// File: project.sol



// SPDX-License-Identifier: MIT

/*
---:::::-----+=-*%%@@@@@@%%%%@%@%%%%%@@@@@@@@@@@@@@%%@%%#**----==+*=---:::::----------:--.
:-:::::::::==--**#%%%@@@@@%@@%%%%@@@@@@@@@@%@@@@@@@@%%@@%%%##++++===+=----------::--:----.
:-::::::::-+::+#+#%%%@%%%@@@@@@@@@@@@@@@@@@%@@@@@@@@@@@@%@@@@@%####*++*+===--------------.
::::::::::=--+*+#*%%%@%@%@@%%%%%%@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@%%**------:::----::::.
::::::::-:--+*%%%%%@@@@%%%%%@@%%%%%@@@@@@@@@@@@@@@@@@@@@%%@@@@@@@@@@@@@%*+=--::::::::::::.
::::::::-=-+**++%%%%%%%%%%%%%%%%%@@@@@@@@%@@@@@@%@%%@@%@%%@@@@%%@@@@@@@@%*+-:::::::::::::.
:::::::::-+++#%%%%%%%@%@%##%%%##%%@%%@%%@%@@@@@@#%@@@%%%@%%@@@@@@@@@%@@@@#+=-::::::::::::.
:::::::-=--=*%%%@%%%@@%%%#%%%##%%%%%@@@@%#%%%@@@@%@@@%@%@@@@%%@%%%%%%@%@@%#=-::::::::::::.
::::::-=-=++#%%%%%%@@%#%#%%###%%%%#%%%#%%%%%%@@@@@@@@%%%@@@%%%@@@@%%%@@@%%#*-::::::::::::.
::::::+-===+*%%%%%%@%%%%%%#%%@%%@%%%#@%%@%%%%%%%@@@%#%%%@@@%@@%%%%%#%@@%%%%#-::::::::::::.
:::::--+:=-*%%%@@%%@%%#%%%%%%%%#%@%%%%%%#%%%%%#%@%#*%%@@@@%%%@%%%%%%%%%%%%%*-::::::::::::.
::::::=-:==%@%@@%%%%%#%#%%%%%%%%@%%%##########%%#####%@@%#%%%%##%%#%%%%%%%*+=::::::::::::.
-:::--:::-=#%%%##%%%#%%@%#%%@@%%@%%%####*###%%#####+-#@##**#**##%%%%#%%%%%+=-:-------::::.
:::::::::=+#%%%%#%%%#%@%%%%%@%%%%%%#####*%###***=+=::=%*+**+**#**#%%%%@%#+=--::::::--:---.
:-::::::-==%#%%@#%%%%%@%@%%@%%%%%%%####*##*+==+:---:::=+---++*+**%%%%@%%**+--::::::::::::.
:-::::::::=##%%%#%%%%%%%%%%@%%%##%##****+--::.-.-:::::::=-:-+==+#%#%%%%%#++::::::::::::::.
:-::::::::==#%%%%%%%%%%**%%+##*=##**+++-::....-.-.::::::::::-=:-**%%%%%%*--::::::::::::::.
--:::-----=+##########+-:**#**=**+==--::........:::::::::::::=::==%%%@%%=-::::-----------.
-----:--:----------======+-*==*+===::::.......::::::::::::::::::-=*%@@%#+=--------:--:---.
::-:::::::------------:--:-+-:-:-::::::.....:::::--===++++****+==**%%%%*--:--:::-::::::::.
::::--------------------::-+####**++++=----==++***++==---======*%%%%%%+=-::::::-:::-::--:.
:::--:::::::--------====::-+++++===+*%%%%%%%%#%=::---==+++===---+%%%%+==--:-:::::::::::::.
:::::::::---::---==-=========+***++===%%%%%%#%*--==++***+++====-=%%#+=+=:--::::::::::::::.
=:::::-:::--:---++#*--====-+**#*++++=-#%*==+#@+--++==+++#++======%#+-+++------:----------:
-:::::::::-:-:-=++#%:----:.:=++=:-==--##=:::+@#---=-::=+*+:.:==-+%+--+==------:----------.
:-:::::::-::::-=+=+%-::::::---=====--*%=-:..:*%*--=======-----::##=:==--:::::::::::::::::.
--::::::::::----+--**:::::::--===--=#%*-:...::=%%*=-====---:::=##+-:-:::::::::----:::::::.
---::::--:::::--+---+##+==---===+*#%#+-:....:::-+#%##*******##*+=-::---:::::-=====-::::::.
--=::::--::::::-+-:::-==+++*******+=-:::...:::::::--==========----::----:::::-==--:::::::.
::-=:::::::::::-+=-::........:::::.........:::::::::::::::::::::----:::::::::::::::::::::.
::-=:::::::::::-+=-:::.....................:::::::::::::::::::::---::::::::::::::::::::::.
::--=:::::::::::+=--::................:....:...:::::::::::::::::----:::::::::::::::::::::.
::---:::::::::::=++==-:...............-==----==-:::::::::::::::--==-:::::::::::::::::::::.
--::::.::::::::-++==+=-...............:::::-:::::::::::::::::::----::::::::::::::::::::::.
