pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165 {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

pragma solidity ^0.8.0;


/**
 * @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 Emitted when `owner` pays to purchase a specific image id.
     */
    event Purchase(address indexed owner, string imageId, string name);

    /**
     * @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;
}

pragma solidity ^0.8.0;

/**
 * @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);
}

pragma solidity ^0.8.0;


/**
 * @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);
}

pragma solidity ^0.8.0;


interface IArtAI is IERC721 {
    function tokenIdForName(string memory _paintingName)
        external
        view
        returns (uint256);

    function tokenInfo(uint256 _tokenId)
        external
        view
        returns (
            string memory _imageHash,
            string memory _imageName,
            string memory _imageId
        );
}

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the amount of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves `amount` tokens from the caller's account to `recipient`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address recipient, uint256 amount)
        external
        returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender)
        external
        view
        returns (uint256);

    /**
     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `sender` to `recipient` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address sender,
        address recipient,
        uint256 amount
    ) external returns (bool);

    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(
        address indexed owner,
        address indexed spender,
        uint256 value
    );
}

pragma solidity ^0.8.0;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize, which returns 0 for contracts in
        // construction, since the code is only stored at the end of the
        // constructor execution.

        uint256 size;
        assembly {
            size := extcodesize(account)
        }
        return size > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(
            address(this).balance >= amount,
            "Address: insufficient balance"
        );

        (bool success, ) = recipient.call{value: amount}("");
        require(
            success,
            "Address: unable to send value, recipient may have reverted"
        );
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data)
        internal
        returns (bytes memory)
    {
        return functionCall(target, data, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return
            functionCallWithValue(
                target,
                data,
                value,
                "Address: low-level call with value failed"
            );
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(
            address(this).balance >= value,
            "Address: insufficient balance for call"
        );
        require(isContract(target), "Address: call to non-contract");

        (bool success, bytes memory returndata) = target.call{value: value}(
            data
        );
        return verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data)
        internal
        view
        returns (bytes memory)
    {
        return
            functionStaticCall(
                target,
                data,
                "Address: low-level static call failed"
            );
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");

        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data)
        internal
        returns (bytes memory)
    {
        return
            functionDelegateCall(
                target,
                data,
                "Address: low-level delegate call failed"
            );
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(isContract(target), "Address: delegate call to non-contract");

        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly

                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

pragma solidity ^0.8.0;

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
}

pragma solidity ^0.8.0;

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _HEX_SYMBOLS = "0123456789abcdef";

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        // Inspired by OraclizeAPI's implementation - MIT licence
        // https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol

        if (value == 0) {
            return "0";
        }
        uint256 temp = value;
        uint256 digits;
        while (temp != 0) {
            digits++;
            temp /= 10;
        }
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
            value /= 10;
        }
        return string(buffer);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        if (value == 0) {
            return "0x00";
        }
        uint256 temp = value;
        uint256 length = 0;
        while (temp != 0) {
            length++;
            temp >>= 8;
        }
        return toHexString(value, length);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length)
        internal
        pure
        returns (string memory)
    {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _HEX_SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }
}

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 ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId)
        public
        view
        virtual
        override
        returns (bool)
    {
        return interfaceId == type(IERC165).interfaceId;
    }
}

pragma solidity ^0.8.0;

contract Ownable {
    address _owner;

    constructor() {
        _owner = msg.sender;
    }

    modifier onlyOwner() {
        require(
            msg.sender == _owner,
            "Only the contract owner may call this function"
        );
        _;
    }

    function owner() public view virtual returns (address) {
        return _owner;
    }

    function transferOwnership(address newOwner) external onlyOwner {
        require(newOwner != address(0));
        _owner = newOwner;
    }

    function withdrawBalance() external onlyOwner {
        payable(_owner).transfer(address(this).balance);
    }

    function withdrawAmountTo(address _recipient, uint256 _amount)
        external
        onlyOwner
    {
        require(address(this).balance >= _amount);
        payable(_recipient).transfer(_amount);
    }
}

