// File: @openzeppelin/contracts-upgradeable/access/IAccessControlEnumerableUpgradeable.sol



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

pragma solidity ^0.8.0;

import "./IAccessControlUpgradeable.sol";

/**
 * @dev External interface of AccessControlEnumerable declared to support ERC165 detection.
 */
interface IAccessControlEnumerableUpgradeable is IAccessControlUpgradeable {
    /**
     * @dev Returns one of the accounts that have `role`. `index` must be a
     * value between 0 and {getRoleMemberCount}, non-inclusive.
     *
     * Role bearers are not sorted in any particular way, and their ordering may
     * change at any point.
     *
     * WARNING: When using {getRoleMember} and {getRoleMemberCount}, make sure
     * you perform all queries on the same block. See the following
     * https://forum.openzeppelin.com/t/iterating-over-elements-on-enumerableset-in-openzeppelin-contracts/2296[forum post]
     * for more information.
     */
    function getRoleMember(bytes32 role, uint256 index) external view returns (address);

    /**
     * @dev Returns the number of accounts that have `role`. Can be used
     * together with {getRoleMember} to enumerate all bearers of a role.
     */
    function getRoleMemberCount(bytes32 role) external view returns (uint256);
}

// File: @openzeppelin/contracts-upgradeable/access/IAccessControlUpgradeable.sol



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

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

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

// File: @openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.1) (proxy/utils/Initializable.sol)

pragma solidity ^0.8.2;

import "../../utils/AddressUpgradeable.sol";

/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;

    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;

    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);

    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts.
     *
     * Similar to `reinitializer(1)`, except that functions marked with `initializer` can be nested in the context of a
     * constructor.
     *
     * Emits an {Initialized} event.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!AddressUpgradeable.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }

    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * A reinitializer may be used after the original initialization step. This is essential to configure modules that
     * are added through upgrades and that require initialization.
     *
     * When `version` is 1, this modifier is similar to `initializer`, except that functions marked with `reinitializer`
     * cannot be nested. If one is invoked in the context of another, execution will revert.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     *
     * WARNING: setting the version to 255 will prevent any future reinitialization.
     *
     * Emits an {Initialized} event.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }

    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }

    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     *
     * Emits an {Initialized} event the first time it is successfully executed.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized < type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }

    /**
     * @dev Returns the highest version that has been initialized. See {reinitializer}.
     */
    function _getInitializedVersion() internal view returns (uint8) {
        return _initialized;
    }

    /**
     * @dev Returns `true` if the contract is currently initializing. See {onlyInitializing}.
     */
    function _isInitializing() internal view returns (bool) {
        return _initializing;
    }
}

// File: @openzeppelin/contracts-upgradeable/token/ERC20/ERC20Upgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.0;

import "./IERC20Upgradeable.sol";
import "./extensions/IERC20MetadataUpgradeable.sol";
import "../../utils/ContextUpgradeable.sol";
import "../../proxy/utils/Initializable.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}.
 * For a generic mechanism see {ERC20PresetMinterPauser}.
 *
 * 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].
 *
 * 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 ERC20
 * applications.
 *
 * Additionally, an {Approval} event is emitted on calls to {transferFrom}.
 * This allows applications to reconstruct the allowance for all accounts just
 * by listening to said events. Other implementations of the EIP may not emit
 * these events, as it isn't required by the specification.
 *
 * Finally, the non-standard {decreaseAllowance} and {increaseAllowance}
 * functions have been added to mitigate the well-known issues around setting
 * allowances. See {IERC20-approve}.
 */
contract ERC20Upgradeable is Initializable, ContextUpgradeable, IERC20Upgradeable, IERC20MetadataUpgradeable {
    mapping(address => uint256) private _balances;

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

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * The default value of {decimals} is 18. To select a different value for
     * {decimals} you should overload it.
     *
     * All two of these values are immutable: they can only be set once during
     * construction.
     */
    function __ERC20_init(string memory name_, string memory symbol_) internal onlyInitializing {
        __ERC20_init_unchained(name_, symbol_);
    }

    function __ERC20_init_unchained(string memory name_, string memory symbol_) internal onlyInitializing {
        _name = name_;
        _symbol = symbol_;
    }

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

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual override 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 value {ERC20} uses, unless this function is
     * 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 override returns (uint8) {
        return 18;
    }

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

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual override 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 `amount`.
     */
    function transfer(address to, uint256 amount) public virtual override returns (bool) {
        address owner = _msgSender();
        _transfer(owner, to, amount);
        return true;
    }

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

    /**
     * @dev See {IERC20-approve}.
     *
     * NOTE: If `amount` 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 amount) public virtual override returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, amount);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Emits an {Approval} event indicating the updated allowance. This is not
     * required by the EIP. See the note at the beginning of {ERC20}.
     *
     * 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 `amount`.
     * - the caller must have allowance for ``from``'s tokens of at least
     * `amount`.
     */
    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) public virtual override returns (bool) {
        address spender = _msgSender();
        _spendAllowance(from, spender, amount);
        _transfer(from, to, amount);
        return true;
    }

    /**
     * @dev Atomically increases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function increaseAllowance(address spender, uint256 addedValue) public virtual returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, allowance(owner, spender) + addedValue);
        return true;
    }

    /**
     * @dev Atomically decreases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `spender` must have allowance for the caller of at least
     * `subtractedValue`.
     */
    function decreaseAllowance(address spender, uint256 subtractedValue) public virtual returns (bool) {
        address owner = _msgSender();
        uint256 currentAllowance = allowance(owner, spender);
        require(currentAllowance >= subtractedValue, "ERC20: decreased allowance below zero");
        unchecked {
            _approve(owner, spender, currentAllowance - subtractedValue);
        }

        return true;
    }

    /**
     * @dev Moves `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.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `from` must have a balance of at least `amount`.
     */
    function _transfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {
        require(from != address(0), "ERC20: transfer from the zero address");
        require(to != address(0), "ERC20: transfer to the zero address");

        _beforeTokenTransfer(from, to, amount);

        uint256 fromBalance = _balances[from];
        require(fromBalance >= amount, "ERC20: transfer amount exceeds balance");
        unchecked {
            _balances[from] = fromBalance - amount;
            // Overflow not possible: the sum of all balances is capped by totalSupply, and the sum is preserved by
            // decrementing then incrementing.
            _balances[to] += amount;
        }

        emit Transfer(from, to, amount);

        _afterTokenTransfer(from, to, amount);
    }

    /** @dev Creates `amount` tokens and assigns them to `account`, increasing
     * the total supply.
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     */
    function _mint(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: mint to the zero address");

        _beforeTokenTransfer(address(0), account, amount);

        _totalSupply += amount;
        unchecked {
            // Overflow not possible: balance + amount is at most totalSupply + amount, which is checked above.
            _balances[account] += amount;
        }
        emit Transfer(address(0), account, amount);

        _afterTokenTransfer(address(0), account, amount);
    }

    /**
     * @dev Destroys `amount` tokens from `account`, reducing the
     * total supply.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens.
     */
    function _burn(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: burn from the zero address");

        _beforeTokenTransfer(account, address(0), amount);

        uint256 accountBalance = _balances[account];
        require(accountBalance >= amount, "ERC20: burn amount exceeds balance");
        unchecked {
            _balances[account] = accountBalance - amount;
            // Overflow not possible: amount <= accountBalance <= totalSupply.
            _totalSupply -= amount;
        }

        emit Transfer(account, address(0), amount);

        _afterTokenTransfer(account, address(0), amount);
    }

    /**
     * @dev Sets `amount` 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.
     */
    function _approve(
        address owner,
        address spender,
        uint256 amount
    ) internal virtual {
        require(owner != address(0), "ERC20: approve from the zero address");
        require(spender != address(0), "ERC20: approve to the zero address");

        _allowances[owner][spender] = amount;
        emit Approval(owner, spender, amount);
    }

    /**
     * @dev Updates `owner` s allowance for `spender` based on spent `amount`.
     *
     * Does not update the allowance amount in case of infinite allowance.
     * Revert if not enough allowance is available.
     *
     * Might emit an {Approval} event.
     */
    function _spendAllowance(
        address owner,
        address spender,
        uint256 amount
    ) internal virtual {
        uint256 currentAllowance = allowance(owner, spender);
        if (currentAllowance != type(uint256).max) {
            require(currentAllowance >= amount, "ERC20: insufficient allowance");
            unchecked {
                _approve(owner, spender, currentAllowance - amount);
            }
        }
    }

    /**
     * @dev Hook that is called before any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * will be transferred to `to`.
     * - when `from` is zero, `amount` tokens will be minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens will be burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {}

    /**
     * @dev Hook that is called after any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * has been transferred to `to`.
     * - when `from` is zero, `amount` tokens have been minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens have been burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _afterTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {}

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[45] private __gap;
}

// File: @openzeppelin/contracts-upgradeable/token/ERC20/extensions/IERC20MetadataUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC20Upgradeable.sol";

/**
 * @dev Interface for the optional metadata functions from the ERC20 standard.
 *
 * _Available since v4.1._
 */
interface IERC20MetadataUpgradeable is IERC20Upgradeable {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

    /**
     * @dev Returns the symbol of the token.
     */
    function symbol() external view returns (string memory);

    /**
     * @dev Returns the decimals places of the token.
     */
    function decimals() external view returns (uint8);
}

// File: @openzeppelin/contracts-upgradeable/token/ERC20/IERC20Upgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20Upgradeable {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the amount of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves `amount` tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 amount) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `from` to `to` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) external returns (bool);
}

// File: @openzeppelin/contracts-upgradeable/utils/AddressUpgradeable.sol



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

pragma solidity ^0.8.1;

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

        return account.code.length > 0;
    }

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

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

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

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

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

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

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

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

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

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

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

// File: @openzeppelin/contracts-upgradeable/utils/ContextUpgradeable.sol



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

pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";

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

    function __Context_init_unchained() internal onlyInitializing {
    }
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

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

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}

// File: @openzeppelin/contracts-upgradeable/utils/structs/EnumerableSetUpgradeable.sol



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

pragma solidity ^0.8.0;