-....::::::::-++=-----::................:::::--::::::::::::::::-:::::::::::::::::::::::::.
=-:::::::::-++==--:-::::.....::::::-=====+=++++++==-::::::::::---::::::::::::::::::--::::.
 .=-::::.:=++--:::::::::::...::::::--------------=--:::::::::-++=::::::::::::::-:---:::::.
  :.::::=+++-:::::::::::::::::::::::::::::::::::::::::::::::=+==-::::::::::::::::--------:
   .:-=+*+--:::::::::::::::::::::........::::::::::::::::::-====::::::::::::::::---------:
--::- .-+-:::::::::::::::::::-:::.......::::::::::::::::::------:::::::::::::::----------:
 :=.....:--::::::::::::::::::-=-:::......::::::::::.....:------::::::::::::::::----------:
   .....-==---:::::::::::::::---=--:....::::::...::...:--------::::::--====---:---------=:
    ..-+=-----::-:::::::::::-=-::--=--:::..::::....:------------:::::--=++++=------------:
     .+=---:::::::::::-:::. -:--:::--=========--======-----------:::::-+++++-:-----------:
      -=--:-::----::::::::  ...  .=--------=========-----:..:---====---++++=::-----------:
    .==---:-::----:::::::.:    .    :--:--------------. =:. .-.::---===++++=-:::--------::
  :==--::::-::::::::::::-     :.   :::. ..-::::-:::::       . ...:-----+++++=====---===-::
:==--:::::::::::::::::::...  .... :   .:.:==-:.  .-+:. .. .:  ..:--:-:-+++++=---=======--:
=--:::::::::::::::::::::. ...     .   .  =+:.==:   ..-. ::  :::  :::::-++++===-----------:
-:::::::::::::::::::::.  .:-- .::-.::.  -=..:.::-.. ...--::...-=:::::::----------::::::--.
:::::::::::-::::::::.      .:.    .   .+-.  .  :..: . ..::-...==  ..:::::::::::::::::::::.
:::::::::::-:::::.          .       .-=+: .. .:-:   ....- ...++      .:::::::::::::::::::.
:::::::::-----:.             . ::.:-=:.. ::: .--::.. :-:. .::=:         .::::::::::::::::.
===+++++++++-.                . .::=.  .  . ..-::. ..  .   .:-             .:::::::::::::.
=========-:                    . :-:-: .:  .  :::= .. .. . -:                .:::::::::::.
-:--::::.                      ..  -. .--     .:    .:-. :-::                   .::::::::.
:::::.                          ..      .  . :-  :---: :-::.                       .:::::.
:::.                             :..:. .    .....:::.   -::.                          .::.
:.                                :...:.  :  ...:..=  .:..-                              .
                                   ..-. .-=     ...    .::.                               
                                   .. ..  ..-: .-. ::: ..-                                
                                    :::. . . .... ..::.:..                                
                                     :-..:  .  . .:. :..-                                 
                                      -- ..:+.     :-..:.                                 
                                       :..  ..:: ..:. .=                                  
                                        -. . . . ..:. ..                                  
                                        -= .  .. .. :.-                                   
                                         =-:..=..:..:-.                                   
                                          :. ... ....-                                    


