creation_sourcecode: // Sources flattened with hardhat v2.22.2 https://hardhat.org
  
  // SPDX-License-Identifier: BSD-4-Clause AND MIT
  
  // File @openzeppelin/contracts-upgradeable/access/IAccessControlUpgradeable.sol@v4.9.6
  
  // Original license: 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/utils/AddressUpgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.9.0) (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
       *
       * Furthermore, `isContract` will also return true if the target contract within
       * the same transaction is already scheduled for destruction by `SELFDESTRUCT`,
       * which only has an effect at the end of a transaction.
       * ====
       *
       * [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://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
       *
       * IMPORTANT: because control is transferred to `recipient`, care must be
       * taken to not create reentrancy vulnerabilities. Consider using
       * {ReentrancyGuard} or the
       * https://solidity.readthedocs.io/en/v0.8.0/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 @openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.9.0) (proxy/utils/Initializable.sol)
  
  pragma solidity ^0.8.2;
  
  /**
   * @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]
   * ```solidity
   * 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/utils/ContextUpgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.9.4) (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 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;
      }
  
      function _contextSuffixLength() internal view virtual returns (uint256) {
          return 0;
      }
  
      /**
       * @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/introspection/IERC165Upgradeable.sol@v4.9.6
  
  // Original license: 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 IERC165Upgradeable {
      /**
       * @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/introspection/ERC165Upgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165.sol)
  
  pragma solidity ^0.8.0;
  
  
  /**
   * @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 ERC165Upgradeable is Initializable, IERC165Upgradeable {
      function __ERC165_init() internal onlyInitializing {
      }
  
      function __ERC165_init_unchained() internal onlyInitializing {
      }
      /**
       * @dev See {IERC165-supportsInterface}.
       */
      function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
          return interfaceId == type(IERC165Upgradeable).interfaceId;
      }
  
      /**
       * @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/math/MathUpgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)
  
  pragma solidity ^0.8.0;
  
  /**
   * @dev Standard math utilities missing in the Solidity language.
   */
  library 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) {
                  // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                  // The surrounding unchecked block does not change this fact.
                  // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                  return prod0 / denominator;
              }
  
              // Make sure the result is less than 2^256. Also prevents denominator == 0.
              require(denominator > prod1, "Math: mulDiv overflow");
  
              ///////////////////////////////////////////////
              // 512 by 256 division.
              ///////////////////////////////////////////////
  
              // Make division exact by subtracting the remainder from [prod1 prod0].
              uint256 remainder;
              assembly {
                  // Compute remainder using mulmod.
                  remainder := mulmod(x, y, denominator)
  
                  // Subtract 256 bit number from 512 bit number.
                  prod1 := sub(prod1, gt(remainder, prod0))
                  prod0 := sub(prod0, remainder)
              }
  
              // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
              // See https://cs.stackexchange.com/q/138556/92363.
  
              // Does not overflow because the denominator cannot be zero at this stage in the function.
              uint256 twos = denominator & (~denominator + 1);
              assembly {
                  // Divide denominator by twos.
                  denominator := div(denominator, twos)
  
                  // Divide [prod1 prod0] by twos.
                  prod0 := div(prod0, twos)
  
                  // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                  twos := add(div(sub(0, twos), twos), 1)
              }
  
              // Shift in bits from prod1 into prod0.
              prod0 |= prod1 * twos;
  
              // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
              // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
              // four bits. That is, denominator * inv = 1 mod 2^4.
              uint256 inverse = (3 * denominator) ^ 2;
  
              // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
              // in modular arithmetic, doubling the correct bits in each step.
              inverse *= 2 - denominator * inverse; // inverse mod 2^8
              inverse *= 2 - denominator * inverse; // inverse mod 2^16
              inverse *= 2 - denominator * inverse; // inverse mod 2^32
              inverse *= 2 - denominator * inverse; // inverse mod 2^64
              inverse *= 2 - denominator * inverse; // inverse mod 2^128
              inverse *= 2 - denominator * inverse; // inverse mod 2^256
  
              // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
              // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
              // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
              // is no longer required.
              result = prod0 * inverse;
              return result;
          }
      }
  
      /**
       * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
       */
      function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
          uint256 result = mulDiv(x, y, denominator);
          if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
              result += 1;
          }
          return result;
      }
  
      /**
       * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
       *
       * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
       */
      function sqrt(uint256 a) internal pure returns (uint256) {
          if (a == 0) {
              return 0;
          }
  
          // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
          //
          // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
          // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
          //
          // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
          // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
          // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
          //
          // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
          uint256 result = 1 << (log2(a) >> 1);
  
          // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
          // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
          // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
          // into the expected uint128 result.
          unchecked {
              result = (result + a / result) >> 1;
              result = (result + a / result) >> 1;
              result = (result + a / result) >> 1;
              result = (result + a / result) >> 1;
              result = (result + a / result) >> 1;
              result = (result + a / result) >> 1;
              result = (result + a / result) >> 1;
              return min(result, a / result);
          }
      }
  
      /**
       * @notice Calculates sqrt(a), following the selected rounding direction.
       */
      function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
          unchecked {
              uint256 result = sqrt(a);
              return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
          }
      }
  
      /**
       * @dev Return the log in base 2, rounded down, of a positive value.
       * Returns 0 if given 0.
       */
      function log2(uint256 value) internal pure returns (uint256) {
          uint256 result = 0;
          unchecked {
              if (value >> 128 > 0) {
                  value >>= 128;
                  result += 128;
              }
              if (value >> 64 > 0) {
                  value >>= 64;
                  result += 64;
              }
              if (value >> 32 > 0) {
                  value >>= 32;
                  result += 32;
              }
              if (value >> 16 > 0) {
                  value >>= 16;
                  result += 16;
              }
              if (value >> 8 > 0) {
                  value >>= 8;
                  result += 8;
              }
              if (value >> 4 > 0) {
                  value >>= 4;
                  result += 4;
              }
              if (value >> 2 > 0) {
                  value >>= 2;
                  result += 2;
              }
              if (value >> 1 > 0) {
                  result += 1;
              }
          }
          return result;
      }
  
      /**
       * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
       * Returns 0 if given 0.
       */
      function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
          unchecked {
              uint256 result = log2(value);
              return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
          }
      }
  
      /**
       * @dev Return the log in base 10, rounded down, of a positive value.
       * Returns 0 if given 0.
       */
      function log10(uint256 value) internal pure returns (uint256) {
          uint256 result = 0;
          unchecked {
              if (value >= 10 ** 64) {
                  value /= 10 ** 64;
                  result += 64;
              }
              if (value >= 10 ** 32) {
                  value /= 10 ** 32;
                  result += 32;
              }
              if (value >= 10 ** 16) {
                  value /= 10 ** 16;
                  result += 16;
              }
              if (value >= 10 ** 8) {
                  value /= 10 ** 8;
                  result += 8;
              }
              if (value >= 10 ** 4) {
                  value /= 10 ** 4;
                  result += 4;
              }
              if (value >= 10 ** 2) {
                  value /= 10 ** 2;
                  result += 2;
              }
              if (value >= 10 ** 1) {
                  result += 1;
              }
          }
          return result;
      }
  
      /**
       * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
       * Returns 0 if given 0.
       */
      function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
          unchecked {
              uint256 result = log10(value);
              return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
          }
      }
  
      /**
       * @dev Return the log in base 256, rounded down, of a positive value.
       * Returns 0 if given 0.
       *
       * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
       */
      function log256(uint256 value) internal pure returns (uint256) {
          uint256 result = 0;
          unchecked {
              if (value >> 128 > 0) {
                  value >>= 128;
                  result += 16;
              }
              if (value >> 64 > 0) {
                  value >>= 64;
                  result += 8;
              }
              if (value >> 32 > 0) {
                  value >>= 32;
                  result += 4;
              }
              if (value >> 16 > 0) {
                  value >>= 16;
                  result += 2;
              }
              if (value >> 8 > 0) {
                  result += 1;
              }
          }
          return result;
      }
  
      /**
       * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
       * Returns 0 if given 0.
       */
      function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
          unchecked {
              uint256 result = log256(value);
              return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);
          }
      }
  }
  
  
  // File @openzeppelin/contracts-upgradeable/utils/math/SignedMathUpgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SignedMath.sol)
  
  pragma solidity ^0.8.0;
  
  /**
   * @dev Standard signed math utilities missing in the Solidity language.
   */
  library SignedMathUpgradeable {
      /**
       * @dev Returns the largest of two signed numbers.
       */
      function max(int256 a, int256 b) internal pure returns (int256) {
          return a > b ? a : b;
      }
  
      /**
       * @dev Returns the smallest of two signed numbers.
       */
      function min(int256 a, int256 b) internal pure returns (int256) {
          return a < b ? a : b;
      }
  
      /**
       * @dev Returns the average of two signed numbers without overflow.
       * The result is rounded towards zero.
       */
      function average(int256 a, int256 b) internal pure returns (int256) {
          // Formula from the book "Hacker's Delight"
          int256 x = (a & b) + ((a ^ b) >> 1);
          return x + (int256(uint256(x) >> 255) & (a ^ b));
      }
  
      /**
       * @dev Returns the absolute unsigned value of a signed value.
       */
      function abs(int256 n) internal pure returns (uint256) {
          unchecked {
              // must be unchecked in order to support `n = type(int256).min`
              return uint256(n >= 0 ? n : -n);
          }
      }
  }
  
  
  // File @openzeppelin/contracts-upgradeable/utils/StringsUpgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.9.0) (utils/Strings.sol)
  
  pragma solidity ^0.8.0;
  
  
  /**
   * @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 `int256` to its ASCII `string` decimal representation.
       */
      function toString(int256 value) internal pure returns (string memory) {
          return string(abi.encodePacked(value < 0 ? "-" : "", toString(SignedMathUpgradeable.abs(value))));
      }
  
      /**
       * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
       */
      function toHexString(uint256 value) internal pure returns (string memory) {
          unchecked {
              return toHexString(value, 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);
      }
  
      /**
       * @dev Returns true if the two strings are equal.
       */
      function equal(string memory a, string memory b) internal pure returns (bool) {
          return keccak256(bytes(a)) == keccak256(bytes(b));
      }
  }
  
  
  // File @openzeppelin/contracts-upgradeable/access/AccessControlUpgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.9.0) (access/AccessControl.sol)
  
  pragma solidity ^0.8.0;
  
  
  
  
  
  /**
   * @dev Contract module that allows children to implement role-based access
   * control mechanisms. This is a lightweight version that doesn't allow enumerating role
   * members except through off-chain means by accessing the contract event logs. Some
   * applications may benefit from on-chain enumerability, for those cases see
   * {AccessControlEnumerable}.
   *
   * Roles are referred to by their `bytes32` identifier. These should be exposed
   * in the external API and be unique. The best way to achieve this is by
   * using `public constant` hash digests:
   *
   * ```solidity
   * bytes32 public constant MY_ROLE = keccak256("MY_ROLE");
   * ```
   *
   * Roles can be used to represent a set of permissions. To restrict access to a
   * function call, use {hasRole}:
   *
   * ```solidity
   * function foo() public {
   *     require(hasRole(MY_ROLE, msg.sender));
   *     ...
   * }
   * ```
   *
   * Roles can be granted and revoked dynamically via the {grantRole} and
   * {revokeRole} functions. Each role has an associated admin role, and only
   * accounts that have a role's admin role can call {grantRole} and {revokeRole}.
   *
   * By default, the admin role for all roles is `DEFAULT_ADMIN_ROLE`, which means
   * that only accounts with this role will be able to grant or revoke other
   * roles. More complex role relationships can be created by using
   * {_setRoleAdmin}.
   *
   * WARNING: The `DEFAULT_ADMIN_ROLE` is also its own admin: it has permission to
   * grant and revoke this role. Extra precautions should be taken to secure
   * accounts that have been granted it. We recommend using {AccessControlDefaultAdminRules}
   * to enforce additional security measures for this role.
   */
  abstract contract AccessControlUpgradeable is Initializable, ContextUpgradeable, IAccessControlUpgradeable, ERC165Upgradeable {
      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);
          _;
      }
  
      function __AccessControl_init() internal onlyInitializing {
      }
  
      function __AccessControl_init_unchained() internal onlyInitializing {
      }
      /**
       * @dev See {IERC165-supportsInterface}.
       */
      function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
          return interfaceId == type(IAccessControlUpgradeable).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 ",
                          StringsUpgradeable.toHexString(account),
                          " is missing role ",
                          StringsUpgradeable.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());
          }
      }
  
      /**
       * @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[49] private __gap;
  }
  
  
  // File @openzeppelin/contracts-upgradeable/interfaces/draft-IERC1822Upgradeable.sol@v4.9.6
  
  // Original license: 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 IERC1822ProxiableUpgradeable {
      /**
       * @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-upgradeable/interfaces/IERC1967Upgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.9.0) (interfaces/IERC1967.sol)
  
  pragma solidity ^0.8.0;
  
  /**
   * @dev ERC-1967: Proxy Storage Slots. This interface contains the events defined in the ERC.
   *
   * _Available since v4.8.3._
   */
  interface IERC1967Upgradeable {
      /**
       * @dev Emitted when the implementation is upgraded.
       */
      event Upgraded(address indexed implementation);
  
      /**
       * @dev Emitted when the admin account has changed.
       */
      event AdminChanged(address previousAdmin, address newAdmin);
  
      /**
       * @dev Emitted when the beacon is changed.
       */
      event BeaconUpgraded(address indexed beacon);
  }
  
  
  // File @openzeppelin/contracts-upgradeable/proxy/beacon/IBeaconUpgradeable.sol@v4.9.6
  
  // Original license: 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 IBeaconUpgradeable {
      /**
       * @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-upgradeable/utils/StorageSlotUpgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.9.0) (utils/StorageSlot.sol)
  // This file was procedurally generated from scripts/generate/templates/StorageSlot.js.
  
  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:
   * ```solidity
   * 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`, `uint256`._
   * _Available since v4.9 for `string`, `bytes`._
   */
  library StorageSlotUpgradeable {
      struct AddressSlot {
          address value;
      }
  
      struct BooleanSlot {
          bool value;
      }
  
      struct Bytes32Slot {
          bytes32 value;
      }
  
      struct Uint256Slot {
          uint256 value;
      }
  
      struct StringSlot {
          string value;
      }
  
      struct BytesSlot {
          bytes 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
          }
      }
  
