pragma solidity ^0.8.20;

/**
 * @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;
    }

    function _contextSuffixLength() internal view virtual returns (uint256) {
        return 0;
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { uMAX_UD60x18, uUNIT } from "./Constants.sol";
import { PRBMath_UD60x18_Convert_Overflow } from "./Errors.sol";
import { UD60x18 } from "./ValueType.sol";

/// @notice Converts a UD60x18 number to a simple integer by dividing it by `UNIT`.
/// @dev The result is rounded toward zero.
/// @param x The UD60x18 number to convert.
/// @return result The same number in basic integer form.
function convert(UD60x18 x) pure returns (uint256 result) {
    result = UD60x18.unwrap(x) / uUNIT;
}

/// @notice Converts a simple integer to UD60x18 by multiplying it by `UNIT`.
///
/// @dev Requirements:
/// - x ≤ MAX_UD60x18 / UNIT
///
/// @param x The basic integer to convert.
/// @return result The same number converted to UD60x18.
function convert(uint256 x) pure returns (UD60x18 result) {
    if (x > uMAX_UD60x18 / uUNIT) {
        revert PRBMath_UD60x18_Convert_Overflow(x);
    }
    unchecked {
        result = UD60x18.wrap(x * uUNIT);
    }
}

// SPDX-License-Identifier: BUSL-1.1
pragma solidity 0.8.28;

import {ISummerToken} from "../interfaces/ISummerToken.sol";
import {IDecayController} from "../interfaces/IDecayController.sol";
import {IGovernanceRewardsManager} from "../interfaces/IGovernanceRewardsManager.sol";

/**
 * @title DecayController
 * @notice Manages decay updates for governance rewards and voting power
 */
abstract contract DecayController is IDecayController {
    ISummerToken private immutable _summerToken;
    IGovernanceRewardsManager private _rewardsManager;

    constructor(address summerToken_) {
        if (summerToken_ == address(0)) {
            revert DecayController__ZeroAddress();
        }
        _summerToken = ISummerToken(summerToken_);
    }

    /**
     * @notice Internal function to set the rewards manager address
     * @dev This function must be called by the inheriting contract after deployment
     * to avoid circular dependencies, as both DecayController and GovernanceRewardsManager
     * need to reference each other. The pattern used is:
     * 1. Deploy DecayController (with rewardsManager unset)
     * 2. Deploy GovernanceRewardsManager (which can reference DecayController)
     * 3. Call this function to set rewardsManager address
     * @param rewardsManager_ Address of the GovernanceRewardsManager contract
     */
    function _setRewardsManager(address rewardsManager_) internal {
        if (rewardsManager_ == address(0)) {
            revert DecayController__ZeroAddress();
        }
        if (address(_rewardsManager) != address(0)) {
            revert DecayController__RewardsManagerAlreadySet();
        }
        _rewardsManager = IGovernanceRewardsManager(rewardsManager_);
    }

    function _updateDecay(address account) internal {
        if (account != address(0)) {
            _summerToken.updateDecayFactor(account);
            _rewardsManager.updateSmoothedDecayFactor(account);
        }
    }

    /**
     * @notice Modifier to update decay before executing a function
     * @param account Address to update decay for
     * @dev Updates both base decay and smoothed decay factors
     */
    modifier updateDecay(address account) {
        _updateDecay(account);
        _;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/structs/DoubleEndedQueue.sol)
pragma solidity ^0.8.20;

import {Panic} from "../Panic.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.
 * ```solidity
 * DoubleEndedQueue.Bytes32Deque queue;
 * ```
 */
library DoubleEndedQueue {
    /**
     * @dev Indices are 128 bits so begin and end are packed in a single storage slot for efficient access.
     *
     * 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.
     *
     * The first item is at data[begin] and the last item is at data[end - 1]. This range can wrap around.
     */
    struct Bytes32Deque {
        uint128 _begin;
        uint128 _end;
        mapping(uint128 index => bytes32) _data;
    }

    /**
     * @dev Inserts an item at the end of the queue.
     *
     * Reverts with {Panic-RESOURCE_ERROR} if the queue is full.
     */
    function pushBack(Bytes32Deque storage deque, bytes32 value) internal {
        unchecked {
            uint128 backIndex = deque._end;
            if (backIndex + 1 == deque._begin) Panic.panic(Panic.RESOURCE_ERROR);
            deque._data[backIndex] = value;
            deque._end = backIndex + 1;
        }
    }

    /**
     * @dev Removes the item at the end of the queue and returns it.
     *
     * Reverts with {Panic-EMPTY_ARRAY_POP} if the queue is empty.
     */
    function popBack(Bytes32Deque storage deque) internal returns (bytes32 value) {
        unchecked {
            uint128 backIndex = deque._end;
            if (backIndex == deque._begin) Panic.panic(Panic.EMPTY_ARRAY_POP);
            --backIndex;
            value = deque._data[backIndex];
            delete deque._data[backIndex];
            deque._end = backIndex;
        }
    }

    /**
     * @dev Inserts an item at the beginning of the queue.
     *
     * Reverts with {Panic-RESOURCE_ERROR} if the queue is full.
     */
    function pushFront(Bytes32Deque storage deque, bytes32 value) internal {
        unchecked {
            uint128 frontIndex = deque._begin - 1;
            if (frontIndex == deque._end) Panic.panic(Panic.RESOURCE_ERROR);
            deque._data[frontIndex] = value;
            deque._begin = frontIndex;
        }
    }

    /**
     * @dev Removes the item at the beginning of the queue and returns it.
     *
     * Reverts with {Panic-EMPTY_ARRAY_POP} if the queue is empty.
     */
    function popFront(Bytes32Deque storage deque) internal returns (bytes32 value) {
        unchecked {
            uint128 frontIndex = deque._begin;
            if (frontIndex == deque._end) Panic.panic(Panic.EMPTY_ARRAY_POP);
            value = deque._data[frontIndex];
            delete deque._data[frontIndex];
            deque._begin = frontIndex + 1;
        }
    }

    /**
     * @dev Returns the item at the beginning of the queue.
     *
     * Reverts with {Panic-ARRAY_OUT_OF_BOUNDS} if the queue is empty.
     */
    function front(Bytes32Deque storage deque) internal view returns (bytes32 value) {
        if (empty(deque)) Panic.panic(Panic.ARRAY_OUT_OF_BOUNDS);
        return deque._data[deque._begin];
    }

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

    /**
     * @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 {Panic-ARRAY_OUT_OF_BOUNDS} if the index is out of bounds.
     */
    function at(Bytes32Deque storage deque, uint256 index) internal view returns (bytes32 value) {
        if (index >= length(deque)) Panic.panic(Panic.ARRAY_OUT_OF_BOUNDS);
        // By construction, length is a uint128, so the check above ensures that index can be safely downcast to uint128
        unchecked {
            return deque._data[deque._begin + uint128(index)];
        }
    }

    /**
     * @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) {
        unchecked {
            return uint256(deque._end - 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 v5.0.0) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.20;

/**
 * @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
    }

    /**
     * @dev The signature derives the `address(0)`.
     */
    error ECDSAInvalidSignature();

    /**
     * @dev The signature has an invalid length.
     */
    error ECDSAInvalidSignatureLength(uint256 length);

    /**
     * @dev The signature has an S value that is in the upper half order.
     */
    error ECDSAInvalidSignatureS(bytes32 s);