/**
 * @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.
 *
 * ```
 * 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 EnumerableSetUpgradeable {
    // 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 of the value in the `values` array, plus 1 because index 0
        // means a value is not in the set.
        mapping(bytes32 => uint256) _indexes;
    }

    /**
     * @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._indexes[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 read and store the value's index to prevent multiple reads from the same storage slot
        uint256 valueIndex = set._indexes[value];

        if (valueIndex != 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 toDeleteIndex = valueIndex - 1;
            uint256 lastIndex = set._values.length - 1;

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

                // Move the last value to the index where the value to delete is
                set._values[toDeleteIndex] = lastValue;
                // Update the index for the moved value
                set._indexes[lastValue] = valueIndex; // Replace lastValue's index to valueIndex
            }

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

            // Delete the index for the deleted slot
            delete set._indexes[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._indexes[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;

        /// @solidity memory-safe-assembly
        assembly {
            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;

        /// @solidity memory-safe-assembly
        assembly {
            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;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }
}

// File: @openzeppelin/contracts/token/ERC20/extensions/draft-IERC20Permit.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/draft-IERC20Permit.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on {IERC20-approve}, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over ``owner``'s tokens,
     * given ``owner``'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) external view returns (uint256);

    /**
     * @dev Returns the domain separator used in the encoding of the signature for {permit}, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view returns (bytes32);
}

// File: @openzeppelin/contracts/token/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the amount of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves `amount` tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 amount) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `from` to `to` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) external returns (bool);
}

// File: @openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";
import "../extensions/draft-IERC20Permit.sol";
import "../../../utils/Address.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using Address for address;

    function safeTransfer(
        IERC20 token,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
    }

    function safeTransferFrom(
        IERC20 token,
        address from,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transferFrom.selector, from, to, value));
    }

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        require(
            (value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

    function safeIncreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        uint256 newAllowance = token.allowance(address(this), spender) + value;
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            uint256 newAllowance = oldAllowance - value;
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
        }
    }

    function safePermit(
        IERC20Permit token,
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        uint256 nonceBefore = token.nonces(owner);
        token.permit(owner, spender, value, deadline, v, r, s);
        uint256 nonceAfter = token.nonces(owner);
        require(nonceAfter == nonceBefore + 1, "SafeERC20: permit did not succeed");
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address-functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

        bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
        if (returndata.length > 0) {
            // Return data is optional
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

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



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

pragma solidity ^0.8.1;

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

        return account.code.length > 0;
    }

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

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

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

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

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

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

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

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

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

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

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

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

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

// File: @prb/math/src/Common.sol



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

/// 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 Emitted when the ending result in the fixed-point version of `mulDiv` would overflow uint256.
error PRBMath_MulDiv18_Overflow(uint256 x, uint256 y);

/// @notice Emitted when the ending result in `mulDiv` would overflow uint256.
error PRBMath_MulDiv_Overflow(uint256 x, uint256 y, uint256 denominator);

/// @notice Emitted when attempting to run `mulDiv` with one of the inputs `type(int256).min`.
error PRBMath_MulDivSigned_InputTooSmall();

/// @notice Emitted when the ending result in the signed version of `mulDiv` would overflow int256.
error PRBMath_MulDivSigned_Overflow(int256 x, int256 y);

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

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

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

/// @dev How many trailing decimals can be represented.
uint256 constant UNIT = 1e18;

/// @dev Largest power of two that is a divisor of `UNIT`.
uint256 constant UNIT_LPOTD = 262144;

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

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

/// @notice Finds the zero-based index of the first one in the binary representation of x.
/// @dev See the note on msb in the "Find First Set" Wikipedia article https://en.wikipedia.org/wiki/Find_first_set
///
/// Each of the steps in this implementation is equivalent to this high-level code:
///
/// ```solidity
/// if (x >= 2 ** 128) {
///     x >>= 128;
///     result += 128;
/// }
/// ```
///
/// Where 128 is swapped with each respective power of two factor. See the full high-level implementation here:
/// https://gist.github.com/PaulRBerg/f932f8693f2733e30c4d479e8e980948
///
/// A list of the Yul instructions used below:
/// - "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 an uint256.
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 floor(x*y÷denominator) with full precision.
///
/// @dev Credits to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
///
/// Requirements:
/// - The denominator cannot be zero.
/// - The result must fit within uint256.
///
/// Caveats:
/// - This function does not work with fixed-point numbers.
///
/// @param x The multiplicand as an uint256.
/// @param y The multiplier as an uint256.
/// @param denominator The divisor as an uint256.
/// @return result The result as an uint256.
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)
    }

    // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
    // See https://cs.stackexchange.com/q/138556/92363.
    unchecked {
        // Does not overflow because the denominator cannot be zero at this stage in the function.
        uint256 lpotdod = denominator & (~denominator + 1);
        assembly ("memory-safe") {
            // Divide denominator by lpotdod.
            denominator := div(denominator, lpotdod)

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

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

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

        // 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 floor(x*y÷1e18) with full precision.
///
/// @dev Variant of `mulDiv` with constant folding, i.e. in which the denominator is always 1e18. Before returning the
/// final result, we add 1 if `(x * y) % UNIT >= HALF_UNIT`. Without this adjustment, 6.6e-19 would be truncated to 0
/// instead of being rounded to 1e-18. See "Listing 6" and text above it at https://accu.org/index.php/journals/1717.
///
/// Requirements:
/// - The result must fit within uint256.
///
/// Caveats:
/// - The body is purposely left uncommented; to understand how this works, see the NatSpec comments in `mulDiv`.
/// - It is assumed that the result can never be `type(uint256).max` when x and y solve the following two equations:
///     1. x * y = type(uint256).max * UNIT
///     2. (x * y) % UNIT >= UNIT / 2
///
/// @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.
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 >= UNIT) {
        revert PRBMath_MulDiv18_Overflow(x, y);
    }

    uint256 remainder;
    assembly ("memory-safe") {
        remainder := mulmod(x, y, UNIT)
    }

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

    assembly ("memory-safe") {
        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 floor(x*y÷denominator) with full precision.
///
/// @dev An extension of `mulDiv` for signed numbers. Works by computing the signs and the absolute values separately.
///
/// Requirements:
/// - None of the inputs can be `type(int256).min`.
/// - The result must fit within 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.
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 absX;
    uint256 absY;
    uint256 absD;
    unchecked {
        absX = x < 0 ? uint256(-x) : uint256(x);
        absY = y < 0 ? uint256(-y) : uint256(y);
        absD = denominator < 0 ? uint256(-denominator) : uint256(denominator);
    }

    // Compute the absolute value of (x*y)÷denominator. The result must fit within int256.
    uint256 rAbs = mulDiv(absX, absY, absD);
    if (rAbs > 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") {
        // This works thanks to two's complement.
        // "sgt" stands for "signed greater than" and "sub(0,1)" is max uint256.
        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(rAbs) : int256(rAbs);
    }
}

/// @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.
function prbExp2(uint256 x) pure returns (uint256 result) {
    unchecked {
        // Start from 0.5 in the 192.64-bit fixed-point format.
        result = 0x800000000000000000000000000000000000000000000000;

        // Multiply the result by root(2, 2^-i) when the bit at position i is 1. None of the intermediary results overflows
        // because the initial result is 2^191 and all magic factors are less than 2^65.
        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 & 0xFF00000000 > 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;
            }
        }

        // We're doing two things at the same time:
        //
        //   1. Multiply the result by 2^n + 1, where "2^n" is the integer part and the one is added to account for
        //      the fact that we initially set the result to 0.5. This is accomplished by subtracting from 191
        //      rather than 192.
        //   2. Convert the result to the unsigned 60.18-decimal fixed-point format.
        //
        // This works because 2^(191-ip) = 2^ip / 2^191, where "ip" is the integer part "2^n".
        result *= UNIT;
        result >>= (191 - (x >> 64));
    }
}

/// @notice Calculates the square root of x, rounding down if x is not a perfect square.
/// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
/// Credits to OpenZeppelin for the explanations in code comments below.
///
/// Caveats:
/// - This function does not work with fixed-point numbers.
///
/// @param x The uint256 number for which to calculate the square root.
/// @return result The result as an uint256.
function prbSqrt(uint256 x) pure returns (uint256 result) {
    if (x == 0) {
        return 0;
    }

    // For our first guess, we get 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;

        // Round down the result in case x is not a perfect square.
        uint256 roundedDownResult = x / result;
        if (result >= roundedDownResult) {
            result = roundedDownResult;
        }
    }
}

// File: @prb/math/src/sd1x18/Casting.sol



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

import { MAX_UINT40 } from "../Common.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import {
    PRBMath_SD1x18_ToUD2x18_Underflow,
    PRBMath_SD1x18_ToUD60x18_Underflow,
    PRBMath_SD1x18_ToUint128_Underflow,
    PRBMath_SD1x18_ToUint256_Underflow,
    PRBMath_SD1x18_ToUint40_Overflow,
    PRBMath_SD1x18_ToUint40_Underflow
} from "./Errors.sol";
import { SD1x18 } from "./ValueType.sol";

/// @notice Casts an SD1x18 number into SD59x18.
/// @dev There is no overflow check because the domain of SD1x18 is a subset of SD59x18.
function intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(SD1x18.unwrap(x)));
}

/// @notice Casts an SD1x18 number into UD2x18.
/// - x must be positive.
function intoUD2x18(SD1x18 x) pure returns (UD2x18 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert PRBMath_SD1x18_ToUD2x18_Underflow(x);
    }
    result = UD2x18.wrap(uint64(xInt));
}

/// @notice Casts an SD1x18 number into UD60x18.
/// @dev Requirements:
/// - x must be positive.
function intoUD60x18(SD1x18 x) pure returns (UD60x18 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert PRBMath_SD1x18_ToUD60x18_Underflow(x);
    }
    result = UD60x18.wrap(uint64(xInt));
}

/// @notice Casts an SD1x18 number into uint256.
/// @dev Requirements:
/// - x must be positive.
function intoUint256(SD1x18 x) pure returns (uint256 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert PRBMath_SD1x18_ToUint256_Underflow(x);
    }
    result = uint256(uint64(xInt));
}

/// @notice Casts an SD1x18 number into uint128.
/// @dev Requirements:
/// - x must be positive.
function intoUint128(SD1x18 x) pure returns (uint128 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert PRBMath_SD1x18_ToUint128_Underflow(x);
    }
    result = uint128(uint64(xInt));
}

/// @notice Casts an SD1x18 number into uint40.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(SD1x18 x) pure returns (uint40 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert PRBMath_SD1x18_ToUint40_Underflow(x);
    }
    if (xInt > int64(uint64(MAX_UINT40))) {
        revert PRBMath_SD1x18_ToUint40_Overflow(x);
    }
    result = uint40(uint64(xInt));
}

/// @notice Alias for the `wrap` function.
function sd1x18(int64 x) pure returns (SD1x18 result) {
    result = wrap(x);
}

/// @notice Unwraps an SD1x18 number into int64.
function unwrap(SD1x18 x) pure returns (int64 result) {
    result = SD1x18.unwrap(x);
}

/// @notice Wraps an int64 number into the SD1x18 value type.
function wrap(int64 x) pure returns (SD1x18 result) {
    result = SD1x18.wrap(x);
}

// File: @prb/math/src/sd1x18/Constants.sol



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

import { SD1x18 } from "./ValueType.sol";

/// @dev Euler's number as an SD1x18 number.
SD1x18 constant E = SD1x18.wrap(2_718281828459045235);

/// @dev The maximum value an SD1x18 number can have.
int64 constant uMAX_SD1x18 = 9_223372036854775807;
SD1x18 constant MAX_SD1x18 = SD1x18.wrap(uMAX_SD1x18);

/// @dev The maximum value an SD1x18 number can have.
int64 constant uMIN_SD1x18 = -9_223372036854775808;
SD1x18 constant MIN_SD1x18 = SD1x18.wrap(uMIN_SD1x18);

/// @dev PI as an SD1x18 number.
SD1x18 constant PI = SD1x18.wrap(3_141592653589793238);

/// @dev The unit amount that implies how many trailing decimals can be represented.
SD1x18 constant UNIT = SD1x18.wrap(1e18);
int256 constant uUNIT = 1e18;

// File: @prb/math/src/sd1x18/Errors.sol



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

import { SD1x18 } from "./ValueType.sol";

/// @notice Emitted when trying to cast a SD1x18 number that doesn't fit in UD2x18.
error PRBMath_SD1x18_ToUD2x18_Underflow(SD1x18 x);

/// @notice Emitted when trying to cast a SD1x18 number that doesn't fit in UD60x18.
error PRBMath_SD1x18_ToUD60x18_Underflow(SD1x18 x);

/// @notice Emitted when trying to cast a SD1x18 number that doesn't fit in uint128.
error PRBMath_SD1x18_ToUint128_Underflow(SD1x18 x);

/// @notice Emitted when trying to cast a SD1x18 number that doesn't fit in uint256.
error PRBMath_SD1x18_ToUint256_Underflow(SD1x18 x);

/// @notice Emitted when trying to cast a SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Overflow(SD1x18 x);

/// @notice Emitted when trying to cast a SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Underflow(SD1x18 x);

// File: @prb/math/src/sd1x18/ValueType.sol



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

import "./Casting.sol" as C;

/// @notice The signed 1.18-decimal fixed-point number representation, which can have up to 1 digit and up to 18 decimals.
/// The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity type int64.
/// This is useful when end users want to use int64 to save gas, e.g. with tight variable packing in contract storage.
type SD1x18 is int64;

/*//////////////////////////////////////////////////////////////////////////
                                    CASTING
//////////////////////////////////////////////////////////////////////////*/

using { C.intoSD59x18, C.intoUD2x18, C.intoUD60x18, C.intoUint256, C.intoUint128, C.intoUint40, C.unwrap } for SD1x18 global;

// File: @prb/math/src/sd59x18/Casting.sol



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

import { MAX_UINT128, MAX_UINT40 } from "../Common.sol";
import { uMAX_SD1x18, uMIN_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import {
    PRBMath_SD59x18_IntoSD1x18_Overflow,
    PRBMath_SD59x18_IntoSD1x18_Underflow,
    PRBMath_SD59x18_IntoUD2x18_Overflow,
    PRBMath_SD59x18_IntoUD2x18_Underflow,
    PRBMath_SD59x18_IntoUD60x18_Underflow,
    PRBMath_SD59x18_IntoUint128_Overflow,
    PRBMath_SD59x18_IntoUint128_Underflow,
    PRBMath_SD59x18_IntoUint256_Underflow,
    PRBMath_SD59x18_IntoUint40_Overflow,
    PRBMath_SD59x18_IntoUint40_Underflow
} from "./Errors.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Casts an SD59x18 number into int256.
/// @dev This is basically a functional alias for the `unwrap` function.
function intoInt256(SD59x18 x) pure returns (int256 result) {
    result = SD59x18.unwrap(x);
}

/// @notice Casts an SD59x18 number into SD1x18.
/// @dev Requirements:
/// - x must be greater than or equal to `uMIN_SD1x18`.
/// - x must be less than or equal to `uMAX_SD1x18`.
function intoSD1x18(SD59x18 x) pure returns (SD1x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < uMIN_SD1x18) {
        revert PRBMath_SD59x18_IntoSD1x18_Underflow(x);
    }
    if (xInt > uMAX_SD1x18) {
        revert PRBMath_SD59x18_IntoSD1x18_Overflow(x);
    }
    result = SD1x18.wrap(int64(xInt));
}

/// @notice Casts an SD59x18 number into UD2x18.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `uMAX_UD2x18`.
function intoUD2x18(SD59x18 x) pure returns (UD2x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert PRBMath_SD59x18_IntoUD2x18_Underflow(x);
    }
    if (xInt > int256(uint256(uMAX_UD2x18))) {
        revert PRBMath_SD59x18_IntoUD2x18_Overflow(x);
    }
    result = UD2x18.wrap(uint64(uint256(xInt)));
}

/// @notice Casts an SD59x18 number into UD60x18.
/// @dev Requirements:
/// - x must be positive.
function intoUD60x18(SD59x18 x) pure returns (UD60x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert PRBMath_SD59x18_IntoUD60x18_Underflow(x);
    }
    result = UD60x18.wrap(uint256(xInt));
}

/// @notice Casts an SD59x18 number into uint256.
/// @dev Requirements:
/// - x must be positive.
function intoUint256(SD59x18 x) pure returns (uint256 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert PRBMath_SD59x18_IntoUint256_Underflow(x);
    }
    result = uint256(xInt);
}

/// @notice Casts an SD59x18 number into uint128.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `uMAX_UINT128`.
function intoUint128(SD59x18 x) pure returns (uint128 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert PRBMath_SD59x18_IntoUint128_Underflow(x);
    }
    if (xInt > int256(uint256(MAX_UINT128))) {
        revert PRBMath_SD59x18_IntoUint128_Overflow(x);
    }
    result = uint128(uint256(xInt));
}

/// @notice Casts an SD59x18 number into uint40.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(SD59x18 x) pure returns (uint40 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert PRBMath_SD59x18_IntoUint40_Underflow(x);
    }
    if (xInt > int256(uint256(MAX_UINT40))) {
        revert PRBMath_SD59x18_IntoUint40_Overflow(x);
    }
    result = uint40(uint256(xInt));
}

/// @notice Alias for the `wrap` function.