      /**
       * @dev Returns an `StringSlot` with member `value` located at `slot`.
       */
      function getStringSlot(bytes32 slot) internal pure returns (StringSlot storage r) {
          /// @solidity memory-safe-assembly
          assembly {
              r.slot := slot
          }
      }
  
      /**
       * @dev Returns an `StringSlot` representation of the string storage pointer `store`.
       */
      function getStringSlot(string storage store) internal pure returns (StringSlot storage r) {
          /// @solidity memory-safe-assembly
          assembly {
              r.slot := store.slot
          }
      }
  
      /**
       * @dev Returns an `BytesSlot` with member `value` located at `slot`.
       */
      function getBytesSlot(bytes32 slot) internal pure returns (BytesSlot storage r) {
          /// @solidity memory-safe-assembly
          assembly {
              r.slot := slot
          }
      }
  
      /**
       * @dev Returns an `BytesSlot` representation of the bytes storage pointer `store`.
       */
      function getBytesSlot(bytes storage store) internal pure returns (BytesSlot storage r) {
          /// @solidity memory-safe-assembly
          assembly {
              r.slot := store.slot
          }
      }
  }
  
  
  // File @openzeppelin/contracts-upgradeable/proxy/ERC1967/ERC1967UpgradeUpgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.9.0) (proxy/ERC1967/ERC1967Upgrade.sol)
  
  pragma solidity ^0.8.2;
  
  
  
  
  
  
  /**
   * @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._
   */
  abstract contract ERC1967UpgradeUpgradeable is Initializable, IERC1967Upgradeable {
      // 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;
  
      function __ERC1967Upgrade_init() internal onlyInitializing {
      }
  
      function __ERC1967Upgrade_init_unchained() internal onlyInitializing {
      }
      /**
       * @dev Returns the current implementation address.
       */
      function _getImplementation() internal view returns (address) {
          return StorageSlotUpgradeable.getAddressSlot(_IMPLEMENTATION_SLOT).value;
      }
  
      /**
       * @dev Stores a new address in the EIP1967 implementation slot.
       */
      function _setImplementation(address newImplementation) private {
          require(AddressUpgradeable.isContract(newImplementation), "ERC1967: new implementation is not a contract");
          StorageSlotUpgradeable.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) {
              AddressUpgradeable.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 (StorageSlotUpgradeable.getBooleanSlot(_ROLLBACK_SLOT).value) {
              _setImplementation(newImplementation);
          } else {
              try IERC1822ProxiableUpgradeable(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 Returns the current admin.
       */
      function _getAdmin() internal view returns (address) {
          return StorageSlotUpgradeable.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");
          StorageSlotUpgradeable.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 Returns the current beacon.
       */
      function _getBeacon() internal view returns (address) {
          return StorageSlotUpgradeable.getAddressSlot(_BEACON_SLOT).value;
      }
  
      /**
       * @dev Stores a new beacon in the EIP1967 beacon slot.
       */
      function _setBeacon(address newBeacon) private {
          require(AddressUpgradeable.isContract(newBeacon), "ERC1967: new beacon is not a contract");
          require(
              AddressUpgradeable.isContract(IBeaconUpgradeable(newBeacon).implementation()),
              "ERC1967: beacon implementation is not a contract"
          );
          StorageSlotUpgradeable.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) {
              AddressUpgradeable.functionDelegateCall(IBeaconUpgradeable(newBeacon).implementation(), 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/proxy/utils/UUPSUpgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.9.0) (proxy/utils/UUPSUpgradeable.sol)
  
  pragma solidity ^0.8.0;
  
  
  
  /**
   * @dev An upgradeability mechanism designed for UUPS proxies. The functions included here can perform an upgrade of an
   * {ERC1967Proxy}, when this contract is set as the implementation behind such a proxy.
   *
   * A security mechanism ensures that an upgrade does not turn off upgradeability accidentally, although this risk is
   * reinstated if the upgrade retains upgradeability but removes the security mechanism, e.g. by replacing
   * `UUPSUpgradeable` with a custom implementation of upgrades.
   *
   * The {_authorizeUpgrade} function must be overridden to include access restriction to the upgrade mechanism.
   *
   * _Available since v4.1._
   */
  abstract contract UUPSUpgradeable is Initializable, IERC1822ProxiableUpgradeable, ERC1967UpgradeUpgradeable {
      /// @custom:oz-upgrades-unsafe-allow state-variable-immutable state-variable-assignment
      address private immutable __self = address(this);
  
      /**
       * @dev Check that the execution is being performed through a delegatecall call and that the execution context is
       * a proxy contract with an implementation (as defined in ERC1967) pointing to self. This should only be the case
       * for UUPS and transparent proxies that are using the current contract as their implementation. Execution of a
       * function through ERC1167 minimal proxies (clones) would not normally pass this test, but is not guaranteed to
       * fail.
       */
      modifier onlyProxy() {
          require(address(this) != __self, "Function must be called through delegatecall");
          require(_getImplementation() == __self, "Function must be called through active proxy");
          _;
      }
  
      /**
       * @dev Check that the execution is not being performed through a delegate call. This allows a function to be
       * callable on the implementing contract but not through proxies.
       */
      modifier notDelegated() {
          require(address(this) == __self, "UUPSUpgradeable: must not be called through delegatecall");
          _;
      }
  
      function __UUPSUpgradeable_init() internal onlyInitializing {
      }
  
      function __UUPSUpgradeable_init_unchained() internal onlyInitializing {
      }
      /**
       * @dev Implementation of the ERC1822 {proxiableUUID} function. This returns the storage slot used by the
       * implementation. It is used to validate the implementation's compatibility when performing an upgrade.
       *
       * 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. This is guaranteed by the `notDelegated` modifier.
       */
      function proxiableUUID() external view virtual override notDelegated returns (bytes32) {
          return _IMPLEMENTATION_SLOT;
      }
  
      /**
       * @dev Upgrade the implementation of the proxy to `newImplementation`.
       *
       * Calls {_authorizeUpgrade}.
       *
       * Emits an {Upgraded} event.
       *
       * @custom:oz-upgrades-unsafe-allow-reachable delegatecall
       */
      function upgradeTo(address newImplementation) public virtual onlyProxy {
          _authorizeUpgrade(newImplementation);
          _upgradeToAndCallUUPS(newImplementation, new bytes(0), false);
      }
  
      /**
       * @dev Upgrade the implementation of the proxy to `newImplementation`, and subsequently execute the function call
       * encoded in `data`.
       *
       * Calls {_authorizeUpgrade}.
       *
       * Emits an {Upgraded} event.
       *
       * @custom:oz-upgrades-unsafe-allow-reachable delegatecall
       */
      function upgradeToAndCall(address newImplementation, bytes memory data) public payable virtual onlyProxy {
          _authorizeUpgrade(newImplementation);
          _upgradeToAndCallUUPS(newImplementation, data, true);
      }
  
      /**
       * @dev Function that should revert when `msg.sender` is not authorized to upgrade the contract. Called by
       * {upgradeTo} and {upgradeToAndCall}.
       *
       * Normally, this function will use an xref:access.adoc[access control] modifier such as {Ownable-onlyOwner}.
       *
       * ```solidity
       * function _authorizeUpgrade(address) internal override onlyOwner {}
       * ```
       */
      function _authorizeUpgrade(address newImplementation) 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[50] private __gap;
  }
  
  
  // File @openzeppelin/contracts-upgradeable/security/PausableUpgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.7.0) (security/Pausable.sol)
  
  pragma solidity ^0.8.0;
  
  
  /**
   * @dev Contract module which allows children to implement an emergency stop
   * mechanism that can be triggered by an authorized account.
   *
   * This module is used through inheritance. It will make available the
   * modifiers `whenNotPaused` and `whenPaused`, which can be applied to
   * the functions of your contract. Note that they will not be pausable by
   * simply including this module, only once the modifiers are put in place.
   */
  abstract contract PausableUpgradeable is Initializable, ContextUpgradeable {
      /**
       * @dev Emitted when the pause is triggered by `account`.
       */
      event Paused(address account);
  
      /**
       * @dev Emitted when the pause is lifted by `account`.
       */
      event Unpaused(address account);
  
      bool private _paused;
  
      /**
       * @dev Initializes the contract in unpaused state.
       */
      function __Pausable_init() internal onlyInitializing {
          __Pausable_init_unchained();
      }
  
      function __Pausable_init_unchained() internal onlyInitializing {
          _paused = false;
      }
  
      /**
       * @dev Modifier to make a function callable only when the contract is not paused.
       *
       * Requirements:
       *
       * - The contract must not be paused.
       */
      modifier whenNotPaused() {
          _requireNotPaused();
          _;
      }
  
      /**
       * @dev Modifier to make a function callable only when the contract is paused.
       *
       * Requirements:
       *
       * - The contract must be paused.
       */
      modifier whenPaused() {
          _requirePaused();
          _;
      }
  
      /**
       * @dev Returns true if the contract is paused, and false otherwise.
       */
      function paused() public view virtual returns (bool) {
          return _paused;
      }
  
      /**
       * @dev Throws if the contract is paused.
       */
      function _requireNotPaused() internal view virtual {
          require(!paused(), "Pausable: paused");
      }
  
      /**
       * @dev Throws if the contract is not paused.
       */
      function _requirePaused() internal view virtual {
          require(paused(), "Pausable: not paused");
      }
  
      /**
       * @dev Triggers stopped state.
       *
       * Requirements:
       *
       * - The contract must not be paused.
       */
      function _pause() internal virtual whenNotPaused {
          _paused = true;
          emit Paused(_msgSender());
      }
  
      /**
       * @dev Returns to normal state.
       *
       * Requirements:
       *
       * - The contract must be paused.
       */
      function _unpause() internal virtual whenPaused {
          _paused = false;
          emit Unpaused(_msgSender());
      }
  
      /**
       * @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[49] private __gap;
  }
  
  
  // File @openzeppelin/contracts-upgradeable/security/ReentrancyGuardUpgradeable.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.9.0) (security/ReentrancyGuard.sol)
  
  pragma solidity ^0.8.0;
  
  /**
   * @dev Contract module that helps prevent reentrant calls to a function.
   *
   * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
   * available, which can be applied to functions to make sure there are no nested
   * (reentrant) calls to them.
   *
   * Note that because there is a single `nonReentrant` guard, functions marked as
   * `nonReentrant` may not call one another. This can be worked around by making
   * those functions `private`, and then adding `external` `nonReentrant` entry
   * points to them.
   *
   * TIP: If you would like to learn more about reentrancy and alternative ways
   * to protect against it, check out our blog post
   * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
   */
  abstract contract ReentrancyGuardUpgradeable is Initializable {
      // Booleans are more expensive than uint256 or any type that takes up a full
      // word because each write operation emits an extra SLOAD to first read the
      // slot's contents, replace the bits taken up by the boolean, and then write
      // back. This is the compiler's defense against contract upgrades and
      // pointer aliasing, and it cannot be disabled.
  