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with `signature` or an error. This will not
     * return address(0) without also returning an error description. Errors are documented using an enum (error type)
     * and a bytes32 providing additional information about the error.
     *
     * If no error is returned, then the address can be used for verification purposes.
     *
     * The `ecrecover` EVM precompile 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 {MessageHashUtils-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]
     */
    function tryRecover(
        bytes32 hash,
        bytes memory signature
    ) internal pure returns (address recovered, RecoverError err, bytes32 errArg) {
        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.
            assembly ("memory-safe") {
                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, bytes32(signature.length));
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM precompile 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 {MessageHashUtils-toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error, bytes32 errorArg) = tryRecover(hash, signature);
        _throwError(error, errorArg);
        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[ERC-2098 short signatures]
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address recovered, RecoverError err, bytes32 errArg) {
        unchecked {
            bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
            // We do not check for an overflow here since the shift operation results in 0 or 1.
            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.
     */
    function recover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address) {
        (address recovered, RecoverError error, bytes32 errorArg) = tryRecover(hash, r, vs);
        _throwError(error, errorArg);
        return recovered;
    }

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

        // 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, bytes32(0));
        }

        return (signer, RecoverError.NoError, bytes32(0));
    }

    /**
     * @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, bytes32 errorArg) = tryRecover(hash, v, r, s);
        _throwError(error, errorArg);
        return recovered;
    }

    /**
     * @dev Optionally reverts with the corresponding custom error according to the `error` argument provided.
     */
    function _throwError(RecoverError error, bytes32 errorArg) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert ECDSAInvalidSignature();
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert ECDSAInvalidSignatureLength(uint256(errorArg));
        } else if (error == RecoverError.InvalidSignatureS) {
            revert ECDSAInvalidSignatureS(errorArg);
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/cryptography/EIP712.sol)

pragma solidity ^0.8.20;

import {MessageHashUtils} from "./MessageHashUtils.sol";
import {ShortStrings, ShortString} from "../ShortStrings.sol";
import {IERC5267} from "../../interfaces/IERC5267.sol";

/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP-712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding scheme specified in the EIP requires a domain separator and a hash of the typed structured data, whose
 * encoding is very generic and therefore its 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 order to
 * produce the hash of their typed data 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].
 *
 * NOTE: In the upgradeable version of this contract, the cached values will correspond to the address, and the domain
 * separator of the implementation contract. This will cause the {_domainSeparatorV4} function to always rebuild the
 * separator from the immutable values, which is cheaper than accessing a cached version in cold storage.
 *
 * @custom:oz-upgrades-unsafe-allow state-variable-immutable
 */
abstract contract EIP712 is IERC5267 {
    using ShortStrings for *;

    bytes32 private constant TYPE_HASH =
        keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)");

    // 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 _cachedDomainSeparator;
    uint256 private immutable _cachedChainId;
    address private immutable _cachedThis;

    bytes32 private immutable _hashedName;
    bytes32 private immutable _hashedVersion;

    ShortString private immutable _name;
    ShortString private immutable _version;
    string private _nameFallback;
    string private _versionFallback;

    /**
     * @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) {
        _name = name.toShortStringWithFallback(_nameFallback);
        _version = version.toShortStringWithFallback(_versionFallback);
        _hashedName = keccak256(bytes(name));
        _hashedVersion = keccak256(bytes(version));

        _cachedChainId = block.chainid;
        _cachedDomainSeparator = _buildDomainSeparator();
        _cachedThis = address(this);
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        if (address(this) == _cachedThis && block.chainid == _cachedChainId) {
            return _cachedDomainSeparator;
        } else {
            return _buildDomainSeparator();
        }
    }

    function _buildDomainSeparator() private view returns (bytes32) {
        return keccak256(abi.encode(TYPE_HASH, _hashedName, _hashedVersion, 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 MessageHashUtils.toTypedDataHash(_domainSeparatorV4(), structHash);
    }

    /**
     * @dev See {IERC-5267}.
     */
    function eip712Domain()
        public
        view
        virtual
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        )
    {
        return (
            hex"0f", // 01111
            _EIP712Name(),
            _EIP712Version(),
            block.chainid,
            address(this),
            bytes32(0),
            new uint256[](0)
        );
    }

    /**
     * @dev The name parameter for the EIP712 domain.
     *
     * NOTE: By default this function reads _name which is an immutable value.
     * It only reads from storage if necessary (in case the value is too large to fit in a ShortString).
     */
    // solhint-disable-next-line func-name-mixedcase
    function _EIP712Name() internal view returns (string memory) {
        return _name.toStringWithFallback(_nameFallback);
    }

    /**
     * @dev The version parameter for the EIP712 domain.
     *
     * NOTE: By default this function reads _version which is an immutable value.
     * It only reads from storage if necessary (in case the value is too large to fit in a ShortString).
     */
    // solhint-disable-next-line func-name-mixedcase
    function _EIP712Version() internal view returns (string memory) {
        return _version.toStringWithFallback(_versionFallback);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/introspection/ERC165.sol)

pragma solidity ^0.8.20;

