// Contract: AuctionERC721SaleNonceHolder
// Target function: function transferFrom(
 function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        return sub(a, b, "SafeMath: subtraction overflow");
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     * - Subtraction cannot overflow.
     *
     * _Available since v2.4.0._
     */
    function sub(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        uint256 c = a - b;

        return c;
    }

    /**
     * @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) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) {
            return 0;
        }

        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");

        return c;
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts 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) internal pure returns (uint256) {
        return div(a, b, "SafeMath: division by zero");
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts 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.
     *
     * _Available since v2.4.0._
     */
    function div(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        // Solidity only automatically asserts when dividing by 0
        require(b > 0, errorMessage);
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold

        return c;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts 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 mod(a, b, "SafeMath: modulo by zero");
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts with custom message 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.
     *
     * _Available since v2.4.0._
     */
    function mod(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        require(b != 0, errorMessage);
        return a % b;
    }
}

/**
 * @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) {
        // According to EIP-1052, 0x0 is the value returned for not-yet created accounts
        // and 0xc5d2460186f7233c927e7db2dcc703c0e500b653ca82273b7bfad8045d85a470 is returned
        // for accounts without code, i.e. `keccak256('')`
        bytes32 codehash;
        bytes32 accountHash =
            0xc5d2460186f7233c927e7db2dcc703c0e500b653ca82273b7bfad8045d85a470;
        // solhint-disable-next-line no-inline-assembly
        assembly {
            codehash := extcodehash(account)
        }
        return (codehash != accountHash && codehash != 0x0);
    }

    /**
     * @dev Converts an `address` into `address payable`. Note that this is
     * simply a type cast: the actual underlying value is not changed.
     *
     * _Available since v2.4.0._
     */
    function toPayable(address account)
        internal
        pure
        returns (address payable)
    {
        return address(uint160(account));
    }

    /**
     * @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].
     *
     * _Available since v2.4.0._
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(
            address(this).balance >= amount,
            "Address: insufficient balance"
        );

        // solhint-disable-next-line avoid-call-value
        (bool success, ) = recipient.call.value(amount)("");
        require(
            success,
            "Address: unable to send value, recipient may have reverted"
        );
    }
}

/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented or decremented by one. This can be used e.g. to track the number
 * of elements in a mapping, issuing ERC721 ids, or counting request ids.
 *
 * Include with `using Counters for Counters.Counter;`
 * Since it is not possible to overflow a 256 bit integer with increments of one, `increment` can skip the {SafeMath}
 * overflow check, thereby saving gas. This does assume however correct usage, in that the underlying `_value` is never
 * directly accessed.
 */
library Counters {
    using SafeMath for uint256;

    struct Counter {
        // This variable should never be directly accessed by users of the library: interactions must be restricted to
        // the library's function. As of Solidity v0.5.2, this cannot be enforced, though there is a proposal to add
        // this feature: see https://github.com/ethereum/solidity/issues/4637
        uint256 _value; // default: 0
    }

    function current(Counter storage counter) internal view returns (uint256) {
        return counter._value;
    }

    function increment(Counter storage counter) internal {
        // The {SafeMath} overflow check can be skipped here, see the comment at the top
        counter._value += 1;
    }

    function decrement(Counter storage counter) internal {
        counter._value = counter._value.sub(1);
    }
}

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts may inherit from this and call {_registerInterface} to declare
 * their support of an interface.
 */
contract ERC165 is IERC165 {
    /*
     * bytes4(keccak256('supportsInterface(bytes4)')) == 0x01ffc9a7
     */
    bytes4 private constant _INTERFACE_ID_ERC165 = 0x01ffc9a7;

    /**
     * @dev Mapping of interface ids to whether or not it's supported.
     */
    mapping(bytes4 => bool) private _supportedInterfaces;

    constructor() internal {
        // Derived contracts need only register support for their own interfaces,
        // we register support for ERC165 itself here
        _registerInterface(_INTERFACE_ID_ERC165);
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     *
     * Time complexity O(1), guaranteed to always use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId)
        external
        view
        returns (bool)
    {
        return _supportedInterfaces[interfaceId];
    }

    /**
     * @dev Registers the contract as an implementer of the interface defined by
     * `interfaceId`. Support of the actual ERC165 interface is automatic and
     * registering its interface id is not required.
     *
     * See {IERC165-supportsInterface}.
     *
     * Requirements:
     *
     * - `interfaceId` cannot be the ERC165 invalid interface (`0xffffffff`).
     */
    function _registerInterface(bytes4 interfaceId) internal {
        require(interfaceId != 0xffffffff, "ERC165: invalid interface id");
        _supportedInterfaces[interfaceId] = true;
    }
}

/**
 * @title ERC721 Non-Fungible Token Standard basic implementation
 * @dev see https://eips.ethereum.org/EIPS/eip-721
 */
contract ERC721 is Context, ERC165, IERC721 {
    using SafeMath for uint256;
    using Address for address;
    using Counters for Counters.Counter;