      // The values being non-zero value makes deployment a bit more expensive,
      // but in exchange the refund on every call to nonReentrant will be lower in
      // amount. Since refunds are capped to a percentage of the total
      // transaction's gas, it is best to keep them low in cases like this one, to
      // increase the likelihood of the full refund coming into effect.
      uint256 private constant _NOT_ENTERED = 1;
      uint256 private constant _ENTERED = 2;
  
      uint256 private _status;
  
      function __ReentrancyGuard_init() internal onlyInitializing {
          __ReentrancyGuard_init_unchained();
      }
  
      function __ReentrancyGuard_init_unchained() internal onlyInitializing {
          _status = _NOT_ENTERED;
      }
  
      /**
       * @dev Prevents a contract from calling itself, directly or indirectly.
       * Calling a `nonReentrant` function from another `nonReentrant`
       * function is not supported. It is possible to prevent this from happening
       * by making the `nonReentrant` function external, and making it call a
       * `private` function that does the actual work.
       */
      modifier nonReentrant() {
          _nonReentrantBefore();
          _;
          _nonReentrantAfter();
      }
  
      function _nonReentrantBefore() private {
          // On the first call to nonReentrant, _status will be _NOT_ENTERED
          require(_status != _ENTERED, "ReentrancyGuard: reentrant call");
  
          // Any calls to nonReentrant after this point will fail
          _status = _ENTERED;
      }
  
      function _nonReentrantAfter() private {
          // By storing the original value once again, a refund is triggered (see
          // https://eips.ethereum.org/EIPS/eip-2200)
          _status = _NOT_ENTERED;
      }
  
      /**
       * @dev Returns true if the reentrancy guard is currently set to "entered", which indicates there is a
       * `nonReentrant` function in the call stack.
       */
      function _reentrancyGuardEntered() internal view returns (bool) {
          return _status == _ENTERED;
      }
  
      /**
       * @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[49] private __gap;
  }
  
  
  // File @openzeppelin/contracts/utils/math/Math.sol@v4.9.6
  
  // Original license: SPDX_License_Identifier: MIT
  // OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)
  
  pragma solidity ^0.8.0;
  
  /**
   * @dev Standard math utilities missing in the Solidity language.
   */
  library Math {
      enum Rounding {
          Down, // Toward negative infinity
          Up, // Toward infinity
          Zero // Toward zero
      }
  
      /**
       * @dev Returns the largest of two numbers.
       */
      function max(uint256 a, uint256 b) internal pure returns (uint256) {
          return a > b ? a : b;
      }
  
      /**
       * @dev Returns the smallest of two numbers.
       */
      function min(uint256 a, uint256 b) internal pure returns (uint256) {
          return a < b ? a : b;
      }
  
      /**
       * @dev Returns the average of two numbers. The result is rounded towards
       * zero.
       */
      function average(uint256 a, uint256 b) internal pure returns (uint256) {
          // (a + b) / 2 can overflow.
          return (a & b) + (a ^ b) / 2;
      }
  
      /**
       * @dev Returns the ceiling of the division of two numbers.
       *
       * This differs from standard division with `/` in that it rounds up instead
       * of rounding down.
       */
      function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
          // (a + b - 1) / b can overflow on addition, so we distribute.
          return a == 0 ? 0 : (a - 1) / b + 1;
      }
  
      /**
       * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
       * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
       * with further edits by Uniswap Labs also under MIT license.
       */
      function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
          unchecked {
              // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
              // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
              // variables such that product = prod1 * 2^256 + prod0.
              uint256 prod0; // Least significant 256 bits of the product
              uint256 prod1; // Most significant 256 bits of the product
              assembly {
                  let mm := mulmod(x, y, not(0))
                  prod0 := mul(x, y)
                  prod1 := sub(sub(mm, prod0), lt(mm, prod0))
              }
  
              // Handle non-overflow cases, 256 by 256 division.
              if (prod1 == 0) {
                  // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                  // The surrounding unchecked block does not change this fact.
                  // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                  return prod0 / denominator;
              }
  
              // Make sure the result is less than 2^256. Also prevents denominator == 0.
              require(denominator > prod1, "Math: mulDiv overflow");
  
              ///////////////////////////////////////////////
              // 512 by 256 division.
              ///////////////////////////////////////////////
  
              // Make division exact by subtracting the remainder from [prod1 prod0].
              uint256 remainder;
              assembly {
                  // Compute remainder using mulmod.
                  remainder := mulmod(x, y, denominator)
  
                  // Subtract 256 bit number from 512 bit number.
                  prod1 := sub(prod1, gt(remainder, prod0))
                  prod0 := sub(prod0, remainder)
              }
  
              // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
              // See https://cs.stackexchange.com/q/138556/92363.
  
              // Does not overflow because the denominator cannot be zero at this stage in the function.
              uint256 twos = denominator & (~denominator + 1);
              assembly {
                  // Divide denominator by twos.
                  denominator := div(denominator, twos)
  
                  // Divide [prod1 prod0] by twos.
                  prod0 := div(prod0, twos)
  
                  // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                  twos := add(div(sub(0, twos), twos), 1)
              }
  
              // Shift in bits from prod1 into prod0.
              prod0 |= prod1 * twos;
  
              // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
              // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
              // four bits. That is, denominator * inv = 1 mod 2^4.
              uint256 inverse = (3 * denominator) ^ 2;
  
              // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
              // in modular arithmetic, doubling the correct bits in each step.
              inverse *= 2 - denominator * inverse; // inverse mod 2^8
              inverse *= 2 - denominator * inverse; // inverse mod 2^16
              inverse *= 2 - denominator * inverse; // inverse mod 2^32
              inverse *= 2 - denominator * inverse; // inverse mod 2^64
              inverse *= 2 - denominator * inverse; // inverse mod 2^128
              inverse *= 2 - denominator * inverse; // inverse mod 2^256
  
              // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
              // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
              // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
              // is no longer required.
              result = prod0 * inverse;
              return result;
          }
      }
  
      /**
       * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
       */
      function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
          uint256 result = mulDiv(x, y, denominator);
          if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
              result += 1;
          }
          return result;
      }
  
      /**
       * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
       *
       * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
       */
      function sqrt(uint256 a) internal pure returns (uint256) {
          if (a == 0) {
              return 0;
          }
  
          // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
          //
          // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
          // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
          //
          // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
          // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
          // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
          //
          // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
          uint256 result = 1 << (log2(a) >> 1);
  
          // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
          // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
          // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
          // into the expected uint128 result.
          unchecked {
              result = (result + a / result) >> 1;
              result = (result + a / result) >> 1;
              result = (result + a / result) >> 1;
              result = (result + a / result) >> 1;
              result = (result + a / result) >> 1;
              result = (result + a / result) >> 1;
              result = (result + a / result) >> 1;
              return min(result, a / result);
          }
      }
  
      /**
       * @notice Calculates sqrt(a), following the selected rounding direction.
       */
      function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
          unchecked {
              uint256 result = sqrt(a);
              return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
          }
      }
  
      /**
       * @dev Return the log in base 2, rounded down, of a positive value.
       * Returns 0 if given 0.
       */
      function log2(uint256 value) internal pure returns (uint256) {
          uint256 result = 0;
          unchecked {
              if (value >> 128 > 0) {
                  value >>= 128;
                  result += 128;
              }
              if (value >> 64 > 0) {
                  value >>= 64;
                  result += 64;
              }
              if (value >> 32 > 0) {
                  value >>= 32;
                  result += 32;
              }
              if (value >> 16 > 0) {
                  value >>= 16;
                  result += 16;
              }
              if (value >> 8 > 0) {
                  value >>= 8;
                  result += 8;
              }
              if (value >> 4 > 0) {
                  value >>= 4;
                  result += 4;
              }
              if (value >> 2 > 0) {
                  value >>= 2;
                  result += 2;
              }
              if (value >> 1 > 0) {
                  result += 1;
              }
          }
          return result;
      }
  
      /**
       * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
       * Returns 0 if given 0.
       */
      function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
          unchecked {
              uint256 result = log2(value);
              return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
          }
      }
  
      /**
       * @dev Return the log in base 10, rounded down, of a positive value.
       * Returns 0 if given 0.
       */
      function log10(uint256 value) internal pure returns (uint256) {
          uint256 result = 0;
          unchecked {
              if (value >= 10 ** 64) {
                  value /= 10 ** 64;
                  result += 64;
              }
              if (value >= 10 ** 32) {
                  value /= 10 ** 32;
                  result += 32;
              }
              if (value >= 10 ** 16) {
                  value /= 10 ** 16;
                  result += 16;
              }
              if (value >= 10 ** 8) {
                  value /= 10 ** 8;
                  result += 8;
              }
              if (value >= 10 ** 4) {
                  value /= 10 ** 4;
                  result += 4;
              }
              if (value >= 10 ** 2) {
                  value /= 10 ** 2;
                  result += 2;
              }
              if (value >= 10 ** 1) {
                  result += 1;
              }
          }
          return result;
      }
  
      /**
       * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
       * Returns 0 if given 0.
       */
      function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
          unchecked {
              uint256 result = log10(value);
              return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
          }
      }
  
      /**
       * @dev Return the log in base 256, rounded down, of a positive value.
       * Returns 0 if given 0.
       *
       * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
       */
      function log256(uint256 value) internal pure returns (uint256) {
          uint256 result = 0;
          unchecked {
              if (value >> 128 > 0) {
                  value >>= 128;
                  result += 16;
              }
              if (value >> 64 > 0) {
                  value >>= 64;
                  result += 8;
              }
              if (value >> 32 > 0) {
                  value >>= 32;
                  result += 4;
              }
              if (value >> 16 > 0) {
                  value >>= 16;
                  result += 2;
              }
              if (value >> 8 > 0) {
                  result += 1;
              }
          }
          return result;
      }
  
      /**
       * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
       * Returns 0 if given 0.
       */
      function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
          unchecked {
              uint256 result = log256(value);
              return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);
          }
      }
  }
  
  
  // File contracts/market/interfaces/IMinter.sol
  
  // Original license: SPDX_License_Identifier: MIT
  pragma solidity ^0.8.17;
  
  interface IMinter {
      function mint(address _to, uint256 _projectId, address sender) external returns (uint256 _tokenId);
  }
  
  
  // File contracts/market/lib/ABDKMathQuad.sol
  
  // Original license: SPDX_License_Identifier: BSD-4-Clause
  /*
   * ABDK Math Quad Smart Contract Library.  Copyright © 2019 by ABDK Consulting.
   * Author: Mikhail Vladimirov <mikhail.vladimirov@gmail.com>
   */
  pragma solidity ^0.8.17;
  
  /**
   * Smart contract library of mathematical functions operating with IEEE 754
   * quadruple-precision binary floating-point numbers (quadruple precision
   * numbers).  As long as quadruple precision numbers are 16-bytes long, they are
   * represented by bytes16 type.
   */
  library ABDKMathQuad {
      /*
      * 0.
      */
      bytes16 private constant POSITIVE_ZERO = 0x00000000000000000000000000000000;
  
      /*
      * -0.
      */
      bytes16 private constant NEGATIVE_ZERO = 0x80000000000000000000000000000000;
  
      /*
      * +Infinity.
      */
      bytes16 private constant POSITIVE_INFINITY = 0x7FFF0000000000000000000000000000;
  
      /*
      * -Infinity.
      */
      bytes16 private constant NEGATIVE_INFINITY = 0xFFFF0000000000000000000000000000;
  
      /*
      * Canonical NaN value.
      */
      bytes16 private constant NaN = 0x7FFF8000000000000000000000000000;
  
      /**
       * Convert signed 256-bit integer number into quadruple precision number.
       *
       * @param x signed 256-bit integer number
       * @return quadruple precision number
       */
      function fromInt(int256 x) internal pure returns (bytes16) {
          unchecked {
              if (x == 0) {
                  return bytes16(0);
              } else {
                  // We rely on overflow behavior here
                  uint256 result = uint256(x > 0 ? x : -x);
  
                  uint256 msb = mostSignificantBit(result);
                  if (msb < 112) result <<= 112 - msb;
                  else if (msb > 112) result >>= msb - 112;
  
                  result = result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 16383 + msb << 112;
                  if (x < 0) result |= 0x80000000000000000000000000000000;
  
                  return bytes16(uint128(result));
              }
          }
      }
  
      /**
       * Convert quadruple precision number into signed 256-bit integer number
       * rounding towards zero.  Revert on overflow.
       *
       * @param x quadruple precision number
       * @return signed 256-bit integer number
       */
      function toInt(bytes16 x) internal pure returns (int256) {
          unchecked {
              uint256 exponent = uint128(x) >> 112 & 0x7FFF;
  
              require(exponent <= 16638); // Overflow
              if (exponent < 16383) return 0; // Underflow
  
              uint256 result = uint256(uint128(x)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 0x10000000000000000000000000000;
  
              if (exponent < 16495) result >>= 16495 - exponent;
              else if (exponent > 16495) result <<= exponent - 16495;
  
              if (uint128(x) >= 0x80000000000000000000000000000000) {
                  // Negative
                  require(result <= 0x8000000000000000000000000000000000000000000000000000000000000000);
                  return -int256(result); // We rely on overflow behavior here
              } else {
                  require(result <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
                  return int256(result);
              }
          }
      }
  