import {IERC165} from "./IERC165.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC-165 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);
 * }
 * ```
 */
abstract contract ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.20;

import {IERC20} from "./IERC20.sol";
import {IERC20Metadata} from "./extensions/IERC20Metadata.sol";
import {Context} from "../../utils/Context.sol";
import {IERC20Errors} from "../../interfaces/draft-IERC6093.sol";

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * The default value of {decimals} is 18. To change this, you should override
 * this function so it returns a different value.
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC-20
 * applications.
 */
abstract contract ERC20 is Context, IERC20, IERC20Metadata, IERC20Errors {
    mapping(address account => uint256) private _balances;

    mapping(address account => mapping(address spender => uint256)) private _allowances;

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * All two of these values are immutable: they can only be set once during
     * construction.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view virtual returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the default value returned by this function, unless
     * it's overridden.
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual returns (uint8) {
        return 18;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() public view virtual returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual returns (uint256) {
        return _balances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `value`.
     */
    function transfer(address to, uint256 value) public virtual returns (bool) {
        address owner = _msgSender();
        _transfer(owner, to, value);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * NOTE: If `value` is the maximum `uint256`, the allowance is not updated on
     * `transferFrom`. This is semantically equivalent to an infinite approval.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 value) public virtual returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, value);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Skips emitting an {Approval} event indicating an allowance update. This is not
     * required by the ERC. See {xref-ERC20-_approve-address-address-uint256-bool-}[_approve].
     *
     * NOTE: Does not update the allowance if the current allowance
     * is the maximum `uint256`.
     *
     * Requirements:
     *
     * - `from` and `to` cannot be the zero address.
     * - `from` must have a balance of at least `value`.
     * - the caller must have allowance for ``from``'s tokens of at least
     * `value`.
     */
    function transferFrom(address from, address to, uint256 value) public virtual returns (bool) {
        address spender = _msgSender();
        _spendAllowance(from, spender, value);
        _transfer(from, to, value);
        return true;
    }

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to`.
     *
     * This internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead.
     */
    function _transfer(address from, address to, uint256 value) internal {
        if (from == address(0)) {
            revert ERC20InvalidSender(address(0));
        }
        if (to == address(0)) {
            revert ERC20InvalidReceiver(address(0));
        }
        _update(from, to, value);
    }

    /**
     * @dev Transfers a `value` amount of tokens from `from` to `to`, or alternatively mints (or burns) if `from`
     * (or `to`) is the zero address. All customizations to transfers, mints, and burns should be done by overriding
     * this function.
     *
     * Emits a {Transfer} event.
     */
    function _update(address from, address to, uint256 value) internal virtual {
        if (from == address(0)) {
            // Overflow check required: The rest of the code assumes that totalSupply never overflows
            _totalSupply += value;
        } else {
            uint256 fromBalance = _balances[from];
            if (fromBalance < value) {
                revert ERC20InsufficientBalance(from, fromBalance, value);
            }
            unchecked {
                // Overflow not possible: value <= fromBalance <= totalSupply.
                _balances[from] = fromBalance - value;
            }
        }

        if (to == address(0)) {
            unchecked {
                // Overflow not possible: value <= totalSupply or value <= fromBalance <= totalSupply.
                _totalSupply -= value;
            }
        } else {
            unchecked {
                // Overflow not possible: balance + value is at most totalSupply, which we know fits into a uint256.
                _balances[to] += value;
            }
        }

        emit Transfer(from, to, value);
    }

    /**
     * @dev Creates a `value` amount of tokens and assigns them to `account`, by transferring it from address(0).
     * Relies on the `_update` mechanism
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead.
     */
    function _mint(address account, uint256 value) internal {
        if (account == address(0)) {
            revert ERC20InvalidReceiver(address(0));
        }
        _update(address(0), account, value);
    }

    /**
     * @dev Destroys a `value` amount of tokens from `account`, lowering the total supply.
     * Relies on the `_update` mechanism.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead
     */
    function _burn(address account, uint256 value) internal {
        if (account == address(0)) {
            revert ERC20InvalidSender(address(0));
        }
        _update(account, address(0), value);
    }

    /**
     * @dev Sets `value` as the allowance of `spender` over the `owner` s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     *
     * Overrides to this logic should be done to the variant with an additional `bool emitEvent` argument.
     */
    function _approve(address owner, address spender, uint256 value) internal {
        _approve(owner, spender, value, true);
    }

    /**
     * @dev Variant of {_approve} with an optional flag to enable or disable the {Approval} event.
     *
     * By default (when calling {_approve}) the flag is set to true. On the other hand, approval changes made by
     * `_spendAllowance` during the `transferFrom` operation set the flag to false. This saves gas by not emitting any
     * `Approval` event during `transferFrom` operations.
     *
     * Anyone who wishes to continue emitting `Approval` events on the`transferFrom` operation can force the flag to
     * true using the following override:
     *
     * ```solidity
     * function _approve(address owner, address spender, uint256 value, bool) internal virtual override {
     *     super._approve(owner, spender, value, true);
     * }
     * ```
     *
     * Requirements are the same as {_approve}.
     */
    function _approve(address owner, address spender, uint256 value, bool emitEvent) internal virtual {
        if (owner == address(0)) {
            revert ERC20InvalidApprover(address(0));
        }
        if (spender == address(0)) {
            revert ERC20InvalidSpender(address(0));
        }
        _allowances[owner][spender] = value;
        if (emitEvent) {
            emit Approval(owner, spender, value);
        }
    }

    /**
     * @dev Updates `owner` s allowance for `spender` based on spent `value`.
     *
     * Does not update the allowance value in case of infinite allowance.
     * Revert if not enough allowance is available.
     *
     * Does not emit an {Approval} event.
     */
    function _spendAllowance(address owner, address spender, uint256 value) internal virtual {
        uint256 currentAllowance = allowance(owner, spender);
        if (currentAllowance != type(uint256).max) {
            if (currentAllowance < value) {
                revert ERC20InsufficientAllowance(spender, currentAllowance, value);
            }
            unchecked {
                _approve(owner, spender, currentAllowance - value, false);
            }
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/extensions/ERC20Wrapper.sol)

pragma solidity ^0.8.20;

import {IERC20, IERC20Metadata, ERC20} from "../ERC20.sol";
import {SafeERC20} from "../utils/SafeERC20.sol";

/**
 * @dev Extension of the ERC-20 token contract to support token wrapping.
 *
 * Users can deposit and withdraw "underlying tokens" and receive a matching number of "wrapped tokens". This is useful
 * in conjunction with other modules. For example, combining this wrapping mechanism with {ERC20Votes} will allow the
 * wrapping of an existing "basic" ERC-20 into a governance token.
 *
 * WARNING: Any mechanism in which the underlying token changes the {balanceOf} of an account without an explicit transfer
 * may desynchronize this contract's supply and its underlying balance. Please exercise caution when wrapping tokens that
 * may undercollateralize the wrapper (i.e. wrapper's total supply is higher than its underlying balance). See {_recover}
 * for recovering value accrued to the wrapper.
 */
abstract contract ERC20Wrapper is ERC20 {
    IERC20 private immutable _underlying;

    /**
     * @dev The underlying token couldn't be wrapped.
     */
    error ERC20InvalidUnderlying(address token);

    constructor(IERC20 underlyingToken) {
        if (underlyingToken == this) {
            revert ERC20InvalidUnderlying(address(this));
        }
        _underlying = underlyingToken;