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 Pausable is Context, Ownable {
    /**
     * @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;
    bool private _allowMinting;
    bool private _allowExtending;

    /**
     * @dev Initializes the contract in paused state.
     */
    constructor() {
        _paused = true;
        _allowMinting = false;
        _allowExtending = false;
    }

    /**
     * @dev Returns true if the contract is paused, and false otherwise.
     */
    function paused() public view virtual returns (bool) {
        return _paused;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is not paused.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    modifier whenNotPaused() {
        require(!paused(), "Pausable: paused");
        _;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is paused.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    modifier whenPaused() {
        require(paused(), "Pausable: not paused");
        _;
    }

    modifier whenMintingOpen() {
        require(!paused() && _allowMinting, "Minting is not open");
        _;
    }

    modifier whenExtendingOpen() {
        require(!paused() && _allowExtending, "Extending is not open");
        _;
    }

    function pause() external onlyOwner {
        _pause();
    }

    function unpause() external onlyOwner {
        _unpause();
    }

    function openExtending() external onlyOwner {
        _openExtending();
    }

    function closeExtending() external onlyOwner {
        _closeExtending();
    }

    function openMinting() external onlyOwner {
        _openMinting();
    }

    function closeMinting() external onlyOwner {
        _closeMinting();
    }

    /**
     * @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());
    }

    function _openMinting() internal virtual whenNotPaused {
        _allowMinting = true;
    }

    function _closeMinting() internal virtual {
        _allowMinting = false;
    }

    function _openExtending() internal virtual whenNotPaused {
        _allowExtending = true;
    }

    function _closeExtending() internal virtual {
        _allowExtending = false;
    }
}

pragma solidity ^0.8.0;


/**
 * @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);
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. 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.
     */
    function recover(bytes32 hash, bytes memory signature)
        internal
        pure
        returns (address)
    {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address, RecoverError) {
        bytes32 s;
        uint8 v;
        assembly {
            s := and(
                vs,
                0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
            )
            v := add(shr(255, vs), 27)
        }
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address, RecoverError) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (
            uint256(s) >
            0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0
        ) {
            return (address(0), RecoverError.InvalidSignatureS);
        }
        if (v != 27 && v != 28) {
            return (address(0), RecoverError.InvalidSignatureV);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash)
        internal
        pure
        returns (bytes32)
    {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return
            keccak256(
                abi.encodePacked("\x19Ethereum Signed Message:\n32", hash)
            );
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s)
        internal
        pure
        returns (bytes32)
    {
        return
            keccak256(
                abi.encodePacked(
                    "\x19Ethereum Signed Message:\n",
                    Strings.toString(s.length),
                    s
                )
            );
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash)
        internal
        pure
        returns (bytes32)
    {
        return
            keccak256(
                abi.encodePacked("\x19\x01", domainSeparator, structHash)
            );
    }
}
pragma solidity ^0.8.0;













contract ArtAI is Context, ERC165, IERC721, IERC721Metadata, Ownable, Pausable {
    /**
     * @dev Implementation of https://eips.ethereum.org/EIPS/eip-721[ERC721] Non-Fungible Token Standard, including
     * the Metadata extension, but not including the Enumerable extension, which is available separately as
     * {ERC721Enumerable}.
     */

    using Address for address;
    using Strings for uint256;
    using ECDSA for bytes;

    event Burn(
        address indexed owner,
        uint256 indexed tokenId1,
        uint256 indexed tokenId2
    );
    event Extend(
        address owner,
        uint256 tokenId,
        string oldHash,
        string newHash,
        string oldName,
        string newName,
        string oldId,
        string newId
    );

    // Max total supply
    uint256 public maxSupply = 5000;
    // Max painting name length
    uint256 private _maxImageNameLength = 100;
    // purchase price
    uint256 public _purchasePrice = 50000000000000000 wei;
    // public signer address
    address private _messageSigner;
    // graveyard address
    address private _graveyardAddress =
        0x000000000000000000000000000000000000dEaD;
    // price in burn tokens for a mint
    uint256 private _mintCostInBurnTokens = 1;
    // Gen 1 Address
    address private _gen1Address = 0xaA20f900e24cA7Ed897C44D92012158f436ef791;