      /**
       * Convert unsigned 256-bit integer number into quadruple precision number.
       *
       * @param x unsigned 256-bit integer number
       * @return quadruple precision number
       */
      function fromUInt(uint256 x) internal pure returns (bytes16) {
          unchecked {
              if (x == 0) {
                  return bytes16(0);
              } else {
                  uint256 result = x;
  
                  uint256 msb = mostSignificantBit(result);
                  if (msb < 112) result <<= 112 - msb;
                  else if (msb > 112) result >>= msb - 112;
  
                  result = result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 16383 + msb << 112;
  
                  return bytes16(uint128(result));
              }
          }
      }
  
      /**
       * Convert quadruple precision number into unsigned 256-bit integer number
       * rounding towards zero.  Revert on underflow.  Note, that negative floating
       * point numbers in range (-1.0 .. 0.0) may be converted to unsigned integer
       * without error, because they are rounded to zero.
       *
       * @param x quadruple precision number
       * @return unsigned 256-bit integer number
       */
      function toUInt(bytes16 x) internal pure returns (uint256) {
          unchecked {
              uint256 exponent = uint128(x) >> 112 & 0x7FFF;
  
              if (exponent < 16383) return 0; // Underflow
  
              require(uint128(x) < 0x80000000000000000000000000000000); // Negative
  
              require(exponent <= 16638); // Overflow
              uint256 result = uint256(uint128(x)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 0x10000000000000000000000000000;
  
              if (exponent < 16495) result >>= 16495 - exponent;
              else if (exponent > 16495) result <<= exponent - 16495;
  
              return result;
          }
      }
  
      /**
       * Convert signed 128.128 bit fixed point number into quadruple precision
       * number.
       *
       * @param x signed 128.128 bit fixed point number
       * @return quadruple precision number
       */
      function from128x128(int256 x) internal pure returns (bytes16) {
          unchecked {
              if (x == 0) {
                  return bytes16(0);
              } else {
                  // We rely on overflow behavior here
                  uint256 result = uint256(x > 0 ? x : -x);
  
                  uint256 msb = mostSignificantBit(result);
                  if (msb < 112) result <<= 112 - msb;
                  else if (msb > 112) result >>= msb - 112;
  
                  result = result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 16255 + msb << 112;
                  if (x < 0) result |= 0x80000000000000000000000000000000;
  
                  return bytes16(uint128(result));
              }
          }
      }
  
      /**
       * Convert quadruple precision number into signed 128.128 bit fixed point
       * number.  Revert on overflow.
       *
       * @param x quadruple precision number
       * @return signed 128.128 bit fixed point number
       */
      function to128x128(bytes16 x) internal pure returns (int256) {
          unchecked {
              uint256 exponent = uint128(x) >> 112 & 0x7FFF;
  
              require(exponent <= 16510); // Overflow
              if (exponent < 16255) return 0; // Underflow
  
              uint256 result = uint256(uint128(x)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 0x10000000000000000000000000000;
  
              if (exponent < 16367) result >>= 16367 - exponent;
              else if (exponent > 16367) result <<= exponent - 16367;
  
              if (uint128(x) >= 0x80000000000000000000000000000000) {
                  // Negative
                  require(result <= 0x8000000000000000000000000000000000000000000000000000000000000000);
                  return -int256(result); // We rely on overflow behavior here
              } else {
                  require(result <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
                  return int256(result);
              }
          }
      }
  
      /**
       * Convert signed 64.64 bit fixed point number into quadruple precision
       * number.
       *
       * @param x signed 64.64 bit fixed point number
       * @return quadruple precision number
       */
      function from64x64(int128 x) internal pure returns (bytes16) {
          unchecked {
              if (x == 0) {
                  return bytes16(0);
              } else {
                  // We rely on overflow behavior here
                  uint256 result = uint128(x > 0 ? x : -x);
  
                  uint256 msb = mostSignificantBit(result);
                  if (msb < 112) result <<= 112 - msb;
                  else if (msb > 112) result >>= msb - 112;
  
                  result = result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 16319 + msb << 112;
                  if (x < 0) result |= 0x80000000000000000000000000000000;
  
                  return bytes16(uint128(result));
              }
          }
      }
  
      /**
       * Convert quadruple precision number into signed 64.64 bit fixed point
       * number.  Revert on overflow.
       *
       * @param x quadruple precision number
       * @return signed 64.64 bit fixed point number
       */
      function to64x64(bytes16 x) internal pure returns (int128) {
          unchecked {
              uint256 exponent = uint128(x) >> 112 & 0x7FFF;
  
              require(exponent <= 16446); // Overflow
              if (exponent < 16319) return 0; // Underflow
  
              uint256 result = uint256(uint128(x)) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF | 0x10000000000000000000000000000;
  
              if (exponent < 16431) result >>= 16431 - exponent;
              else if (exponent > 16431) result <<= exponent - 16431;
  
              if (uint128(x) >= 0x80000000000000000000000000000000) {
                  // Negative
                  require(result <= 0x80000000000000000000000000000000);
                  return -int128(int256(result)); // We rely on overflow behavior here
              } else {
                  require(result <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
                  return int128(int256(result));
              }
          }
      }
  
      /**
       * Convert octuple precision number into quadruple precision number.
       *
       * @param x octuple precision number
       * @return quadruple precision number
       */
      function fromOctuple(bytes32 x) internal pure returns (bytes16) {
          unchecked {
              bool negative = x & 0x8000000000000000000000000000000000000000000000000000000000000000 > 0;
  
              uint256 exponent = uint256(x) >> 236 & 0x7FFFF;
              uint256 significand = uint256(x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
  
              if (exponent == 0x7FFFF) {
                  if (significand > 0) return NaN;
                  else return negative ? NEGATIVE_INFINITY : POSITIVE_INFINITY;
              }
  
              if (exponent > 278526) {
                  return negative ? NEGATIVE_INFINITY : POSITIVE_INFINITY;
              } else if (exponent < 245649) {
                  return negative ? NEGATIVE_ZERO : POSITIVE_ZERO;
              } else if (exponent < 245761) {
                  significand =
                      (significand | 0x100000000000000000000000000000000000000000000000000000000000) >> 245885 - exponent;
                  exponent = 0;
              } else {
                  significand >>= 124;
                  exponent -= 245760;
              }
  
              uint128 result = uint128(significand | exponent << 112);
              if (negative) result |= 0x80000000000000000000000000000000;
  
              return bytes16(result);
          }
      }
  
      /**
       * Convert quadruple precision number into octuple precision number.
       *
       * @param x quadruple precision number
       * @return octuple precision number
       */
      function toOctuple(bytes16 x) internal pure returns (bytes32) {
          unchecked {
              uint256 exponent = uint128(x) >> 112 & 0x7FFF;
  
              uint256 result = uint128(x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
  
              if (exponent == 0x7FFF) {
                  exponent = 0x7FFFF;
              } // Infinity or NaN
              else if (exponent == 0) {
                  if (result > 0) {
                      uint256 msb = mostSignificantBit(result);
                      result = result << 236 - msb & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                      exponent = 245649 + msb;
                  }
              } else {
                  result <<= 124;
                  exponent += 245760;
              }
  
              result |= exponent << 236;
              if (uint128(x) >= 0x80000000000000000000000000000000) {
                  result |= 0x8000000000000000000000000000000000000000000000000000000000000000;
              }
  
              return bytes32(result);
          }
      }
  
      /**
       * Convert double precision number into quadruple precision number.
       *
       * @param x double precision number
       * @return quadruple precision number
       */
      function fromDouble(bytes8 x) internal pure returns (bytes16) {
          unchecked {
              uint256 exponent = uint64(x) >> 52 & 0x7FF;
  
              uint256 result = uint64(x) & 0xFFFFFFFFFFFFF;
  
              if (exponent == 0x7FF) {
                  exponent = 0x7FFF;
              } // Infinity or NaN
              else if (exponent == 0) {
                  if (result > 0) {
                      uint256 msb = mostSignificantBit(result);
                      result = result << 112 - msb & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                      exponent = 15309 + msb;
                  }
              } else {
                  result <<= 60;
                  exponent += 15360;
              }
  
              result |= exponent << 112;
              if (x & 0x8000000000000000 > 0) {
                  result |= 0x80000000000000000000000000000000;
              }
  
              return bytes16(uint128(result));
          }
      }
  
      /**
       * Convert quadruple precision number into double precision number.
       *
       * @param x quadruple precision number
       * @return double precision number
       */
      function toDouble(bytes16 x) internal pure returns (bytes8) {
          unchecked {
              bool negative = uint128(x) >= 0x80000000000000000000000000000000;
  
              uint256 exponent = uint128(x) >> 112 & 0x7FFF;
              uint256 significand = uint128(x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
  
              if (exponent == 0x7FFF) {
                  if (significand > 0) {
                      return 0x7FF8000000000000;
                  } // NaN
                  else {
                      return negative
                          ? bytes8(0xFFF0000000000000) // -Infinity
                          : bytes8(0x7FF0000000000000);
                  } // Infinity
              }
  
              if (exponent > 17406) {
                  return negative
                      ? bytes8(0xFFF0000000000000) // -Infinity
                      : bytes8(0x7FF0000000000000);
              } // Infinity
              else if (exponent < 15309) {
                  return negative
                      ? bytes8(0x8000000000000000) // -0
                      : bytes8(0x0000000000000000);
              } // 0
              else if (exponent < 15361) {
                  significand = (significand | 0x10000000000000000000000000000) >> 15421 - exponent;
                  exponent = 0;
              } else {
                  significand >>= 60;
                  exponent -= 15360;
              }
  
              uint64 result = uint64(significand | exponent << 52);
              if (negative) result |= 0x8000000000000000;
  
              return bytes8(result);
          }
      }
  
      /**
       * Test whether given quadruple precision number is NaN.
       *
       * @param x quadruple precision number
       * @return true if x is NaN, false otherwise
       */
      function isNaN(bytes16 x) internal pure returns (bool) {
          unchecked {
              return uint128(x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF > 0x7FFF0000000000000000000000000000;
          }
      }
  
      /**
       * Test whether given quadruple precision number is positive or negative
       * infinity.
       *
       * @param x quadruple precision number
       * @return true if x is positive or negative infinity, false otherwise
       */
      function isInfinity(bytes16 x) internal pure returns (bool) {
          unchecked {
              return uint128(x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0x7FFF0000000000000000000000000000;
          }
      }
  
      /**
       * Calculate sign of x, i.e. -1 if x is negative, 0 if x if zero, and 1 if x
       * is positive.  Note that sign (-0) is zero.  Revert if x is NaN.
       *
       * @param x quadruple precision number
       * @return sign of x
       */
      function sign(bytes16 x) internal pure returns (int8) {
          unchecked {
              uint128 absoluteX = uint128(x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
  
              require(absoluteX <= 0x7FFF0000000000000000000000000000); // Not NaN
  
              if (absoluteX == 0) return 0;
              else if (uint128(x) >= 0x80000000000000000000000000000000) return -1;
              else return 1;
          }
      }
  
      /**
       * Calculate sign (x - y).  Revert if either argument is NaN, or both
       * arguments are infinities of the same sign.
       *
       * @param x quadruple precision number
       * @param y quadruple precision number
       * @return sign (x - y)
       */
      function cmp(bytes16 x, bytes16 y) internal pure returns (int8) {
          unchecked {
              uint128 absoluteX = uint128(x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
  
              require(absoluteX <= 0x7FFF0000000000000000000000000000); // Not NaN
  
              uint128 absoluteY = uint128(y) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
  
              require(absoluteY <= 0x7FFF0000000000000000000000000000); // Not NaN
  
              // Not infinities of the same sign
              require(x != y || absoluteX < 0x7FFF0000000000000000000000000000);
  
              if (x == y) {
                  return 0;
              } else {
                  bool negativeX = uint128(x) >= 0x80000000000000000000000000000000;
                  bool negativeY = uint128(y) >= 0x80000000000000000000000000000000;
  
                  if (negativeX) {
                      if (negativeY) return absoluteX > absoluteY ? -1 : int8(1);
                      else return -1;
                  } else {
                      if (negativeY) return 1;
                      else return absoluteX > absoluteY ? int8(1) : -1;
                  }
              }
          }
      }
  
      /**
       * Test whether x equals y.  NaN, infinity, and -infinity are not equal to
       * anything.
       *
       * @param x quadruple precision number
       * @param y quadruple precision number
       * @return true if x equals to y, false otherwise
       */
      function eq(bytes16 x, bytes16 y) internal pure returns (bool) {
          unchecked {
              if (x == y) {
                  return uint128(x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF < 0x7FFF0000000000000000000000000000;
              } else {
                  return false;
              }
          }
      }
  
