// File: contracts/vaults/SpiceFiNFTFactory.sol



// SPDX-License-Identifier: BUSL-1.1
pragma solidity 0.8.17;

import "@openzeppelin/contracts/access/AccessControlEnumerable.sol";
import "@openzeppelin/contracts/proxy/beacon/BeaconProxy.sol";
import "@openzeppelin/contracts-upgradeable/utils/StringsUpgradeable.sol";

/**
 * @title SpiceFiNFTFactory
 * @author Spice Finance Inc
 */
contract SpiceFiNFTFactory is AccessControlEnumerable {
    using StringsUpgradeable for uint256;

    /// @notice Beacon address
    address public immutable beacon;

    /// @notice Spice dev wallet
    address public dev;

    /// @notice Spice Multisig address
    address public multisig;

    /// @notice Fee recipient address
    address public feeRecipient;

    /*************/
    /* Constants */
    /*************/

    /// @notice Asset role
    bytes32 public constant ASSET_ROLE = keccak256("ASSET_ROLE");

    /// @notice Vault role
    bytes32 public constant VAULT_ROLE = keccak256("VAULT_ROLE");

    /// @notice Aggregator role
    bytes32 public constant AGGREGATOR_ROLE = keccak256("AGGREGATOR_ROLE");

    /**********/
    /* Errors */
    /**********/

    /// @notice Invalid address (e.g. zero address)
    error InvalidAddress();

    /// @notice Parameter out of bounds
    error ParameterOutOfBounds();

    /**********/
    /* Events */
    /**********/

    /// @notice Emitted when new vault is created
    /// @param owner Owner addres
    /// @param vault Vault address
    event VaultCreated(address indexed owner, address vault);

    /// @notice Emitted when dev is updated
    /// @param dev New dev address
    event DevUpdated(address dev);

    /// @notice Emitted when multisig is updated
    /// @param multisig New multisig address
    event MultisigUpdated(address multisig);

    /// @notice Emitted when fee recipient is updated
    /// @param feeRecipient New fee recipient address
    event FeeRecipientUpdated(address feeRecipient);

    /***************/
    /* Constructor */
    /***************/

    /// @notice Constructor
    /// @param _beacon Beacon address
    /// @param _dev Initial dev address
    /// @param _multisig Initial multisig address
    /// @param _feeRecipient Initial fee recipient address
    constructor(
        address _beacon,
        address _dev,
        address _multisig,
        address _feeRecipient
    ) {
        if (_beacon == address(0)) {
            revert InvalidAddress();
        }
        if (_dev == address(0)) {
            revert InvalidAddress();
        }
        if (_multisig == address(0)) {
            revert InvalidAddress();
        }
        if (_feeRecipient == address(0)) {
            revert InvalidAddress();
        }

        _setupRole(DEFAULT_ADMIN_ROLE, _msgSender());

        beacon = _beacon;
        dev = _dev;
        multisig = _multisig;
        feeRecipient = _feeRecipient;
    }

    /***********/
    /* Setters */
    /***********/

    /// @notice Set the dev wallet address
    ///
    /// Emits a {DevUpdated} event.
    ///
    /// @param _dev New dev wallet
    function setDev(address _dev) external onlyRole(DEFAULT_ADMIN_ROLE) {
        if (_dev == address(0)) {
            revert InvalidAddress();
        }
        dev = _dev;
        emit DevUpdated(_dev);
    }

    /// @notice Set the multisig address
    ///
    /// Emits a {MultisigUpdated} event.
    ///
    /// @param _multisig New multisig address
    function setMultisig(
        address _multisig
    ) external onlyRole(DEFAULT_ADMIN_ROLE) {
        if (_multisig == address(0)) {
            revert InvalidAddress();
        }
        multisig = _multisig;
        emit MultisigUpdated(_multisig);
    }

    /// @notice Set the fee recipient address
    ///
    /// Emits a {FeeRecipientUpdated} event.
    ///
    /// @param _feeRecipient New fee recipient address
    function setFeeRecipient(
        address _feeRecipient
    ) external onlyRole(DEFAULT_ADMIN_ROLE) {
        if (_feeRecipient == address(0)) {
            revert InvalidAddress();
        }
        feeRecipient = _feeRecipient;
        emit FeeRecipientUpdated(_feeRecipient);
    }