    // Equals to `bytes4(keccak256("onERC721Received(address,address,uint256,bytes)"))`
    // which can be also obtained as `IERC721Receiver(0).onERC721Received.selector`
    bytes4 private constant _ERC721_RECEIVED = 0x150b7a02;

    // Mapping from token ID to owner
    mapping(uint256 => address) private _tokenOwner;

    // Mapping from token ID to approved address
    mapping(uint256 => address) private _tokenApprovals;

    // Mapping from owner to number of owned token
    mapping(address => Counters.Counter) private _ownedTokensCount;

    // Mapping from owner to operator approvals
    mapping(address => mapping(address => bool)) private _operatorApprovals;

    /*
     *     bytes4(keccak256('balanceOf(address)')) == 0x70a08231
     *     bytes4(keccak256('ownerOf(uint256)')) == 0x6352211e
     *     bytes4(keccak256('approve(address,uint256)')) == 0x095ea7b3
     *     bytes4(keccak256('getApproved(uint256)')) == 0x081812fc
     *     bytes4(keccak256('setApprovalForAll(address,bool)')) == 0xa22cb465
     *     bytes4(keccak256('isApprovedForAll(address,address)')) == 0xe985e9c5
     *     bytes4(keccak256('transferFrom(address,address,uint256)')) == 0x23b872dd
     *     bytes4(keccak256('safeTransferFrom(address,address,uint256)')) == 0x42842e0e
     *     bytes4(keccak256('safeTransferFrom(address,address,uint256,bytes)')) == 0xb88d4fde
     *
     *     => 0x70a08231 ^ 0x6352211e ^ 0x095ea7b3 ^ 0x081812fc ^
     *        0xa22cb465 ^ 0xe985e9c ^ 0x23b872dd ^ 0x42842e0e ^ 0xb88d4fde == 0x80ac58cd
     */
    bytes4 private constant _INTERFACE_ID_ERC721 = 0x80ac58cd;

    constructor() public {
        // register the supported interfaces to conform to ERC721 via ERC165
        _registerInterface(_INTERFACE_ID_ERC721);
    }

    /**
     * @dev Gets the balance of the specified address.
     * @param owner address to query the balance of
     * @return uint256 representing the amount owned by the passed address
     */
    function balanceOf(address owner) public view returns (uint256) {
        require(
            owner != address(0),
            "ERC721: balance query for the zero address"
        );

        return _ownedTokensCount[owner].current();
    }

    /**
     * @dev Gets the owner of the specified token ID.
     * @param tokenId uint256 ID of the token to query the owner of
     * @return address currently marked as the owner of the given token ID
     */
    function ownerOf(uint256 tokenId) public view returns (address) {
        address owner = _tokenOwner[tokenId];
        require(
            owner != address(0),
            "ERC721: owner query for nonexistent token"
        );

        return owner;
    }

    /**
     * @dev Approves another address to transfer the given token ID
     * The zero address indicates there is no approved address.
     * There can only be one approved address per token at a given time.
     * Can only be called by the token owner or an approved operator.
     * @param to address to be approved for the given token ID
     * @param tokenId uint256 ID of the token to be approved
     */
    function approve(address to, uint256 tokenId) public {
        address owner = ownerOf(tokenId);
        require(to != owner, "ERC721: approval to current owner");

        require(
            _msgSender() == owner || isApprovedForAll(owner, _msgSender()),
            "ERC721: approve caller is not owner nor approved for all"
        );

        _tokenApprovals[tokenId] = to;
        emit Approval(owner, to, tokenId);
    }

    /**
     * @dev Gets the approved address for a token ID, or zero if no address set
     * Reverts if the token ID does not exist.
     * @param tokenId uint256 ID of the token to query the approval of
     * @return address currently approved for the given token ID
     */
    function getApproved(uint256 tokenId) public view returns (address) {
        require(
            _exists(tokenId),
            "ERC721: approved query for nonexistent token"
        );

        return _tokenApprovals[tokenId];
    }

    /**
     * @dev Sets or unsets the approval of a given operator
     * An operator is allowed to transfer all tokens of the sender on their behalf.
     * @param to operator address to set the approval
     * @param approved representing the status of the approval to be set
     */
    function setApprovalForAll(address to, bool approved) public {
        require(to != _msgSender(), "ERC721: approve to caller");

        _operatorApprovals[_msgSender()][to] = approved;
        emit ApprovalForAll(_msgSender(), to, approved);
    }

    /**
     * @dev Tells whether an operator is approved by a given owner.
     * @param owner owner address which you want to query the approval of
     * @param operator operator address which you want to query the approval of
     * @return bool whether the given operator is approved by the given owner
     */
    function isApprovedForAll(address owner, address operator)
        public
        view
        returns (bool)
    {
        return _operatorApprovals[owner][operator];
    }