// Contract: DogZone721
// Target function: function recover(bytes32 hash, bytes memory signature) internal pure returns (address)
/pull/522
      if (a == 0) return (true, 0);
      uint256 c = a * b;
      if (c / a != b) return (false, 0);
      return (true, c);
    }
  }

  /**
   * @dev Returns the division of two unsigned integers, with a division by zero flag.
   *
   * _Available since v3.4._
   */
  function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
    unchecked {
      if (b == 0) return (false, 0);
      return (true, a / b);
    }
  }

  /**
   * @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
   *
   * _Available since v3.4._
   */
  function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
    unchecked {
      if (b == 0) return (false, 0);
      return (true, a % b);
    }
  }

  /**
   * @dev Returns the addition of two unsigned integers, reverting on
   * overflow.
   *
   * Counterpart to Solidity's `+` operator.
   *
   * Requirements:
   *
   * - Addition cannot overflow.
   */
  function add(uint256 a, uint256 b) internal pure returns (uint256) {
    return a + b;
  }

  /**
   * @dev Returns the subtraction of two unsigned integers, reverting on
   * overflow (when the result is negative).
   *
   * Counterpart to Solidity's `-` operator.
   *
   * Requirements:
   *
   * - Subtraction cannot overflow.
   */
  function sub(uint256 a, uint256 b) internal pure returns (uint256) {
    return a - b;
  }

  /**
   * @dev Returns the multiplication of two unsigned integers, reverting on
   * overflow.
   *
   * Counterpart to Solidity's `*` operator.
   *
   * Requirements:
   *
   * - Multiplication cannot overflow.
   */
  function mul(uint256 a, uint256 b) internal pure returns (uint256) {
    return a * b;
  }

  /**
   * @dev Returns the integer division of two unsigned integers, reverting on
   * division by zero. The result is rounded towards zero.
   *
   * Counterpart to Solidity's `/` operator.
   *
   * Requirements:
   *
   * - The divisor cannot be zero.
   */
  function div(uint256 a, uint256 b) internal pure returns (uint256) {
    return a / b;
  }

  /**
   * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
   * reverting when dividing by zero.
   *
   * Counterpart to Solidity's `%` operator. This function uses a `revert`
   * opcode (which leaves remaining gas untouched) while Solidity uses an
   * invalid opcode to revert (consuming all remaining gas).
   *
   * Requirements:
   *
   * - The divisor cannot be zero.
   */
  function mod(uint256 a, uint256 b) internal pure returns (uint256) {
    return a % b;
  }

  /**
   * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
   * overflow (when the result is negative).
   *
   * CAUTION: This function is deprecated because it requires allocating memory for the error
   * message unnecessarily. For custom revert reasons use {trySub}.
   *
   * Counterpart to Solidity's `-` operator.
   *
   * Requirements:
   *
   * - Subtraction cannot overflow.
   */
  function sub(
    uint256 a,
    uint256 b,
    string memory errorMessage
  ) internal pure returns (uint256) {
    unchecked {
      require(b <= a, errorMessage);
      return a - b;
    }
  }

  /**
   * @dev Returns the integer division of two unsigned integers, reverting with custom message on
   * division by zero. The result is rounded towards zero.
   *
   * Counterpart to Solidity's `/` operator. Note: this function uses a
   * `revert` opcode (which leaves remaining gas untouched) while Solidity
   * uses an invalid opcode to revert (consuming all remaining gas).
   *
   * Requirements:
   *
   * - The divisor cannot be zero.
   */
  function div(
    uint256 a,
    uint256 b,
    string memory errorMessage
  ) internal pure returns (uint256) {
    unchecked {
      require(b > 0, errorMessage);
      return a / b;
    }
  }

  /**
   * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
   * reverting with custom message when dividing by zero.
   *
   * CAUTION: This function is deprecated because it requires allocating memory for the error
   * message unnecessarily. For custom revert reasons use {tryMod}.
   *
   * Counterpart to Solidity's `%` operator. This function uses a `revert`
   * opcode (which leaves remaining gas untouched) while Solidity uses an
   * invalid opcode to revert (consuming all remaining gas).
   *
   * Requirements:
   *
   * - The divisor cannot be zero.
   */
  function mod(
    uint256 a,
    uint256 b,
    string memory errorMessage
  ) internal pure returns (uint256) {
    unchecked {
      require(b > 0, errorMessage);
      return a % b;
    }
  }
}