    /*************/
    /* Functions */
    /*************/

    /// @notice Creates new BeaconProxy for SpiceFi4626 vault
    /// @param _asset Asset address for the vault
    /// @param _mintPrice NFT mint price
    /// @param _maxSupply Max total supply
    /// @param _vaults Default vault addresses
    /// @return vault Created vault address
    function createVault(
        address _asset,
        uint256 _mintPrice,
        uint256 _maxSupply,
        address[] calldata _vaults
    ) external returns (address vault) {
        if (_asset == address(0)) {
            revert InvalidAddress();
        }
        if (_maxSupply == 0) {
            revert ParameterOutOfBounds();
        }

        _checkRole(ASSET_ROLE, _asset);

        uint256 length = _vaults.length;
        for (uint256 i; i != length; ++i) {
            _checkRole(VAULT_ROLE, _vaults[i]);
        }

        uint256 vaultId = getRoleMemberCount(AGGREGATOR_ROLE) + 1;
        vault = address(
            new BeaconProxy(
                beacon,
                abi.encodeWithSignature(
                    "initialize(string,string,address,uint256,uint256,address[],address,address,address,address)",
                    string(abi.encodePacked("Spice", vaultId.toString())),
                    string(abi.encodePacked("s", vaultId.toString())),
                    _asset,
                    _mintPrice,
                    _maxSupply,
                    _vaults,
                    msg.sender,
                    dev,
                    multisig,
                    feeRecipient
                )
            )
        );

        // grant AGGREGATOR_ROLE for tracking
        _grantRole(AGGREGATOR_ROLE, address(vault));

        emit VaultCreated(msg.sender, vault);
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (access/AccessControlEnumerable.sol)

pragma solidity ^0.8.0;

import "./IAccessControlEnumerable.sol";
import "./AccessControl.sol";
import "../utils/structs/EnumerableSet.sol";

/**
 * @dev Extension of {AccessControl} that allows enumerating the members of each role.
 */
abstract contract AccessControlEnumerable is IAccessControlEnumerable, AccessControl {
    using EnumerableSet for EnumerableSet.AddressSet;

    mapping(bytes32 => EnumerableSet.AddressSet) private _roleMembers;

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

    /**
     * @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) public view virtual override returns (address) {
        return _roleMembers[role].at(index);
    }

    /**
     * @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) public view virtual override returns (uint256) {
        return _roleMembers[role].length();
    }

    /**
     * @dev Overload {_grantRole} to track enumerable memberships
     */
    function _grantRole(bytes32 role, address account) internal virtual override {
        super._grantRole(role, account);
        _roleMembers[role].add(account);
    }

    /**
     * @dev Overload {_revokeRole} to track enumerable memberships
     */
    function _revokeRole(bytes32 role, address account) internal virtual override {
        super._revokeRole(role, account);
        _roleMembers[role].remove(account);
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0-rc.1) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/MathUpgradeable.sol";

/**
 * @dev String operations.
 */
library StringsUpgradeable {
    bytes16 private constant _SYMBOLS = "0123456789abcdef";
    uint8 private constant _ADDRESS_LENGTH = 20;

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = MathUpgradeable.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, MathUpgradeable.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
    }
}

// File: @openzeppelin/contracts/proxy/beacon/BeaconProxy.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (proxy/beacon/BeaconProxy.sol)

pragma solidity ^0.8.0;

import "./IBeacon.sol";
import "../Proxy.sol";
import "../ERC1967/ERC1967Upgrade.sol";

/**
 * @dev This contract implements a proxy that gets the implementation address for each call from an {UpgradeableBeacon}.
 *
 * The beacon address is stored in storage slot `uint256(keccak256('eip1967.proxy.beacon')) - 1`, so that it doesn't
 * conflict with the storage layout of the implementation behind the proxy.
 *
 * _Available since v3.4._
 */
contract BeaconProxy is Proxy, ERC1967Upgrade {
    /**
     * @dev Initializes the proxy with `beacon`.
     *
     * If `data` is nonempty, it's used as data in a delegate call to the implementation returned by the beacon. This
     * will typically be an encoded function call, and allows initializing the storage of the proxy like a Solidity
     * constructor.
     *
     * Requirements:
     *
     * - `beacon` must be a contract with the interface {IBeacon}.
     */
    constructor(address beacon, bytes memory data) payable {
        _upgradeBeaconToAndCall(beacon, data, false);
    }

    /**
     * @dev Returns the current beacon address.
     */
    function _beacon() internal view virtual returns (address) {
        return _getBeacon();
    }

    /**
     * @dev Returns the current implementation address of the associated beacon.
     */
    function _implementation() internal view virtual override returns (address) {
        return IBeacon(_getBeacon()).implementation();
    }