function sd(int256 x) pure returns (SD59x18 result) {
    result = wrap(x);
}

/// @notice Alias for the `wrap` function.
function sd59x18(int256 x) pure returns (SD59x18 result) {
    result = wrap(x);
}

/// @notice Unwraps an SD59x18 number into int256.
function unwrap(SD59x18 x) pure returns (int256 result) {
    result = SD59x18.unwrap(x);
}

/// @notice Wraps an int256 number into the SD59x18 value type.
function wrap(int256 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(x);
}

// File: @prb/math/src/sd59x18/Constants.sol



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

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

/// NOTICE: the "u" prefix stands for "unwrapped".

/// @dev Euler's number as an SD59x18 number.
SD59x18 constant E = SD59x18.wrap(2_718281828459045235);

/// @dev Half the UNIT number.
int256 constant uHALF_UNIT = 0.5e18;
SD59x18 constant HALF_UNIT = SD59x18.wrap(uHALF_UNIT);

/// @dev log2(10) as an SD59x18 number.
int256 constant uLOG2_10 = 3_321928094887362347;
SD59x18 constant LOG2_10 = SD59x18.wrap(uLOG2_10);

/// @dev log2(e) as an SD59x18 number.
int256 constant uLOG2_E = 1_442695040888963407;
SD59x18 constant LOG2_E = SD59x18.wrap(uLOG2_E);

/// @dev The maximum value an SD59x18 number can have.
int256 constant uMAX_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_792003956564819967;
SD59x18 constant MAX_SD59x18 = SD59x18.wrap(uMAX_SD59x18);

/// @dev The maximum whole value an SD59x18 number can have.
int256 constant uMAX_WHOLE_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_000000000000000000;
SD59x18 constant MAX_WHOLE_SD59x18 = SD59x18.wrap(uMAX_WHOLE_SD59x18);

/// @dev The minimum value an SD59x18 number can have.
int256 constant uMIN_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_792003956564819968;
SD59x18 constant MIN_SD59x18 = SD59x18.wrap(uMIN_SD59x18);

/// @dev The minimum whole value an SD59x18 number can have.
int256 constant uMIN_WHOLE_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_000000000000000000;
SD59x18 constant MIN_WHOLE_SD59x18 = SD59x18.wrap(uMIN_WHOLE_SD59x18);

/// @dev PI as an SD59x18 number.
SD59x18 constant PI = SD59x18.wrap(3_141592653589793238);

/// @dev The unit amount that implies how many trailing decimals can be represented.
int256 constant uUNIT = 1e18;
SD59x18 constant UNIT = SD59x18.wrap(1e18);

/// @dev Zero as an SD59x18 number.
SD59x18 constant ZERO = SD59x18.wrap(0);

// File: @prb/math/src/sd59x18/Errors.sol



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

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

/// @notice Emitted when taking the absolute value of `MIN_SD59x18`.
error PRBMath_SD59x18_Abs_MinSD59x18();

/// @notice Emitted when ceiling a number overflows SD59x18.
error PRBMath_SD59x18_Ceil_Overflow(SD59x18 x);

/// @notice Emitted when converting a basic integer to the fixed-point format overflows SD59x18.
error PRBMath_SD59x18_Convert_Overflow(int256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format underflows SD59x18.
error PRBMath_SD59x18_Convert_Underflow(int256 x);

/// @notice Emitted when dividing two numbers and one of them is `MIN_SD59x18`.
error PRBMath_SD59x18_Div_InputTooSmall();

/// @notice Emitted when dividing two numbers and one of the intermediary unsigned results overflows SD59x18.
error PRBMath_SD59x18_Div_Overflow(SD59x18 x, SD59x18 y);

/// @notice Emitted when taking the natural exponent of a base greater than 133.084258667509499441.
error PRBMath_SD59x18_Exp_InputTooBig(SD59x18 x);

/// @notice Emitted when taking the binary exponent of a base greater than 192.
error PRBMath_SD59x18_Exp2_InputTooBig(SD59x18 x);

/// @notice Emitted when flooring a number underflows SD59x18.
error PRBMath_SD59x18_Floor_Underflow(SD59x18 x);

/// @notice Emitted when taking the geometric mean of two numbers and their product is negative.
error PRBMath_SD59x18_Gm_NegativeProduct(SD59x18 x, SD59x18 y);

/// @notice Emitted when taking the geometric mean of two numbers and multiplying them overflows SD59x18.
error PRBMath_SD59x18_Gm_Overflow(SD59x18 x, SD59x18 y);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Overflow(SD59x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Underflow(SD59x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Overflow(SD59x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Underflow(SD59x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in UD60x18.
error PRBMath_SD59x18_IntoUD60x18_Underflow(SD59x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Overflow(SD59x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Underflow(SD59x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in uint256.
error PRBMath_SD59x18_IntoUint256_Underflow(SD59x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Overflow(SD59x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Underflow(SD59x18 x);

/// @notice Emitted when taking the logarithm of a number less than or equal to zero.
error PRBMath_SD59x18_Log_InputTooSmall(SD59x18 x);

/// @notice Emitted when multiplying two numbers and one of the inputs is `MIN_SD59x18`.
error PRBMath_SD59x18_Mul_InputTooSmall();

/// @notice Emitted when multiplying two numbers and the intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Mul_Overflow(SD59x18 x, SD59x18 y);

/// @notice Emitted when raising a number to a power and hte intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Powu_Overflow(SD59x18 x, uint256 y);

/// @notice Emitted when taking the square root of a negative number.
error PRBMath_SD59x18_Sqrt_NegativeInput(SD59x18 x);

/// @notice Emitted when the calculating the square root overflows SD59x18.
error PRBMath_SD59x18_Sqrt_Overflow(SD59x18 x);

// File: @prb/math/src/sd59x18/Helpers.sol



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

import { unwrap, 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(unwrap(x) + unwrap(y));
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

// File: @prb/math/src/sd59x18/Math.sol



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

import { MAX_UINT128, MAX_UINT40, msb, mulDiv, mulDiv18, prbExp2, prbSqrt } from "../Common.sol";
import {
    uHALF_UNIT,
    uLOG2_10,
    uLOG2_E,
    uMAX_SD59x18,
    uMAX_WHOLE_SD59x18,
    uMIN_SD59x18,
    uMIN_WHOLE_SD59x18,
    UNIT,
    uUNIT,
    ZERO
} from "./Constants.sol";
import {
    PRBMath_SD59x18_Abs_MinSD59x18,
    PRBMath_SD59x18_Ceil_Overflow,
    PRBMath_SD59x18_Div_InputTooSmall,
    PRBMath_SD59x18_Div_Overflow,
    PRBMath_SD59x18_Exp_InputTooBig,
    PRBMath_SD59x18_Exp2_InputTooBig,
    PRBMath_SD59x18_Floor_Underflow,
    PRBMath_SD59x18_Gm_Overflow,
    PRBMath_SD59x18_Gm_NegativeProduct,
    PRBMath_SD59x18_Log_InputTooSmall,
    PRBMath_SD59x18_Mul_InputTooSmall,
    PRBMath_SD59x18_Mul_Overflow,
    PRBMath_SD59x18_Powu_Overflow,
    PRBMath_SD59x18_Sqrt_NegativeInput,
    PRBMath_SD59x18_Sqrt_Overflow
} from "./Errors.sol";
import { unwrap, wrap } from "./Helpers.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Calculate the absolute value of x.
///
/// @dev Requirements:
/// - x must be greater than `MIN_SD59x18`.
///
/// @param x The SD59x18 number for which to calculate the absolute value.
/// @param result The absolute value of x as an SD59x18 number.
function abs(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    if (xInt == uMIN_SD59x18) {
        revert PRBMath_SD59x18_Abs_MinSD59x18();
    }
    result = xInt < 0 ? wrap(-xInt) : x;
}

/// @notice Calculates the arithmetic average of x and y, rounding towards zero.
/// @param x The first operand as an SD59x18 number.
/// @param y The second operand as an SD59x18 number.
/// @return result The arithmetic average as an SD59x18 number.
function avg(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    int256 yInt = unwrap(y);

    unchecked {
        // This is equivalent to "x / 2 +  y / 2" but faster.
        // This operation can never overflow.
        int256 sum = (xInt >> 1) + (yInt >> 1);

        if (sum < 0) {
            // If at least one of x and y is odd, we add 1 to the result, since shifting negative numbers to the right rounds
            // down to infinity. The right part is equivalent to "sum + (x % 2 == 1 || y % 2 == 1)" but faster.
            assembly ("memory-safe") {
                result := add(sum, and(or(xInt, yInt), 1))
            }
        } else {
            // We need to add 1 if both x and y are odd to account for the double 0.5 remainder that is truncated after shifting.
            result = wrap(sum + (xInt & yInt & 1));
        }
    }
}

/// @notice Yields the smallest whole SD59x18 number greater than or equal to x.
///
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be less than or equal to `MAX_WHOLE_SD59x18`.
///
/// @param x The SD59x18 number to ceil.
/// @param result The least number greater than or equal to x, as an SD59x18 number.
function ceil(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    if (xInt > uMAX_WHOLE_SD59x18) {
        revert PRBMath_SD59x18_Ceil_Overflow(x);
    }

    int256 remainder = xInt % uUNIT;
    if (remainder == 0) {
        result = x;
    } else {
        unchecked {
            // Solidity uses C fmod style, which returns a modulus with the same sign as x.
            int256 resultInt = xInt - remainder;
            if (xInt > 0) {
                resultInt += uUNIT;
            }
            result = wrap(resultInt);
        }
    }
}

/// @notice Divides two SD59x18 numbers, returning a new SD59x18 number. Rounds towards zero.
///
/// @dev This is a variant of `mulDiv` that works with signed numbers. Works by computing the signs and the absolute values
/// separately.
///
/// Requirements:
/// - All from `Common.mulDiv`.
/// - None of the inputs can be `MIN_SD59x18`.
/// - The denominator cannot be zero.
/// - The result must fit within int256.
///
/// Caveats:
/// - All from `Common.mulDiv`.
///
/// @param x The numerator as an SD59x18 number.
/// @param y The denominator as an SD59x18 number.
/// @param result The quotient as an SD59x18 number.
function div(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    int256 yInt = unwrap(y);
    if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {
        revert PRBMath_SD59x18_Div_InputTooSmall();
    }

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

    // Compute the absolute value (x*UNIT)÷y. The resulting value must fit within int256.
    uint256 resultAbs = mulDiv(xAbs, uint256(uUNIT), yAbs);
    if (resultAbs > uint256(uMAX_SD59x18)) {
        revert PRBMath_SD59x18_Div_Overflow(x, y);
    }

    // Check if x and y have the same sign. This works thanks to two's complement; the left-most bit is the sign bit.
    bool sameSign = (xInt ^ yInt) > -1;

    // If the inputs don't have the same sign, the result should be negative. Otherwise, it should be positive.
    unchecked {
        result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));
    }
}

/// @notice Calculates the natural exponent of x.
///
/// @dev Based on the formula:
///
/// $$
/// e^x = 2^{x * log_2{e}}
/// $$
///
/// Requirements:
/// - All from `log2`.
/// - x must be less than 133.084258667509499441.
///
/// Caveats:
/// - All from `exp2`.
/// - For any x less than -41.446531673892822322, the result is zero.
///
/// @param x The exponent as an SD59x18 number.
/// @return result The result as an SD59x18 number.
function exp(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    // Without this check, the value passed to `exp2` would be less than -59.794705707972522261.
    if (xInt < -41_446531673892822322) {
        return ZERO;
    }

    // Without this check, the value passed to `exp2` would be greater than 192.
    if (xInt >= 133_084258667509499441) {
        revert PRBMath_SD59x18_Exp_InputTooBig(x);
    }

    unchecked {
        // Do the fixed-point multiplication inline to save gas.
        int256 doubleUnitProduct = xInt * uLOG2_E;
        result = exp2(wrap(doubleUnitProduct / uUNIT));
    }
}

/// @notice Calculates the binary exponent of x using the binary fraction method.
///
/// @dev Based on the formula:
///
/// $$
/// 2^{-x} = \frac{1}{2^x}
/// $$
///
/// See https://ethereum.stackexchange.com/q/79903/24693.
///
/// Requirements:
/// - x must be 192 or less.
/// - The result must fit within `MAX_SD59x18`.
///
/// Caveats:
/// - For any x less than -59.794705707972522261, the result is zero.
///
/// @param x The exponent as an SD59x18 number.
/// @return result The result as an SD59x18 number.
function exp2(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    if (xInt < 0) {
        // 2^59.794705707972522262 is the maximum number whose inverse does not truncate down to zero.
        if (xInt < -59_794705707972522261) {
            return ZERO;
        }

        unchecked {
            // Do the fixed-point inversion $1/2^x$ inline to save gas. 1e36 is UNIT * UNIT.
            result = wrap(1e36 / unwrap(exp2(wrap(-xInt))));
        }
    } else {
        // 2^192 doesn't fit within the 192.64-bit format used internally in this function.
        if (xInt >= 192e18) {
            revert PRBMath_SD59x18_Exp2_InputTooBig(x);
        }

        unchecked {
            // Convert x to the 192.64-bit fixed-point format.
            uint256 x_192x64 = uint256((xInt << 64) / uUNIT);

            // It is safe to convert the result to int256 with no checks because the maximum input allowed in this function is 192.
            result = wrap(int256(prbExp2(x_192x64)));
        }
    }
}

/// @notice Yields the greatest whole SD59x18 number less than or equal to x.
///
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be greater than or equal to `MIN_WHOLE_SD59x18`.
///
/// @param x The SD59x18 number to floor.
/// @param result The greatest integer less than or equal to x, as an SD59x18 number.
function floor(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    if (xInt < uMIN_WHOLE_SD59x18) {
        revert PRBMath_SD59x18_Floor_Underflow(x);
    }

    int256 remainder = xInt % uUNIT;
    if (remainder == 0) {
        result = x;
    } else {
        unchecked {
            // Solidity uses C fmod style, which returns a modulus with the same sign as x.
            int256 resultInt = xInt - remainder;
            if (xInt < 0) {
                resultInt -= uUNIT;
            }
            result = wrap(resultInt);
        }
    }
}

/// @notice Yields the excess beyond the floor of x for positive numbers and the part of the number to the right.
/// of the radix point for negative numbers.
/// @dev Based on the odd function definition. https://en.wikipedia.org/wiki/Fractional_part
/// @param x The SD59x18 number to get the fractional part of.
/// @param result The fractional part of x as an SD59x18 number.
function frac(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(unwrap(x) % uUNIT);
}

/// @notice Calculates the geometric mean of x and y, i.e. sqrt(x * y), rounding down.
///
/// @dev Requirements:
/// - x * y must fit within `MAX_SD59x18`, lest it overflows.
/// - x * y must not be negative, since this library does not handle complex numbers.
///
/// @param x The first operand as an SD59x18 number.
/// @param y The second operand as an SD59x18 number.
/// @return result The result as an SD59x18 number.
function gm(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    int256 yInt = unwrap(y);
    if (xInt == 0 || yInt == 0) {
        return ZERO;
    }

    unchecked {
        // Equivalent to "xy / x != y". Checking for overflow this way is faster than letting Solidity do it.
        int256 xyInt = xInt * yInt;
        if (xyInt / xInt != yInt) {
            revert PRBMath_SD59x18_Gm_Overflow(x, y);
        }

        // The product must not be negative, since this library does not handle complex numbers.
        if (xyInt < 0) {
            revert PRBMath_SD59x18_Gm_NegativeProduct(x, y);
        }

        // We don't need to multiply the result by `UNIT` here because the x*y product had picked up a factor of `UNIT`
        // during multiplication. See the comments within the `prbSqrt` function.
        uint256 resultUint = prbSqrt(uint256(xyInt));
        result = wrap(int256(resultUint));
    }
}

/// @notice Calculates 1 / x, rounding toward zero.
///
/// @dev Requirements:
/// - x cannot be zero.
///
/// @param x The SD59x18 number for which to calculate the inverse.
/// @return result The inverse as an SD59x18 number.
function inv(SD59x18 x) pure returns (SD59x18 result) {
    // 1e36 is UNIT * UNIT.
    result = wrap(1e36 / unwrap(x));
}

/// @notice Calculates the natural logarithm of x.
///
/// @dev Based on the formula:
///
/// $$
/// ln{x} = log_2{x} / log_2{e}$$.
/// $$
///
/// Requirements:
/// - All from `log2`.
///
/// Caveats:
/// - All from `log2`.
/// - This doesn't return exactly 1 for 2.718281828459045235, for that more fine-grained precision is needed.
///
/// @param x The SD59x18 number for which to calculate the natural logarithm.
/// @return result The natural logarithm as an SD59x18 number.
function ln(SD59x18 x) pure returns (SD59x18 result) {
    // Do the fixed-point multiplication inline to save gas. This is overflow-safe because the maximum value that log2(x)
    // can return is 195.205294292027477728.
    result = wrap((unwrap(log2(x)) * uUNIT) / uLOG2_E);
}

/// @notice Calculates the common logarithm of x.
///
/// @dev First checks if x is an exact power of ten and it stops if yes. If it's not, calculates the common
/// logarithm based on the formula:
///
/// $$
/// log_{10}{x} = log_2{x} / log_2{10}
/// $$
///
/// Requirements:
/// - All from `log2`.
///
/// Caveats:
/// - All from `log2`.
///
/// @param x The SD59x18 number for which to calculate the common logarithm.
/// @return result The common logarithm as an SD59x18 number.
function log10(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    if (xInt < 0) {
        revert PRBMath_SD59x18_Log_InputTooSmall(x);
    }

    // Note that the `mul` in this block is the assembly mul operation, not the SD59x18 `mul`.
    // prettier-ignore
    assembly ("memory-safe") {
        switch x
        case 1 { result := mul(uUNIT, sub(0, 18)) }
        case 10 { result := mul(uUNIT, sub(1, 18)) }
        case 100 { result := mul(uUNIT, sub(2, 18)) }
        case 1000 { result := mul(uUNIT, sub(3, 18)) }
        case 10000 { result := mul(uUNIT, sub(4, 18)) }
        case 100000 { result := mul(uUNIT, sub(5, 18)) }
        case 1000000 { result := mul(uUNIT, sub(6, 18)) }
        case 10000000 { result := mul(uUNIT, sub(7, 18)) }
        case 100000000 { result := mul(uUNIT, sub(8, 18)) }
        case 1000000000 { result := mul(uUNIT, sub(9, 18)) }
        case 10000000000 { result := mul(uUNIT, sub(10, 18)) }
        case 100000000000 { result := mul(uUNIT, sub(11, 18)) }
        case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }
        case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }
        case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }
        case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }
        case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }
        case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }
        case 1000000000000000000 { result := 0 }
        case 10000000000000000000 { result := uUNIT }
        case 100000000000000000000 { result := mul(uUNIT, 2) }
        case 1000000000000000000000 { result := mul(uUNIT, 3) }
        case 10000000000000000000000 { result := mul(uUNIT, 4) }
        case 100000000000000000000000 { result := mul(uUNIT, 5) }
        case 1000000000000000000000000 { result := mul(uUNIT, 6) }
        case 10000000000000000000000000 { result := mul(uUNIT, 7) }
        case 100000000000000000000000000 { result := mul(uUNIT, 8) }
        case 1000000000000000000000000000 { result := mul(uUNIT, 9) }
        case 10000000000000000000000000000 { result := mul(uUNIT, 10) }
        case 100000000000000000000000000000 { result := mul(uUNIT, 11) }
        case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }
        case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }
        case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }
        case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }
        case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }
        case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }
        case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }
        case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }
        case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }
        case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }
        case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }
        case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }
        case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }
        case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }
        case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }
        case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }
        case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }
        case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }
        case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }
        case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }