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
  function _msgSender() internal view virtual returns (address) {
    return msg.sender;
  }

  function _msgData() internal view virtual returns (bytes calldata) {
    return msg.data;
  }
}

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165 {
  /**
   * @dev Returns true if this contract implements the interface defined by
   * `interfaceId`. See the corresponding
   * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
   * to learn more about how these ids are created.
   *
   * This function call must use less than 30 000 gas.
   */
  function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

/**
 * @dev Required interface of an ERC721 compliant contract.
 */
interface IERC721 is IERC165 {
  /**
   * @dev Emitted when `tokenId` token is transferred from `from` to `to`.
   */
  event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);

  /**
   * @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.
   */
  event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);

  /**
   * @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.
   */
  event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

  /**
   * @dev Returns the number of tokens in ``owner``'s account.
   */
  function balanceOf(address owner) external view returns (uint256 balance);

  /**
   * @dev Returns the owner of the `tokenId` token.
   *
   * Requirements:
   *
   * - `tokenId` must exist.
   */
  function ownerOf(uint256 tokenId) external view returns (address owner);

  /**
   * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
   * are aware of the ERC721 protocol to prevent tokens from being forever locked.
   *
   * Requirements:
   *
   * - `from` cannot be the zero address.
   * - `to` cannot be the zero address.
   * - `tokenId` token must exist and be owned by `from`.
   * - If the caller is not `from`, it must be have been allowed to move this token by either {approve} or {setApprovalForAll}.
   * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
   *
   * Emits a {Transfer} event.
   */
  function safeTransferFrom(
    address from,
    address to,
    uint256 tokenId
  ) external;

  /**
   * @dev Transfers `tokenId` token from `from` to `to`.
   *
   * WARNING: Usage of this method is discouraged, use {safeTransferFrom} whenever possible.
   *
   * Requirements:
   *
   * - `from` cannot be the zero address.
   * - `to` cannot be the zero address.
   * - `tokenId` token must be owned by `from`.
   * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
   *
   * Emits a {Transfer} event.
   */
  function transferFrom(
    address from,
    address to,
    uint256 tokenId
  ) external;

  /**
   * @dev Gives permission to `to` to transfer `tokenId` token to another account.
   * The approval is cleared when the token is transferred.
   *
   * Only a single account can be approved at a time, so approving the zero address clears previous approvals.
   *
   * Requirements:
   *
   * - The caller must own the token or be an approved operator.
   * - `tokenId` must exist.
   *
   * Emits an {Approval} event.
   */
  function approve(address to, uint256 tokenId) external;

  /**
   * @dev Returns the account approved for `tokenId` token.
   *
   * Requirements:
   *
   * - `tokenId` must exist.
   */
  function getApproved(uint256 tokenId) external view returns (address operator);

  /**
   * @dev Approve or remove `operator` as an operator for the caller.
   * Operators can call {transferFrom} or {safeTransferFrom} for any token owned by the caller.
   *
   * Requirements:
   *
   * - The `operator` cannot be the caller.
   *
   * Emits an {ApprovalForAll} event.
   */
  function setApprovalForAll(address operator, bool _approved) external;

  /**
   * @dev Returns if the `operator` is allowed to manage all of the assets of `owner`.
   *
   * See {setApprovalForAll}
   */
  function isApprovedForAll(address owner, address operator) external view returns (bool);

  /**
   * @dev Safely transfers `tokenId` token from `from` to `to`.
   *
   * Requirements:
   *
   * - `from` cannot be the zero address.
   * - `to` cannot be the zero address.
   * - `tokenId` token must exist and be owned by `from`.
   * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
   * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
   *
   * Emits a {Transfer} event.
   */
  function safeTransferFrom(
    address from,
    address to,
    uint256 tokenId,
    bytes calldata data
  ) external;
}