    /**
     * @dev Changes the proxy to use a new beacon. Deprecated: see {_upgradeBeaconToAndCall}.
     *
     * If `data` is nonempty, it's used as data in a delegate call to the implementation returned by the beacon.
     *
     * Requirements:
     *
     * - `beacon` must be a contract.
     * - The implementation returned by `beacon` must be a contract.
     */
    function _setBeacon(address beacon, bytes memory data) internal virtual {
        _upgradeBeaconToAndCall(beacon, data, false);
    }
}

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



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

pragma solidity ^0.8.0;

import "./IAccessControl.sol";

/**
 * @dev External interface of AccessControlEnumerable declared to support ERC165 detection.
 */
interface IAccessControlEnumerable is IAccessControl {
    /**
     * @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/access/AccessControl.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (access/AccessControl.sol)

pragma solidity ^0.8.0;

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

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

    mapping(bytes32 => RoleData) private _roles;

    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;

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

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

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

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

    /**
     * @dev Revert with a standard message if `account` is missing `role`.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     */
    function _checkRole(bytes32 role, address account) internal view virtual {
        if (!hasRole(role, account)) {
            revert(
                string(
                    abi.encodePacked(
                        "AccessControl: account ",
                        Strings.toHexString(uint160(account), 20),
                        " is missing role ",
                        Strings.toHexString(uint256(role), 32)
                    )
                )
            );
        }
    }

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

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

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

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

        _revokeRole(role, account);
    }

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

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

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

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

// File: @openzeppelin/contracts/utils/structs/EnumerableSet.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/structs/EnumerableSet.sol)

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 EnumerableSet {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Set type with
    // bytes32 values.
    // The Set implementation uses private functions, and user-facing
    // implementations (such as AddressSet) are just wrappers around the
    // underlying Set.
    // This means that we can only create new EnumerableSets for types that fit
    // in bytes32.

    struct Set {
        // Storage of set values
        bytes32[] _values;
        // Position 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) {
        return _values(set._inner);
    }

    // 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 on 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/access/IAccessControl.sol



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

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

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

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



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

pragma solidity ^0.8.0;

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

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

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/Strings.sol)

pragma solidity ^0.8.0;

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _HEX_SYMBOLS = "0123456789abcdef";
    uint8 private constant _ADDRESS_LENGTH = 20;

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        // Inspired by OraclizeAPI's implementation - MIT licence
        // https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol

        if (value == 0) {
            return "0";
        }
        uint256 temp = value;
        uint256 digits;
        while (temp != 0) {
            digits++;
            temp /= 10;
        }
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
            value /= 10;
        }
        return string(buffer);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        if (value == 0) {
            return "0x00";
        }
        uint256 temp = value;
        uint256 length = 0;
        while (temp != 0) {
            length++;
            temp >>= 8;
        }
        return toHexString(value, length);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _HEX_SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
    }
}

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



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

pragma solidity ^0.8.0;

import "./IERC165.sol";

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

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



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

pragma solidity ^0.8.0;

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

// File: @openzeppelin/contracts-upgradeable/utils/math/MathUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0-rc.1) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library MathUpgradeable {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

// File: @openzeppelin/contracts/proxy/Proxy.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (proxy/Proxy.sol)

pragma solidity ^0.8.0;

/**
 * @dev This abstract contract provides a fallback function that delegates all calls to another contract using the EVM
 * instruction `delegatecall`. We refer to the second contract as the _implementation_ behind the proxy, and it has to
 * be specified by overriding the virtual {_implementation} function.
 *
 * Additionally, delegation to the implementation can be triggered manually through the {_fallback} function, or to a
 * different contract through the {_delegate} function.
 *
 * The success and return data of the delegated call will be returned back to the caller of the proxy.
 */
abstract contract Proxy {
    /**
     * @dev Delegates the current call to `implementation`.
     *
     * This function does not return to its internal call site, it will return directly to the external caller.
     */
    function _delegate(address implementation) internal virtual {
        assembly {
            // Copy msg.data. We take full control of memory in this inline assembly
            // block because it will not return to Solidity code. We overwrite the
            // Solidity scratch pad at memory position 0.
            calldatacopy(0, 0, calldatasize())

            // Call the implementation.
            // out and outsize are 0 because we don't know the size yet.
            let result := delegatecall(gas(), implementation, 0, calldatasize(), 0, 0)

            // Copy the returned data.
            returndatacopy(0, 0, returndatasize())

            switch result
            // delegatecall returns 0 on error.
            case 0 {
                revert(0, returndatasize())
            }
            default {
                return(0, returndatasize())
            }
        }
    }

    /**
     * @dev This is a virtual function that should be overridden so it returns the address to which the fallback function
     * and {_fallback} should delegate.
     */
    function _implementation() internal view virtual returns (address);