      /**
       * Calculate x + y.  Special values behave in the following way:
       *
       * NaN + x = NaN for any x.
       * Infinity + x = Infinity for any finite x.
       * -Infinity + x = -Infinity for any finite x.
       * Infinity + Infinity = Infinity.
       * -Infinity + -Infinity = -Infinity.
       * Infinity + -Infinity = -Infinity + Infinity = NaN.
       *
       * @param x quadruple precision number
       * @param y quadruple precision number
       * @return quadruple precision number
       */
      function add(bytes16 x, bytes16 y) internal pure returns (bytes16) {
          unchecked {
              uint256 xExponent = uint128(x) >> 112 & 0x7FFF;
              uint256 yExponent = uint128(y) >> 112 & 0x7FFF;
  
              if (xExponent == 0x7FFF) {
                  if (yExponent == 0x7FFF) {
                      if (x == y) return x;
                      else return NaN;
                  } else {
                      return x;
                  }
              } else if (yExponent == 0x7FFF) {
                  return y;
              } else {
                  bool xSign = uint128(x) >= 0x80000000000000000000000000000000;
                  uint256 xSignifier = uint128(x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                  if (xExponent == 0) xExponent = 1;
                  else xSignifier |= 0x10000000000000000000000000000;
  
                  bool ySign = uint128(y) >= 0x80000000000000000000000000000000;
                  uint256 ySignifier = uint128(y) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                  if (yExponent == 0) yExponent = 1;
                  else ySignifier |= 0x10000000000000000000000000000;
  
                  if (xSignifier == 0) {
                      return y == NEGATIVE_ZERO ? POSITIVE_ZERO : y;
                  } else if (ySignifier == 0) {
                      return x == NEGATIVE_ZERO ? POSITIVE_ZERO : x;
                  } else {
                      int256 delta = int256(xExponent) - int256(yExponent);
  
                      if (xSign == ySign) {
                          if (delta > 112) {
                              return x;
                          } else if (delta > 0) {
                              ySignifier >>= uint256(delta);
                          } else if (delta < -112) {
                              return y;
                          } else if (delta < 0) {
                              xSignifier >>= uint256(-delta);
                              xExponent = yExponent;
                          }
  
                          xSignifier += ySignifier;
  
                          if (xSignifier >= 0x20000000000000000000000000000) {
                              xSignifier >>= 1;
                              xExponent += 1;
                          }
  
                          if (xExponent == 0x7FFF) {
                              return xSign ? NEGATIVE_INFINITY : POSITIVE_INFINITY;
                          } else {
                              if (xSignifier < 0x10000000000000000000000000000) xExponent = 0;
                              else xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
  
                              return bytes16(
                                  uint128(
                                      (xSign ? 0x80000000000000000000000000000000 : 0) | (xExponent << 112) | xSignifier
                                  )
                              );
                          }
                      } else {
                          if (delta > 0) {
                              xSignifier <<= 1;
                              xExponent -= 1;
                          } else if (delta < 0) {
                              ySignifier <<= 1;
                              xExponent = yExponent - 1;
                          }
  
                          if (delta > 112) ySignifier = 1;
                          else if (delta > 1) ySignifier = (ySignifier - 1 >> uint256(delta - 1)) + 1;
                          else if (delta < -112) xSignifier = 1;
                          else if (delta < -1) xSignifier = (xSignifier - 1 >> uint256(-delta - 1)) + 1;
  
                          if (xSignifier >= ySignifier) {
                              xSignifier -= ySignifier;
                          } else {
                              xSignifier = ySignifier - xSignifier;
                              xSign = ySign;
                          }
  
                          if (xSignifier == 0) {
                              return POSITIVE_ZERO;
                          }
  
                          uint256 msb = mostSignificantBit(xSignifier);
  
                          if (msb == 113) {
                              xSignifier = xSignifier >> 1 & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                              xExponent += 1;
                          } else if (msb < 112) {
                              uint256 shift = 112 - msb;
                              if (xExponent > shift) {
                                  xSignifier = xSignifier << shift & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                                  xExponent -= shift;
                              } else {
                                  xSignifier <<= xExponent - 1;
                                  xExponent = 0;
                              }
                          } else {
                              xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                          }
  
                          if (xExponent == 0x7FFF) {
                              return xSign ? NEGATIVE_INFINITY : POSITIVE_INFINITY;
                          } else {
                              return bytes16(
                                  uint128(
                                      (xSign ? 0x80000000000000000000000000000000 : 0) | (xExponent << 112) | xSignifier
                                  )
                              );
                          }
                      }
                  }
              }
          }
      }
  
      /**
       * Calculate x - y.  Special values behave in the following way:
       *
       * NaN - x = NaN for any x.
       * Infinity - x = Infinity for any finite x.
       * -Infinity - x = -Infinity for any finite x.
       * Infinity - -Infinity = Infinity.
       * -Infinity - Infinity = -Infinity.
       * Infinity - Infinity = -Infinity - -Infinity = NaN.
       *
       * @param x quadruple precision number
       * @param y quadruple precision number
       * @return quadruple precision number
       */
      function sub(bytes16 x, bytes16 y) internal pure returns (bytes16) {
          unchecked {
              return add(x, y ^ 0x80000000000000000000000000000000);
          }
      }
  
      /**
       * Calculate x * y.  Special values behave in the following way:
       *
       * NaN * x = NaN for any x.
       * Infinity * x = Infinity for any finite positive x.
       * Infinity * x = -Infinity for any finite negative x.
       * -Infinity * x = -Infinity for any finite positive x.
       * -Infinity * x = Infinity for any finite negative x.
       * Infinity * 0 = NaN.
       * -Infinity * 0 = NaN.
       * Infinity * Infinity = Infinity.
       * Infinity * -Infinity = -Infinity.
       * -Infinity * Infinity = -Infinity.
       * -Infinity * -Infinity = Infinity.
       *
       * @param x quadruple precision number
       * @param y quadruple precision number
       * @return quadruple precision number
       */
      function mul(bytes16 x, bytes16 y) internal pure returns (bytes16) {
          unchecked {
              uint256 xExponent = uint128(x) >> 112 & 0x7FFF;
              uint256 yExponent = uint128(y) >> 112 & 0x7FFF;
  
              if (xExponent == 0x7FFF) {
                  if (yExponent == 0x7FFF) {
                      if (x == y) return x ^ y & 0x80000000000000000000000000000000;
                      else if (x ^ y == 0x80000000000000000000000000000000) return x | y;
                      else return NaN;
                  } else {
                      if (y & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) return NaN;
                      else return x ^ y & 0x80000000000000000000000000000000;
                  }
              } else if (yExponent == 0x7FFF) {
                  if (x & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) return NaN;
                  else return y ^ x & 0x80000000000000000000000000000000;
              } else {
                  uint256 xSignifier = uint128(x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                  if (xExponent == 0) xExponent = 1;
                  else xSignifier |= 0x10000000000000000000000000000;
  
                  uint256 ySignifier = uint128(y) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                  if (yExponent == 0) yExponent = 1;
                  else ySignifier |= 0x10000000000000000000000000000;
  
                  xSignifier *= ySignifier;
                  if (xSignifier == 0) {
                      return (x ^ y) & 0x80000000000000000000000000000000 > 0 ? NEGATIVE_ZERO : POSITIVE_ZERO;
                  }
  
                  xExponent += yExponent;
  
                  uint256 msb = xSignifier >= 0x200000000000000000000000000000000000000000000000000000000
                      ? 225
                      : xSignifier >= 0x100000000000000000000000000000000000000000000000000000000
                          ? 224
                          : mostSignificantBit(xSignifier);
  
                  if (xExponent + msb < 16496) {
                      // Underflow
                      xExponent = 0;
                      xSignifier = 0;
                  } else if (xExponent + msb < 16608) {
                      // Subnormal
                      if (xExponent < 16496) {
                          xSignifier >>= 16496 - xExponent;
                      } else if (xExponent > 16496) {
                          xSignifier <<= xExponent - 16496;
                      }
                      xExponent = 0;
                  } else if (xExponent + msb > 49373) {
                      xExponent = 0x7FFF;
                      xSignifier = 0;
                  } else {
                      if (msb > 112) {
                          xSignifier >>= msb - 112;
                      } else if (msb < 112) {
                          xSignifier <<= 112 - msb;
                      }
  
                      xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
  
                      xExponent = xExponent + msb - 16607;
                  }
  
                  return bytes16(
                      uint128(uint128((x ^ y) & 0x80000000000000000000000000000000) | xExponent << 112 | xSignifier)
                  );
              }
          }
      }
  
      /**
       * Calculate x / y.  Special values behave in the following way:
       *
       * NaN / x = NaN for any x.
       * x / NaN = NaN for any x.
       * Infinity / x = Infinity for any finite non-negative x.
       * Infinity / x = -Infinity for any finite negative x including -0.
       * -Infinity / x = -Infinity for any finite non-negative x.
       * -Infinity / x = Infinity for any finite negative x including -0.
       * x / Infinity = 0 for any finite non-negative x.
       * x / -Infinity = -0 for any finite non-negative x.
       * x / Infinity = -0 for any finite non-negative x including -0.
       * x / -Infinity = 0 for any finite non-negative x including -0.
       *
       * Infinity / Infinity = NaN.
       * Infinity / -Infinity = -NaN.
       * -Infinity / Infinity = -NaN.
       * -Infinity / -Infinity = NaN.
       *
       * Division by zero behaves in the following way:
       *
       * x / 0 = Infinity for any finite positive x.
       * x / -0 = -Infinity for any finite positive x.
       * x / 0 = -Infinity for any finite negative x.
       * x / -0 = Infinity for any finite negative x.
       * 0 / 0 = NaN.
       * 0 / -0 = NaN.
       * -0 / 0 = NaN.
       * -0 / -0 = NaN.
       *
       * @param x quadruple precision number
       * @param y quadruple precision number
       * @return quadruple precision number
       */
      function div(bytes16 x, bytes16 y) internal pure returns (bytes16) {
          unchecked {
              uint256 xExponent = uint128(x) >> 112 & 0x7FFF;
              uint256 yExponent = uint128(y) >> 112 & 0x7FFF;
  
              if (xExponent == 0x7FFF) {
                  if (yExponent == 0x7FFF) return NaN;
                  else return x ^ y & 0x80000000000000000000000000000000;
              } else if (yExponent == 0x7FFF) {
                  if (y & 0x0000FFFFFFFFFFFFFFFFFFFFFFFFFFFF != 0) return NaN;
                  else return POSITIVE_ZERO | (x ^ y) & 0x80000000000000000000000000000000;
              } else if (y & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) {
                  if (x & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) return NaN;
                  else return POSITIVE_INFINITY | (x ^ y) & 0x80000000000000000000000000000000;
              } else {
                  uint256 ySignifier = uint128(y) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                  if (yExponent == 0) yExponent = 1;
                  else ySignifier |= 0x10000000000000000000000000000;
  
                  uint256 xSignifier = uint128(x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                  if (xExponent == 0) {
                      if (xSignifier != 0) {
                          uint256 shift = 226 - mostSignificantBit(xSignifier);
  
                          xSignifier <<= shift;
  
                          xExponent = 1;
                          yExponent += shift - 114;
                      }
                  } else {
                      xSignifier = (xSignifier | 0x10000000000000000000000000000) << 114;
                  }
  
                  xSignifier = xSignifier / ySignifier;
                  if (xSignifier == 0) {
                      return (x ^ y) & 0x80000000000000000000000000000000 > 0 ? NEGATIVE_ZERO : POSITIVE_ZERO;
                  }
  
                  assert(xSignifier >= 0x1000000000000000000000000000);
  
                  uint256 msb = xSignifier >= 0x80000000000000000000000000000
                      ? mostSignificantBit(xSignifier)
                      : xSignifier >= 0x40000000000000000000000000000
                          ? 114
                          : xSignifier >= 0x20000000000000000000000000000 ? 113 : 112;
  
                  if (xExponent + msb > yExponent + 16497) {
                      // Overflow
                      xExponent = 0x7FFF;
                      xSignifier = 0;
                  } else if (xExponent + msb + 16380 < yExponent) {
                      // Underflow
                      xExponent = 0;
                      xSignifier = 0;
                  } else if (xExponent + msb + 16268 < yExponent) {
                      // Subnormal
                      if (xExponent + 16380 > yExponent) {
                          xSignifier <<= xExponent + 16380 - yExponent;
                      } else if (xExponent + 16380 < yExponent) {
                          xSignifier >>= yExponent - xExponent - 16380;
                      }
  
                      xExponent = 0;
                  } else {
                      // Normal
                      if (msb > 112) {
                          xSignifier >>= msb - 112;
                      }
  
                      xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
  
                      xExponent = xExponent + msb + 16269 - yExponent;
                  }
  
                  return bytes16(
                      uint128(uint128((x ^ y) & 0x80000000000000000000000000000000) | xExponent << 112 | xSignifier)
                  );
              }
          }
      }
  