    }

    /**
     * @dev See {ERC20-decimals}.
     */
    function decimals() public view virtual override returns (uint8) {
        try IERC20Metadata(address(_underlying)).decimals() returns (uint8 value) {
            return value;
        } catch {
            return super.decimals();
        }
    }

    /**
     * @dev Returns the address of the underlying ERC-20 token that is being wrapped.
     */
    function underlying() public view returns (IERC20) {
        return _underlying;
    }

    /**
     * @dev Allow a user to deposit underlying tokens and mint the corresponding number of wrapped tokens.
     */
    function depositFor(address account, uint256 value) public virtual returns (bool) {
        address sender = _msgSender();
        if (sender == address(this)) {
            revert ERC20InvalidSender(address(this));
        }
        if (account == address(this)) {
            revert ERC20InvalidReceiver(account);
        }
        SafeERC20.safeTransferFrom(_underlying, sender, address(this), value);
        _mint(account, value);
        return true;
    }

    /**
     * @dev Allow a user to burn a number of wrapped tokens and withdraw the corresponding number of underlying tokens.
     */
    function withdrawTo(address account, uint256 value) public virtual returns (bool) {
        if (account == address(this)) {
            revert ERC20InvalidReceiver(account);
        }
        _burn(_msgSender(), value);
        SafeERC20.safeTransfer(_underlying, account, value);
        return true;
    }

    /**
     * @dev Mint wrapped token to cover any underlyingTokens that would have been transferred by mistake or acquired from
     * rebasing mechanisms. Internal function that can be exposed with access control if desired.
     */
    function _recover(address account) internal virtual returns (uint256) {
        uint256 value = _underlying.balanceOf(address(this)) - totalSupply();
        _mint(account, value);
        return value;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/structs/EnumerableSet.sol)
// This file was procedurally generated from scripts/generate/templates/EnumerableSet.js.

pragma solidity ^0.8.20;

/**
 * @dev Library for managing
 * https://en.wikipedia.org/wiki/Set_(abstract_data_type)[sets] of primitive
 * types.
 *
 * Sets have the following properties:
 *
 * - Elements are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Elements are enumerated in O(n). No guarantees are made on the ordering.
 *
 * ```solidity
 * contract Example {
 *     // Add the library methods
 *     using EnumerableSet for EnumerableSet.AddressSet;
 *
 *     // Declare a set state variable
 *     EnumerableSet.AddressSet private mySet;
 * }
 * ```
 *
 * As of v3.3.0, sets of type `bytes32` (`Bytes32Set`), `address` (`AddressSet`)
 * and `uint256` (`UintSet`) are supported.
 *
 * [WARNING]
 * ====
 * Trying to delete such a structure from storage will likely result in data corruption, rendering the structure
 * unusable.
 * See https://github.com/ethereum/solidity/pull/11843[ethereum/solidity#11843] for more info.
 *
 * In order to clean an EnumerableSet, you can either remove all elements one by one or create a fresh instance using an
 * array of EnumerableSet.
 * ====
 */
library EnumerableSet {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Set type with
    // bytes32 values.
    // The Set implementation uses private functions, and user-facing
    // implementations (such as AddressSet) are just wrappers around the
    // underlying Set.
    // This means that we can only create new EnumerableSets for types that fit
    // in bytes32.

    struct Set {
        // Storage of set values
        bytes32[] _values;
        // Position is the index of the value in the `values` array plus 1.
        // Position 0 is used to mean a value is not in the set.
        mapping(bytes32 value => uint256) _positions;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function _add(Set storage set, bytes32 value) private returns (bool) {
        if (!_contains(set, value)) {
            set._values.push(value);
            // The value is stored at length-1, but we add 1 to all indexes
            // and use 0 as a sentinel value
            set._positions[value] = set._values.length;
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function _remove(Set storage set, bytes32 value) private returns (bool) {
        // We cache the value's position to prevent multiple reads from the same storage slot
        uint256 position = set._positions[value];

        if (position != 0) {
            // Equivalent to contains(set, value)
            // To delete an element from the _values array in O(1), we swap the element to delete with the last one in
            // the array, and then remove the last element (sometimes called as 'swap and pop').
            // This modifies the order of the array, as noted in {at}.

            uint256 valueIndex = position - 1;
            uint256 lastIndex = set._values.length - 1;

            if (valueIndex != lastIndex) {
                bytes32 lastValue = set._values[lastIndex];

                // Move the lastValue to the index where the value to delete is
                set._values[valueIndex] = lastValue;
                // Update the tracked position of the lastValue (that was just moved)
                set._positions[lastValue] = position;
            }

            // Delete the slot where the moved value was stored
            set._values.pop();

            // Delete the tracked position for the deleted slot
            delete set._positions[value];

            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function _contains(Set storage set, bytes32 value) private view returns (bool) {
        return set._positions[value] != 0;
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function _length(Set storage set) private view returns (uint256) {
        return set._values.length;
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function _at(Set storage set, uint256 index) private view returns (bytes32) {
        return set._values[index];
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function _values(Set storage set) private view returns (bytes32[] memory) {
        return set._values;
    }

    // Bytes32Set

    struct Bytes32Set {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _add(set._inner, value);
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _remove(set._inner, value);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(Bytes32Set storage set, bytes32 value) internal view returns (bool) {
        return _contains(set._inner, value);
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(Bytes32Set storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(Bytes32Set storage set, uint256 index) internal view returns (bytes32) {
        return _at(set._inner, index);
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(Bytes32Set storage set) internal view returns (bytes32[] memory) {
        bytes32[] memory store = _values(set._inner);
        bytes32[] memory result;

        assembly ("memory-safe") {
            result := store
        }

        return result;
    }

    // AddressSet

    struct AddressSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(AddressSet storage set, address value) internal returns (bool) {
        return _add(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(AddressSet storage set, address value) internal returns (bool) {
        return _remove(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(AddressSet storage set, address value) internal view returns (bool) {
        return _contains(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(AddressSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(AddressSet storage set, uint256 index) internal view returns (address) {
        return address(uint160(uint256(_at(set._inner, index))));
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(AddressSet storage set) internal view returns (address[] memory) {
        bytes32[] memory store = _values(set._inner);
        address[] memory result;

        assembly ("memory-safe") {
            result := store
        }

        return result;
    }

    // UintSet

    struct UintSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(UintSet storage set, uint256 value) internal returns (bool) {
        return _add(set._inner, bytes32(value));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(UintSet storage set, uint256 value) internal returns (bool) {
        return _remove(set._inner, bytes32(value));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(UintSet storage set, uint256 value) internal view returns (bool) {
        return _contains(set._inner, bytes32(value));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(UintSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(UintSet storage set, uint256 index) internal view returns (uint256) {
        return uint256(_at(set._inner, index));
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(UintSet storage set) internal view returns (uint256[] memory) {
        bytes32[] memory store = _values(set._inner);
        uint256[] memory result;

        assembly ("memory-safe") {
            result := store
        }

        return result;
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.20;

/**
 * @dev Collection of common custom errors used in multiple contracts
 *
 * IMPORTANT: Backwards compatibility is not guaranteed in future versions of the library.