    // Paintbrush ERC20 address
    address private _paintbrushAddress;

    // baseURI for Metadata
    string private _metadataURI = "https://art-ai.com/api/gen2/metadata/";

    // Min Paintbrush balance to extend
    uint256 public _minPaintbrushesToExtend;

    // Token name
    string private _name;

    // Token symbol
    string private _symbol;

    // Token supply
    uint256 public _tokenSupply;

    // Mapping from token ID to owner address
    mapping(uint256 => address) private _owners;

    // Mapping owner address to token count
    mapping(address => uint256) private _balances;

    // Mapping from token ID to approved address
    mapping(uint256 => address) private _tokenApprovals;

    // Mapping from owner to operator approvals
    mapping(address => mapping(address => bool)) private _operatorApprovals;

    // Mapping from image name to its purchased status
    mapping(string => bool) private _namePurchases;

    // Mapping from image name to its token id
    mapping(string => uint256) private _nameToTokenId;

    // Token Id to image hash
    mapping(uint256 => string) private _tokenImageHashes;

    // Token Id to image name
    mapping(uint256 => string) private _tokenIdToName;

    // Token Id to image id
    mapping(uint256 => string) private _tokenIdToImageId;

    // Status of signed messages
    mapping(bytes => bool) private _usedSignedMessages;

    // used IPFS hashes
    mapping(string => bool) private _usedIPFSHashes;

    // used image IDs
    mapping(string => bool) private _usedImageIds;

    // Burn counts 'tokens' for addresses
    mapping(address => uint256) private _burnTokens;

    // Gen 1 Available names for address
    mapping(address => mapping(string => bool)) private _availableBurnedNames;

    // Gen 2 available names for a token id
    mapping(uint256 => mapping(string => bool)) private _availableExtendedNames;

    /**
     * @dev Initializes the contract by setting a `name` and a `symbol` to the token collection.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    function isExtensionNameAvailableForToken(
        uint256 _tokenId,
        string memory _imageName
    ) external view returns (bool) {
        return _availableExtendedNames[_tokenId][_imageName];
    }

    function isNameAvailableForAddress(
        address _address,
        string memory _imageName
    ) external view returns (bool) {
        return _availableBurnedNames[_address][_imageName];
    }

    function setPaintbrushAddress(address newAddress) external onlyOwner {
        _paintbrushAddress = newAddress;
    }

    function setMinPaintbrushesToExtend(uint256 amount) external onlyOwner {
        _minPaintbrushesToExtend = amount;
    }

    function setGen1Address(address newAddress) external onlyOwner {
        _gen1Address = newAddress;
    }

    function tokenIdForName(string memory _paintingName)
        external
        view
        returns (uint256)
    {
        return _nameToTokenId[_paintingName];
    }

    function setBaseURI(string memory newURI) external onlyOwner {
        _metadataURI = newURI;
    }

    function setPurchasePrice(uint256 newPrice) external onlyOwner {
        _purchasePrice = newPrice;
    }

    function totalSupply() external view returns (uint256) {
        return maxSupply;
    }

    function setMessageSigner(address newSigner) external onlyOwner {
        _messageSigner = newSigner;
    }

    function burnTokenBalance(address owner) public view returns (uint256) {
        return _burnTokens[owner];
    }

    function lockMinting() external onlyOwner {
        maxSupply = _tokenSupply;
        _closeMinting();
    }

    function _burn(uint256 _tokenId1, uint256 _tokenId2) private {
        IArtAI(_gen1Address).safeTransferFrom(
            msg.sender,
            _graveyardAddress,
            _tokenId1
        );
        IArtAI(_gen1Address).safeTransferFrom(
            msg.sender,
            _graveyardAddress,
            _tokenId2
        );
        (, string memory _name1, ) = IArtAI(_gen1Address).tokenInfo(_tokenId1);
        (, string memory _name2, ) = IArtAI(_gen1Address).tokenInfo(_tokenId2);