      /**
       * Calculate -x.
       *
       * @param x quadruple precision number
       * @return quadruple precision number
       */
      function neg(bytes16 x) internal pure returns (bytes16) {
          unchecked {
              return x ^ 0x80000000000000000000000000000000;
          }
      }
  
      /**
       * Calculate |x|.
       *
       * @param x quadruple precision number
       * @return quadruple precision number
       */
      function abs(bytes16 x) internal pure returns (bytes16) {
          unchecked {
              return x & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
          }
      }
  
      /**
       * Calculate square root of x.  Return NaN on negative x excluding -0.
       *
       * @param x quadruple precision number
       * @return quadruple precision number
       */
      function sqrt(bytes16 x) internal pure returns (bytes16) {
          unchecked {
              if (uint128(x) > 0x80000000000000000000000000000000) {
                  return NaN;
              } else {
                  uint256 xExponent = uint128(x) >> 112 & 0x7FFF;
                  if (xExponent == 0x7FFF) {
                      return x;
                  } else {
                      uint256 xSignifier = uint128(x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                      if (xExponent == 0) xExponent = 1;
                      else xSignifier |= 0x10000000000000000000000000000;
  
                      if (xSignifier == 0) return POSITIVE_ZERO;
  
                      bool oddExponent = xExponent & 0x1 == 0;
                      xExponent = xExponent + 16383 >> 1;
  
                      if (oddExponent) {
                          if (xSignifier >= 0x10000000000000000000000000000) {
                              xSignifier <<= 113;
                          } else {
                              uint256 msb = mostSignificantBit(xSignifier);
                              uint256 shift = (226 - msb) & 0xFE;
                              xSignifier <<= shift;
                              xExponent -= shift - 112 >> 1;
                          }
                      } else {
                          if (xSignifier >= 0x10000000000000000000000000000) {
                              xSignifier <<= 112;
                          } else {
                              uint256 msb = mostSignificantBit(xSignifier);
                              uint256 shift = (225 - msb) & 0xFE;
                              xSignifier <<= shift;
                              xExponent -= shift - 112 >> 1;
                          }
                      }
  
                      uint256 r = 0x10000000000000000000000000000;
                      r = (r + xSignifier / r) >> 1;
                      r = (r + xSignifier / r) >> 1;
                      r = (r + xSignifier / r) >> 1;
                      r = (r + xSignifier / r) >> 1;
                      r = (r + xSignifier / r) >> 1;
                      r = (r + xSignifier / r) >> 1;
                      r = (r + xSignifier / r) >> 1; // Seven iterations should be enough
                      uint256 r1 = xSignifier / r;
                      if (r1 < r) r = r1;
  
                      return bytes16(uint128(xExponent << 112 | r & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF));
                  }
              }
          }
      }
  
      /**
       * Calculate binary logarithm of x.  Return NaN on negative x excluding -0.
       *
       * @param x quadruple precision number
       * @return quadruple precision number
       */
      function log_2(bytes16 x) internal pure returns (bytes16) {
          unchecked {
              if (uint128(x) > 0x80000000000000000000000000000000) {
                  return NaN;
              } else if (x == 0x3FFF0000000000000000000000000000) {
                  return POSITIVE_ZERO;
              } else {
                  uint256 xExponent = uint128(x) >> 112 & 0x7FFF;
                  if (xExponent == 0x7FFF) {
                      return x;
                  } else {
                      uint256 xSignifier = uint128(x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                      if (xExponent == 0) xExponent = 1;
                      else xSignifier |= 0x10000000000000000000000000000;
  
                      if (xSignifier == 0) return NEGATIVE_INFINITY;
  
                      bool resultNegative;
                      uint256 resultExponent = 16495;
                      uint256 resultSignifier;
  
                      if (xExponent >= 0x3FFF) {
                          resultNegative = false;
                          resultSignifier = xExponent - 0x3FFF;
                          xSignifier <<= 15;
                      } else {
                          resultNegative = true;
                          if (xSignifier >= 0x10000000000000000000000000000) {
                              resultSignifier = 0x3FFE - xExponent;
                              xSignifier <<= 15;
                          } else {
                              uint256 msb = mostSignificantBit(xSignifier);
                              resultSignifier = 16493 - msb;
                              xSignifier <<= 127 - msb;
                          }
                      }
  
                      if (xSignifier == 0x80000000000000000000000000000000) {
                          if (resultNegative) resultSignifier += 1;
                          uint256 shift = 112 - mostSignificantBit(resultSignifier);
                          resultSignifier <<= shift;
                          resultExponent -= shift;
                      } else {
                          uint256 bb = resultNegative ? 1 : 0;
                          while (resultSignifier < 0x10000000000000000000000000000) {
                              resultSignifier <<= 1;
                              resultExponent -= 1;
  
                              xSignifier *= xSignifier;
                              uint256 b = xSignifier >> 255;
                              resultSignifier += b ^ bb;
                              xSignifier >>= 127 + b;
                          }
                      }
  
                      return bytes16(
                          uint128(
                              (resultNegative ? 0x80000000000000000000000000000000 : 0) | resultExponent << 112
                                  | resultSignifier & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF
                          )
                      );
                  }
              }
          }
      }
  
      /**
       * Calculate natural logarithm of x.  Return NaN on negative x excluding -0.
       *
       * @param x quadruple precision number
       * @return quadruple precision number
       */
      function ln(bytes16 x) internal pure returns (bytes16) {
          unchecked {
              return mul(log_2(x), 0x3FFE62E42FEFA39EF35793C7673007E5);
          }
      }
  
      /**
       * Calculate 2^x.
       *
       * @param x quadruple precision number
       * @return quadruple precision number
       */
      function pow_2(bytes16 x) internal pure returns (bytes16) {
          unchecked {
              bool xNegative = uint128(x) > 0x80000000000000000000000000000000;
              uint256 xExponent = uint128(x) >> 112 & 0x7FFF;
              uint256 xSignifier = uint128(x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
  
              if (xExponent == 0x7FFF && xSignifier != 0) {
                  return NaN;
              } else if (xExponent > 16397) {
                  return xNegative ? POSITIVE_ZERO : POSITIVE_INFINITY;
              } else if (xExponent < 16255) {
                  return 0x3FFF0000000000000000000000000000;
              } else {
                  if (xExponent == 0) xExponent = 1;
                  else xSignifier |= 0x10000000000000000000000000000;
  
                  if (xExponent > 16367) {
                      xSignifier <<= xExponent - 16367;
                  } else if (xExponent < 16367) {
                      xSignifier >>= 16367 - xExponent;
                  }
  
                  if (xNegative && xSignifier > 0x406E00000000000000000000000000000000) {
                      return POSITIVE_ZERO;
                  }
  
                  if (!xNegative && xSignifier > 0x3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF) {
                      return POSITIVE_INFINITY;
                  }
  
                  uint256 resultExponent = xSignifier >> 128;
                  xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                  if (xNegative && xSignifier != 0) {
                      xSignifier = ~xSignifier;
                      resultExponent += 1;
                  }
  