 * It is recommended to avoid relying on the error API for critical functionality.
 *
 * _Available since v5.1._
 */
library Errors {
    /**
     * @dev The ETH balance of the account is not enough to perform the operation.
     */
    error InsufficientBalance(uint256 balance, uint256 needed);

    /**
     * @dev A call to an address target failed. The target may have reverted.
     */
    error FailedCall();

    /**
     * @dev The deployment failed.
     */
    error FailedDeployment();

    /**
     * @dev A necessary precompile is missing.
     */
    error MissingPrecompile(address);
}

// SPDX-License-Identifier: BUSL-1.1
pragma solidity 0.8.28;

import {ReentrancyGuardTransient} from "@summerfi/dependencies/openzeppelin-next/ReentrancyGuardTransient.sol";
import {StakingRewardsManagerBase} from "@summerfi/rewards-contracts/contracts/StakingRewardsManagerBase.sol";
import {IStakingRewardsManagerBase} from "@summerfi/rewards-contracts/interfaces/IStakingRewardsManagerBase.sol";
import {ProtocolAccessManaged} from "@summerfi/access-contracts/contracts/ProtocolAccessManaged.sol";
import {IERC20, SafeERC20} from "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import {IGovernanceRewardsManager} from "../interfaces/IGovernanceRewardsManager.sol";
import {EnumerableSet} from "@openzeppelin/contracts/utils/structs/EnumerableSet.sol";
import {Constants} from "@summerfi/constants/Constants.sol";
import {ISummerToken} from "../interfaces/ISummerToken.sol";
import {DecayController} from "./DecayController.sol";
import {WrappedStakingToken} from "./WrappedStakingToken.sol";

/**
 * @title GovernanceRewardsManager
 * @notice Contract for managing governance rewards with multiple reward tokens in the Summer protocol
 * @dev Implements IGovernanceRewardsManager interface and inherits from StakingRewardsManagerBase
 */
contract GovernanceRewardsManager is
    IGovernanceRewardsManager,
    StakingRewardsManagerBase,
    DecayController
{
    using SafeERC20 for IERC20;
    using EnumerableSet for EnumerableSet.AddressSet;

    /*//////////////////////////////////////////////////////////////
                            STATE VARIABLES
    //////////////////////////////////////////////////////////////*/

    /**
     * @notice Smoothing factor base for decay calculations (1e18)
     */
    uint256 public constant DECAY_SMOOTHING_FACTOR_BASE = Constants.WAD;

    /**
     * @notice Smoothing factor for decay calculations (0.2 * 1e18)
     */
    uint256 public constant DECAY_SMOOTHING_FACTOR =
        DECAY_SMOOTHING_FACTOR_BASE / 5; // represents 0.2

    /**
     * @notice Mapping of user addresses to their smoothed decay factors
     */
    mapping(address account => uint256 smoothedDecayFactor)
        public userSmoothedDecayFactor;

    /**
     * @notice Wrapped version of staking token for rewards
     */
    address public immutable wrappedStakingToken;

    /**
     * @notice Updates rewards for an account before executing a function
     * @param account The address of the account to update rewards for
     * @dev Updates reward data for all reward tokens
     */
    modifier updateReward(address account) override {
        _updateReward(account);
        _;
    }

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

    /**
     * @notice Initializes the contract with the protocol access manager
     * @param _stakingToken Address of the staking token
     * @param accessManager Address of the ProtocolAccessManager contract
     */
    constructor(
        address _stakingToken,
        address accessManager
    ) StakingRewardsManagerBase(accessManager) DecayController(_stakingToken) {
        stakingToken = _stakingToken;
        wrappedStakingToken = address(new WrappedStakingToken(stakingToken));
        _setRewardsManager(address(this));
    }

    /*//////////////////////////////////////////////////////////////
                            MUTATIVE FUNCTIONS
    //////////////////////////////////////////////////////////////*/

    /// @inheritdoc IStakingRewardsManagerBase
    function stakeOnBehalfOf(address, uint256) external pure override {
        revert StakeOnBehalfOfNotSupported();
    }

    /**
     * @notice No op function to satisfy interface requirements. Emits an event but performs no state changes.
     * @dev This operation is not supported and will only emit an event
     */
    function unstakeAndWithdrawOnBehalfOf(
        address,
        uint256,
        bool
    ) external pure override {
        revert UnstakeOnBehalfOfNotSupported();
    }

    /// @inheritdoc IStakingRewardsManagerBase
    function stake(
        uint256 amount
    )
        external
        override(IStakingRewardsManagerBase, StakingRewardsManagerBase)
        updateDecay(_msgSender())
        updateReward(_msgSender())
    {
        _stake(_msgSender(), _msgSender(), amount);
    }

    /// @inheritdoc IStakingRewardsManagerBase
    function unstake(
        uint256 amount
    )
        external
        override(IStakingRewardsManagerBase, StakingRewardsManagerBase)
        updateReward(_msgSender())
        updateDecay(_msgSender())
    {
        _unstake(_msgSender(), _msgSender(), amount);
    }

    /**
     * @notice External function to update smoothed decay factor
     * @param account The address to update
     * @dev Only callable by the SummerToken or this contract
     */
    function updateSmoothedDecayFactor(
        address account
    ) external onlyDecayController {
        _updateSmoothedDecayFactor(account);
    }

    /*//////////////////////////////////////////////////////////////
                            VIEWS
    //////////////////////////////////////////////////////////////*/

    /// @inheritdoc IGovernanceRewardsManager
    function balanceOf(
        address account
    )
        public
        view
        override(IGovernanceRewardsManager, StakingRewardsManagerBase)
        returns (uint256)
    {
        return super.balanceOf(account);
    }

    /// @inheritdoc IStakingRewardsManagerBase
    function earned(
        address account,
        address rewardToken
    )
        public
        view
        override(IStakingRewardsManagerBase, StakingRewardsManagerBase)
        returns (uint256)
    {
        uint256 rawEarned = _earned(account, rewardToken);
        uint256 latestSmoothedDecayFactor = _calculateSmoothedDecayFactor(
            account
        );

        return (rawEarned * latestSmoothedDecayFactor) / Constants.WAD;
    }

    /// @inheritdoc IGovernanceRewardsManager
    function calculateSmoothedDecayFactor(
        address account
    ) external view returns (uint256) {
        return _calculateSmoothedDecayFactor(account);
    }

    /*//////////////////////////////////////////////////////////////
                                INTERNAL
    //////////////////////////////////////////////////////////////*/

    /**
     * @notice Updates the smoothed decay factor for a given account
     * @param account The address of the account to update
     */
    function _updateSmoothedDecayFactor(address account) internal {
        if (account != address(0)) {
            userSmoothedDecayFactor[account] = _calculateSmoothedDecayFactor(
                account
            );
        }
    }

    /**
     * @notice Calculates the smoothed decay factor for a given account without modifying state
     * @param account The address of the account to calculate for
     * @return The calculated smoothed decay factor
     */
    function _calculateSmoothedDecayFactor(
        address account
    ) internal view returns (uint256) {
        uint256 currentDecayFactor = ISummerToken(address(stakingToken))
            .getDecayFactor(account);

        // If there's no existing smoothed factor, return the current factor
        if (userSmoothedDecayFactor[account] == 0) {
            return currentDecayFactor;
        }

        // Apply exponential moving average (EMA) smoothing
        // Formula: EMA = α * currentValue + (1 - α) * previousEMA
        // Where α is the smoothing factor (DECAY_SMOOTHING_FACTOR / DECAY_SMOOTHING_FACTOR_BASE)
        return
            ((currentDecayFactor * DECAY_SMOOTHING_FACTOR) +
                (userSmoothedDecayFactor[account] *
                    (DECAY_SMOOTHING_FACTOR_BASE - DECAY_SMOOTHING_FACTOR))) /
            DECAY_SMOOTHING_FACTOR_BASE;
    }

    /**
     * @notice Override _stake to wrap tokens
     * @param from The address to transfer tokens from
     * @param receiver The address to receive tokens
     * @param amount The amount of tokens to transfer
     */
    function _stake(
        address from,
        address receiver,
        uint256 amount
    ) internal override {
        if (receiver == address(0)) revert CannotStakeToZeroAddress();
        if (amount == 0) revert CannotStakeZero();
        if (address(stakingToken) == address(0)) {
            revert StakingTokenNotInitialized();
        }

        address delegate = ISummerToken(address(stakingToken)).delegates(
            receiver
        );
        if (delegate == address(0)) {
            revert NotDelegated();
        }

        totalSupply += amount;
        _balances[receiver] += amount;

        IERC20(stakingToken).safeTransferFrom(from, address(this), amount);
        IERC20(stakingToken).forceApprove(wrappedStakingToken, amount);
        WrappedStakingToken(wrappedStakingToken).depositFor(
            address(this),
            amount
        );

        emit Staked(from, receiver, amount);