        case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }
        case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }
        case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }
        case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }
        case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }
        case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }
        case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }
        case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }
        case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }
        case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }
        case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }
        case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }
        case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }
        case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }
        case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }
        case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }
        case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }
        case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }
        case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }
        default {
            result := uMAX_SD59x18
        }
    }

    if (unwrap(result) == uMAX_SD59x18) {
        unchecked {
            // Do the fixed-point division inline to save gas.
            result = wrap((unwrap(log2(x)) * uUNIT) / uLOG2_10);
        }
    }
}

/// @notice Calculates the binary logarithm of x.
///
/// @dev Based on the iterative approximation algorithm.
/// https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
///
/// Requirements:
/// - x must be greater than zero.
///
/// Caveats:
/// - The results are not perfectly accurate to the last decimal, due to the lossy precision of the iterative approximation.
///
/// @param x The SD59x18 number for which to calculate the binary logarithm.
/// @return result The binary logarithm as an SD59x18 number.
function log2(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    if (xInt <= 0) {
        revert PRBMath_SD59x18_Log_InputTooSmall(x);
    }

    unchecked {
        // This works because of:
        //
        // $$
        // log_2{x} = -log_2{\frac{1}{x}}
        // $$
        int256 sign;
        if (xInt >= uUNIT) {
            sign = 1;
        } else {
            sign = -1;
            // Do the fixed-point inversion inline to save gas. The numerator is UNIT * UNIT.
            xInt = 1e36 / xInt;
        }

        // Calculate the integer part of the logarithm and add it to the result and finally calculate $y = x * 2^(-n)$.
        uint256 n = msb(uint256(xInt / uUNIT));

        // This is the integer part of the logarithm as an SD59x18 number. The operation can't overflow
        // because n is maximum 255, UNIT is 1e18 and sign is either 1 or -1.
        int256 resultInt = int256(n) * uUNIT;

        // This is $y = x * 2^{-n}$.
        int256 y = xInt >> n;

        // If y is 1, the fractional part is zero.
        if (y == uUNIT) {
            return wrap(resultInt * sign);
        }

        // Calculate the fractional part via the iterative approximation.
        // The "delta >>= 1" part is equivalent to "delta /= 2", but shifting bits is faster.
        int256 DOUBLE_UNIT = 2e18;
        for (int256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {
            y = (y * y) / uUNIT;

            // Is $y^2 > 2$ and so in the range [2,4)?
            if (y >= DOUBLE_UNIT) {
                // Add the 2^{-m} factor to the logarithm.
                resultInt = resultInt + delta;

                // Corresponds to z/2 on Wikipedia.
                y >>= 1;
            }
        }
        resultInt *= sign;
        result = wrap(resultInt);
    }
}

/// @notice Multiplies two SD59x18 numbers together, returning a new SD59x18 number.
///
/// @dev This is a variant of `mulDiv` that works with signed numbers and employs constant folding, i.e. the denominator
/// is always 1e18.
///
/// Requirements:
/// - All from `Common.mulDiv18`.
/// - None of the inputs can be `MIN_SD59x18`.
/// - The result must fit within `MAX_SD59x18`.
///
/// Caveats:
/// - To understand how this works in detail, see the NatSpec comments in `Common.mulDivSigned`.
///
/// @param x The multiplicand as an SD59x18 number.
/// @param y The multiplier as an SD59x18 number.
/// @return result The product as an SD59x18 number.
function mul(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    int256 yInt = unwrap(y);
    if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {
        revert PRBMath_SD59x18_Mul_InputTooSmall();
    }

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

    uint256 resultAbs = mulDiv18(xAbs, yAbs);
    if (resultAbs > uint256(uMAX_SD59x18)) {
        revert PRBMath_SD59x18_Mul_Overflow(x, y);
    }

    // Check if x and y have the same sign. This works thanks to two's complement; the left-most bit is the sign bit.
    bool sameSign = (xInt ^ yInt) > -1;

    // If the inputs have the same sign, the result should be negative. Otherwise, it should be positive.
    unchecked {
        result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));
    }
}

/// @notice Raises x to the power of y.
///
/// @dev Based on the formula:
///
/// $$
/// x^y = 2^{log_2{x} * y}
/// $$
///
/// Requirements:
/// - All from `exp2`, `log2` and `mul`.
/// - x cannot be zero.
///
/// Caveats:
/// - All from `exp2`, `log2` and `mul`.
/// - Assumes 0^0 is 1.
///
/// @param x Number to raise to given power y, as an SD59x18 number.
/// @param y Exponent to raise x to, as an SD59x18 number
/// @return result x raised to power y, as an SD59x18 number.
function pow(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    int256 yInt = unwrap(y);

    if (xInt == 0) {
        result = yInt == 0 ? UNIT : ZERO;
    } else {
        if (yInt == uUNIT) {
            result = x;
        } else {
            result = exp2(mul(log2(x), y));
        }
    }
}

/// @notice Raises x (an SD59x18 number) to the power y (unsigned basic integer) using the famous algorithm
/// algorithm "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring
///
/// Requirements:
/// - All from `abs` and `Common.mulDiv18`.
/// - The result must fit within `MAX_SD59x18`.
///
/// Caveats:
/// - All from `Common.mulDiv18`.
/// - Assumes 0^0 is 1.
///
/// @param x The base as an SD59x18 number.
/// @param y The exponent as an uint256.
/// @return result The result as an SD59x18 number.
function powu(SD59x18 x, uint256 y) pure returns (SD59x18 result) {
    uint256 xAbs = uint256(unwrap(abs(x)));

    // Calculate the first iteration of the loop in advance.
    uint256 resultAbs = y & 1 > 0 ? xAbs : uint256(uUNIT);

    // Equivalent to "for(y /= 2; y > 0; y /= 2)" but faster.
    uint256 yAux = y;
    for (yAux >>= 1; yAux > 0; yAux >>= 1) {
        xAbs = mulDiv18(xAbs, xAbs);

        // Equivalent to "y % 2 == 1" but faster.
        if (yAux & 1 > 0) {
            resultAbs = mulDiv18(resultAbs, xAbs);
        }
    }

    // The result must fit within `MAX_SD59x18`.
    if (resultAbs > uint256(uMAX_SD59x18)) {
        revert PRBMath_SD59x18_Powu_Overflow(x, y);
    }

    unchecked {
        // Is the base negative and the exponent an odd number?
        int256 resultInt = int256(resultAbs);
        bool isNegative = unwrap(x) < 0 && y & 1 == 1;
        if (isNegative) {
            resultInt = -resultInt;
        }
        result = wrap(resultInt);
    }
}

/// @notice Calculates the square root of x, rounding down. Only the positive root is returned.
/// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Requirements:
/// - x cannot be negative, since this library does not handle complex numbers.
/// - x must be less than `MAX_SD59x18` divided by `UNIT`.
///
/// @param x The SD59x18 number for which to calculate the square root.
/// @return result The result as an SD59x18 number.
function sqrt(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = unwrap(x);
    if (xInt < 0) {
        revert PRBMath_SD59x18_Sqrt_NegativeInput(x);
    }
    if (xInt > uMAX_SD59x18 / uUNIT) {
        revert PRBMath_SD59x18_Sqrt_Overflow(x);
    }

    unchecked {
        // Multiply x by `UNIT` to account for the factor of `UNIT` that is picked up when multiplying two SD59x18
        // numbers together (in this case, the two numbers are both the square root).
        uint256 resultUint = prbSqrt(uint256(xInt * uUNIT));
        result = wrap(int256(resultUint));
    }
}

// File: @prb/math/src/sd59x18/ValueType.sol



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

import "./Casting.sol" as C;
import "./Helpers.sol" as H;
import "./Math.sol" as M;

/// @notice The signed 59.18-decimal fixed-point number representation, which can have up to 59 digits and up to 18 decimals.
/// The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity type int256.
type SD59x18 is int256;

/*//////////////////////////////////////////////////////////////////////////
                                    CASTING
//////////////////////////////////////////////////////////////////////////*/

using {
    C.intoInt256,
    C.intoSD1x18,
    C.intoUD2x18,
    C.intoUD60x18,
    C.intoUint256,
    C.intoUint128,
    C.intoUint40,
    C.unwrap
} for SD59x18 global;

/*//////////////////////////////////////////////////////////////////////////
                            MATHEMATICAL FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

using {
    M.abs,
    M.avg,
    M.ceil,
    M.div,
    M.exp,
    M.exp2,
    M.floor,
    M.frac,
    M.gm,
    M.inv,
    M.log10,
    M.log2,
    M.ln,
    M.mul,
    M.pow,
    M.powu,
    M.sqrt
} for SD59x18 global;

/*//////////////////////////////////////////////////////////////////////////
                                HELPER FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

using {
    H.add,
    H.and,
    H.eq,
    H.gt,
    H.gte,
    H.isZero,
    H.lshift,
    H.lt,
    H.lte,
    H.mod,
    H.neq,
    H.or,
    H.rshift,
    H.sub,
    H.uncheckedAdd,
    H.uncheckedSub,
    H.uncheckedUnary,
    H.xor
} for SD59x18 global;

// File: @prb/math/src/ud2x18/Casting.sol



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

import { MAX_UINT40 } from "../Common.sol";
import { uMAX_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { PRBMath_UD2x18_IntoSD1x18_Overflow, PRBMath_UD2x18_IntoUint40_Overflow } from "./Errors.sol";
import { UD2x18 } from "./ValueType.sol";

/// @notice Casts an UD2x18 number into SD1x18.
/// - x must be less than or equal to `uMAX_SD1x18`.
function intoSD1x18(UD2x18 x) pure returns (SD1x18 result) {
    uint64 xUint = UD2x18.unwrap(x);
    if (xUint > uint64(uMAX_SD1x18)) {
        revert PRBMath_UD2x18_IntoSD1x18_Overflow(x);
    }
    result = SD1x18.wrap(int64(xUint));
}

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

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

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

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

/// @notice Casts an UD2x18 number into uint40.
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(UD2x18 x) pure returns (uint40 result) {
    uint64 xUint = UD2x18.unwrap(x);
    if (xUint > uint64(MAX_UINT40)) {
        revert PRBMath_UD2x18_IntoUint40_Overflow(x);
    }
    result = uint40(xUint);
}

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

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

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

// File: @prb/math/src/ud2x18/Constants.sol



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

import { UD2x18 } from "./ValueType.sol";

/// @dev Euler's number as an UD2x18 number.
UD2x18 constant E = UD2x18.wrap(2_718281828459045235);

/// @dev The maximum value an UD2x18 number can have.
uint64 constant uMAX_UD2x18 = 18_446744073709551615;
UD2x18 constant MAX_UD2x18 = UD2x18.wrap(uMAX_UD2x18);

/// @dev PI as an UD2x18 number.
UD2x18 constant PI = UD2x18.wrap(3_141592653589793238);

/// @dev The unit amount that implies how many trailing decimals can be represented.
uint256 constant uUNIT = 1e18;
UD2x18 constant UNIT = UD2x18.wrap(1e18);

// File: @prb/math/src/ud2x18/Errors.sol



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

import { UD2x18 } from "./ValueType.sol";

/// @notice Emitted when trying to cast a UD2x18 number that doesn't fit in SD1x18.
error PRBMath_UD2x18_IntoSD1x18_Overflow(UD2x18 x);

/// @notice Emitted when trying to cast a UD2x18 number that doesn't fit in uint40.
error PRBMath_UD2x18_IntoUint40_Overflow(UD2x18 x);

// File: @prb/math/src/ud2x18/ValueType.sol



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

import "./Casting.sol" as C;

/// @notice The unsigned 2.18-decimal fixed-point number representation, which can have up to 2 digits and up to 18 decimals.
/// The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity type uint64.
/// This is useful when end users want to use uint64 to save gas, e.g. with tight variable packing in contract storage.
type UD2x18 is uint64;

/*//////////////////////////////////////////////////////////////////////////
                                    CASTING
//////////////////////////////////////////////////////////////////////////*/

using { C.intoSD1x18, C.intoSD59x18, C.intoUD60x18, C.intoUint256, C.intoUint128, C.intoUint40, C.unwrap } for UD2x18 global;

// File: @prb/math/src/UD60x18.sol



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

import "./ud60x18/Casting.sol";
import "./ud60x18/Constants.sol";
import "./ud60x18/Conversions.sol";
import "./ud60x18/Errors.sol";
import "./ud60x18/Helpers.sol";
import "./ud60x18/Math.sol";
import "./ud60x18/ValueType.sol";

// File: @prb/math/src/ud60x18/Casting.sol



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

import { MAX_UINT128, MAX_UINT40 } from "../Common.sol";
import { uMAX_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { uMAX_SD59x18 } from "../sd59x18/Constants.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import {
    PRBMath_UD60x18_IntoSD1x18_Overflow,
    PRBMath_UD60x18_IntoUD2x18_Overflow,
    PRBMath_UD60x18_IntoSD59x18_Overflow,
    PRBMath_UD60x18_IntoUint128_Overflow,
    PRBMath_UD60x18_IntoUint40_Overflow
} from "./Errors.sol";
import { UD60x18 } from "./ValueType.sol";

/// @notice Casts an UD60x18 number into SD1x18.
/// @dev Requirements:
/// - x must be less than or equal to `uMAX_SD1x18`.
function intoSD1x18(UD60x18 x) pure returns (SD1x18 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > uint256(int256(uMAX_SD1x18))) {
        revert PRBMath_UD60x18_IntoSD1x18_Overflow(x);
    }
    result = SD1x18.wrap(int64(uint64(xUint)));
}

/// @notice Casts an UD60x18 number into UD2x18.
/// @dev Requirements:
/// - x must be less than or equal to `uMAX_UD2x18`.
function intoUD2x18(UD60x18 x) pure returns (UD2x18 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > uMAX_UD2x18) {
        revert PRBMath_UD60x18_IntoUD2x18_Overflow(x);
    }
    result = UD2x18.wrap(uint64(xUint));
}

/// @notice Casts an UD60x18 number into SD59x18.
/// @dev Requirements:
/// - x must be less than or equal to `uMAX_SD59x18`.
function intoSD59x18(UD60x18 x) pure returns (SD59x18 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > uint256(uMAX_SD59x18)) {
        revert PRBMath_UD60x18_IntoSD59x18_Overflow(x);
    }
    result = SD59x18.wrap(int256(xUint));
}

/// @notice Casts an UD60x18 number into uint128.
/// @dev This is basically a functional alias for the `unwrap` function.
function intoUint256(UD60x18 x) pure returns (uint256 result) {
    result = UD60x18.unwrap(x);
}

/// @notice Casts an UD60x18 number into uint128.
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UINT128`.
function intoUint128(UD60x18 x) pure returns (uint128 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > MAX_UINT128) {
        revert PRBMath_UD60x18_IntoUint128_Overflow(x);
    }
    result = uint128(xUint);
}

/// @notice Casts an UD60x18 number into uint40.
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(UD60x18 x) pure returns (uint40 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > MAX_UINT40) {
        revert PRBMath_UD60x18_IntoUint40_Overflow(x);
    }
    result = uint40(xUint);
}

/// @notice Alias for the `wrap` function.
function ud(uint256 x) pure returns (UD60x18 result) {
    result = wrap(x);
}

/// @notice Alias for the `wrap` function.
function ud60x18(uint256 x) pure returns (UD60x18 result) {
    result = wrap(x);
}

/// @notice Unwraps an UD60x18 number into uint256.
function unwrap(UD60x18 x) pure returns (uint256 result) {
    result = UD60x18.unwrap(x);
}

/// @notice Wraps an uint256 number into the UD60x18 value type.
function wrap(uint256 x) pure returns (UD60x18 result) {
    result = UD60x18.wrap(x);
}

// File: @prb/math/src/ud60x18/Constants.sol



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

import { UD60x18 } from "./ValueType.sol";

/// @dev Euler's number as an UD60x18 number.
UD60x18 constant E = UD60x18.wrap(2_718281828459045235);

/// @dev Half the UNIT number.
uint256 constant uHALF_UNIT = 0.5e18;
UD60x18 constant HALF_UNIT = UD60x18.wrap(uHALF_UNIT);

/// @dev log2(10) as an UD60x18 number.
uint256 constant uLOG2_10 = 3_321928094887362347;
UD60x18 constant LOG2_10 = UD60x18.wrap(uLOG2_10);

/// @dev log2(e) as an UD60x18 number.
uint256 constant uLOG2_E = 1_442695040888963407;
UD60x18 constant LOG2_E = UD60x18.wrap(uLOG2_E);

/// @dev The maximum value an UD60x18 number can have.
uint256 constant uMAX_UD60x18 = 115792089237316195423570985008687907853269984665640564039457_584007913129639935;
UD60x18 constant MAX_UD60x18 = UD60x18.wrap(uMAX_UD60x18);

/// @dev The maximum whole value an UD60x18 number can have.
uint256 constant uMAX_WHOLE_UD60x18 = 115792089237316195423570985008687907853269984665640564039457_000000000000000000;
UD60x18 constant MAX_WHOLE_UD60x18 = UD60x18.wrap(uMAX_WHOLE_UD60x18);

/// @dev PI as an UD60x18 number.
UD60x18 constant PI = UD60x18.wrap(3_141592653589793238);

/// @dev The unit amount that implies how many trailing decimals can be represented.
uint256 constant uUNIT = 1e18;
UD60x18 constant UNIT = UD60x18.wrap(uUNIT);

/// @dev Zero as an UD60x18 number.
UD60x18 constant ZERO = UD60x18.wrap(0);

// File: @prb/math/src/ud60x18/Conversions.sol



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

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

/// @notice Converts an UD60x18 number to a simple integer by dividing it by `UNIT`. Rounds towards zero in the process.
/// @dev Rounds down in the process.
/// @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 must be less than or equal to `MAX_UD60x18` divided by `UNIT`.
///
/// @param x The basic integer to convert.
/// @param 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);
    }
}

/// @notice Alias for the `convert` function defined above.
/// @dev Here for backward compatibility. Will be removed in V4.
function fromUD60x18(UD60x18 x) pure returns (uint256 result) {
    result = convert(x);
}

/// @notice Alias for the `convert` function defined above.
/// @dev Here for backward compatibility. Will be removed in V4.
function toUD60x18(uint256 x) pure returns (UD60x18 result) {
    result = convert(x);
}

// File: @prb/math/src/ud60x18/Errors.sol



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

import { UD60x18 } from "./ValueType.sol";

/// @notice Emitted when ceiling a number overflows UD60x18.
error PRBMath_UD60x18_Ceil_Overflow(UD60x18 x);

/// @notice Emitted when converting a basic integer to the fixed-point format overflows UD60x18.
error PRBMath_UD60x18_Convert_Overflow(uint256 x);

/// @notice Emitted when taking the natural exponent of a base greater than 133.084258667509499441.
error PRBMath_UD60x18_Exp_InputTooBig(UD60x18 x);

/// @notice Emitted when taking the binary exponent of a base greater than 192.
error PRBMath_UD60x18_Exp2_InputTooBig(UD60x18 x);

/// @notice Emitted when taking the geometric mean of two numbers and multiplying them overflows UD60x18.
error PRBMath_UD60x18_Gm_Overflow(UD60x18 x, UD60x18 y);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in SD1x18.
error PRBMath_UD60x18_IntoSD1x18_Overflow(UD60x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in SD59x18.
error PRBMath_UD60x18_IntoSD59x18_Overflow(UD60x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in UD2x18.
error PRBMath_UD60x18_IntoUD2x18_Overflow(UD60x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in uint128.
error PRBMath_UD60x18_IntoUint128_Overflow(UD60x18 x);

/// @notice Emitted when trying to cast an UD60x18 number that doesn't fit in uint40.
error PRBMath_UD60x18_IntoUint40_Overflow(UD60x18 x);

/// @notice Emitted when taking the logarithm of a number less than 1.
error PRBMath_UD60x18_Log_InputTooSmall(UD60x18 x);

/// @notice Emitted when calculating the square root overflows UD60x18.
error PRBMath_UD60x18_Sqrt_Overflow(UD60x18 x);

// File: @prb/math/src/ud60x18/Helpers.sol



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

import { unwrap, wrap } from "./Casting.sol";
import { UD60x18 } from "./ValueType.sol";

/// @notice Implements the checked addition operation (+) in the UD60x18 type.