                  uint256 resultSignifier = 0x80000000000000000000000000000000;
                  if (xSignifier & 0x80000000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x16A09E667F3BCC908B2FB1366EA957D3E >> 128;
                  }
                  if (xSignifier & 0x40000000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1306FE0A31B7152DE8D5A46305C85EDEC >> 128;
                  }
                  if (xSignifier & 0x20000000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1172B83C7D517ADCDF7C8C50EB14A791F >> 128;
                  }
                  if (xSignifier & 0x10000000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10B5586CF9890F6298B92B71842A98363 >> 128;
                  }
                  if (xSignifier & 0x8000000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1059B0D31585743AE7C548EB68CA417FD >> 128;
                  }
                  if (xSignifier & 0x4000000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x102C9A3E778060EE6F7CACA4F7A29BDE8 >> 128;
                  }
                  if (xSignifier & 0x2000000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10163DA9FB33356D84A66AE336DCDFA3F >> 128;
                  }
                  if (xSignifier & 0x1000000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100B1AFA5ABCBED6129AB13EC11DC9543 >> 128;
                  }
                  if (xSignifier & 0x800000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10058C86DA1C09EA1FF19D294CF2F679B >> 128;
                  }
                  if (xSignifier & 0x400000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1002C605E2E8CEC506D21BFC89A23A00F >> 128;
                  }
                  if (xSignifier & 0x200000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100162F3904051FA128BCA9C55C31E5DF >> 128;
                  }
                  if (xSignifier & 0x100000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000B175EFFDC76BA38E31671CA939725 >> 128;
                  }
                  if (xSignifier & 0x80000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100058BA01FB9F96D6CACD4B180917C3D >> 128;
                  }
                  if (xSignifier & 0x40000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10002C5CC37DA9491D0985C348C68E7B3 >> 128;
                  }
                  if (xSignifier & 0x20000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000162E525EE054754457D5995292026 >> 128;
                  }
                  if (xSignifier & 0x10000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000B17255775C040618BF4A4ADE83FC >> 128;
                  }
                  if (xSignifier & 0x8000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000058B91B5BC9AE2EED81E9B7D4CFAB >> 128;
                  }
                  if (xSignifier & 0x4000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100002C5C89D5EC6CA4D7C8ACC017B7C9 >> 128;
                  }
                  if (xSignifier & 0x2000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000162E43F4F831060E02D839A9D16D >> 128;
                  }
                  if (xSignifier & 0x1000000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000B1721BCFC99D9F890EA06911763 >> 128;
                  }
                  if (xSignifier & 0x800000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000058B90CF1E6D97F9CA14DBCC1628 >> 128;
                  }
                  if (xSignifier & 0x400000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000002C5C863B73F016468F6BAC5CA2B >> 128;
                  }
                  if (xSignifier & 0x200000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000162E430E5A18F6119E3C02282A5 >> 128;
                  }
                  if (xSignifier & 0x100000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000B1721835514B86E6D96EFD1BFE >> 128;
                  }
                  if (xSignifier & 0x80000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000058B90C0B48C6BE5DF846C5B2EF >> 128;
                  }
                  if (xSignifier & 0x40000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000002C5C8601CC6B9E94213C72737A >> 128;
                  }
                  if (xSignifier & 0x20000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000162E42FFF037DF38AA2B219F06 >> 128;
                  }
                  if (xSignifier & 0x10000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000B17217FBA9C739AA5819F44F9 >> 128;
                  }
                  if (xSignifier & 0x8000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000058B90BFCDEE5ACD3C1CEDC823 >> 128;
                  }
                  if (xSignifier & 0x4000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000002C5C85FE31F35A6A30DA1BE50 >> 128;
                  }
                  if (xSignifier & 0x2000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000162E42FF0999CE3541B9FFFCF >> 128;
                  }
                  if (xSignifier & 0x1000000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000B17217F80F4EF5AADDA45554 >> 128;
                  }
                  if (xSignifier & 0x800000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000058B90BFBF8479BD5A81B51AD >> 128;
                  }
                  if (xSignifier & 0x400000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000002C5C85FDF84BD62AE30A74CC >> 128;
                  }
                  if (xSignifier & 0x200000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000162E42FEFB2FED257559BDAA >> 128;
                  }
                  if (xSignifier & 0x100000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000B17217F7D5A7716BBA4A9AE >> 128;
                  }
                  if (xSignifier & 0x80000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000058B90BFBE9DDBAC5E109CCE >> 128;
                  }
                  if (xSignifier & 0x40000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000002C5C85FDF4B15DE6F17EB0D >> 128;
                  }
                  if (xSignifier & 0x20000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000162E42FEFA494F1478FDE05 >> 128;
                  }
                  if (xSignifier & 0x10000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000B17217F7D20CF927C8E94C >> 128;
                  }
                  if (xSignifier & 0x8000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000058B90BFBE8F71CB4E4B33D >> 128;
                  }
                  if (xSignifier & 0x4000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000002C5C85FDF477B662B26945 >> 128;
                  }
                  if (xSignifier & 0x2000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000162E42FEFA3AE53369388C >> 128;
                  }
                  if (xSignifier & 0x1000000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000B17217F7D1D351A389D40 >> 128;
                  }
                  if (xSignifier & 0x800000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000058B90BFBE8E8B2D3D4EDE >> 128;
                  }
                  if (xSignifier & 0x400000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000002C5C85FDF4741BEA6E77E >> 128;
                  }
                  if (xSignifier & 0x200000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000162E42FEFA39FE95583C2 >> 128;
                  }
                  if (xSignifier & 0x100000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000B17217F7D1CFB72B45E1 >> 128;
                  }
                  if (xSignifier & 0x80000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000058B90BFBE8E7CC35C3F0 >> 128;
                  }
                  if (xSignifier & 0x40000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000002C5C85FDF473E242EA38 >> 128;
                  }
                  if (xSignifier & 0x20000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000162E42FEFA39F02B772C >> 128;
                  }
                  if (xSignifier & 0x10000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000B17217F7D1CF7D83C1A >> 128;
                  }
                  if (xSignifier & 0x8000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000058B90BFBE8E7BDCBE2E >> 128;
                  }
                  if (xSignifier & 0x4000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000002C5C85FDF473DEA871F >> 128;
                  }
                  if (xSignifier & 0x2000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000162E42FEFA39EF44D91 >> 128;
                  }
                  if (xSignifier & 0x1000000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000B17217F7D1CF79E949 >> 128;
                  }
                  if (xSignifier & 0x800000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000058B90BFBE8E7BCE544 >> 128;
                  }
                  if (xSignifier & 0x400000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000002C5C85FDF473DE6ECA >> 128;
                  }
                  if (xSignifier & 0x200000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000162E42FEFA39EF366F >> 128;
                  }
                  if (xSignifier & 0x100000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000B17217F7D1CF79AFA >> 128;
                  }
                  if (xSignifier & 0x80000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000058B90BFBE8E7BCD6D >> 128;
                  }
                  if (xSignifier & 0x40000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000002C5C85FDF473DE6B2 >> 128;
                  }
                  if (xSignifier & 0x20000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000162E42FEFA39EF358 >> 128;
                  }
                  if (xSignifier & 0x10000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000B17217F7D1CF79AB >> 128;
                  }
                  if (xSignifier & 0x8000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000058B90BFBE8E7BCD5 >> 128;
                  }
                  if (xSignifier & 0x4000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000002C5C85FDF473DE6A >> 128;
                  }
                  if (xSignifier & 0x2000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000162E42FEFA39EF34 >> 128;
                  }
                  if (xSignifier & 0x1000000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000B17217F7D1CF799 >> 128;
                  }
                  if (xSignifier & 0x800000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000058B90BFBE8E7BCC >> 128;
                  }
                  if (xSignifier & 0x400000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000002C5C85FDF473DE5 >> 128;
                  }
                  if (xSignifier & 0x200000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000162E42FEFA39EF2 >> 128;
                  }
                  if (xSignifier & 0x100000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000B17217F7D1CF78 >> 128;
                  }
                  if (xSignifier & 0x80000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000058B90BFBE8E7BB >> 128;
                  }
                  if (xSignifier & 0x40000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000002C5C85FDF473DD >> 128;
                  }
                  if (xSignifier & 0x20000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000162E42FEFA39EE >> 128;
                  }
                  if (xSignifier & 0x10000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000B17217F7D1CF6 >> 128;
                  }
                  if (xSignifier & 0x8000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000058B90BFBE8E7A >> 128;
                  }
                  if (xSignifier & 0x4000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000002C5C85FDF473C >> 128;
                  }
                  if (xSignifier & 0x2000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000162E42FEFA39D >> 128;
                  }
                  if (xSignifier & 0x1000000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000B17217F7D1CE >> 128;
                  }
                  if (xSignifier & 0x800000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000058B90BFBE8E6 >> 128;
                  }
                  if (xSignifier & 0x400000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000002C5C85FDF472 >> 128;
                  }
                  if (xSignifier & 0x200000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000162E42FEFA38 >> 128;
                  }
                  if (xSignifier & 0x100000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000B17217F7D1B >> 128;
                  }
                  if (xSignifier & 0x80000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000058B90BFBE8D >> 128;
                  }
                  if (xSignifier & 0x40000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000002C5C85FDF46 >> 128;
                  }
                  if (xSignifier & 0x20000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000162E42FEFA2 >> 128;
                  }
                  if (xSignifier & 0x10000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000B17217F7D0 >> 128;
                  }
                  if (xSignifier & 0x8000000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000058B90BFBE7 >> 128;
                  }
                  if (xSignifier & 0x4000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000002C5C85FDF3 >> 128;
                  }
                  if (xSignifier & 0x2000000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000162E42FEF9 >> 128;
                  }
                  if (xSignifier & 0x1000000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000B17217F7C >> 128;
                  }
                  if (xSignifier & 0x800000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000058B90BFBD >> 128;
                  }
                  if (xSignifier & 0x400000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000002C5C85FDE >> 128;
                  }
                  if (xSignifier & 0x200000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000162E42FEE >> 128;
                  }
                  if (xSignifier & 0x100000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000000B17217F6 >> 128;
                  }
                  if (xSignifier & 0x80000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000058B90BFA >> 128;
                  }
                  if (xSignifier & 0x40000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000002C5C85FC >> 128;
                  }
                  if (xSignifier & 0x20000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000000162E42FD >> 128;
                  }
                  if (xSignifier & 0x10000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000000B17217E >> 128;
                  }
                  if (xSignifier & 0x8000000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000000058B90BE >> 128;
                  }
                  if (xSignifier & 0x4000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000002C5C85E >> 128;
                  }
                  if (xSignifier & 0x2000000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000000162E42E >> 128;
                  }
                  if (xSignifier & 0x1000000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000000B17216 >> 128;
                  }
                  if (xSignifier & 0x800000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000000058B90A >> 128;
                  }
                  if (xSignifier & 0x400000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000000002C5C84 >> 128;
                  }
                  if (xSignifier & 0x200000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000000162E41 >> 128;
                  }
                  if (xSignifier & 0x100000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000000000B1720 >> 128;
                  }
                  if (xSignifier & 0x80000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000000058B8F >> 128;
                  }
                  if (xSignifier & 0x40000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000000002C5C7 >> 128;
                  }
                  if (xSignifier & 0x20000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000000000162E3 >> 128;
                  }
                  if (xSignifier & 0x10000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000000000B171 >> 128;
                  }
                  if (xSignifier & 0x8000 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000000000058B8 >> 128;
                  }
                  if (xSignifier & 0x4000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000000002C5B >> 128;
                  }
                  if (xSignifier & 0x2000 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000000000162D >> 128;
                  }
                  if (xSignifier & 0x1000 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000000000B16 >> 128;
                  }
                  if (xSignifier & 0x800 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000000000058A >> 128;
                  }
                  if (xSignifier & 0x400 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000000000002C4 >> 128;
                  }
                  if (xSignifier & 0x200 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000000000161 >> 128;
                  }
                  if (xSignifier & 0x100 > 0) {
                      resultSignifier = resultSignifier * 0x1000000000000000000000000000000B0 >> 128;
                  }
                  if (xSignifier & 0x80 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000000000057 >> 128;
                  }
                  if (xSignifier & 0x40 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000000000002B >> 128;
                  }
                  if (xSignifier & 0x20 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000000000015 >> 128;
                  }
                  if (xSignifier & 0x10 > 0) {
                      resultSignifier = resultSignifier * 0x10000000000000000000000000000000A >> 128;
                  }
                  if (xSignifier & 0x8 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000000000004 >> 128;
                  }
                  if (xSignifier & 0x4 > 0) {
                      resultSignifier = resultSignifier * 0x100000000000000000000000000000001 >> 128;
                  }
  
                  if (!xNegative) {
                      resultSignifier = resultSignifier >> 15 & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                      resultExponent += 0x3FFF;
                  } else if (resultExponent <= 0x3FFE) {
                      resultSignifier = resultSignifier >> 15 & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                      resultExponent = 0x3FFF - resultExponent;
                  } else {
                      resultSignifier = resultSignifier >> resultExponent - 16367;
                      resultExponent = 0;
                  }
  
                  return bytes16(uint128(resultExponent << 112 | resultSignifier));
              }
          }
      }
  
      /**
       * Calculate e^x.
       *
       * @param x quadruple precision number
       * @return quadruple precision number
       */
      function exp(bytes16 x) internal pure returns (bytes16) {
          unchecked {
              return pow_2(mul(x, 0x3FFF71547652B82FE1777D0FFDA0D23A));
          }
      }
  
      /**
       * Get index of the most significant non-zero bit in binary representation of
       * x.  Reverts if x is zero.
       *
       * @return index of the most significant non-zero bit in binary representation
       *         of x
       */
      function mostSignificantBit(uint256 x) private pure returns (uint256) {
          unchecked {
              require(x > 0);
  
              uint256 result = 0;
  
              if (x >= 0x100000000000000000000000000000000) {
                  x >>= 128;
                  result += 128;
              }
              if (x >= 0x10000000000000000) {
                  x >>= 64;
                  result += 64;
              }
              if (x >= 0x100000000) {
                  x >>= 32;
                  result += 32;
              }
              if (x >= 0x10000) {
                  x >>= 16;
                  result += 16;
              }
              if (x >= 0x100) {
                  x >>= 8;
                  result += 8;
              }
              if (x >= 0x10) {
                  x >>= 4;
                  result += 4;
              }
              if (x >= 0x4) {
                  x >>= 2;
                  result += 2;
              }
              if (x >= 0x2) result += 1; // No need to shift x anymore
  
              return result;
          }
      }
  }
  
  
  // File contracts/market/DutchAuctionMinter.sol
  
  // Original license: SPDX_License_Identifier: MIT
  pragma solidity ^0.8.17;
  
  
  
  
  
  
  
  contract DutchAuctionMinter is PausableUpgradeable, AccessControlUpgradeable, ReentrancyGuardUpgradeable, UUPSUpgradeable {
      /// minterType for this minter
      string public constant minterType = "DutchAuctionMinter";
      // @notice Role for operate
      bytes32 public constant OPERATE_ROLE = keccak256("OPERATE_ROLE");
  
      // @notice Role for withdraw
      bytes32 public constant WITHDRAW_ROLE = keccak256("WITHDRAW_ROLE");
  
  
      struct ReturnConfig {
          uint256 startTime;
          uint256 endTime;
          uint256 startPrice;
          uint256 restPrice;
          uint256 priceDropSlot;
          uint256 halfPeriod;
          uint256 maxSupply;
          uint256 totalSupply;
          uint256 decayTime;
          uint256 maxPerwallet;
      }
  
      struct ProjectConfig {
          /// @notice ERC-721 pass contract whose tokens are minted by this auction
          /// @dev Must implement mint(address)
          IMinter passes;
          /// @notice Timestamp when this auction starts allowing minting
          uint256 startTime;
          /// @notice Timestamp when this auction end
          uint256 endTime;
          /// @notice Starting price for the Dutch auction
          uint256 startPrice;
          /// @notice Resting price where price descent ends
          uint256 restPrice;
          // @notice Amount of time in seconds after each price drops
          uint256 priceDropSlot;
          /// @notice time of half period
          uint256 halfPeriod;
          /// @notice maximum amount of passes which can be minted
          uint256 maxSupply;
          uint256 projectId;
          uint256 maxPerwallet;
      }
  
      ProjectConfig internal config;
      
      /// @notice total amount of minted passes
      uint256 public totalSupply;
      /// @notice the minest price of user bid for
      uint256 public minPrice;
  
      bytes16 internal HalfPeriod;
      bytes16 internal BaseValue;
      uint256 internal pauseStart;
      uint256 internal pastPauseDelay;
      address internal beneficiary;
      bool internal isNeedRefund;
      bool internal isRefund;
      bool internal isClear;
  
      struct mintInfo {
          uint256 amount;
          uint256 totalPay;
      }
  
      mapping(address => mintInfo) private _mintInfos;
      address[] private _mintAddresses;
  
      /// @notice An event to be emitted upon pass purchases for the benefit of the UI
      event Purchase(address purchaser, uint256 tokenId, uint256 price);
  
      /// @notice An event emitted when mint being open for everyone or not.
      /// @dev open - true if mint open for everyone, false if not
      event MintPublicUpdated(bool open);
  
      /// @notice An event emitted when mint passes contract changed
      /// @dev newMintPasses - address of new mint passes contract
      event MintPassesUpdated(address newMintPasses);
  
      /// @notice An error returned when the auction has already started.
      error AlreadyStarted();
      /// @notice An error returned when the auction has not yet started.
      error NotYetStarted();
      /// @notice An error returned when funds transfer was not passed.
      error FailedPaying(address payee, bytes data);
  
      constructor() {
           _disableInitializers();
      }
      
      modifier onGoing() {
          require(block.timestamp >= config.startTime && block.timestamp <= config.endTime, "Not on going");
          _;
      }
  
      modifier started() {
          if (!isStarted()) revert NotYetStarted();
          _;
      }
  
      modifier unstarted() {
          if (isStarted()) revert AlreadyStarted();
          _;
      }
  
      // required by the OZ UUPS module
      function _authorizeUpgrade(address) internal override onlyRole(DEFAULT_ADMIN_ROLE) {}
  
      function initialize(address __owner, address __operator, address __withdraw) external initializer {
          __Pausable_init();
          __AccessControl_init();
          __ReentrancyGuard_init();
          __UUPSUpgradeable_init();
  