    /**
     * @dev Delegates the current call to the address returned by `_implementation()`.
     *
     * This function does not return to its internal call site, it will return directly to the external caller.
     */
    function _fallback() internal virtual {
        _beforeFallback();
        _delegate(_implementation());
    }

    /**
     * @dev Fallback function that delegates calls to the address returned by `_implementation()`. Will run if no other
     * function in the contract matches the call data.
     */
    fallback() external payable virtual {
        _fallback();
    }

    /**
     * @dev Fallback function that delegates calls to the address returned by `_implementation()`. Will run if call data
     * is empty.
     */
    receive() external payable virtual {
        _fallback();
    }

    /**
     * @dev Hook that is called before falling back to the implementation. Can happen as part of a manual `_fallback`
     * call, or as part of the Solidity `fallback` or `receive` functions.
     *
     * If overridden should call `super._beforeFallback()`.
     */
    function _beforeFallback() internal virtual {}
}

// File: @openzeppelin/contracts/proxy/beacon/IBeacon.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (proxy/beacon/IBeacon.sol)

pragma solidity ^0.8.0;

/**
 * @dev This is the interface that {BeaconProxy} expects of its beacon.
 */
interface IBeacon {
    /**
     * @dev Must return an address that can be used as a delegate call target.
     *
     * {BeaconProxy} will check that this address is a contract.
     */
    function implementation() external view returns (address);
}

// File: @openzeppelin/contracts/proxy/ERC1967/ERC1967Upgrade.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (proxy/ERC1967/ERC1967Upgrade.sol)

pragma solidity ^0.8.2;

import "../beacon/IBeacon.sol";
import "../../interfaces/draft-IERC1822.sol";
import "../../utils/Address.sol";
import "../../utils/StorageSlot.sol";

/**
 * @dev This abstract contract provides getters and event emitting update functions for
 * https://eips.ethereum.org/EIPS/eip-1967[EIP1967] slots.
 *
 * _Available since v4.1._
 *
 * @custom:oz-upgrades-unsafe-allow delegatecall
 */
abstract contract ERC1967Upgrade {
    // This is the keccak-256 hash of "eip1967.proxy.rollback" subtracted by 1
    bytes32 private constant _ROLLBACK_SLOT = 0x4910fdfa16fed3260ed0e7147f7cc6da11a60208b5b9406d12a635614ffd9143;

    /**
     * @dev Storage slot with the address of the current implementation.
     * This is the keccak-256 hash of "eip1967.proxy.implementation" subtracted by 1, and is
     * validated in the constructor.
     */
    bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;

    /**
     * @dev Emitted when the implementation is upgraded.
     */
    event Upgraded(address indexed implementation);

    /**
     * @dev Returns the current implementation address.
     */
    function _getImplementation() internal view returns (address) {
        return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
    }

    /**
     * @dev Stores a new address in the EIP1967 implementation slot.
     */
    function _setImplementation(address newImplementation) private {
        require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
        StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
    }

    /**
     * @dev Perform implementation upgrade
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeTo(address newImplementation) internal {
        _setImplementation(newImplementation);
        emit Upgraded(newImplementation);
    }

    /**
     * @dev Perform implementation upgrade with additional setup call.
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeToAndCall(
        address newImplementation,
        bytes memory data,
        bool forceCall
    ) internal {
        _upgradeTo(newImplementation);
        if (data.length > 0 || forceCall) {
            Address.functionDelegateCall(newImplementation, data);
        }
    }

    /**
     * @dev Perform implementation upgrade with security checks for UUPS proxies, and additional setup call.
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeToAndCallUUPS(
        address newImplementation,
        bytes memory data,
        bool forceCall
    ) internal {
        // Upgrades from old implementations will perform a rollback test. This test requires the new
        // implementation to upgrade back to the old, non-ERC1822 compliant, implementation. Removing
        // this special case will break upgrade paths from old UUPS implementation to new ones.
        if (StorageSlot.getBooleanSlot(_ROLLBACK_SLOT).value) {
            _setImplementation(newImplementation);
        } else {
            try IERC1822Proxiable(newImplementation).proxiableUUID() returns (bytes32 slot) {
                require(slot == _IMPLEMENTATION_SLOT, "ERC1967Upgrade: unsupported proxiableUUID");
            } catch {
                revert("ERC1967Upgrade: new implementation is not UUPS");
            }
            _upgradeToAndCall(newImplementation, data, forceCall);
        }
    }