function add(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(unwrap(x) + unwrap(y));
}

/// @notice Implements the AND (&) bitwise operation in the UD60x18 type.
function and(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {
    result = wrap(unwrap(x) & bits);
}

/// @notice Implements the equal operation (==) in the UD60x18 type.
function eq(UD60x18 x, UD60x18 y) pure returns (bool result) {
    result = unwrap(x) == unwrap(y);
}

/// @notice Implements the greater than operation (>) in the UD60x18 type.
function gt(UD60x18 x, UD60x18 y) pure returns (bool result) {
    result = unwrap(x) > unwrap(y);
}

/// @notice Implements the greater than or equal to operation (>=) in the UD60x18 type.
function gte(UD60x18 x, UD60x18 y) pure returns (bool result) {
    result = unwrap(x) >= unwrap(y);
}

/// @notice Implements a zero comparison check function in the UD60x18 type.
function isZero(UD60x18 x) pure returns (bool result) {
    // This wouldn't work if x could be negative.
    result = unwrap(x) == 0;
}

/// @notice Implements the left shift operation (<<) in the UD60x18 type.
function lshift(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {
    result = wrap(unwrap(x) << bits);
}

/// @notice Implements the lower than operation (<) in the UD60x18 type.
function lt(UD60x18 x, UD60x18 y) pure returns (bool result) {
    result = unwrap(x) < unwrap(y);
}

/// @notice Implements the lower than or equal to operation (<=) in the UD60x18 type.
function lte(UD60x18 x, UD60x18 y) pure returns (bool result) {
    result = unwrap(x) <= unwrap(y);
}

/// @notice Implements the checked modulo operation (%) in the UD60x18 type.
function mod(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(unwrap(x) % unwrap(y));
}

/// @notice Implements the not equal operation (!=) in the UD60x18 type
function neq(UD60x18 x, UD60x18 y) pure returns (bool result) {
    result = unwrap(x) != unwrap(y);
}

/// @notice Implements the OR (|) bitwise operation in the UD60x18 type.
function or(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(unwrap(x) | unwrap(y));
}

/// @notice Implements the right shift operation (>>) in the UD60x18 type.
function rshift(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {
    result = wrap(unwrap(x) >> bits);
}

/// @notice Implements the checked subtraction operation (-) in the UD60x18 type.
function sub(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(unwrap(x) - unwrap(y));
}

/// @notice Implements the unchecked addition operation (+) in the UD60x18 type.
function uncheckedAdd(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    unchecked {
        result = wrap(unwrap(x) + unwrap(y));
    }
}

/// @notice Implements the unchecked subtraction operation (-) in the UD60x18 type.
function uncheckedSub(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    unchecked {
        result = wrap(unwrap(x) - unwrap(y));
    }
}

/// @notice Implements the XOR (^) bitwise operation in the UD60x18 type.
function xor(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(unwrap(x) ^ unwrap(y));
}

// File: @prb/math/src/ud60x18/Math.sol



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

import { msb, mulDiv, mulDiv18, prbExp2, prbSqrt } from "../Common.sol";
import { unwrap, wrap } from "./Casting.sol";
import { uHALF_UNIT, uLOG2_10, uLOG2_E, uMAX_UD60x18, uMAX_WHOLE_UD60x18, UNIT, uUNIT, ZERO } from "./Constants.sol";
import {
    PRBMath_UD60x18_Ceil_Overflow,
    PRBMath_UD60x18_Exp_InputTooBig,
    PRBMath_UD60x18_Exp2_InputTooBig,
    PRBMath_UD60x18_Gm_Overflow,
    PRBMath_UD60x18_Log_InputTooSmall,
    PRBMath_UD60x18_Sqrt_Overflow
} from "./Errors.sol";
import { UD60x18 } from "./ValueType.sol";

/*//////////////////////////////////////////////////////////////////////////
                            MATHEMATICAL FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

/// @notice Calculates the arithmetic average of x and y, rounding down.
///
/// @dev Based on the formula:
///
/// $$
/// avg(x, y) = (x & y) + ((xUint ^ yUint) / 2)
/// $$
//
/// In English, what this formula does is:
///
/// 1. AND x and y.
/// 2. Calculate half of XOR x and y.
/// 3. Add the two results together.
///
/// This technique is known as SWAR, which stands for "SIMD within a register". You can read more about it here:
/// https://devblogs.microsoft.com/oldnewthing/20220207-00/?p=106223
///
/// @param x The first operand as an UD60x18 number.
/// @param y The second operand as an UD60x18 number.
/// @return result The arithmetic average as an UD60x18 number.
function avg(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    uint256 xUint = unwrap(x);
    uint256 yUint = unwrap(y);
    unchecked {
        result = wrap((xUint & yUint) + ((xUint ^ yUint) >> 1));
    }
}

/// @notice Yields the smallest whole UD60x18 number greater than or equal to x.
///
/// @dev This is optimized for fractional value inputs, because for every whole value there are "1e18 - 1" fractional
/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x must be less than or equal to `MAX_WHOLE_UD60x18`.
///
/// @param x The UD60x18 number to ceil.
/// @param result The least number greater than or equal to x, as an UD60x18 number.
function ceil(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = unwrap(x);
    if (xUint > uMAX_WHOLE_UD60x18) {
        revert PRBMath_UD60x18_Ceil_Overflow(x);
    }

    assembly ("memory-safe") {
        // Equivalent to "x % UNIT" but faster.
        let remainder := mod(x, uUNIT)

        // Equivalent to "UNIT - remainder" but faster.
        let delta := sub(uUNIT, remainder)

        // Equivalent to "x + delta * (remainder > 0 ? 1 : 0)" but faster.
        result := add(x, mul(delta, gt(remainder, 0)))
    }
}

/// @notice Divides two UD60x18 numbers, returning a new UD60x18 number. Rounds towards zero.
///
/// @dev Uses `mulDiv` to enable overflow-safe multiplication and division.
///
/// Requirements:
/// - The denominator cannot be zero.
///
/// @param x The numerator as an UD60x18 number.
/// @param y The denominator as an UD60x18 number.
/// @param result The quotient as an UD60x18 number.
function div(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(mulDiv(unwrap(x), uUNIT, unwrap(y)));
}

/// @notice Calculates the natural exponent of x.
///
/// @dev Based on the formula:
///
/// $$
/// e^x = 2^{x * log_2{e}}
/// $$
///
/// Requirements:
/// - All from `log2`.
/// - x must be less than 133.084258667509499441.
///
/// @param x The exponent as an UD60x18 number.
/// @return result The result as an UD60x18 number.
function exp(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = unwrap(x);

    // Without this check, the value passed to `exp2` would be greater than 192.
    if (xUint >= 133_084258667509499441) {
        revert PRBMath_UD60x18_Exp_InputTooBig(x);
    }

    unchecked {
        // We do the fixed-point multiplication inline rather than via the `mul` function to save gas.
        uint256 doubleUnitProduct = xUint * uLOG2_E;
        result = exp2(wrap(doubleUnitProduct / uUNIT));
    }
}

/// @notice Calculates the binary exponent of x using the binary fraction method.
///
/// @dev See https://ethereum.stackexchange.com/q/79903/24693.
///
/// Requirements:
/// - x must be 192 or less.
/// - The result must fit within `MAX_UD60x18`.
///
/// @param x The exponent as an UD60x18 number.
/// @return result The result as an UD60x18 number.
function exp2(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = unwrap(x);

    // Numbers greater than or equal to 2^192 don't fit within the 192.64-bit format.
    if (xUint >= 192e18) {
        revert PRBMath_UD60x18_Exp2_InputTooBig(x);
    }

    // Convert x to the 192.64-bit fixed-point format.
    uint256 x_192x64 = (xUint << 64) / uUNIT;

    // Pass x to the `prbExp2` function, which uses the 192.64-bit fixed-point number representation.
    result = wrap(prbExp2(x_192x64));
}

/// @notice Yields the greatest whole UD60x18 number less than or equal to x.
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
/// @param x The UD60x18 number to floor.
/// @param result The greatest integer less than or equal to x, as an UD60x18 number.
function floor(UD60x18 x) pure returns (UD60x18 result) {
    assembly ("memory-safe") {
        // Equivalent to "x % UNIT" but faster.
        let remainder := mod(x, uUNIT)

        // Equivalent to "x - remainder * (remainder > 0 ? 1 : 0)" but faster.
        result := sub(x, mul(remainder, gt(remainder, 0)))
    }
}

/// @notice Yields the excess beyond the floor of x.
/// @dev Based on the odd function definition https://en.wikipedia.org/wiki/Fractional_part.
/// @param x The UD60x18 number to get the fractional part of.
/// @param result The fractional part of x as an UD60x18 number.
function frac(UD60x18 x) pure returns (UD60x18 result) {
    assembly ("memory-safe") {
        result := mod(x, uUNIT)
    }
}

/// @notice Calculates the geometric mean of x and y, i.e. $$sqrt(x * y)$$, rounding down.
///
/// @dev Requirements:
/// - x * y must fit within `MAX_UD60x18`, lest it overflows.
///
/// @param x The first operand as an UD60x18 number.
/// @param y The second operand as an UD60x18 number.
/// @return result The result as an UD60x18 number.
function gm(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    uint256 xUint = unwrap(x);
    uint256 yUint = unwrap(y);
    if (xUint == 0 || yUint == 0) {
        return ZERO;
    }

    unchecked {
        // Checking for overflow this way is faster than letting Solidity do it.
        uint256 xyUint = xUint * yUint;
        if (xyUint / xUint != yUint) {
            revert PRBMath_UD60x18_Gm_Overflow(x, y);
        }

        // We don't need to multiply the result by `UNIT` here because the x*y product had picked up a factor of `UNIT`
        // during multiplication. See the comments in the `prbSqrt` function.
        result = wrap(prbSqrt(xyUint));
    }
}

/// @notice Calculates 1 / x, rounding toward zero.
///
/// @dev Requirements:
/// - x cannot be zero.
///
/// @param x The UD60x18 number for which to calculate the inverse.
/// @return result The inverse as an UD60x18 number.
function inv(UD60x18 x) pure returns (UD60x18 result) {
    unchecked {
        // 1e36 is UNIT * UNIT.
        result = wrap(1e36 / unwrap(x));
    }
}

/// @notice Calculates the natural logarithm of x.
///
/// @dev Based on the formula:
///
/// $$
/// ln{x} = log_2{x} / log_2{e}$$.
/// $$
///
/// Requirements:
/// - All from `log2`.
///
/// Caveats:
/// - All from `log2`.
/// - This doesn't return exactly 1 for 2.718281828459045235, for that more fine-grained precision is needed.
///
/// @param x The UD60x18 number for which to calculate the natural logarithm.
/// @return result The natural logarithm as an UD60x18 number.
function ln(UD60x18 x) pure returns (UD60x18 result) {
    unchecked {
        // We do the fixed-point multiplication inline to save gas. This is overflow-safe because the maximum value
        // that `log2` can return is 196.205294292027477728.
        result = wrap((unwrap(log2(x)) * uUNIT) / uLOG2_E);
    }
}

/// @notice Calculates the common logarithm of x.
///
/// @dev First checks if x is an exact power of ten and it stops if yes. If it's not, calculates the common
/// logarithm based on the formula:
///
/// $$
/// log_{10}{x} = log_2{x} / log_2{10}
/// $$
///
/// Requirements:
/// - All from `log2`.
///
/// Caveats:
/// - All from `log2`.
///
/// @param x The UD60x18 number for which to calculate the common logarithm.
/// @return result The common logarithm as an UD60x18 number.
function log10(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = unwrap(x);
    if (xUint < uUNIT) {
        revert PRBMath_UD60x18_Log_InputTooSmall(x);
    }

    // Note that the `mul` in this assembly block is the assembly multiplication operation, not the UD60x18 `mul`.
    // prettier-ignore
    assembly ("memory-safe") {
        switch x
        case 1 { result := mul(uUNIT, sub(0, 18)) }
        case 10 { result := mul(uUNIT, sub(1, 18)) }
        case 100 { result := mul(uUNIT, sub(2, 18)) }
        case 1000 { result := mul(uUNIT, sub(3, 18)) }
        case 10000 { result := mul(uUNIT, sub(4, 18)) }
        case 100000 { result := mul(uUNIT, sub(5, 18)) }
        case 1000000 { result := mul(uUNIT, sub(6, 18)) }
        case 10000000 { result := mul(uUNIT, sub(7, 18)) }
        case 100000000 { result := mul(uUNIT, sub(8, 18)) }
        case 1000000000 { result := mul(uUNIT, sub(9, 18)) }
        case 10000000000 { result := mul(uUNIT, sub(10, 18)) }
        case 100000000000 { result := mul(uUNIT, sub(11, 18)) }
        case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }
        case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }
        case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }
        case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }
        case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }
        case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }
        case 1000000000000000000 { result := 0 }
        case 10000000000000000000 { result := uUNIT }
        case 100000000000000000000 { result := mul(uUNIT, 2) }
        case 1000000000000000000000 { result := mul(uUNIT, 3) }
        case 10000000000000000000000 { result := mul(uUNIT, 4) }
        case 100000000000000000000000 { result := mul(uUNIT, 5) }
        case 1000000000000000000000000 { result := mul(uUNIT, 6) }
        case 10000000000000000000000000 { result := mul(uUNIT, 7) }
        case 100000000000000000000000000 { result := mul(uUNIT, 8) }
        case 1000000000000000000000000000 { result := mul(uUNIT, 9) }
        case 10000000000000000000000000000 { result := mul(uUNIT, 10) }
        case 100000000000000000000000000000 { result := mul(uUNIT, 11) }
        case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }
        case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }
        case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }
        case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }
        case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }
        case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }
        case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }
        case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }
        case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }
        case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }
        case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }
        case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }
        case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }
        case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }
        case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }
        case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }
        case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }
        case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }
        case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }
        case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }
        case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }
        case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }
        case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }
        case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }
        case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }
        case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }
        case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }
        case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }
        case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }
        case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }
        case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }
        case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }
        case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }
        case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }
        case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }
        case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }
        case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }
        case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }
        case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 59) }
        default {
            result := uMAX_UD60x18
        }
    }

    if (unwrap(result) == uMAX_UD60x18) {
        unchecked {
            // Do the fixed-point division inline to save gas.
            result = wrap((unwrap(log2(x)) * uUNIT) / uLOG2_10);
        }
    }
}

/// @notice Calculates the binary logarithm of x.
///
/// @dev Based on the iterative approximation algorithm.
/// https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
///
/// Requirements:
/// - x must be greater than or equal to UNIT, otherwise the result would be negative.
///
/// Caveats:
/// - The results are nor perfectly accurate to the last decimal, due to the lossy precision of the iterative approximation.
///
/// @param x The UD60x18 number for which to calculate the binary logarithm.
/// @return result The binary logarithm as an UD60x18 number.
function log2(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = unwrap(x);

    if (xUint < uUNIT) {
        revert PRBMath_UD60x18_Log_InputTooSmall(x);
    }

    unchecked {
        // Calculate the integer part of the logarithm, add it to the result and finally calculate y = x * 2^(-n).
        uint256 n = msb(xUint / uUNIT);

        // This is the integer part of the logarithm as an UD60x18 number. The operation can't overflow because n
        // n is maximum 255 and UNIT is 1e18.
        uint256 resultUint = n * uUNIT;

        // This is $y = x * 2^{-n}$.
        uint256 y = xUint >> n;

        // If y is 1, the fractional part is zero.
        if (y == uUNIT) {
            return wrap(resultUint);
        }

        // Calculate the fractional part via the iterative approximation.
        // The "delta.rshift(1)" part is equivalent to "delta /= 2", but shifting bits is faster.
        uint256 DOUBLE_UNIT = 2e18;
        for (uint256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {
            y = (y * y) / uUNIT;

            // Is y^2 > 2 and so in the range [2,4)?
            if (y >= DOUBLE_UNIT) {
                // Add the 2^{-m} factor to the logarithm.
                resultUint += delta;

                // Corresponds to z/2 on Wikipedia.
                y >>= 1;
            }
        }
        result = wrap(resultUint);
    }
}

/// @notice Multiplies two UD60x18 numbers together, returning a new UD60x18 number.
/// @dev See the documentation for the `Common.mulDiv18` function.
/// @param x The multiplicand as an UD60x18 number.
/// @param y The multiplier as an UD60x18 number.
/// @return result The product as an UD60x18 number.
function mul(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(mulDiv18(unwrap(x), unwrap(y)));
}

/// @notice Raises x to the power of y.
///
/// @dev Based on the formula:
///
/// $$
/// x^y = 2^{log_2{x} * y}
/// $$
///
/// Requirements:
/// - All from `exp2`, `log2` and `mul`.
///
/// Caveats:
/// - All from `exp2`, `log2` and `mul`.
/// - Assumes 0^0 is 1.
///
/// @param x Number to raise to given power y, as an UD60x18 number.
/// @param y Exponent to raise x to, as an UD60x18 number.
/// @return result x raised to power y, as an UD60x18 number.
function pow(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    uint256 xUint = unwrap(x);
    uint256 yUint = unwrap(y);

    if (xUint == 0) {
        result = yUint == 0 ? UNIT : ZERO;
    } else {
        if (yUint == uUNIT) {
            result = x;
        } else {
            result = exp2(mul(log2(x), y));
        }
    }
}

/// @notice Raises x (an UD60x18 number) to the power y (unsigned basic integer) using the famous algorithm
/// "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring
///
/// Requirements:
/// - The result must fit within `MAX_UD60x18`.
///
/// Caveats:
/// - All from "Common.mulDiv18".
/// - Assumes 0^0 is 1.
///
/// @param x The base as an UD60x18 number.
/// @param y The exponent as an uint256.
/// @return result The result as an UD60x18 number.
function powu(UD60x18 x, uint256 y) pure returns (UD60x18 result) {
    // Calculate the first iteration of the loop in advance.
    uint256 xUint = unwrap(x);
    uint256 resultUint = y & 1 > 0 ? xUint : uUNIT;

    // Equivalent to "for(y /= 2; y > 0; y /= 2)" but faster.
    for (y >>= 1; y > 0; y >>= 1) {
        xUint = mulDiv18(xUint, xUint);

        // Equivalent to "y % 2 == 1" but faster.
        if (y & 1 > 0) {
            resultUint = mulDiv18(resultUint, xUint);
        }
    }
    result = wrap(resultUint);
}

/// @notice Calculates the square root of x, rounding down.
/// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Requirements:
/// - x must be less than `MAX_UD60x18` divided by `UNIT`.
///
/// @param x The UD60x18 number for which to calculate the square root.
/// @return result The result as an UD60x18 number.
function sqrt(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = unwrap(x);

    unchecked {
        if (xUint > uMAX_UD60x18 / uUNIT) {