*/

pragma solidity ^0.6.6;

import "ERC721A.sol";
import "Ownable.sol";
import "ReentrancyGuard.sol";
import "MerkleProof.sol";

contract COOLOOKS is Ownable, ERC721A, ReentrancyGuard {
    uint256 public maxSupply = 888;
    uint256 public maxMintPerTx = 10;
    uint256 public price = 0.088 * 10 ** 18;
    bytes32 public whitelistMerkleRoot =
        0x55b0851e01d00b0f631e74f760828de41ba90c07505faee442c89ea3cf6ef78f;
    bool public publicPaused = true;
    bool public revealed = false;
    string public baseURI;
    string public hiddenMetadataUri =
        "ipfs://QmNU7DuogsbrnsDQzCQ7ExCk5D71VJ5b2SF1RY4MtfmSEt";

    constructor() public ERC721A("COOLOOKS", "COOLOOKS", 888, 888) {}

    function mlnt(
        uint256 amount,
        bytes32[] calldata _merkleProof
    ) public payable {
        bytes32 leaf = keccak256(abi.encodePacked(msg.sender));
        uint256 ts = totalSupply();
        require(ts + amount <= maxSupply, "Purchase would exceed max tokens");

        require(
            MerkleProof.verify(_merkleProof, whitelistMerkleRoot, leaf),
            "Invalid proof!"
        );

        {
            _safeMint(msg.sender, amount);
        }
    }

    function mint(uint256 amount) external payable {
        uint256 ts = totalSupply();
        require(publicPaused == false, "Mint not open for public");
        require(ts + amount <= maxSupply, "Purchase would exceed max tokens");
        require(
            amount <= maxMintPerTx,
            "Amount should not exceed max mint number"
        );

        require(msg.value >= price * amount, "Please send the exact amount.");

        _safeMint(msg.sender, amount);
    }

    function openPublicMint(bool paused) external onlyOwner {
        publicPaused = paused;
    }

    function setWhitelistMerkleRoot(bytes32 _merkleRoot) external onlyOwner {
        whitelistMerkleRoot = _merkleRoot;
    }

    function setPrice(uint256 _price) external onlyOwner {
        price = _price;
    }

    function whitelistStop(uint256 _maxSupply) external onlyOwner {
        maxSupply = _maxSupply;
    }

    function setMaxPerTx(uint256 _maxMintPerTx) external onlyOwner {
        maxMintPerTx = _maxMintPerTx;
    }

    function setRevealed(bool _state) public onlyOwner {
        revealed = _state;
    }

    function setBaseURI(string calldata newBaseURI) external onlyOwner {
        baseURI = newBaseURI;
    }

    function _baseURI() internal view override returns (string memory) {
        return baseURI;
    }

    function setHiddenMetadataUri(
        string memory _hiddenMetadataUri
    ) public onlyOwner {
        hiddenMetadataUri = _hiddenMetadataUri;
    }

    function tokenURI(
        uint256 _tokenId
    ) public view virtual override returns (string memory) {
        require(
            _exists(_tokenId),
            "ERC721Metadata: URI query for nonexistent token"
        );

        if (revealed == false) {
            return hiddenMetadataUri;
        }

        string memory currentBaseURI = _baseURI();
        return
            bytes(currentBaseURI).length > 0
                ? string(abi.encodePacked(currentBaseURI, _tokenId.toString()))
                : "";
    }

    function withdraw() external onlyOwner nonReentrant {
        (bool success, ) = msg.sender.call{value: address(this).balance}("");
        require(success, "Transfer failed.");
    }
}

// File: ERC721A.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "IERC721.sol";
import "IERC721Receiver.sol";
import "IERC721Metadata.sol";
import "IERC721Enumerable.sol";
import "Address.sol";
import "Context.sol";
import "Strings.sol";
import "ERC165.sol";