        _availableBurnedNames[msg.sender][_name1] = true;
        _availableBurnedNames[msg.sender][_name2] = true;
        _burnTokens[msg.sender] += 1;

        emit Burn(msg.sender, _tokenId1, _tokenId2);
    }

    function _verifyName(string memory _imageName) private view returns (bool) {
        if (_namePurchases[_imageName]) {
            return false;
        }
        if (IArtAI(_gen1Address).tokenIdForName(_imageName) != 0) {
            return _availableBurnedNames[msg.sender][_imageName];
        }
        return true;
    }

    function _verifyName(string memory _imageName, uint256 _tokenId)
        private
        view
        returns (bool)
    {
        if (_availableExtendedNames[_tokenId][_imageName]) {
            return true;
        }
        return _verifyName(_imageName);
    }

    function _mint(
        address _owner,
        string memory _imageName,
        string memory _imageHash,
        string memory _imageId,
        bytes memory _signedMessage
    ) private returns (uint256) {
        uint256 _newTokenId = _tokenSupply + 1;

        _safeMint(_owner, _newTokenId);
        _updateStoredValues(
            _imageName,
            _imageHash,
            _imageId,
            _signedMessage,
            _newTokenId
        );
        _burnTokens[msg.sender] -= 1;

        return _newTokenId;
    }

    function _verifySignedMessage(
        string memory _imageHash,
        string memory _imageId,
        string memory _imageName,
        bytes memory _signedMessage
    ) internal returns (bool) {
        if (_usedSignedMessages[_signedMessage]) {
            return false;
        }

        bytes32 _message = ECDSA.toEthSignedMessageHash(
            abi.encodePacked(_imageId, _imageHash, _imageName)
        );

        address signer = ECDSA.recover(_message, _signedMessage);

        if (signer != _messageSigner) {
            return false;
        }

        _usedSignedMessages[_signedMessage] = true;
        return true;
    }

    function _verifyParams(
        string memory _imageName,
        string memory _imageHash,
        string memory _imageId,
        bytes memory _signedMessage
    ) internal {
        require(!_usedImageIds[_imageId], "ImageID");
        require(!_usedIPFSHashes[_imageHash], "IPFS hash");
        require(bytes(_imageName).length <= _maxImageNameLength, "Name");
        require(msg.value >= _purchasePrice, "value");
        require(_verifyName(_imageName), "name purchased");
        require(
            _verifySignedMessage(
                _imageHash,
                _imageId,
                _imageName,
                _signedMessage
            ),
            "Signature"
        );
    }

    function _verifyParams(
        string memory _imageName,
        string memory _imageHash,
        string memory _imageId,
        bytes memory _signedMessage,
        uint256 _tokenId
    ) internal {
        require(!_usedImageIds[_imageId], "ImageID");
        require(!_usedIPFSHashes[_imageHash], "IPFS hash");
        require(bytes(_imageName).length <= _maxImageNameLength, "Name");
        require(msg.value >= _purchasePrice, "value");
        require(_verifyName(_imageName, _tokenId), "name purchased");
        require(
            _verifySignedMessage(
                _imageHash,
                _imageId,
                _imageName,
                _signedMessage
            ),
            "Signature"
        );
    }

    function _updateStoredValues(
        string memory _imageName,
        string memory _imageHash,
        string memory _imageId,
        bytes memory _signedMessage,
        uint256 _tokenId
    ) private {
        _namePurchases[_imageName] = true;
        _usedSignedMessages[_signedMessage] = true;
        _usedImageIds[_imageId] = true;
        _usedIPFSHashes[_imageHash] = true;
        _availableExtendedNames[_tokenId][_imageName] = true;