            revert PRBMath_UD60x18_Sqrt_Overflow(x);
        }
        // Multiply x by `UNIT` to account for the factor of `UNIT` that is picked up when multiplying two UD60x18
        // numbers together (in this case, the two numbers are both the square root).
        result = wrap(prbSqrt(xUint * uUNIT));
    }
}

// File: @prb/math/src/ud60x18/ValueType.sol



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

import "./Casting.sol" as C;
import "./Helpers.sol" as H;
import "./Math.sol" as M;

/// @notice The unsigned 60.18-decimal fixed-point number representation, which can have up to 60 digits and up to 18 decimals.
/// The values of this are bound by the minimum and the maximum values permitted by the Solidity type uint256.
/// @dev The value type is defined here so it can be imported in all other files.
type UD60x18 is uint256;

/*//////////////////////////////////////////////////////////////////////////
                                    CASTING
//////////////////////////////////////////////////////////////////////////*/

using { C.intoSD1x18, C.intoUD2x18, C.intoSD59x18, C.intoUint128, C.intoUint256, C.intoUint40, C.unwrap } for UD60x18 global;

/*//////////////////////////////////////////////////////////////////////////
                            MATHEMATICAL FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

/// The global "using for" directive makes the functions in this library callable on the UD60x18 type.
using {
    M.avg,
    M.ceil,
    M.div,
    M.exp,
    M.exp2,
    M.floor,
    M.frac,
    M.gm,
    M.inv,
    M.ln,
    M.log10,
    M.log2,
    M.mul,
    M.pow,
    M.powu,
    M.sqrt
} for UD60x18 global;

/*//////////////////////////////////////////////////////////////////////////
                                HELPER FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

/// The global "using for" directive makes the functions in this library callable on the UD60x18 type.
using {
    H.add,
    H.and,
    H.eq,
    H.gt,
    H.gte,
    H.isZero,
    H.lshift,
    H.lt,
    H.lte,
    H.mod,
    H.neq,
    H.or,
    H.rshift,
    H.sub,
    H.uncheckedAdd,
    H.uncheckedSub,
    H.xor
} for UD60x18 global;

// File: contracts/implementations/swETH.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity 0.8.16;

import {UD60x18, wrap} from "@prb/math/src/UD60x18.sol";
import {ERC20Upgradeable} from "@openzeppelin/contracts-upgradeable/token/ERC20/ERC20Upgradeable.sol";
import {Initializable} from "@openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol";
import {AddressUpgradeable} from "@openzeppelin/contracts-upgradeable/utils/AddressUpgradeable.sol";
import {EnumerableSetUpgradeable} from "@openzeppelin/contracts-upgradeable/utils/structs/EnumerableSetUpgradeable.sol";
import {IERC20} from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import {SafeERC20} from "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";

import {Whitelist} from "./Whitelist.sol";

import {SwellLib} from "../libraries/SwellLib.sol";

import {IswETH} from "../interfaces/IswETH.sol";
import {IAccessControlManager} from "../interfaces/IAccessControlManager.sol";
import {INodeOperatorRegistry} from "../interfaces/INodeOperatorRegistry.sol";
import {IRateProvider} from "../vendors/IRateProvider.sol";

/**
 * @title swETH
 * @notice Contract for handling user deposits in ETH in exchange for swETH at the stored rate. Also handles the rate updates from the BOT wallet which will occur at a fixed interval.
 * @author https://github.com/max-taylor
 * @dev This contract inherits the Whitelist contract which holds the Access control manager state variable and the checkRole modifier
 */
contract swETH is
  Initializable,
  Whitelist,
  IswETH,
  IRateProvider,
  ERC20Upgradeable
{
  using SafeERC20 for IERC20;
  using EnumerableSetUpgradeable for EnumerableSetUpgradeable.AddressSet;

  uint256 public override lastRepriceETHReserves;
  uint256 private swETHToETHRateFixed;

  uint256 public override swellTreasuryRewardPercentage;
  uint256 public override nodeOperatorRewardPercentage;

  uint256 public override lastRepriceUNIX;

  uint256 public override totalETHDeposited;

  uint256 public override minimumRepriceTime;
  uint256 public override maximumRepriceDifferencePercentage;
  uint256 public override maximumRepriceswETHDifferencePercentage;

  /// @custom:oz-upgrades-unsafe-allow constructor
  constructor() {
    _disableInitializers();
  }

  fallback() external {
    revert SwellLib.InvalidMethodCall();
  }

  function initialize(
    IAccessControlManager _accessControlManager
  ) external initializer checkZeroAddress(address(_accessControlManager)) {
    __ERC20_init("swETH", "swETH");

    __Whitelist_init(_accessControlManager);
  }

  // ************************************
  // ***** External methods ******

  function withdrawERC20(
    IERC20 _token
  ) external override checkRole(SwellLib.PLATFORM_ADMIN) {
    uint256 contractBalance = _token.balanceOf(address(this));
    if (contractBalance == 0) {
      revert SwellLib.NoTokensToWithdraw();
    }

    _token.safeTransfer(msg.sender, contractBalance);
  }

  function setSwellTreasuryRewardPercentage(
    uint256 _newSwellTreasuryRewardPercentage
  ) external override checkRole(SwellLib.PLATFORM_ADMIN) {
    // Joined percentage total cannot exeed 100% (1 ether)
    if (
      nodeOperatorRewardPercentage + _newSwellTreasuryRewardPercentage > 1 ether
    ) {
      revert RewardPercentageTotalOverflow();
    }

    emit SwellTreasuryRewardPercentageUpdate(
      swellTreasuryRewardPercentage,
      _newSwellTreasuryRewardPercentage
    );

    swellTreasuryRewardPercentage = _newSwellTreasuryRewardPercentage;
  }

  function setNodeOperatorRewardPercentage(
    uint256 _newNodeOperatorRewardPercentage
  ) external override checkRole(SwellLib.PLATFORM_ADMIN) {
    // Joined percentage total cannot exeed 100% (1 ether)
    if (
      swellTreasuryRewardPercentage + _newNodeOperatorRewardPercentage > 1 ether
    ) {
      revert RewardPercentageTotalOverflow();
    }

    emit NodeOperatorRewardPercentageUpdate(
      nodeOperatorRewardPercentage,
      _newNodeOperatorRewardPercentage
    );

    nodeOperatorRewardPercentage = _newNodeOperatorRewardPercentage;
  }

  function setMinimumRepriceTime(
    uint256 _minimumRepriceTime
  ) external checkRole(SwellLib.PLATFORM_ADMIN) {
    emit MinimumRepriceTimeUpdated(minimumRepriceTime, _minimumRepriceTime);

    minimumRepriceTime = _minimumRepriceTime;
  }

  function setMaximumRepriceswETHDifferencePercentage(
    uint256 _maximumRepriceswETHDifferencePercentage
  ) external checkRole(SwellLib.PLATFORM_ADMIN) {
    emit MaximumRepriceswETHDifferencePercentageUpdated(
      maximumRepriceswETHDifferencePercentage,
      _maximumRepriceswETHDifferencePercentage
    );

    maximumRepriceswETHDifferencePercentage = _maximumRepriceswETHDifferencePercentage;
  }

  function setMaximumRepriceDifferencePercentage(
    uint256 _maximumRepriceDifferencePercentage
  ) external checkRole(SwellLib.PLATFORM_ADMIN) {
    emit MaximumRepriceDifferencePercentageUpdated(
      maximumRepriceDifferencePercentage,
      _maximumRepriceDifferencePercentage
    );

    maximumRepriceDifferencePercentage = _maximumRepriceDifferencePercentage;
  }

  function swETHToETHRate() external view override returns (uint256) {
    return _swETHToETHRate().unwrap();
  }

  function ethToSwETHRate() external view override returns (uint256) {
    return _ethToSwETHRate().unwrap();
  }

  function getRate() external view override returns (uint256) {
    // This method is identical to swETHToETHRate but is required for the Balancer Metastable pools. Keeping this and the swETHToETHRate method because the swETHToETHRate method is more readable for integrations.
    return _swETHToETHRate().unwrap();
  }

  function deposit() external payable override checkWhitelist(msg.sender) {
    if (AccessControlManager.coreMethodsPaused()) {
      revert SwellLib.CoreMethodsPaused();
    }

    if (msg.value == 0) {
      revert SwellLib.InvalidETHDeposit();
    }

    uint256 swETHAmount = wrap(msg.value).mul(_ethToSwETHRate()).unwrap();

    _mint(msg.sender, swETHAmount);

    totalETHDeposited += msg.value;

    AddressUpgradeable.sendValue(
      payable(address(AccessControlManager.DepositManager())),
      msg.value
    );

    emit ETHDepositReceived(
      msg.sender,
      msg.value,
      swETHAmount,
      totalETHDeposited
    );
  }

  function reprice(
    uint256 _preRewardETHReserves,
    uint256 _newETHRewards,
    uint256 _swETHTotalSupply
  ) external override checkRole(SwellLib.BOT) {
    if (AccessControlManager.botMethodsPaused()) {
      revert SwellLib.BotMethodsPaused();
    }

    uint256 currSupply = totalSupply();

    if (_swETHTotalSupply == 0 || currSupply == 0) {
      revert CannotRepriceWithZeroSwETHSupply();
    }

    if (_preRewardETHReserves == 0) {
      revert InvalidPreRewardETHReserves();
    }

    uint256 timeSinceLastReprice = block.timestamp - lastRepriceUNIX;

    if (timeSinceLastReprice < minimumRepriceTime) {
      revert NotEnoughTimeElapsedForReprice(
        minimumRepriceTime - timeSinceLastReprice
      );
    }

    uint256 totalReserves = _preRewardETHReserves + _newETHRewards;

    uint256 rewardPercentageTotal = swellTreasuryRewardPercentage +
      nodeOperatorRewardPercentage;

    UD60x18 rewardsInETH = wrap(_newETHRewards).mul(
      wrap(rewardPercentageTotal)
    );

    UD60x18 rewardsInSwETH = wrap(_swETHTotalSupply).mul(rewardsInETH).div(
      wrap(_preRewardETHReserves - rewardsInETH.unwrap() + _newETHRewards)
    );

    // Also including the amount of new swETH that was minted alongside the provided swETH total supply
    uint256 updatedSwETHToETHRateFixed = wrap(totalReserves)
      .div(wrap(_swETHTotalSupply + rewardsInSwETH.unwrap()))
      .unwrap();

    // Ensure that the reprice differences are within expected ranges, only if the reprice method has been called before
    if (lastRepriceUNIX != 0) {
      // Check repricing rate difference
      uint256 repriceDiff = _absolute(
        updatedSwETHToETHRateFixed,
        swETHToETHRateFixed
      );

      uint256 maximumRepriceDiff = wrap(swETHToETHRateFixed)
        .mul(wrap(maximumRepriceDifferencePercentage))
        .unwrap();

      if (repriceDiff > maximumRepriceDiff) {
        revert RepriceDifferenceTooLarge(repriceDiff, maximumRepriceDiff);
      }
    }

    // Check swETH supply provided with actual current supply
    uint256 swETHSupplyDiff = _absolute(currSupply, _swETHTotalSupply);

    uint256 maximumswETHDiff = (currSupply *
      maximumRepriceswETHDifferencePercentage) / 1 ether;

    if (swETHSupplyDiff > maximumswETHDiff) {
      revert RepriceswETHDifferenceTooLarge(swETHSupplyDiff, maximumswETHDiff);
    }

    uint256 nodeOperatorRewards;
    uint256 swellTreasuryRewards;

    if (rewardsInSwETH.unwrap() != 0) {
      _mint(address(this), rewardsInSwETH.unwrap());

      UD60x18 nodeOperatorRewardPortion = wrap(nodeOperatorRewardPercentage)
        .div(wrap(rewardPercentageTotal));

      nodeOperatorRewards = nodeOperatorRewardPortion
        .mul(rewardsInSwETH)
        .unwrap();

      if (nodeOperatorRewards != 0) {
        INodeOperatorRegistry nodeOperatorRegistry = AccessControlManager
          .NodeOperatorRegistry();

        uint128 totalOperators = nodeOperatorRegistry.numOperators();

        UD60x18 totalActiveValidators = wrap(
          nodeOperatorRegistry.getPoRAddressListLength()
        );

        if (totalActiveValidators.unwrap() == 0) {
          revert NoActiveValidators();
        }

        // Operator Id's start at 1
        for (uint128 i = 1; i <= totalOperators; ) {
          (
            address rewardAddress,
            uint256 operatorActiveValidators
          ) = nodeOperatorRegistry.getRewardDetailsForOperatorId(i);

          if (operatorActiveValidators != 0) {
            uint256 operatorsRewardShare = wrap(operatorActiveValidators)
              .div(totalActiveValidators)
              .mul(wrap(nodeOperatorRewards))
              .unwrap();

            _transfer(address(this), rewardAddress, operatorsRewardShare);
          }

          // Will never overflow as the total operators are capped at uint128
          unchecked {
            ++i;
          }
        }
      }

      // Transfer the remaining tokens to the treasury, this includes the swell treasury percentage and if there are any remainder tokens after NO distribution
      swellTreasuryRewards = balanceOf(address(this));

      if (swellTreasuryRewards != 0) {
        _transfer(
          address(this),
          AccessControlManager.SwellTreasury(),
          swellTreasuryRewards
        );
      }
    }

    lastRepriceETHReserves = totalReserves;
    lastRepriceUNIX = block.timestamp;
    swETHToETHRateFixed = updatedSwETHToETHRateFixed;

    emit Reprice(
      lastRepriceETHReserves,
      swETHToETHRateFixed,
      nodeOperatorRewards,
      swellTreasuryRewards,
      totalETHDeposited
    );
  }

  // ************************************
  // ***** Internal methods ******

  /**
   * @dev Returns the ETH -> swETH rate, if no PoR reading has come through the rate is 1:1
   * @return The rate as a fixed-point type
   */
  function _ethToSwETHRate() internal view returns (UD60x18) {
    return wrap(1 ether).div(_swETHToETHRate());
  }

  /**
   * @dev Returns the swETH -> ETH rate, if no PoR reading has come in the rate is 1:1
   * @return The rate as a fixed-point type
   */
  function _swETHToETHRate() internal view returns (UD60x18) {
    if (swETHToETHRateFixed == 0) {
      return wrap(1 ether);
    }

    return wrap(swETHToETHRateFixed);
  }

  /**
   * @dev Returns the absolute difference between two uint256 values
   */
  function _absolute(uint256 _a, uint256 _b) internal pure returns (uint256) {
    if (_a < _b) {
      return _b - _a;
    }

    return _a - _b;
  }
}

// File: contracts/implementations/Whitelist.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity 0.8.16;

import {Initializable} from "@openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol";

import {IAccessControlManager} from "../interfaces/IAccessControlManager.sol";
import {IWhitelist} from "../interfaces/IWhitelist.sol";

import {SwellLib} from "../libraries/SwellLib.sol";

/**
  @title Whitelist
  @author https://github.com/max-taylor 
  @dev Contract to manage a whitelist, used in the swETH contract to handle allowed depositors
*/
contract Whitelist is Initializable, IWhitelist {
  IAccessControlManager public AccessControlManager;

  mapping(address => bool) public override whitelistedAddresses;

  bool public override whitelistEnabled;

  /// @custom:oz-upgrades-unsafe-allow constructor
  constructor() {
    _disableInitializers();
  }

  /**
   * @dev Modifier to check for empty addresses
   * @param _address The address to check
   */
  modifier checkZeroAddress(address _address) {
    SwellLib._checkZeroAddress(_address);

    _;
  }

  /**
   * Helper to check the sender against the given role
   * @param role The role to check for the msg.sender
   */
  modifier checkRole(bytes32 role) {
    AccessControlManager.checkRole(role, msg.sender);

    _;
  }

  /**
   * @dev Method checks if the whitelist is enabled and also whether the address is in the whitelist, reverting if true.
   * @param _address The address to check in the whitelist
   */
  modifier checkWhitelist(address _address) {
    if (whitelistEnabled && !whitelistedAddresses[_address]) {
      revert NotInWhitelist();
    }

    _;
  }

  /**
   * @dev This contract is intended to be inherited from a parent contract, so using an onlyInitializing modifier to allow that.
   * @param _accessControlManager The access control manager to use for role management
   */
  function __Whitelist_init(
    IAccessControlManager _accessControlManager
  ) internal onlyInitializing checkZeroAddress(address(_accessControlManager)) {
    AccessControlManager = _accessControlManager;

    whitelistEnabled = true;
  }

  // ************************************
  // ***** External methods ******

  function addToWhitelist(
    address _address
  ) external override checkRole(SwellLib.PLATFORM_ADMIN) {
    _checkAndAddToWhitelist(_address);
  }

  function batchAddToWhitelist(
    address[] calldata _addresses
  ) external checkRole(SwellLib.PLATFORM_ADMIN) {
    for (uint256 i; i < _addresses.length; ) {
      _checkAndAddToWhitelist(_addresses[i]);

      unchecked {
        ++i;
      }
    }
  }

  function removeFromWhitelist(
    address _address
  ) external override checkRole(SwellLib.PLATFORM_ADMIN) {
    _checkAndRemoveFromWhitelist(_address);
  }

  function batchRemoveFromWhitelist(
    address[] calldata _addresses
  ) external checkRole(SwellLib.PLATFORM_ADMIN) {
    for (uint256 i; i < _addresses.length; ) {
      _checkAndRemoveFromWhitelist(_addresses[i]);

      unchecked {
        ++i;
      }
    }
  }

  function enableWhitelist()
    external
    override
    checkRole(SwellLib.PLATFORM_ADMIN)
  {
    if (whitelistEnabled) {
      revert WhitelistAlreadyEnabled();
    }

    whitelistEnabled = true;

    emit WhitelistEnabled();
  }

  function disableWhitelist()
    external
    override
    checkRole(SwellLib.PLATFORM_ADMIN)
  {
    if (!whitelistEnabled) {
      revert WhitelistAlreadyDisabled();
    }

    whitelistEnabled = false;

    emit WhitelistDisabled();
  }

  // ************************************
  // ***** Internal methods ******

  /**
   * @dev This method checks if the given address is the zero address or is in the whitelist already, reverting if true; otherwise the address is added and an event is emitted
   * @param _address The address to check and add to the whitelist
   */
  function _checkAndAddToWhitelist(address _address) internal {
    SwellLib._checkZeroAddress(_address);

    if (whitelistedAddresses[_address]) {
      revert AddressAlreadyInWhitelist(_address);
    }

    whitelistedAddresses[_address] = true;

    emit AddedToWhitelist(_address);
  }

  /**
   * @dev This method checks if the address doesn't exist within the whitelist and reverts if true, otherwise the address is removed from the whitelist and an event is emitted
   * @param _address The address to check and remove from the whitelist
   */
  function _checkAndRemoveFromWhitelist(address _address) internal {
    if (!whitelistedAddresses[_address]) {
      revert AddressMissingFromWhitelist(_address);
    }

    whitelistedAddresses[_address] = false;

    emit RemovedFromWhitelist(_address);
  }

  /**
   * @dev Gap for upgrades
   */
  uint256[45] private __gap;
}

// File: contracts/interfaces/IAccessControlManager.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity 0.8.16;

import {IAccessControlEnumerableUpgradeable} from "@openzeppelin/contracts-upgradeable/access/IAccessControlEnumerableUpgradeable.sol";
import {IERC20} from "@openzeppelin/contracts/token/ERC20/IERC20.sol";

import {IDepositManager} from "./IDepositManager.sol";
import {IswETH} from "./IswETH.sol";
import {INodeOperatorRegistry} from "./INodeOperatorRegistry.sol";

/**
  @title IAccessControlManager
  @author https://github.com/max-taylor 
  @dev The interface for the Access Control Manager, which manages roles and permissions for contracts within the Swell ecosystem
*/
interface IAccessControlManager is IAccessControlEnumerableUpgradeable {
  // ***** Structs ******

  /**
    @dev Parameters for initializing the contract.
    @param admin The admin address
    @param swellTreasury The swell treasury address
  */
  struct InitializeParams {
    address admin;
    address swellTreasury;
  }

  // ***** Errors ******

  /**
    @dev Error thrown when attempting to pause an already-paused boolean
  */
  error AlreadyPaused();

  /**
    @dev Error thrown when attempting to unpause an already-unpaused boolean
  */
  error AlreadyUnpaused();

  // ***** Events ******

  /**
    @dev Emitted when a new DepositManager contract address is set.
    @param newAddress The new DepositManager contract address.
    @param oldAddress The old DepositManager contract address.
  */
  event UpdatedDepositManager(address newAddress, address oldAddress);

  /**
    @dev Emitted when a new NodeOperatorRegistry contract address is set.
    @param newAddress The new NodeOperatorRegistry contract address.
    @param oldAddress The old NodeOperatorRegistry contract address.
  */
  event UpdatedNodeOperatorRegistry(address newAddress, address oldAddress);

  /**
    @dev Emitted when a new SwellTreasury contract address is set.
    @param newAddress The new SwellTreasury contract address.
    @param oldAddress The old SwellTreasury contract address.
  */
  event UpdatedSwellTreasury(address newAddress, address oldAddress);

  /**
    @dev Emitted when a new SwETH contract address is set.
    @param newAddress The new SwETH contract address.
    @param oldAddress The old SwETH contract address.
  */
  event UpdatedSwETH(address newAddress, address oldAddress);

  /**
    @dev Emitted when core methods functionality is paused or unpaused.
    @param newPausedStatus The new paused status.
  */
  event CoreMethodsPause(bool newPausedStatus);

  /**
    @dev Emitted when bot methods functionality is paused or unpaused.