    /**
     * @dev Storage slot with the admin of the contract.
     * This is the keccak-256 hash of "eip1967.proxy.admin" subtracted by 1, and is
     * validated in the constructor.
     */
    bytes32 internal constant _ADMIN_SLOT = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;

    /**
     * @dev Emitted when the admin account has changed.
     */
    event AdminChanged(address previousAdmin, address newAdmin);

    /**
     * @dev Returns the current admin.
     */
    function _getAdmin() internal view returns (address) {
        return StorageSlot.getAddressSlot(_ADMIN_SLOT).value;
    }

    /**
     * @dev Stores a new address in the EIP1967 admin slot.
     */
    function _setAdmin(address newAdmin) private {
        require(newAdmin != address(0), "ERC1967: new admin is the zero address");
        StorageSlot.getAddressSlot(_ADMIN_SLOT).value = newAdmin;
    }

    /**
     * @dev Changes the admin of the proxy.
     *
     * Emits an {AdminChanged} event.
     */
    function _changeAdmin(address newAdmin) internal {
        emit AdminChanged(_getAdmin(), newAdmin);
        _setAdmin(newAdmin);
    }

    /**
     * @dev The storage slot of the UpgradeableBeacon contract which defines the implementation for this proxy.
     * This is bytes32(uint256(keccak256('eip1967.proxy.beacon')) - 1)) and is validated in the constructor.
     */
    bytes32 internal constant _BEACON_SLOT = 0xa3f0ad74e5423aebfd80d3ef4346578335a9a72aeaee59ff6cb3582b35133d50;

    /**
     * @dev Emitted when the beacon is upgraded.
     */
    event BeaconUpgraded(address indexed beacon);

    /**
     * @dev Returns the current beacon.
     */
    function _getBeacon() internal view returns (address) {
        return StorageSlot.getAddressSlot(_BEACON_SLOT).value;
    }

    /**
     * @dev Stores a new beacon in the EIP1967 beacon slot.
     */
    function _setBeacon(address newBeacon) private {
        require(Address.isContract(newBeacon), "ERC1967: new beacon is not a contract");
        require(
            Address.isContract(IBeacon(newBeacon).implementation()),
            "ERC1967: beacon implementation is not a contract"
        );
        StorageSlot.getAddressSlot(_BEACON_SLOT).value = newBeacon;
    }

    /**
     * @dev Perform beacon upgrade with additional setup call. Note: This upgrades the address of the beacon, it does
     * not upgrade the implementation contained in the beacon (see {UpgradeableBeacon-_setImplementation} for that).
     *
     * Emits a {BeaconUpgraded} event.
     */
    function _upgradeBeaconToAndCall(
        address newBeacon,
        bytes memory data,
        bool forceCall
    ) internal {
        _setBeacon(newBeacon);
        emit BeaconUpgraded(newBeacon);
        if (data.length > 0 || forceCall) {
            Address.functionDelegateCall(IBeacon(newBeacon).implementation(), data);
        }
    }
}

// File: @openzeppelin/contracts/interfaces/draft-IERC1822.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (interfaces/draft-IERC1822.sol)

pragma solidity ^0.8.0;

/**
 * @dev ERC1822: Universal Upgradeable Proxy Standard (UUPS) documents a method for upgradeability through a simplified
 * proxy whose upgrades are fully controlled by the current implementation.
 */
interface IERC1822Proxiable {
    /**
     * @dev Returns the storage slot that the proxiable contract assumes is being used to store the implementation
     * address.
     *
     * IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
     * bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
     * function revert if invoked through a proxy.
     */
    function proxiableUUID() external view returns (bytes32);
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (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 functionCall(target, data, "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");
        require(isContract(target), "Address: call to non-contract");

        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(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) {
        require(isContract(target), "Address: static call to non-contract");

        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(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) {
        require(isContract(target), "Address: delegate call to non-contract");

        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason 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 {
            // 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/utils/StorageSlot.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/StorageSlot.sol)

pragma solidity ^0.8.0;

/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC1967 implementation slot:
 * ```
 * contract ERC1967 {
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * _Available since v4.1 for `address`, `bool`, `bytes32`, and `uint256`._
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }

    struct BooleanSlot {
        bool value;
    }

    struct Bytes32Slot {
        bytes32 value;
    }

    struct Uint256Slot {
        uint256 value;
    }

    /**
     * @dev Returns an `AddressSlot` with member `value` located at `slot`.
     */
    function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BooleanSlot` with member `value` located at `slot`.
     */
    function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Bytes32Slot` with member `value` located at `slot`.
     */
    function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Uint256Slot` with member `value` located at `slot`.
     */
    function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }
}