        _nameToTokenId[_imageName] = _tokenId;
        _tokenImageHashes[_tokenId] = _imageHash;
        _tokenIdToName[_tokenId] = _imageName;
        _tokenIdToImageId[_tokenId] = _imageId;
    }

    function _extend(
        uint256 _tokenId,
        string memory _imageHash,
        string memory _imageName,
        string memory _imageId,
        bytes memory _signedMessage
    ) private {
        string memory oldHash = _tokenImageHashes[_tokenId];
        string memory oldName = _tokenIdToName[_tokenId];
        string memory oldId = _tokenIdToImageId[_tokenId];

        _updateStoredValues(
            _imageName,
            _imageHash,
            _imageId,
            _signedMessage,
            _tokenId
        );

        emit Extend(
            msg.sender,
            _tokenId,
            oldHash,
            _imageHash,
            oldName,
            _imageName,
            oldId,
            _imageId
        );
    }

    function extend(
        uint256 _tokenId,
        string memory _imageHash,
        string memory _imageName,
        string memory _imageId,
        bytes memory _signedMessage
    ) external payable whenExtendingOpen {
        require(ownerOf(_tokenId) == msg.sender, "Ownership");
        require(
            IERC721(_gen1Address).balanceOf(msg.sender) > 0 ||
                IERC20(_paintbrushAddress).balanceOf(msg.sender) >=
                _minPaintbrushesToExtend,
            "Balance"
        );
        _verifyParams(
            _imageName,
            _imageHash,
            _imageId,
            _signedMessage,
            _tokenId
        );

        _extend(_tokenId, _imageHash, _imageName, _imageId, _signedMessage);
    }

    function burn(uint256 _tokenId1, uint256 _tokenId2)
        external
        whenMintingOpen
    {
        require(_tokenId1 != _tokenId2, "same tokens");
        IERC721 iface = IERC721(_gen1Address);
        require(iface.ownerOf(_tokenId1) == msg.sender, "Ownership");
        require(iface.ownerOf(_tokenId2) == msg.sender, "Ownership");
        require(
            iface.isApprovedForAll(msg.sender, address(this)),
            "transfer perms"
        );

        _burn(_tokenId1, _tokenId2);
    }

    function mint(
        string memory _imageHash,
        string memory _imageName,
        string memory _imageId,
        bytes memory _signedMessage
    ) external payable whenMintingOpen returns (uint256) {
        require(_tokenSupply < maxSupply, "Maximum supply");
        require(
            _burnTokens[msg.sender] >= _mintCostInBurnTokens,
            "burn tokens"
        );
        _verifyParams(_imageName, _imageHash, _imageId, _signedMessage);
        uint256 _newTokenId = _mint(
            msg.sender,
            _imageName,
            _imageHash,
            _imageId,
            _signedMessage
        );

        return _newTokenId;
    }

    function tokenInfo(uint256 _tokenId)
        external
        view
        returns (
            string memory _imageHash,
            string memory _imageName,
            string memory _imageId
        )
    {
        return (
            _tokenImageHashes[_tokenId],
            _tokenIdToName[_tokenId],
            _tokenIdToImageId[_tokenId]
        );
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId)
        public
        view
        virtual
        override(ERC165, IERC165)
        returns (bool)
    {
        return
            interfaceId == type(IERC721).interfaceId ||
            interfaceId == type(IERC721Metadata).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC721-balanceOf}.
     */
    function balanceOf(address owner)
        public
        view
        virtual
        override
        returns (uint256)
    {
        require(owner != address(0), "ERC721: zero address");
        return _balances[owner];
    }

    /**
     * @dev See {IERC721-ownerOf}.
     */
    function ownerOf(uint256 tokenId)
        public
        view
        virtual
        override
        returns (address)
    {
        address owner = _owners[tokenId];
        require(owner != address(0), "ERC721: nonexistent token");
        return owner;
    }