    }

    /**
     * @notice Override _unstake to unwrap tokens
     * @param from The address to transfer tokens from
     * @param receiver The address to receive tokens
     * @param amount The amount of tokens to transfer
     */
    function _unstake(
        address from,
        address receiver,
        uint256 amount
    ) internal virtual override {
        if (amount == 0) revert CannotUnstakeZero();

        address delegate = ISummerToken(address(stakingToken)).delegates(
            receiver
        );
        if (delegate == address(0)) {
            revert NotDelegated();
        }

        totalSupply -= amount;
        _balances[from] -= amount;

        // Send direct to receiver to avoid any interim state where voting units might be incorrectly calculated
        WrappedStakingToken(wrappedStakingToken).withdrawTo(receiver, amount);

        emit Unstaked(from, receiver, amount);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (governance/Governor.sol)

pragma solidity ^0.8.20;

import {IERC721Receiver} from "../token/ERC721/IERC721Receiver.sol";
import {IERC1155Receiver} from "../token/ERC1155/IERC1155Receiver.sol";
import {EIP712} from "../utils/cryptography/EIP712.sol";
import {SignatureChecker} from "../utils/cryptography/SignatureChecker.sol";
import {IERC165, ERC165} from "../utils/introspection/ERC165.sol";
import {SafeCast} from "../utils/math/SafeCast.sol";
import {DoubleEndedQueue} from "../utils/structs/DoubleEndedQueue.sol";
import {Address} from "../utils/Address.sol";
import {Context} from "../utils/Context.sol";
import {Nonces} from "../utils/Nonces.sol";
import {IGovernor, IERC6372} from "./IGovernor.sol";

/**
 * @dev Core of the governance system, designed to be extended through various modules.
 *
 * This contract is abstract and requires several functions to be implemented in various modules:
 *
 * - A counting module must implement {quorum}, {_quorumReached}, {_voteSucceeded} and {_countVote}
 * - A voting module must implement {_getVotes}
 * - Additionally, {votingPeriod} must also be implemented
 */
abstract contract Governor is Context, ERC165, EIP712, Nonces, IGovernor, IERC721Receiver, IERC1155Receiver {
    using DoubleEndedQueue for DoubleEndedQueue.Bytes32Deque;

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

    struct ProposalCore {
        address proposer;
        uint48 voteStart;
        uint32 voteDuration;
        bool executed;
        bool canceled;
        uint48 etaSeconds;
    }

    bytes32 private constant ALL_PROPOSAL_STATES_BITMAP = bytes32((2 ** (uint8(type(ProposalState).max) + 1)) - 1);
    string private _name;

    mapping(uint256 proposalId => 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 {execute}, consumed by the
    // {onlyGovernance} modifier and eventually reset after {_executeOperations} completes. 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() {
        _checkGovernance();
        _;
    }

    /**
     * @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 {
        if (_executor() != address(this)) {
            revert GovernorDisabledDeposit();
        }
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override(IERC165, ERC165) returns (bool) {
        return
            interfaceId == type(IGovernor).interfaceId ||
            interfaceId == type(IERC1155Receiver).interfaceId ||
            super.supportsInterface(interfaceId);
    }

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

    /**
     * @dev See {IGovernor-version}.
     */
    function version() public view virtual 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 returns (uint256) {
        return uint256(keccak256(abi.encode(targets, values, calldatas, descriptionHash)));
    }

    /**
     * @dev See {IGovernor-state}.
     */
    function state(uint256 proposalId) public view virtual returns (ProposalState) {
        // We read the struct fields into the stack at once so Solidity emits a single SLOAD
        ProposalCore storage proposal = _proposals[proposalId];
        bool proposalExecuted = proposal.executed;
        bool proposalCanceled = proposal.canceled;

        if (proposalExecuted) {
            return ProposalState.Executed;
        }

        if (proposalCanceled) {
            return ProposalState.Canceled;
        }

        uint256 snapshot = proposalSnapshot(proposalId);

        if (snapshot == 0) {
            revert GovernorNonexistentProposal(proposalId);
        }

        uint256 currentTimepoint = clock();

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

        uint256 deadline = proposalDeadline(proposalId);

        if (deadline >= currentTimepoint) {
            return ProposalState.Active;
        } else if (!_quorumReached(proposalId) || !_voteSucceeded(proposalId)) {
            return ProposalState.Defeated;
        } else if (proposalEta(proposalId) == 0) {
            return ProposalState.Succeeded;
        } else {
            return ProposalState.Queued;
        }
    }

    /**
     * @dev See {IGovernor-proposalThreshold}.
     */
    function proposalThreshold() public view virtual returns (uint256) {
        return 0;
    }

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

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

    /**
     * @dev See {IGovernor-proposalProposer}.
     */
    function proposalProposer(uint256 proposalId) public view virtual returns (address) {
        return _proposals[proposalId].proposer;
    }

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

    /**
     * @dev See {IGovernor-proposalNeedsQueuing}.
     */
    function proposalNeedsQueuing(uint256) public view virtual returns (bool) {
        return false;
    }

    /**
     * @dev Reverts if the `msg.sender` is not the executor. In case the executor is not this contract
     * itself, the function reverts if `msg.data` is not whitelisted as a result of an {execute}
     * operation. See {onlyGovernance}.
     */
    function _checkGovernance() internal virtual {
        if (_executor() != _msgSender()) {
            revert GovernorOnlyExecutor(_msgSender());
        }
        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 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 `timepoint`, for a vote as described by `params`.
     */
    function _getVotes(address account, uint256 timepoint, 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 totalWeight,
        bytes memory params
    ) internal virtual returns (uint256);

    /**
     * @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}. This function has opt-in frontrunning protection, described in {_isValidDescriptionForProposer}.
     */
    function propose(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        string memory description
    ) public virtual returns (uint256) {
        address proposer = _msgSender();

        // check description restriction
        if (!_isValidDescriptionForProposer(proposer, description)) {
            revert GovernorRestrictedProposer(proposer);
        }

        // check proposal threshold
        uint256 votesThreshold = proposalThreshold();
        if (votesThreshold > 0) {
            uint256 proposerVotes = getVotes(proposer, clock() - 1);
            if (proposerVotes < votesThreshold) {
                revert GovernorInsufficientProposerVotes(proposer, proposerVotes, votesThreshold);
            }
        }

        return _propose(targets, values, calldatas, description, proposer);
    }

    /**
     * @dev Internal propose mechanism. Can be overridden to add more logic on proposal creation.
     *
     * Emits a {IGovernor-ProposalCreated} event.
     */
    function _propose(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        string memory description,
        address proposer
    ) internal virtual returns (uint256 proposalId) {
        proposalId = hashProposal(targets, values, calldatas, keccak256(bytes(description)));

        if (targets.length != values.length || targets.length != calldatas.length || targets.length == 0) {
            revert GovernorInvalidProposalLength(targets.length, calldatas.length, values.length);
        }
        if (_proposals[proposalId].voteStart != 0) {
            revert GovernorUnexpectedProposalState(proposalId, state(proposalId), bytes32(0));
        }

        uint256 snapshot = clock() + votingDelay();
        uint256 duration = votingPeriod();

        ProposalCore storage proposal = _proposals[proposalId];
        proposal.proposer = proposer;
        proposal.voteStart = SafeCast.toUint48(snapshot);
        proposal.voteDuration = SafeCast.toUint32(duration);

        emit ProposalCreated(
            proposalId,
            proposer,
            targets,
            values,
            new string[](targets.length),
            calldatas,
            snapshot,
            snapshot + duration,
            description
        );

        // Using a named return variable to avoid stack too deep errors
    }

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

        _validateStateBitmap(proposalId, _encodeStateBitmap(ProposalState.Succeeded));

        uint48 etaSeconds = _queueOperations(proposalId, targets, values, calldatas, descriptionHash);

        if (etaSeconds != 0) {
            _proposals[proposalId].etaSeconds = etaSeconds;
            emit ProposalQueued(proposalId, etaSeconds);
        } else {
            revert GovernorQueueNotImplemented();
        }

        return proposalId;
    }

    /**