          _grantRole(DEFAULT_ADMIN_ROLE, __owner);
          _grantRole(OPERATE_ROLE, __operator);
          _grantRole(WITHDRAW_ROLE, __withdraw);
      }
  
      function setProject(
          ProjectConfig memory config_,
          address beneficiary_,
          bool isNeedRefund_
      ) external onlyRole(OPERATE_ROLE) {
          // CHECKS inputs
          require(address(config_.passes) != address(0), "Pass contract must not be the zero address");
          require(config_.startTime < config_.endTime, "Invalid time");
          require(config_.startPrice >= config_.restPrice, "Start price must not be lower than rest price");
          require(config_.priceDropSlot > 0, "Price drop slot must be greater than 0");
          require(config_.halfPeriod > 0, "Half period must be greater than 0");
          require(beneficiary_ != address(0), "Beneficiary must not be the zero address");
          require(config_.maxSupply > 0, "Max mint must be greater than 0");
  
          // EFFECTS
          config = config_;
          beneficiary = beneficiary_;
  
          HalfPeriod = ABDKMathQuad.fromUInt(config_.halfPeriod);
          BaseValue = ABDKMathQuad.fromUInt(config_.startPrice);
  
          if (isNeedRefund_) {
              isRefund = false;
          } else {
              isRefund = true;
          }
  
          isNeedRefund = isNeedRefund_;
          
          isClear = false;
  
          require(config_.endTime -  config_.startTime > decayTime(), "The period is too short");
      }
  
      // PUBLIC FUNCTIONS
  
  /*
      /// @notice Mint a pass on the `passes` contract. Must include at least `currentPrice`.
      function mint() external payable onGoing whenNotPaused nonReentrant {
          // CHECKS inputs
          uint256 price = msg.value;
          uint256 cPrice = currentPrice();
          require(price >= cPrice, "Insufficient payment");
          require(totalSupply < maxSupply, "Maximum mint reached");
  
          if (isNeedRefund) {
              if (_mintInfos[msg.sender].amount == 0) {
                  _mintAddresses.push(msg.sender);
              }
          }
  
          // EFFECTS
          unchecked {
              _mintInfos[msg.sender].amount++;
              _mintInfos[msg.sender].totalPay += price;
              minPrice = cPrice;
              totalSupply++;
          }
  
          uint256 id = passes.mint(msg.sender, projectId, msg.sender);
  
          emit Purchase(msg.sender, id, price);
      }
  */
  
      /// @notice Mint up to three passes on the `passes` contract. Must include at least `currentPrice` * `quantity`.
      /// @param quantity The number of passes to mint: must be 1, 2, or 3
      function mint(uint256 quantity) external payable onGoing whenNotPaused nonReentrant {
          // CHECKS inputs
          require(quantity > 0, "Must mint at least one pass");
          uint256 payment = msg.value;
          uint256 price = payment / quantity;
          uint256 cPrice = currentPrice();
          require(price >= cPrice, "Insufficient payment");
          require(totalSupply + quantity <= config.maxSupply, "Maximum mint reached");
          require(_mintInfos[msg.sender].amount + quantity <= config.maxPerwallet, "Maximum per wallet mint reached");
          
          if (isNeedRefund) {
              require(!isContract(msg.sender), "only EOA");
  
              if (_mintInfos[msg.sender].amount == 0) {
                  _mintAddresses.push(msg.sender);
              }
          }
  
          // EFFECTS
          unchecked {
              _mintInfos[msg.sender].amount += quantity;
              _mintInfos[msg.sender].totalPay += payment;
  
              minPrice = cPrice;
              // Unchecked arithmetic: totalSupply cannot exceed max mint
              totalSupply = totalSupply + quantity;
          }
  
          // EFFECTS + INTERACTIONS: call mint on known contract (passes.mint contains no external interactions)
          // One call without try/catch to make sure at least one is minted.
          for (uint256 i = 0; i < quantity; i++) {
              uint256 id = config.passes.mint(msg.sender, config.projectId, msg.sender);
              emit Purchase(msg.sender, id, price);
          }
      }
  
      function isContract(address account) internal view returns (bool) {
          uint256 size;
          assembly {
              size := extcodesize(account)
          }
          return size > 0;
      }
      // OWNER FUNCTIONS
  
      function setProjectId(uint256 projectId_) external unstarted onlyRole(OPERATE_ROLE) {
          config.projectId = projectId_;
      }
  
      /// @notice Update the passes contract address
      /// @dev Can only be called by the contract `owner`. Reverts if the auction has already started.
      function setPasses(IMinter passes_) external unstarted onlyRole(OPERATE_ROLE) {
          // CHECKS inputs
          require(address(passes_) != address(0), "Pass contract must not be the zero address");
          config.passes = passes_;
      }
  
      /// @notice Pause this contract
      /// @dev Can only be called by the contract `owner`
      function pause() public onlyRole(OPERATE_ROLE) {
          super._pause();
          // More EFFECTS
          pauseStart = block.timestamp;
      }
  
      /// @notice Resume this contract
      /// @dev Can only be called by the contract `owner`. Pricing tiers will pick up where they left off.
      function unpause() public onlyRole(OPERATE_ROLE) {
          // CHECKS + EFFECTS: `Pausable` handles checking permissions and setting pause state
          super._unpause();
          // More EFFECTS
          if (block.timestamp <= config.startTime) {
              return;
          }
          // Find the amount time the auction should have been live, but was paused
          unchecked {
              // Unchecked arithmetic: computed value will be < block.timestamp and >= 0
              if (pauseStart < config.startTime) {
                  pastPauseDelay = block.timestamp - config.startTime;
              } else {
                  pastPauseDelay += (block.timestamp - pauseStart);
              }
          }
      }
  
      function setTime(uint256 startTime_, uint256 endTime_)
          external
          unstarted
          onlyRole(OPERATE_ROLE)
      {
          // CHECKS inputs
          require(startTime_ >= block.timestamp, "New start time cannot be in the past");
          require(endTime_ > startTime_, "New end time cannot be small than start time");
          // EFFECTS
          config.startTime = startTime_;
          config.endTime = endTime_;
      }
  
      /// @notice Update the auction start time
      /// @dev Can only be called by the contract `owner`. Reverts if the auction has already started.
      function setMaxSupply(uint256 maxSupply_) external unstarted onlyRole(OPERATE_ROLE) {
          // CHECKS inputs
          require(maxSupply_ > 0, "Max mint must be greater than 0");
          // EFFECTS
          config.maxSupply = maxSupply_;
      }
  
      /// @notice Update the auction price range and rate of decrease
      /// @dev Since the values are validated against each other, they are all set together. Can only be called by the
      ///  contract `owner`. Reverts if the auction has already started.
      function setPriceRange(uint256 startPrice_, uint256 restPrice_, uint256 priceDropSlot_, uint256 halfPeriod_)
          external
          unstarted
          onlyRole(OPERATE_ROLE)
      {
          // CHECKS inputs
          require(startPrice_ > 1e15, "Start price too low: check that prices are in wei");
          require(restPrice_ > 1e15, "Rest price too low: check that prices are in wei");
          require(startPrice_ >= restPrice_, "Start price must not be lower than rest price");
          require(priceDropSlot_ > 0, "Price drop slot must be greater than 0");
          require(halfPeriod_ > 0, "Half period must be greater than 0");
  
          // EFFECTS
          config.startPrice = startPrice_;
          config.restPrice = restPrice_;
          config.priceDropSlot = priceDropSlot_;
          config.halfPeriod = halfPeriod_;
  
          HalfPeriod = ABDKMathQuad.fromUInt(halfPeriod_);
          BaseValue = ABDKMathQuad.fromUInt(startPrice_);
      }
  
      // VIEW FUNCTIONS
  
      /// @notice Query the current price
      function currentPrice() public view returns (uint256) {
          uint256 time = timeElapsed();
          unchecked {
              time = (time / config.priceDropSlot) * config.priceDropSlot;
          }
  
          //function fromUInt (uint256 x) internal pure returns (bytes16)
          bytes16 currentTime = ABDKMathQuad.fromUInt(time);
  
          //first: currentTime / half period
          bytes16 step0 = ABDKMathQuad.div(currentTime, HalfPeriod);
  
          //second: pow_2
          bytes16 step1 = ABDKMathQuad.pow_2(step0);
  
          //then: startPrice / step1
          bytes16 step2 = ABDKMathQuad.div(BaseValue, step1);
  
          //last
          uint256 value = ABDKMathQuad.toUInt(step2);
  
          if (value < config.restPrice) {
              value = config.restPrice;
          }
  
          return value;
      }
  
      /// @notice Returns time of total decay period
      function decayTime() public view returns (uint256) {
          bytes16 step0 = ABDKMathQuad.log_2(BaseValue);
          bytes16 step1 = ABDKMathQuad.log_2(ABDKMathQuad.fromUInt(config.restPrice));
  
          bytes16 result = ABDKMathQuad.mul(HalfPeriod, ABDKMathQuad.sub(step0, step1));
          uint256 t = ABDKMathQuad.toUInt(result);
          unchecked {
              //padding 10
              t = ((t + 10) / 10) * 10;
          }
  
          return t;
      }
  
      /// @notice Returns timestamp of next price drop
      function nextPriceDrop() public view returns (uint256) {
          if (!isStarted()) return config.startTime + config.priceDropSlot;
  
          uint256 timeUntilNextDrop = config.priceDropSlot - (timeElapsed() % config.priceDropSlot);
  
          return block.timestamp + timeUntilNextDrop;
      }
  
      function endTime() public view returns (uint256) {
          return config.startTime + decayTime() + pastPauseDelay;
      }
  
      function isStarted() internal view returns (bool) {
          return (paused() ? pauseStart : block.timestamp) >= config.startTime;
      }
  
      function timeElapsed() internal view returns (uint256) {
          if (!isStarted()) return 0;
          unchecked {
              // pastPauseDelay cannot be greater than the time passed since startTime.
              if (!paused()) {
                  return block.timestamp - config.startTime - pastPauseDelay;
              }
  
              // pastPauseDelay cannot be greater than the time between startTime and pauseStart.
              return pauseStart - config.startTime - pastPauseDelay;
          }
      }
  
      function getMintInfo(address user) external view returns (uint256 minted) {
          minted = _mintInfos[user].amount;
      }
  
      function getProjectInfo() external view returns (ReturnConfig memory result) {
          result.startTime = config.startTime;
          result.endTime = config.endTime;
          result.startPrice = config.startPrice;
          result.restPrice = config.restPrice;
          result.priceDropSlot = config.priceDropSlot;
          result.halfPeriod = config.halfPeriod;
  
          result.maxSupply = config.maxSupply;
          result.totalSupply = totalSupply;
          result.maxPerwallet = config.maxPerwallet;
          result.decayTime = decayTime();
      }
  
      function clearAllStepOne() external onlyRole(OPERATE_ROLE) {
          require(!isClear, "has set step one");
          require(block.timestamp > config.endTime, "sale not end");
          isClear = true;
      }
  
      function clearAllStepTwo() external onlyRole(OPERATE_ROLE) {
          require(isClear, "step one not set");
  
          HalfPeriod = bytes16(0);
          BaseValue = bytes16(0);
          delete config;
          totalSupply = 0;
          minPrice = 0;
          pauseStart = 0;
          pastPauseDelay = 0;
          beneficiary = address(0);
          isRefund = false;
          isClear = false;
          for (uint256 i = 0; i < _mintAddresses.length;) {
              delete _mintInfos[_mintAddresses[i]];
              unchecked {
                  i++;
              }
          }
          delete _mintAddresses;
      }
  
      //////////////////////////////////////////////////////////////////////////////////////////////////
      ////                                                                                          ////
      ////                              WITHDRAW_ROLE                                               ////
      ////                                                                                          ////
      //////////////////////////////////////////////////////////////////////////////////////////////////
      function refund() external onlyRole(WITHDRAW_ROLE) {
          require(isNeedRefund, "not need refund");
          require(!isRefund, "has refunded");
          isRefund = true;
          uint256 refunds;
          address user;
  
          for (uint256 i = 0; i < _mintAddresses.length; i++) {
              user = _mintAddresses[i];
              refunds = _mintInfos[user].totalPay - _mintInfos[user].amount * minPrice;
  
              assembly {
                  if gt(refunds, 0) { let callStatus := call(gas(), user, refunds, 0, 0, 0, 0) }
              }
          }
      }
  
      function withdraw() public onlyRole(WITHDRAW_ROLE) {
          require(isRefund, "refund first");
          uint256 balanceAvailable = address(this).balance;
          (bool success, bytes memory data) = beneficiary.call{value: balanceAvailable}("");
          if (!success) revert FailedPaying(beneficiary, data);
      }
  }