    /**
     * @dev See {IERC721Metadata-name}.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev See {IERC721Metadata-symbol}.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev See {IERC721Metadata-tokenURI}.
     */
    function tokenURI(uint256 tokenId)
        public
        view
        virtual
        override
        returns (string memory)
    {
        require(_exists(tokenId), "ERC721Metadata: nonexistent token");

        string memory baseURI = _baseURI();
        return
            bytes(baseURI).length > 0
                ? string(abi.encodePacked(baseURI, tokenId.toString()))
                : "";
    }

    /**
     * @dev Base URI for computing {tokenURI}. If set, the resulting URI for each
     * token will be the concatenation of the `baseURI` and the `tokenId`. Empty
     * by default, can be overriden in child contracts.
     */
    function _baseURI() internal view virtual returns (string memory) {
        return _metadataURI;
    }

    /**
     * @dev See {IERC721-approve}.
     */
    function approve(address to, uint256 tokenId) public virtual override {
        address owner = ArtAI.ownerOf(tokenId);
        require(to != owner, "ERC721: current owner");

        require(
            _msgSender() == owner || isApprovedForAll(owner, _msgSender()),
            "ERC721: approve caller is not owner nor approved for all"
        );

        _approve(to, tokenId);
    }

    /**
     * @dev See {IERC721-getApproved}.
     */
    function getApproved(uint256 tokenId)
        public
        view
        virtual
        override
        returns (address)
    {
        require(_exists(tokenId), "ERC721: nonexistent token");

        return _tokenApprovals[tokenId];
    }

    /**
     * @dev See {IERC721-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved)
        public
        virtual
        override
    {
        require(operator != _msgSender(), "ERC721: approve to caller");

        _operatorApprovals[_msgSender()][operator] = approved;
        emit ApprovalForAll(_msgSender(), operator, approved);
    }

    /**
     * @dev See {IERC721-isApprovedForAll}.
     */
    function isApprovedForAll(address owner, address operator)
        public
        view
        virtual
        override
        returns (bool)
    {
        return _operatorApprovals[owner][operator];
    }

    /**
     * @dev See {IERC721-transferFrom}.
     */
    function transferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public virtual override {
        //solhint-disable-next-line max-line-length
        require(
            _isApprovedOrOwner(_msgSender(), tokenId),
            "ERC721: not owner nor approved"
        );

        _transfer(from, to, tokenId);
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public virtual override {
        safeTransferFrom(from, to, tokenId, "");
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId,
        bytes memory _data
    ) public virtual override {
        require(
            _isApprovedOrOwner(_msgSender(), tokenId),
            "ERC721: not owner nor approved"
        );
        _safeTransfer(from, to, tokenId, _data);
    }

    /**
     * @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.
     *
     * `_data` is additional data, it has no specified format and it is sent in call to `to`.
     *
     * This internal function is equivalent to {safeTransferFrom}, and can be used to e.g.
     * implement alternative mechanisms to perform token transfer, such as signature-based.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeTransfer(
        address from,
        address to,
        uint256 tokenId,
        bytes memory _data
    ) internal virtual {
        _transfer(from, to, tokenId);
        require(
            _checkOnERC721Received(from, to, tokenId, _data),
            "ERC721: non ERC721Receiver implementer"
        );
    }

    /**
     * @dev Returns whether `tokenId` exists.
     *
     * Tokens can be managed by their owner or approved accounts via {approve} or {setApprovalForAll}.
     *
     * Tokens start existing when they are minted (`_mint`),
     * and stop existing when they are burned (`_burn`).
     */
    function _exists(uint256 tokenId) internal view virtual returns (bool) {
        return _owners[tokenId] != address(0);
    }

    /**
     * @dev Returns whether `spender` is allowed to manage `tokenId`.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function _isApprovedOrOwner(address spender, uint256 tokenId)
        internal
        view
        virtual
        returns (bool)
    {
        require(_exists(tokenId), "ERC721: nonexistent token");
        address owner = ArtAI.ownerOf(tokenId);
        return (spender == owner ||
            getApproved(tokenId) == spender ||
            isApprovedForAll(owner, spender));
    }