     * @dev Internal queuing mechanism. Can be overridden (without a super call) to modify the way queuing is
     * performed (for example adding a vault/timelock).
     *
     * This is empty by default, and must be overridden to implement queuing.
     *
     * This function returns a timestamp that describes the expected ETA for execution. If the returned value is 0
     * (which is the default value), the core will consider queueing did not succeed, and the public {queue} function
     * will revert.
     *
     * NOTE: Calling this function directly will NOT check the current state of the proposal, or emit the
     * `ProposalQueued` event. Queuing a proposal should be done using {queue}.
     */
    function _queueOperations(
        uint256 /*proposalId*/,
        address[] memory /*targets*/,
        uint256[] memory /*values*/,
        bytes[] memory /*calldatas*/,
        bytes32 /*descriptionHash*/
    ) internal virtual returns (uint48) {
        return 0;
    }

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

        _validateStateBitmap(
            proposalId,
            _encodeStateBitmap(ProposalState.Succeeded) | _encodeStateBitmap(ProposalState.Queued)
        );

        // mark as executed before calls to avoid reentrancy
        _proposals[proposalId].executed = true;

        // before execute: register governance call in queue.
        if (_executor() != address(this)) {
            for (uint256 i = 0; i < targets.length; ++i) {
                if (targets[i] == address(this)) {
                    _governanceCall.pushBack(keccak256(calldatas[i]));
                }
            }
        }

        _executeOperations(proposalId, targets, values, calldatas, descriptionHash);

        // after execute: cleanup governance call queue.
        if (_executor() != address(this) && !_governanceCall.empty()) {
            _governanceCall.clear();
        }

        emit ProposalExecuted(proposalId);

        return proposalId;
    }

    /**
     * @dev Internal execution mechanism. Can be overridden (without a super call) to modify the way execution is
     * performed (for example adding a vault/timelock).
     *
     * NOTE: Calling this function directly will NOT check the current state of the proposal, set the executed flag to
     * true or emit the `ProposalExecuted` event. Executing a proposal should be done using {execute} or {_execute}.
     */
    function _executeOperations(
        uint256 /* proposalId */,
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 /*descriptionHash*/
    ) internal virtual {
        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);
        }
    }

    /**
     * @dev See {IGovernor-cancel}.
     */
    function cancel(
        address[] memory targets,
        uint256[] memory values,
        bytes[] memory calldatas,
        bytes32 descriptionHash
    ) public virtual returns (uint256) {
        // The proposalId will be recomputed in the `_cancel` call further down. However we need the value before we
        // do the internal call, because we need to check the proposal state BEFORE the internal `_cancel` call
        // changes it. The `hashProposal` duplication has a cost that is limited, and that we accept.
        uint256 proposalId = hashProposal(targets, values, calldatas, descriptionHash);

        // public cancel restrictions (on top of existing _cancel restrictions).
        _validateStateBitmap(proposalId, _encodeStateBitmap(ProposalState.Pending));
        if (_msgSender() != proposalProposer(proposalId)) {
            revert GovernorOnlyProposer(_msgSender());
        }

        return _cancel(targets, values, calldatas, descriptionHash);
    }

    /**
     * @dev Internal cancel mechanism with minimal restrictions. A proposal can be cancelled in any state other than
     * Canceled, Expired, or Executed. Once cancelled a proposal can't be re-submitted.
     *
     * 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);

        _validateStateBitmap(
            proposalId,
            ALL_PROPOSAL_STATES_BITMAP ^
                _encodeStateBitmap(ProposalState.Canceled) ^
                _encodeStateBitmap(ProposalState.Expired) ^
                _encodeStateBitmap(ProposalState.Executed)
        );

        _proposals[proposalId].canceled = true;
        emit ProposalCanceled(proposalId);

        return proposalId;
    }

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

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

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

    /**
     * @dev See {IGovernor-castVoteBySig}.
     */
    function castVoteBySig(
        uint256 proposalId,
        uint8 support,
        address voter,
        bytes memory signature
    ) public virtual returns (uint256) {
        bool valid = SignatureChecker.isValidSignatureNow(
            voter,
            _hashTypedDataV4(keccak256(abi.encode(BALLOT_TYPEHASH, proposalId, support, voter, _useNonce(voter)))),
            signature
        );

        if (!valid) {
            revert GovernorInvalidSignature(voter);
        }

        return _castVote(proposalId, voter, support, "");
    }

    /**
     * @dev See {IGovernor-castVoteWithReasonAndParamsBySig}.
     */
    function castVoteWithReasonAndParamsBySig(
        uint256 proposalId,
        uint8 support,
        address voter,
        string calldata reason,
        bytes memory params,
        bytes memory signature
    ) public virtual returns (uint256) {
        bool valid = SignatureChecker.isValidSignatureNow(
            voter,
            _hashTypedDataV4(
                keccak256(
                    abi.encode(
                        EXTENDED_BALLOT_TYPEHASH,
                        proposalId,
                        support,
                        voter,
                        _useNonce(voter),
                        keccak256(bytes(reason)),
                        keccak256(params)
                    )
                )
            ),
            signature
        );

        if (!valid) {
            revert GovernorInvalidSignature(voter);
        }

        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) {
        _validateStateBitmap(proposalId, _encodeStateBitmap(ProposalState.Active));

        uint256 totalWeight = _getVotes(account, proposalSnapshot(proposalId), params);
        uint256 votedWeight = _countVote(proposalId, account, support, totalWeight, params);

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

        return votedWeight;
    }

    /**
     * @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);
    }

    /**
     * @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}.
     * Receiving tokens is disabled if the governance executor is other than the governor itself (eg. when using with a timelock).
     */
    function onERC721Received(address, address, uint256, bytes memory) public virtual returns (bytes4) {
        if (_executor() != address(this)) {
            revert GovernorDisabledDeposit();
        }
        return this.onERC721Received.selector;
    }

    /**
     * @dev See {IERC1155Receiver-onERC1155Received}.
     * Receiving tokens is disabled if the governance executor is other than the governor itself (eg. when using with a timelock).
     */
    function onERC1155Received(address, address, uint256, uint256, bytes memory) public virtual returns (bytes4) {
        if (_executor() != address(this)) {
            revert GovernorDisabledDeposit();
        }
        return this.onERC1155Received.selector;
    }

    /**
     * @dev See {IERC1155Receiver-onERC1155BatchReceived}.
     * Receiving tokens is disabled if the governance executor is other than the governor itself (eg. when using with a timelock).
     */
    function onERC1155BatchReceived(
        address,
        address,
        uint256[] memory,
        uint256[] memory,
        bytes memory
    ) public virtual returns (bytes4) {
        if (_executor() != address(this)) {
            revert GovernorDisabledDeposit();
        }
        return this.onERC1155BatchReceived.selector;
    }

    /**
     * @dev Encodes a `ProposalState` into a `bytes32` representation where each bit enabled corresponds to
     * the underlying position in the `ProposalState` enum. For example:
     *
     * 0x000...10000
     *   ^^^^^^------ ...
     *         ^----- Succeeded
     *          ^---- Defeated
     *           ^--- Canceled
     *            ^-- Active
     *             ^- Pending
     */
    function _encodeStateBitmap(ProposalState proposalState) internal pure returns (bytes32) {
        return bytes32(1 << uint8(proposalState));
    }

    /**
     * @dev Check that the current state of a proposal matches the requirements described by the `allowedStates` bitmap.
     * This bitmap should be built using `_encodeStateBitmap`.
     *
     * If requirements are not met, reverts with a {GovernorUnexpectedProposalState} error.
     */
    function _validateStateBitmap(uint256 proposalId, bytes32 allowedStates) private view returns (ProposalState) {
        ProposalState currentState = state(proposalId);
        if (_encodeStateBitmap(currentState) & allowedStates == bytes32(0)) {
            revert GovernorUnexpectedProposalState(proposalId, currentState, allowedStates);
        }
        return currentState;
    }

    /*
     * @dev Check if the proposer is authorized to submit a proposal with the given description.
     *
     * If the proposal description ends with `#proposer=0x???`, where `0x???` is an address written as a hex string