    @param newPausedStatus The new paused status.
  */
  event BotMethodsPause(bool newPausedStatus);

  /**
    @dev Emitted when operator methods functionality is paused or unpaused.
    @param newPausedStatus The new paused status.
  */
  event OperatorMethodsPause(bool newPausedStatus);

  /**
    @dev Emitted when withdrawals functionality is paused or unpaused.
    @param newPausedStatus The new paused status.
  */
  event WithdrawalsPause(bool newPausedStatus);

  // ************************************
  // ***** External Methods ******

  /**
   * @dev Pass-through method to call the _checkRole method on the inherited access control contract. This method is to be used by external contracts that are using this centralised access control manager, this ensures that if the check fails it reverts with the correct access control error message
   * @param role The role to check
   * @param account The account to check for
   */
  function checkRole(bytes32 role, address account) external view;

  // ***** Setters ******

  /**
   * @notice Sets the `swETH` address to `_swETH`.
   * @dev This function is only callable by the `PLATFORM_ADMIN` role.
   * @param _swETH The address of the `swETH` contract.
   */
  function setSwETH(IswETH _swETH) external;

  /**
   * @notice Sets the `DepositManager` address to `_depositManager`.
   * @dev This function is only callable by the `PLATFORM_ADMIN` role.
   * @param _depositManager The address of the `DepositManager` contract.
   */
  function setDepositManager(IDepositManager _depositManager) external;

  /**
   * @notice Sets the `NodeOperatorRegistry` address to `_NodeOperatorRegistry`.
   * @dev This function is only callable by the `PLATFORM_ADMIN` role.
   * @param _NodeOperatorRegistry The address of the `NodeOperatorRegistry` contract.
   */
  function setNodeOperatorRegistry(
    INodeOperatorRegistry _NodeOperatorRegistry
  ) external;

  /**
   * @notice Sets the `SwellTreasury` address to `_swellTreasury`.
   * @dev This function is only callable by the `PLATFORM_ADMIN` role.
   * @param _swellTreasury The new address of the `SwellTreasury` contract.
   */
  function setSwellTreasury(address _swellTreasury) external;

  // ***** Getters ******

  /**
    @dev Returns the PLATFORM_ADMIN role.
    @return The bytes32 representation of the PLATFORM_ADMIN role.
  */
  function PLATFORM_ADMIN() external pure returns (bytes32);

  /**
    @dev Returns the Swell ETH contract.
    @return The Swell ETH contract.
  */
  function swETH() external returns (IswETH);

  /**
    @dev Returns the address of the Swell Treasury contract.
    @return The address of the Swell Treasury contract.
  */
  function SwellTreasury() external returns (address);

  /**
    @dev Returns the Deposit Manager contract.
    @return The Deposit Manager contract.
  */
  function DepositManager() external returns (IDepositManager);

  /**
    @dev Returns the Node Operator Registry contract.
    @return The Node Operator Registry contract.
  */
  function NodeOperatorRegistry() external returns (INodeOperatorRegistry);

  /**
    @dev Returns true if core methods are currently paused.
    @return Whether core methods are paused.
  */
  function coreMethodsPaused() external returns (bool);

  /**
    @dev Returns true if bot methods are currently paused.
    @return Whether bot methods are paused.
  */
  function botMethodsPaused() external returns (bool);

  /**
    @dev Returns true if operator methods are currently paused.
    @return Whether operator methods are paused.
  */
  function operatorMethodsPaused() external returns (bool);

  /**
    @dev Returns true if withdrawals are currently paused.
    @dev ! Note that this is completely unused in the current implementation and is a placeholder that will be used once the withdrawals are implemented.
    @return Whether withdrawals are paused.
  */
  function withdrawalsPaused() external returns (bool);

  // ***** Pausable methods ******

  /**
    @dev Pauses the core methods of the Swell ecosystem, only callable by the PLATFORM_ADMIN
  */
  function pauseCoreMethods() external;

  /**
    @dev Unpauses the core methods of the Swell ecosystem, only callable by the PLATFORM_ADMIN
  */
  function unpauseCoreMethods() external;

  /**
    @dev Pauses the bot specific methods, only callable by the PLATFORM_ADMIN
  */
  function pauseBotMethods() external;

  /**
    @dev Unpauses the bot specific methods, only callable by the PLATFORM_ADMIN
  */
  function unpauseBotMethods() external;

  /**
    @dev Pauses the operator methods in the NO registry contract, only callable by the PLATFORM_ADMIN
  */
  function pauseOperatorMethods() external;

  /**
    @dev Unpauses the operator methods in the NO registry contract, only callable by the PLATFORM_ADMIN
  */
  function unpauseOperatorMethods() external;

  /**
    @dev Pauses the withdrawals of the Swell ecosystem, only callable by the PLATFORM_ADMIN
  */
  function pauseWithdrawals() external;

  /**
    @dev Unpauses the withdrawals of the Swell ecosystem, only callable by the PLATFORM_ADMIN
  */
  function unpauseWithdrawals() external;

  /**
   * @dev This method withdraws contract's _token balance to a platform admin
   * @param _token The ERC20 token to withdraw from the contract
   */
  function withdrawERC20(IERC20 _token) external;
}

// File: contracts/interfaces/IDepositManager.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity 0.8.16;

import {IERC20} from "@openzeppelin/contracts/token/ERC20/IERC20.sol";

/**
 * @title IDepositManager
 * @author https://github.com/max-taylor
 * @notice The interface for the deposit manager contract
 */
interface IDepositManager {
  // ***** Errors ******

  /**
   * @dev Error thrown when calling the withdrawETH method from an account that isn't the swETH contract
   */
  error InvalidETHWithdrawCaller();

  /**
   * @dev Error thrown when the depositDataRoot parameter in the setupValidators contract doesn't match the onchain deposit data root from the deposit contract
   */
  error InvalidDepositDataRoot();

  /**
   * @dev Error thrown when setting up new validators and the contract doesn't hold enough ETH to be able to set them up.
   */
  error InsufficientETHBalance();

  // ***** Events ******

  /**
   * Emitted when new validators are setup
   * @param pubKeys The pubKeys that have been used for validator setup
   */
  event ValidatorsSetup(bytes[] pubKeys);

  /**
   * @dev Event is fired when some contracts receive ETH
   * @param from The account that sent the ETH
   * @param amount The amount of ETH received
   */
  event ETHReceived(address indexed from, uint256 amount);

  // ************************************
  // ***** External methods ******

  /**
   * @dev This method withdraws contract's _token balance to a platform admin
   * @param _token The ERC20 token to withdraw from the contract
   */
  function withdrawERC20(IERC20 _token) external;

  /**
   * @dev Formats ETH1 the withdrawal credentials according to the following standard: https://github.com/ethereum/consensus-specs/blob/dev/specs/phase0/validator.md#eth1_address_withdrawal_prefix
   * @dev It doesn't outline the withdrawal prefixes, they can be found here: https://eth2book.info/altair/part3/config/constants#withdrawal-prefixes
   * @dev As the DepositManager on the execution layer is going to be the withdrawal contract, we will be doing ETH1 withdrawals. The standard for this is a 32 byte response where; the first byte stores the withdrawal prefix (0x01), the following 11 bytes are empty and the last 20 bytes are the address
   */
  function getWithdrawalCredentials()
    external
    view
    returns (bytes memory withdrawalCredentials);

  /**
   * @dev This method allows setting up of new validators in the beacon deposit contract, it ensures the provided pubKeys are unused in the NO registry
   * @notice An off-chain service provides front-running protection by validating each pubKey ensuring that it hasn't been used for a validator setup. This service snapshots the depositDataRoot of the deposit contract, then this value is re-read from the deposit contract within setupValdiators() and ensures that they match, this consistency provides the front-running protection. Read more here: https://research.lido.fi/t/mitigations-for-deposit-front-running-vulnerability/1239
   * @param _pubKeys The pubKeys to setup
   * @param _depositDataRoot The deposit contracts deposit root which MUST match the current beacon deposit contract deposit data root otherwise the contract will revert due to the risk of the front-running vulnerability.
   */
  function setupValidators(
    bytes[] calldata _pubKeys,
    bytes32 _depositDataRoot
  ) external;
}

// File: contracts/interfaces/INodeOperatorRegistry.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity 0.8.16;

import {IERC20} from "@openzeppelin/contracts/token/ERC20/IERC20.sol";

import {IAccessControlManager} from "../interfaces/IAccessControlManager.sol";

import {IPoRAddresses} from "../vendors/IPoRAddresses.sol";

/**
 * @title INodeOperatorRegistry
 * @author https://github.com/max-taylor
 * @notice Interface for the Node Operator Registry contract.
 */
interface INodeOperatorRegistry is IPoRAddresses {
  /**
   * @dev  Struct containing the required details to setup a validator on the beacon chain
   * @param pubKey Public key of the validator
   * @param signature The signature of the validator
   */
  struct ValidatorDetails {
    bytes pubKey;
    bytes signature;
  }

  /**
   * @dev  Struct containing operator details
   * @param enabled Flag indicating if the operator is enabled or disabled
   * @param rewardAddress Address to sending repricing rewards to
   * @param controllingAddress The address that can control the operator account
   * @param name The name of the operator
   * @param activeValidators The amount of active validators for the operator
   */
  struct Operator {
    bool enabled;
    address rewardAddress;
    address controllingAddress;
    string name;
    uint128 activeValidators;
  }

  // ***** Events *****
  /**
   * @dev  Emitted when a new operator is added.
   * @param operatorAddress  The address of the newly added operator.
   * @param rewardAddress    The address associated with the reward for the operator.
   */
  event OperatorAdded(address operatorAddress, address rewardAddress);

  /**
   * @dev  Emitted when an operator is enabled.
   * @param operator  The address of the operator that was enabled.
   */
  event OperatorEnabled(address indexed operator);

  /**
   * @dev  Emitted when an operator is disabled.
   * @param operator  The address of the operator that was disabled.
   */
  event OperatorDisabled(address indexed operator);

  /**
   * @dev  Emitted when the validator details for an operator are added.
   * @param operator  The address of the operator for which the validator details were added.
   * @param pubKeys   An array of `ValidatorDetails` for the operator.
   */
  event OperatorAddedValidatorDetails(
    address indexed operator,
    ValidatorDetails[] pubKeys
  );

  /**
   * @dev  Emitted when active public keys are deleted.
   * @param pubKeys  An array of public keys that were deleted.
   */
  event ActivePubKeysDeleted(bytes[] pubKeys);

  /**
   * @dev  Emitted when pending public keys are deleted.
   * @param pubKeys  An array of public keys that were deleted.
   */
  event PendingPubKeysDeleted(bytes[] pubKeys);

  /**
   * @dev  Emitted when public keys are used for validator setup.
   * @param pubKeys  An array of public keys that were used for validator setup.
   */
  event PubKeysUsedForValidatorSetup(bytes[] pubKeys);

  // ***** Errors *****
  /**
   * @dev Thrown when an operator is not found.
   * @param operator  The address of the operator that was not found.
   */
  error NoOperatorFound(address operator);

  /**
   * @dev Thrown when an operator already exists.
   * @param operator The address of the operator that already exists.
   */
  error OperatorAlreadyExists(address operator);

  /**
   * @dev Thrown when an operator is already enabled.
   */
  error OperatorAlreadyEnabled();

  /**
   * @dev Thrown when an operator is already disabled.
   */
  error OperatorAlreadyDisabled();

  /**
   * @dev Thrown when an array length of zero is invalid.
   */
  error InvalidArrayLengthOfZero();

  /**
   * @dev Thrown when an operator is adding new validator details and this causes the total amount of operator's validator details to exceed uint128
   */
  error AmountOfValidatorDetailsExceedsLimit();

  /**
   * @dev Thrown during setup of new validators, when comparing the next operator's public key to the provided public key they should match. This ensures consistency in the tracking of the active and pending validator details.
   * @param foundPubKey The operator's next available public key
   * @param providedPubKey The public key that was passed in as an argument
   */
  error NextOperatorPubKeyMismatch(bytes foundPubKey, bytes providedPubKey);

  /**
   * @dev Thrown during the setup of new validators and when the operator that has no pending details left to use
   */
  error OperatorOutOfPendingKeys();

  /**
   * @dev Thrown when the given pubKey hasn't been added to the registry and cannot be found
   * @param pubKey  The public key that was not found.
   */
  error NoPubKeyFound(bytes pubKey);

  /**
   * @dev Thrown when an operator tries to use the node operator registry whilst they are disabled
   */
  error CannotUseDisabledOperator();

  /**
   * @dev Thrown when a duplicate public key is added.
   * @param existingKey  The public key that already exists.
   */
  error CannotAddDuplicatePubKey(bytes existingKey);

  /**
   * @dev Thrown when the given pubKey doesn't exist in the pending validator details sets
   * @param pubKey  The missing pubKey
   */
  error MissingPendingValidatorDetails(bytes pubKey);

  /**
   * @dev Thrown when the pubKey doesn't exist in the active validator details set
   * @param pubKey  The missing pubKey
   */
  error MissingActiveValidatorDetails(bytes pubKey);

  /**
   * @dev Throw when the msg.sender isn't the Deposit Manager contract
   */
  error InvalidPubKeySetupCaller();

  /**
   * @dev Thrown when an operator is trying to add validator details and a provided pubKey isn't the correct length
   */
  error InvalidPubKeyLength();

  /**
   * @dev Thrown when an operator is trying to add validator details and a provided signature isn't the correct length
   */
  error InvalidSignatureLength();

  // ************************************
  // ***** External  methods ******

  /**
   * @dev This method withdraws contract's _token balance to a platform admin
   * @param _token The ERC20 token to withdraw from the contract
   */
  function withdrawERC20(IERC20 _token) external;

  /**
   * @dev  Gets the next available validator details, ordered by operators with the least amount of active validators. There may be less available validators then the provided _numNewValidators amount, in that case the function will return an array of length equal to _numNewValidators but all indexes after the second return value; foundValidators, will be 0x0 values
   * @param _numNewValidators The number of new validators to get details for.
   * @return An array of ValidatorDetails and the length of the array of non-zero validator details
   * @notice This method tries to return enough validator details to equal the provided _numNewValidators, but if there aren't enough validator details to find, it will simply return what it found, and the caller will need to check for empty values.
   */
  function getNextValidatorDetails(
    uint256 _numNewValidators
  ) external view returns (ValidatorDetails[] memory, uint256 foundValidators);

  /**
   * @dev  Allows the DepositManager to move provided _pubKeys from the pending validator details arrays into the active validator details array. It also returns the validator details, so that the DepositManager can pass the signature along to the ETH2 deposit contract.
   * @param _pubKeys Array of public keys to use for validator setup.
   * @return validatorDetails The associated validator details for the given public keys
   * @notice This method will be called when the DepositManager is setting up new validators.
   */
  function usePubKeysForValidatorSetup(
    bytes[] calldata _pubKeys
  ) external returns (ValidatorDetails[] memory validatorDetails);

  // ** Operator management methods **

  /**
   * @dev  Adds new validator details to the registry.
  /**
   * @dev  Callable by node operator's to add their validator details to the setup queue
   * @param _validatorDetails Array of ValidatorDetails to add.
  */
  function addNewValidatorDetails(
    ValidatorDetails[] calldata _validatorDetails
  ) external;

  // ** PLATFORM_ADMIN management methods **

  /**
   * @dev  Adds a new operator to the registry.
   * @param _name Name of the operator.
   * @param _operatorAddress Address of the operator.
   * @param _rewardAddress Address of the reward recipient for this operator.
   * @notice Throws if an operator already exists with the given _operatorAddress
   */
  function addOperator(
    string calldata _name,
    address _operatorAddress,
    address _rewardAddress
  ) external;

  /**
   * @dev  Enables an operator in the registry.
   * @param _operatorAddress Address of the operator to enable.
   * @notice Throws NoOperatorFound if the operator address is not found in the registry
   */
  function enableOperator(address _operatorAddress) external;

  /**
   * @dev  Disables an operator in the registry.
   * @param _operatorAddress Address of the operator to disable.
   * @notice Throws NoOperatorFound if the operator address is not found in the registry
   */
  function disableOperator(address _operatorAddress) external;

  /**
   * @dev  Updates the controlling address of an operator in the registry.
   * @param _operatorAddress Current address of the operator.
   * @param _newOperatorAddress New address of the operator.
   * @notice Throws NoOperatorFound if the operator address is not found in the registry
   */
  function updateOperatorControllingAddress(
    address _operatorAddress,
    address _newOperatorAddress
  ) external;

  /**
   * @dev  Updates the reward address of an operator in the registry.
   * @param _operatorAddress Address of the operator to update.
   * @param _newRewardAddress New reward address for the operator.
   * @notice Throws NoOperatorFound if the operator address is not found in the registry
   */
  function updateOperatorRewardAddress(
    address _operatorAddress,
    address _newRewardAddress
  ) external;

  /**
   * @dev  Updates the name of an operator in the registry
   * @param _operatorAddress The address of the operator to update
   * @param _name The new name for the operator
   * @notice Throws NoOperatorFound if the operator address is not found in the registry
   */
  function updateOperatorName(
    address _operatorAddress,
    string calldata _name
  ) external;

  /**
   * @dev  Allows the PLATFORM_ADMIN to delete validators that are pending. This is likely to be called via an admin if a public key fails the front-running checks
   * @notice Throws InvalidArrayLengthOfZero if the length of _pubKeys is 0
   * @notice Throws NoPubKeyFound if any of the provided pubKeys is not found in the pending validators set
   * @param _pubKeys The public keys of the pending validators to delete
   */
  function deletePendingValidators(bytes[] calldata _pubKeys) external;

  /**
   * @dev  Allows the PLATFORM_ADMIN to delete validator public keys that have been used to setup a validator and that validator has now exited
   * @notice Throws NoPubKeyFound if any of the provided pubKeys is not found in the active validators set
   * @notice Throws InvalidArrayLengthOfZero if the length of _pubKeys is 0
   * @param _pubKeys The public keys of the active validators to delete
   */
  function deleteActiveValidators(bytes[] calldata _pubKeys) external;

  /**
   * @dev  Returns the address of the AccessControlManager contract
   */
  function AccessControlManager() external returns (IAccessControlManager);

  /**
   * @dev  Returns the operator details for a given operator address
   * @notice Throws NoOperatorFound if the operator address is not found in the registry
   * @param _operatorAddress The address of the operator to retrieve
   * @return operator The operator details, including name, reward address, and enabled status
   * @return totalValidatorDetails The total amount of validator details for an operator
   * @return operatorId The operator's Id
   */
  function getOperator(
    address _operatorAddress
  )
    external
    view
    returns (
      Operator memory operator,
      uint128 totalValidatorDetails,
      uint128 operatorId
    );

  /**
   * @dev  Returns the pending validator details for a given operator address
   * @notice Throws NoOperatorFound if the operator address is not found in the registry
   * @param _operatorAddress The address of the operator to retrieve pending validator details for
   * @return validatorDetails The pending validator details for the given operator
   */