    /**
     * @dev Safely mints `tokenId` and transfers it to `to`.
     *
     * Requirements:
     *
     * - `tokenId` must not exist.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeMint(address to, uint256 tokenId) internal virtual {
        _safeMint(to, tokenId, "");
    }

    /**
     * @dev Same as {xref-ERC721-_safeMint-address-uint256-}[`_safeMint`], with an additional `data` parameter which is
     * forwarded in {IERC721Receiver-onERC721Received} to contract recipients.
     */
    function _safeMint(
        address to,
        uint256 tokenId,
        bytes memory _data
    ) internal virtual {
        _mint(to, tokenId);
        require(
            _checkOnERC721Received(address(0), to, tokenId, _data),
            "ERC721: non ERC721Receiver implementer"
        );
    }

    /**
     * @dev Mints `tokenId` and transfers it to `to`.
     *
     * WARNING: Usage of this method is discouraged, use {_safeMint} whenever possible
     *
     * Requirements:
     *
     * - `tokenId` must not exist.
     * - `to` cannot be the zero address.
     *
     * Emits a {Transfer} event.
     */
    function _mint(address to, uint256 tokenId) internal virtual {
        require(to != address(0), "ERC721: zero address");
        require(!_exists(tokenId), "ERC721: token already minted");

        _beforeTokenTransfer(address(0), to, tokenId);

        _balances[to] += 1;
        _owners[tokenId] = to;
        _tokenSupply += 1;

        emit Transfer(address(0), to, tokenId);
    }

    /**
     * @dev Transfers `tokenId` from `from` to `to`.
     *  As opposed to {transferFrom}, this imposes no restrictions on msg.sender.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     *
     * Emits a {Transfer} event.
     */
    function _transfer(
        address from,
        address to,
        uint256 tokenId
    ) internal virtual {
        require(ArtAI.ownerOf(tokenId) == from, "ERC721: not own");
        require(to != address(0), "ERC721: zero address");

        _beforeTokenTransfer(from, to, tokenId);

        // Clear approvals from the previous owner
        _approve(address(0), tokenId);

        _balances[from] -= 1;
        _balances[to] += 1;
        _owners[tokenId] = to;

        emit Transfer(from, to, tokenId);
    }

    /**
     * @dev Approve `to` to operate on `tokenId`
     *
     * Emits a {Approval} event.
     */
    function _approve(address to, uint256 tokenId) internal virtual {
        _tokenApprovals[tokenId] = to;
        emit Approval(ArtAI.ownerOf(tokenId), to, tokenId);
    }

    /**
     * @dev Internal function to invoke {IERC721Receiver-onERC721Received} on a target address.
     * The call is not executed if the target address is not a contract.
     *
     * @param from address representing the previous owner of the given token ID
     * @param to target address that will receive the tokens
     * @param tokenId uint256 ID of the token to be transferred
     * @param _data bytes optional data to send along with the call
     * @return bool whether the call correctly returned the expected magic value
     */
    function _checkOnERC721Received(
        address from,
        address to,
        uint256 tokenId,
        bytes memory _data
    ) private returns (bool) {
        if (to.isContract()) {
            try
                IERC721Receiver(to).onERC721Received(
                    _msgSender(),
                    from,
                    tokenId,
                    _data
                )
            returns (bytes4 retval) {
                return retval == IERC721Receiver.onERC721Received.selector;
            } catch (bytes memory reason) {
                if (reason.length == 0) {
                    revert("ERC721: non ERC721Receiver implementer");
                } else {
                    assembly {
                        revert(add(32, reason), mload(reason))
                    }
                }
            }
        } else {
            return true;
        }
    }

    /**
     * @dev Hook that is called before any token transfer. This includes minting
     * and burning.
     *
     * Calling conditions:
     *
     * - When `from` and `to` are both non-zero, ``from``'s `tokenId` will be
     * transferred to `to`.
     * - When `from` is zero, `tokenId` will be minted for `to`.
     * - When `to` is zero, ``from``'s `tokenId` will be burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 tokenId
    ) internal virtual {}
}