     * (case insensitive), then the submission of this proposal will only be authorized to said address.
     *
     * This is used for frontrunning protection. By adding this pattern at the end of their proposal, one can ensure
     * that no other address can submit the same proposal. An attacker would have to either remove or change that part,
     * which would result in a different proposal id.
     *
     * If the description does not match this pattern, it is unrestricted and anyone can submit it. This includes:
     * - If the `0x???` part is not a valid hex string.
     * - If the `0x???` part is a valid hex string, but does not contain exactly 40 hex digits.
     * - If it ends with the expected suffix followed by newlines or other whitespace.
     * - If it ends with some other similar suffix, e.g. `#other=abc`.
     * - If it does not end with any such suffix.
     */
    function _isValidDescriptionForProposer(
        address proposer,
        string memory description
    ) internal view virtual returns (bool) {
        uint256 len = bytes(description).length;

        // Length is too short to contain a valid proposer suffix
        if (len < 52) {
            return true;
        }

        // Extract what would be the `#proposer=0x` marker beginning the suffix
        bytes12 marker;
        assembly ("memory-safe") {
            // - Start of the string contents in memory = description + 32
            // - First character of the marker = len - 52
            //   - Length of "#proposer=0x0000000000000000000000000000000000000000" = 52
            // - We read the memory word starting at the first character of the marker:
            //   - (description + 32) + (len - 52) = description + (len - 20)
            // - Note: Solidity will ignore anything past the first 12 bytes
            marker := mload(add(description, sub(len, 20)))
        }

        // If the marker is not found, there is no proposer suffix to check
        if (marker != bytes12("#proposer=0x")) {
            return true;
        }

        // Parse the 40 characters following the marker as uint160
        uint160 recovered = 0;
        for (uint256 i = len - 40; i < len; ++i) {
            (bool isHex, uint8 value) = _tryHexToUint(bytes(description)[i]);
            // If any of the characters is not a hex digit, ignore the suffix entirely
            if (!isHex) {
                return true;
            }
            recovered = (recovered << 4) | value;
        }

        return recovered == uint160(proposer);
    }

    /**
     * @dev Try to parse a character from a string as a hex value. Returns `(true, value)` if the char is in
     * `[0-9a-fA-F]` and `(false, 0)` otherwise. Value is guaranteed to be in the range `0 <= value < 16`
     */
    function _tryHexToUint(bytes1 char) private pure returns (bool isHex, uint8 value) {
        uint8 c = uint8(char);
        unchecked {
            // Case 0-9
            if (47 < c && c < 58) {
                return (true, c - 48);
            }
            // Case A-F
            else if (64 < c && c < 71) {
                return (true, c - 55);
            }
            // Case a-f
            else if (96 < c && c < 103) {
                return (true, c - 87);
            }
            // Else: not a hex char
            else {
                return (false, 0);
            }
        }
    }

    /**
     * @inheritdoc IERC6372
     */
    function clock() public view virtual returns (uint48);

    /**
     * @inheritdoc IERC6372
     */
    // solhint-disable-next-line func-name-mixedcase
    function CLOCK_MODE() public view virtual returns (string memory);

    /**
     * @inheritdoc IGovernor
     */
    function votingDelay() public view virtual returns (uint256);

    /**
     * @inheritdoc IGovernor
     */
    function votingPeriod() public view virtual returns (uint256);

    /**
     * @inheritdoc IGovernor
     */
    function quorum(uint256 timepoint) public view virtual returns (uint256);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (governance/extensions/GovernorVotes.sol)

pragma solidity ^0.8.20;

import {Governor} from "../Governor.sol";
import {IVotes} from "../utils/IVotes.sol";
import {IERC5805} from "../../interfaces/IERC5805.sol";
import {SafeCast} from "../../utils/math/SafeCast.sol";
import {Time} from "../../utils/types/Time.sol";

/**
 * @dev Extension of {Governor} for voting weight extraction from an {ERC20Votes} token, or since v4.5 an {ERC721Votes}
 * token.
 */
abstract contract GovernorVotes is Governor {
    IERC5805 private immutable _token;

    constructor(IVotes tokenAddress) {
        _token = IERC5805(address(tokenAddress));
    }

    /**
     * @dev The token that voting power is sourced from.
     */
    function token() public view virtual returns (IERC5805) {
        return _token;
    }

    /**
     * @dev Clock (as specified in ERC-6372) is set to match the token's clock. Fallback to block numbers if the token
     * does not implement ERC-6372.
     */
    function clock() public view virtual override returns (uint48) {
        try token().clock() returns (uint48 timepoint) {
            return timepoint;
        } catch {
            return Time.blockNumber();
        }
    }

    /**
     * @dev Machine-readable description of the clock as specified in ERC-6372.
     */
    // solhint-disable-next-line func-name-mixedcase
    function CLOCK_MODE() public view virtual override returns (string memory) {
        try token().CLOCK_MODE() returns (string memory clockmode) {
            return clockmode;
        } catch {
            return "mode=blocknumber&from=default";
        }
    }

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

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { wrap } from "./Casting.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Implements the checked addition operation (+) in the SD59x18 type.
function add(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    return wrap(x.unwrap() + y.unwrap());
}

/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.
function and(SD59x18 x, int256 bits) pure returns (SD59x18 result) {
    return wrap(x.unwrap() & bits);
}

/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.
function and2(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    return wrap(x.unwrap() & y.unwrap());
}

/// @notice Implements the equal (=) operation in the SD59x18 type.
function eq(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() == y.unwrap();
}

/// @notice Implements the greater than operation (>) in the SD59x18 type.
function gt(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() > y.unwrap();
}

/// @notice Implements the greater than or equal to operation (>=) in the SD59x18 type.
function gte(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() >= y.unwrap();
}

/// @notice Implements a zero comparison check function in the SD59x18 type.
function isZero(SD59x18 x) pure returns (bool result) {
    result = x.unwrap() == 0;
}

/// @notice Implements the left shift operation (<<) in the SD59x18 type.
function lshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() << bits);
}

/// @notice Implements the lower than operation (<) in the SD59x18 type.
function lt(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() < y.unwrap();
}

/// @notice Implements the lower than or equal to operation (<=) in the SD59x18 type.
function lte(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() <= y.unwrap();
}

/// @notice Implements the unchecked modulo operation (%) in the SD59x18 type.
function mod(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() % y.unwrap());
}

/// @notice Implements the not equal operation (!=) in the SD59x18 type.
function neq(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() != y.unwrap();
}

/// @notice Implements the NOT (~) bitwise operation in the SD59x18 type.
function not(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(~x.unwrap());
}

/// @notice Implements the OR (|) bitwise operation in the SD59x18 type.
function or(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() | y.unwrap());
}

/// @notice Implements the right shift operation (>>) in the SD59x18 type.
function rshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() >> bits);
}

/// @notice Implements the checked subtraction operation (-) in the SD59x18 type.
function sub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() - y.unwrap());
}

/// @notice Implements the checked unary minus operation (-) in the SD59x18 type.
function unary(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(-x.unwrap());
}

/// @notice Implements the unchecked addition operation (+) in the SD59x18 type.
function uncheckedAdd(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    unchecked {
        result = wrap(x.unwrap() + y.unwrap());
    }
}

/// @notice Implements the unchecked subtraction operation (-) in the SD59x18 type.
function uncheckedSub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    unchecked {
        result = wrap(x.unwrap() - y.unwrap());
    }
}

/// @notice Implements the unchecked unary minus operation (-) in the SD59x18 type.
function uncheckedUnary(SD59x18 x) pure returns (SD59x18 result) {
    unchecked {
        result = wrap(-x.unwrap());
    }
}

/// @notice Implements the XOR (^) bitwise operation in the SD59x18 type.
function xor(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() ^ y.unwrap());
}