/**
 * @title ERC-721 Non-Fungible Token Standard, optional metadata extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721Metadata is IERC721 {
  /**
   * @dev Returns the token collection name.
   */
  function name() external view returns (string memory);

  /**
   * @dev Returns the token collection symbol.
   */
  function symbol() external view returns (string memory);

  /**
   * @dev Returns the Uniform Resource Identifier (URI) for `tokenId` token.
   */
  function tokenURI(uint256 tokenId) external view returns (string memory);
}

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 *
 * Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
 */
abstract contract ERC165 is IERC165 {
  /**
   * @dev See {IERC165-supportsInterface}.
   */
  function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
    return interfaceId == type(IERC165).interfaceId;
  }
}

/**
 * @title ERC721 token receiver interface
 * @dev Interface for any contract that wants to support safeTransfers
 * from ERC721 asset contracts.
 */
interface IERC721Receiver {
  /**
   * @dev Whenever an {IERC721} `tokenId` token is transferred to this contract via {IERC721-safeTransferFrom}
   * by `operator` from `from`, this function is called.
   *
   * It must return its Solidity selector to confirm the token transfer.
   * If any other value is returned or the interface is not implemented by the recipient, the transfer will be reverted.
   *
   * The selector can be obtained in Solidity with `IERC721.onERC721Received.selector`.
   */
  function onERC721Received(
    address operator,
    address from,
    uint256 tokenId,
    bytes calldata data
  ) external returns (bytes4);
}

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
  enum RecoverError {
    NoError,
    InvalidSignature,
    InvalidSignatureLength,
    InvalidSignatureS,
    InvalidSignatureV
  }

  function _throwError(RecoverError error) private pure {
    if (error == RecoverError.NoError) {
      return; // no error: do nothing
    } else if (error == RecoverError.InvalidSignature) {
      revert("ECDSA: invalid signature");
    } else if (error == RecoverError.InvalidSignatureLength) {
      revert("ECDSA: invalid signature length");
    } else if (error == RecoverError.InvalidSignatureS) {
      revert("ECDSA: invalid signature 's' value");
    } else if (error == RecoverError.InvalidSignatureV) {
      revert("ECDSA: invalid signature 'v' value");
    }
  }

  /**
   * @dev Returns the address that signed a hashed message (`hash`) with
   * `signature` or error string. This address can then be used for verification purposes.
   *
   * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
   * this function rejects them by requiring the `s` value to be in the lower
   * half order, and the `v` value to be either 27 or 28.
   *
   * IMPORTANT: `hash` _must_ be the result of a hash operation for the
   * verification to be secure: it is possible to craft signatures that
   * recover to arbitrary addresses for non-hashed data. A safe way to ensure
   * this is by receiving a hash of the original message (which may otherwise
   * be too long), and then calling {toEthSignedMessageHash} on it.
   *
   * Documentation for signature generation:
   * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
   * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
   *
   * _Available since v4.3._
   */
  function tryRecover(bytes32 hash, bytes memory signature)
    internal
    pure
    returns (address, RecoverError)
  {
    // Check the signature length
    // - case 65: r,s,v signature (standard)
    // - case 64: r,vs signature (cf https://eips.ethereum.org/EIPS/eip-2098) _Available since v4.1._
    if (signature.length == 65) {
      bytes32 r;
      bytes32 s;
      uint8 v;
      // ecrecover takes the signature parameters, and the only way to get them
      // currently is to use assembly.
      assembly {
        r := mload(add(signature, 0x20))
        s := mload(add(signature, 0x40))
        v := byte(0, mload(add(signature, 0x60)))
      }
      return tryRecover(hash, v, r, s);
    } else if (signature.length == 64) {
      bytes32 r;
      bytes32 vs;
      // ecrecover takes the signature parameters, and the only way to get them
      // currently is to use assembly.
      assembly {
        r := mload(add(signature, 0x20))
        vs := mload(add(signature, 0x40))
      }
      return tryRecover(hash, r, vs);
    } else {
      return (address(0), RecoverError.InvalidSignatureLength);
    }
  }