  function getOperatorsPendingValidatorDetails(
    address _operatorAddress
  ) external returns (ValidatorDetails[] memory);

  /**
   * @dev  Returns the active validator details for a given operator address
   * @notice Throws NoOperatorFound if the operator address is not found in the registry
   * @param _operatorAddress The address of the operator to retrieve active validator details for
   * @return validatorDetails The active validator details for the given operator
   */
  function getOperatorsActiveValidatorDetails(
    address _operatorAddress
  ) external returns (ValidatorDetails[] memory validatorDetails);

  /**
   * @dev  Returns the reward details for a given operator Id, this method is used in the swETH contract when paying swETH rewards
   * @param _operatorId The operator Id to get the reward details for
   * @return rewardAddress The reward address of the operator
   * @return activeValidators The amount of active validators for the operator
   */
  function getRewardDetailsForOperatorId(
    uint128 _operatorId
  ) external returns (address rewardAddress, uint128 activeValidators);

  /**
   * @dev  Returns the number of operators in the registry
   */
  function numOperators() external returns (uint128);

  /**
   * @dev  Returns the amount of pending validator keys in the registry
   */
  function numPendingValidators() external returns (uint256);

  /**
   * @dev  Returns the operator ID for a given operator address
   * @notice Throws NoOperatorFound if the operator address is not found in the registry
   * @param _operator The address of the operator to retrieve the operator ID for
   * @return _operatorId The operator ID for the given operator
   */
  function getOperatorIdForAddress(
    address _operator
  ) external returns (uint128 _operatorId);

  /**
   * @dev Returns the `operatorId` associated with the given `pubKey`.
   * @param pubKey  The public key to lookup the `operatorId` for.
   * @notice Returns 0 if no operatorId controls the pubKey
   */
  function getOperatorIdForPubKey(
    bytes calldata pubKey
  ) external returns (uint128);
}

// File: contracts/interfaces/IswETH.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity 0.8.16;

import {IERC20Upgradeable} from "@openzeppelin/contracts-upgradeable/token/ERC20/IERC20Upgradeable.sol";
import {IERC20} from "@openzeppelin/contracts/token/ERC20/IERC20.sol";

/**
 * @title SwETH Interface
 * @author https://github.com/max-taylor
 * @dev This interface provides the methods to interact with the SwETH contract.
 */
interface IswETH is IERC20Upgradeable {
  // ***** Errors ******

  /**
   * @dev Error thrown when attempting to reprice with zero SwETH supply.
   */
  error CannotRepriceWithZeroSwETHSupply();

  /**
   * @dev Error thrown when passing a preRewardETHReserves value equal to 0 into the repricing function
   */
  error InvalidPreRewardETHReserves();

  /**
   * @dev Error thrown when repricing the rate and distributing rewards to NOs when they are no active validators. This condition should never happen; it means that no active validators were running but we still have rewards, despite this it's still here for security
   */
  error NoActiveValidators();

  /**
   * @dev Error thrown when updating the reward percentage for either the NOs or the swell treasury and the update will cause the NO percentage + swell treasury percentage to exceed 100%.
   */
  error RewardPercentageTotalOverflow();

  /**
   * @dev Thrown when calling the reprice function and not enough time has elapsed between the previous repriace and the current reprice.
   * @param remainingTime Remaining time until reprice can be called
   */
  error NotEnoughTimeElapsedForReprice(uint256 remainingTime);

  /**
   * @dev Thrown when repricing the rate and the difference in reserves values is greater than expected
   * @param repriceDiff The difference between the previous swETH rate and what would be the updated rate
   * @param maximumRepriceDiff The maximum allowed difference in swETH rate
   */
  error RepriceDifferenceTooLarge(
    uint256 repriceDiff,
    uint256 maximumRepriceDiff
  );

  /**
   * @dev Thrown during repricing when the difference in swETH supplied to repricing compared to the actual supply is too great
   * @param repriceswETHDiff The difference between the swETH supplied to repricing and actual supply
   * @param maximumswETHRepriceDiff The maximum allowed difference in swETH supply
   */
  error RepriceswETHDifferenceTooLarge(
    uint256 repriceswETHDiff,
    uint256 maximumswETHRepriceDiff
  );

  // ***** Events *****

  /**
   * @dev Event emitted when a user withdraws ETH for swETH
   * @param to Address of the recipient.
   * @param swETHBurned Amount of SwETH burned in the transaction.
   * @param ethReturned Amount of ETH returned in the transaction.
   */
  event ETHWithdrawn(
    address indexed to,
    uint256 swETHBurned,
    uint256 ethReturned
  );

  /**
   * @dev Event emitted when the swell treasury reward percentage is updated.
   * @dev Only callable by the platform admin
   * @param oldPercentage The previous swell treasury reward percentage.
   * @param newPercentage The new swell treasury reward percentage.
   */
  event SwellTreasuryRewardPercentageUpdate(
    uint256 oldPercentage,
    uint256 newPercentage
  );

  /**
   * @dev Event emitted when the node operator reward percentage is updated.
   * @dev Only callable by the platform admin
   * @param oldPercentage The previous node operator reward percentage.
   * @param newPercentage The new node operator reward percentage.
   */
  event NodeOperatorRewardPercentageUpdate(
    uint256 oldPercentage,
    uint256 newPercentage
  );

  /**
   * @dev Event emitted when the swETH - ETH rate is updated
   * @param newEthReserves The new ETH reserves for the swell protocol
   * @param newSwETHToETHRate The new SwETH to ETH rate.
   * @param nodeOperatorRewards The rewards for the node operator's.
   * @param swellTreasuryRewards The rewards for the swell treasury.
   * @param totalETHDeposited Current total ETH staked at time of reprice.
   */
  event Reprice(
    uint256 newEthReserves,
    uint256 newSwETHToETHRate,
    uint256 nodeOperatorRewards,
    uint256 swellTreasuryRewards,
    uint256 totalETHDeposited
  );

  /**
   * @dev Event is fired when some contracts receive ETH
   * @param from The account that sent the ETH
   * @param swETHMinted The amount of swETH minted to the caller
   * @param amount The amount of ETH received
   */
  event ETHDepositReceived(
    address indexed from,
    uint256 amount,
    uint256 swETHMinted,
    uint256 newTotalETHDeposited
  );

  /**
   * @dev Event emitted on a successful call to setMinimumRepriceTime
   * @param _oldMinimumRepriceTime The old reprice time
   * @param _newMinimumRepriceTime The new updated reprice time
   */
  event MinimumRepriceTimeUpdated(
    uint256 _oldMinimumRepriceTime,
    uint256 _newMinimumRepriceTime
  );

  /**
   * @dev Event emitted on a successful call to setMaximumRepriceswETHDifferencePercentage
   * @param _oldMaximumRepriceswETHDifferencePercentage The old maximum swETH supply difference
   * @param _newMaximumRepriceswETHDifferencePercentage The new updated swETH supply difference
   */
  event MaximumRepriceswETHDifferencePercentageUpdated(
    uint256 _oldMaximumRepriceswETHDifferencePercentage,
    uint256 _newMaximumRepriceswETHDifferencePercentage
  );

  /**
   * @dev Event emitted on a successful call to setMaximumRepriceDifferencePercentage
   * @param _oldMaximumRepriceDifferencePercentage The old maximum reprice difference
   * @param _newMaximumRepriceDifferencePercentage The new updated maximum reprice difference
   */
  event MaximumRepriceDifferencePercentageUpdated(
    uint256 _oldMaximumRepriceDifferencePercentage,
    uint256 _newMaximumRepriceDifferencePercentage
  );

  // ************************************
  // ***** External Methods ******

  /**
   * @dev This method withdraws contract's _token balance to a platform admin
   * @param _token The ERC20 token to withdraw from the contract
   */
  function withdrawERC20(IERC20 _token) external;

  /**
   * @dev Returns the ETH reserves that were provided in the most recent call to the reprice function
   * @return The last recorded ETH reserves
   */
  function lastRepriceETHReserves() external returns (uint256);

  /**
   * @dev Returns the last time the reprice method was called in UNIX
   * @return The UNIX timestamp of the last time reprice was called
   */
  function lastRepriceUNIX() external returns (uint256);

  /**
   * @dev Returns the total ETH that has been deposited over the protocols lifespan
   * @return The current total amount of ETH that has been deposited
   */
  function totalETHDeposited() external returns (uint256);

  /**
   * @dev Returns the current swell treasury reward percentage.
   * @return The current swell treasury reward percentage.
   */
  function swellTreasuryRewardPercentage() external returns (uint256);

  /**
   * @dev Returns the current node operator reward percentage.
   * @return The current node operator reward percentage.
   */
  function nodeOperatorRewardPercentage() external returns (uint256);

  /**
   * @dev Returns the current SwETH to ETH rate, returns 1:1 if no reprice has occurred otherwise it returns the swETHToETHRateFixed rate.
   * @return The current SwETH to ETH rate.
   */
  function swETHToETHRate() external returns (uint256);

  /**
   * @dev Returns the current ETH to SwETH rate.
   * @return The current ETH to SwETH rate.
   */
  function ethToSwETHRate() external returns (uint256);

  /**
   * @dev Returns the minimum reprice time
   * @return The minimum reprice time
   */
  function minimumRepriceTime() external returns (uint256);

  /**
   * @dev Returns the maximum percentage difference with 1e18 precision
   * @return The maximum percentage difference
   */
  function maximumRepriceDifferencePercentage() external returns (uint256);

  /**
   * @dev Returns the maximum percentage difference with 1e18 precision
   * @return The maximum percentage difference in suppled and actual swETH supply
   */
  function maximumRepriceswETHDifferencePercentage() external returns (uint256);

  /**
   * @dev Sets the new swell treasury reward percentage.
   * @notice Only a platform admin can call this function.
   * @param _newSwellTreasuryRewardPercentage The new swell treasury reward percentage to set.
   */
  function setSwellTreasuryRewardPercentage(
    uint256 _newSwellTreasuryRewardPercentage
  ) external;

  /**
   * @dev Sets the new node operator reward percentage.
   * @notice Only a platform admin can call this function.
   * @param _newNodeOperatorRewardPercentage The new node operator reward percentage to set.
   */
  function setNodeOperatorRewardPercentage(
    uint256 _newNodeOperatorRewardPercentage
  ) external;

  /**
   * @dev Sets the minimum permitted time between successful repricing calls using the block timestamp.
   * @notice Only a platform admin can call this function.
   * @param _minimumRepriceTime The new minimum time between successful repricing calls
   */
  function setMinimumRepriceTime(uint256 _minimumRepriceTime) external;

  /**
   * @dev Sets the maximum percentage allowable difference in swETH supplied to repricing compared to current swETH supply.
   * @notice Only a platform admin can call this function.
   * @param _maximumRepriceswETHDifferencePercentage The new maximum percentage swETH supply difference allowed.
   */
  function setMaximumRepriceswETHDifferencePercentage(
    uint256 _maximumRepriceswETHDifferencePercentage
  ) external;

  /**
   * @dev Sets the maximum percentage allowable difference in swETH to ETH price changes for a repricing call.
   * @notice Only a platform admin can call this function.
   * @param _maximumRepriceDifferencePercentage The new maximum percentage difference in repricing rate.
   */
  function setMaximumRepriceDifferencePercentage(
    uint256 _maximumRepriceDifferencePercentage
  ) external;

  /**
   * @dev Deposits ETH into the contract
   * @notice The amount of ETH deposited will be converted to SwETH at the current SwETH to ETH rate
   */
  function deposit() external payable;

  /**
  //  * TODO: Reword
   * @dev This method reprices the swETH -> ETH rate, this will be called via an offchain service on a regular interval, likely ~1 day. The swETH total supply is passed as an argument to avoid a potential race conditions between the off-chain reserve calculations and the on-chain repricing
   * @dev This method also mints a percentage of swETH as rewards to be claimed by NO's and the swell treasury. The formula for determining the amount of swETH to mint is the following: swETHToMint = (swETHSupply * newETHRewards * feeRate) / (preRewardETHReserves - newETHRewards * feeRate + newETHRewards)
   * @dev The formula is quite complicated because it needs to factor in the updated exchange rate whilst it calculates the amount of swETH rewards to mint. This ensures the rewards aren't double-minted and are backed by ETH.
   * @param _preRewardETHReserves The PoR value exclusive of the new ETH rewards earned
   * @param _newETHRewards The total amount of new ETH earnt over the period.
   * @param _swETHTotalSupply The total swETH supply at the time of off-chain reprice calculation
   */
  function reprice(
    uint256 _preRewardETHReserves,
    uint256 _newETHRewards,
    uint256 _swETHTotalSupply
  ) external;
}

// File: contracts/interfaces/IWhitelist.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity 0.8.16;

/**
 * @title IWhitelist
 * @author https://github.com/max-taylor
 * @dev Interface for managing a whitelist of addresses.
 */
interface IWhitelist {
  // ***** Events ******
  /**
   * @dev Emitted when an address is added to the whitelist.
   * @param _address The address that was added to the whitelist.
   */
  event AddedToWhitelist(address indexed _address);

  /**
   * @dev Emitted when an address is removed from the whitelist.
   * @param _address The address that was removed from the whitelist.
   */
  event RemovedFromWhitelist(address indexed _address);

  /**
   * @dev Emitted when the whitelist is enabled.
   */
  event WhitelistEnabled();

  /**
   * @dev Emitted when the whitelist is disabled.
   */
  event WhitelistDisabled();

  // ***** Errors ******
  /**
   * @dev Throws an error indicating that the address is already in the whitelist.
   * @param _address The address that already exists in the whitelist.
   */
  error AddressAlreadyInWhitelist(address _address);

  /**
   * @dev Throws an error indicating that the address is missing from the whitelist.
   * @param _address The address that is missing from the whitelist.
   */
  error AddressMissingFromWhitelist(address _address);

  /**
   * @dev Throws an error indicating that the whitelist is already enabled.
   */
  error WhitelistAlreadyEnabled();

  /**
   * @dev Throws an error indicating that the whitelist is already disabled.
   */
  error WhitelistAlreadyDisabled();

  /**
   * @dev Throws an error indicating that the address is not in the whitelist.
   */
  error NotInWhitelist();

  // ************************************
  // ***** External Methods ******

  /**
   * @dev Returns true if the whitelist is enabled, false otherwise.
    @return bool representing whether the whitelist is enabled.
  */
  function whitelistEnabled() external returns (bool);

  /**
   * @dev Returns true if the address is in the whitelist, false otherwise.

   * @param _address The address to check.
    @return bool representing whether the address is in the whitelist.
  */
  function whitelistedAddresses(address _address) external returns (bool);

  /**
   * @dev Adds the specified address to the whitelist, reverts if not the platform admin
   * @param _address The address to add.
   */
  function addToWhitelist(address _address) external;

  /**
   * @dev Adds the array of addresses to the whitelist, reverts if not the platform admin.
   * @param _addresses The address to add.
   */
  function batchAddToWhitelist(address[] calldata _addresses) external;

  /**
   * @dev Removes the specified address from the whitelist, reverts if not the platform admin
   * @param _address The address to remove.
   */
  function removeFromWhitelist(address _address) external;

  /**
   * @dev Removes the array of addresses from the whitelist, reverts if not the platform admin
   * @param _addresses The array of addresses to remove.
   */
  function batchRemoveFromWhitelist(address[] calldata _addresses) external;

  /**
   * @dev Enables the whitelist, allowing only whitelisted addresses to interact with the contract. Reverts if the caller is not the platform admin
   */
  function enableWhitelist() external;

  /**
   * @dev Disables the whitelist, allowing all addresses to interact with the contract. Reverts if the caller is not the platform admin
   */
  function disableWhitelist() external;
}

// File: contracts/libraries/SwellLib.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity 0.8.16;

/**
 * @title SwellLib
 * @author https://github.com/max-taylor
 * @notice This library contains roles, errors, events and functions that are widely used throughout the protocol
 */
library SwellLib {
  // ***** Roles *****
  /**
   * @dev The platform admin role
   */
  bytes32 public constant PLATFORM_ADMIN = keccak256("PLATFORM_ADMIN");

  /**
   * @dev The bot role
   */
  bytes32 public constant BOT = keccak256("BOT");

  // ***** Errors *****
  /**
   * @dev Thrown when _checkZeroAddress is called with the zero address
   */
  error CannotBeZeroAddress();

  /**
   * @dev Thrown in some contracts when the contract call is received by the fallback method
   */
  error InvalidMethodCall();

  /**
   * @dev Thrown in some contracts when ETH is sent directly to the contract
   */
  error InvalidETHDeposit();

  /**
   * @dev Thrown when interacting with a method on the protocol that is disabled via the coreMethodsPaused bool
   */
  error CoreMethodsPaused();

  /**
   * @dev Thrown when interacting with a method on the protocol that is disabled via the botMethodsPaused bool
   */
  error BotMethodsPaused();

  /**
   * @dev Thrown when interacting with a method on the protocol that is disabled via the operatorMethodsPaused bool
   */
  error OperatorMethodsPaused();

  /**
   * @dev Thrown when interacting with a method on the protocol that is disabled via the withdrawalsPaused bool
   */
  error WithdrawalsPaused();

  /**
   * @dev Thrown when calling the withdrawERC20 method and the contracts balance is 0
   */
  error NoTokensToWithdraw();

  // ************************************
  // ***** Internal Methods *****
  /**
   * @dev This helper is used throughout the protocol to guard against zero addresses being passed as parameters
   * @param _address The address to check if it is the zero address
   */
  function _checkZeroAddress(address _address) internal pure {
    if (_address == address(0)) {
      revert CannotBeZeroAddress();
    }
  }
}

// File: contracts/vendors/IPoRAddresses.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.16;

/**
 * @title Chainlink Proof-of-Reserve address list interface.
 * @notice This interface enables Chainlink nodes to get the list addresses to be used in a PoR feed. A single
 * contract that implements this interface can only store an address list for a single PoR feed.
 * @dev All functions in this interface are expected to be called off-chain, so gas usage is not a big concern.
 * This makes it possible to store addresses in optimized data types and convert them to human-readable strings
 * in `getPoRAddressList()`.
 */
interface IPoRAddresses {
  /**
   * @notice Get total number of addresses in the list.
   * @return The array length
   */
  function getPoRAddressListLength() external view returns (uint256);

  /**
   * @notice Get a batch of human-readable addresses from the address list.
   * @dev Due to limitations of gas usage in off-chain calls, we need to support fetching the addresses in batches.
   * EVM addresses need to be converted to human-readable strings. The address strings need to be in the same format
   * that would be used when querying the balance of that address.
   * @param startIndex The index of the first address in the batch.
   * @param endIndex The index of the last address in the batch. If `endIndex > getPoRAddressListLength()-1`,
   * endIndex need to default to `getPoRAddressListLength()-1`. If `endIndex < startIndex`, the result would be an
   * empty array.
   * @return Array of addresses as strings.
   */
  function getPoRAddressList(
    uint256 startIndex,
    uint256 endIndex
  ) external view returns (string[] memory);
}

// File: contracts/vendors/IRateProvider.sol



// SPDX-License-Identifier: UNLICENSED
pragma solidity 0.8.16;

/**
 * @title IRateProvider
 * @notice This interface ensure compatibility with Balancer's Metastable pools, the getRate() method is used as the pool rate. This reduces arbitrages whenever the swETH rate increases from a repricing event.
 * @dev https://github.com/balancer-labs/metastable-rate-providers/blob/master/contracts/interfaces/IRateProvider.sol
 */
interface IRateProvider {
  function getRate() external view returns (uint256);
}