/**
 * @dev Implementation of https://eips.ethereum.org/EIPS/eip-721[ERC721] Non-Fungible Token Standard, including
 * the Metadata and Enumerable extension. Built to optimize for lower gas during batch mints.
 *
 * Assumes serials are sequentially minted starting at 0 (e.g. 0, 1, 2, 3..).
 *
 * Assumes the number of issuable tokens (collection size) is capped and fits in a uint128.
 *
 * Does not support burning tokens to address(0).
 */
contract ERC721A is
    Context,
    ERC165,
    IERC721,
    IERC721Metadata,
    IERC721Enumerable
{
    using Address for address;
    using Strings for uint256;

    struct TokenOwnership {
        address addr;
        uint64 startTimestamp;
    }

    struct AddressData {
        uint128 balance;
        uint128 numberMinted;
    }

    uint256 private currentIndex = 0;

    uint256 internal immutable collectionSize;
    uint256 internal immutable maxBatchSize;

    // Token name
    string private _name;

    // Token symbol
    string private _symbol;

    // Mapping from token ID to ownership details
    // An empty struct value does not necessarily mean the token is unowned. See ownershipOf implementation for details.
    mapping(uint256 => TokenOwnership) private _ownerships;

    // Mapping owner address to address data
    mapping(address => AddressData) private _addressData;

    // 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;

    /**
     * @dev
     * `maxBatchSize` refers to how much a minter can mint at a time.
     * `collectionSize_` refers to how many tokens are in the collection.
     */
    constructor(
        string memory name_,
        string memory symbol_,
        uint256 maxBatchSize_,
        uint256 collectionSize_
    ) public {
        require(
            collectionSize_ > 0,
            "ERC721A: collection must have a nonzero supply"
        );
        require(maxBatchSize_ > 0, "ERC721A: max batch size must be nonzero");
        _name = name_;
        _symbol = symbol_;
        maxBatchSize = maxBatchSize_;
        collectionSize = collectionSize_;
    }

    /**
     * @dev See {IERC721Enumerable-totalSupply}.
     */
    function totalSupply() public view override returns (uint256) {
        return currentIndex;
    }

    /**
     * @dev See {IERC721Enumerable-tokenByIndex}.
     */
    function tokenByIndex(uint256 index)
        public
        view
        override
        returns (uint256)
    {
        require(index < totalSupply(), "ERC721A: global index out of bounds");
        return index;
    }

    /**
     * @dev See {IERC721Enumerable-tokenOfOwnerByIndex}.
     * This read function is O(collectionSize). If calling from a separate contract, be sure to test gas first.
     * It may also degrade with extremely large collection sizes (e.g >> 10000), test for your use case.
     */
    function tokenOfOwnerByIndex(address owner, uint256 index)
        public
        view
        override
        returns (uint256)
    {
        require(index < balanceOf(owner), "ERC721A: owner index out of bounds");
        uint256 numMintedSoFar = totalSupply();
        uint256 tokenIdsIdx = 0;
        address currOwnershipAddr = address(0);
        for (uint256 i = 0; i < numMintedSoFar; i++) {
            TokenOwnership memory ownership = _ownerships[i];
            if (ownership.addr != address(0)) {
                currOwnershipAddr = ownership.addr;
            }
            if (currOwnershipAddr == owner) {
                if (tokenIdsIdx == index) {
                    return i;
                }
                tokenIdsIdx++;
            }
        }
        revert("ERC721A: unable to get token of owner by index");
    }

    /**
     * @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 ||
            interfaceId == type(IERC721Enumerable).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC721-balanceOf}.
     */
    function balanceOf(address owner) public view override returns (uint256) {
        require(
            owner != address(0),
            "ERC721A: balance query for the zero address"
        );
        return uint256(_addressData[owner].balance);
    }

    function _numberMinted(address owner) internal view returns (uint256) {
        require(
            owner != address(0),
            "ERC721A: number minted query for the zero address"
        );
        return uint256(_addressData[owner].numberMinted);
    }

    function ownershipOf(uint256 tokenId)
        internal
        view
        returns (TokenOwnership memory)
    {
        require(_exists(tokenId), "ERC721A: owner query for nonexistent token");

        uint256 lowestTokenToCheck;
        if (tokenId >= maxBatchSize) {
            lowestTokenToCheck = tokenId - maxBatchSize + 1;
        }

        for (uint256 curr = tokenId; curr >= lowestTokenToCheck; curr--) {
            TokenOwnership memory ownership = _ownerships[curr];
            if (ownership.addr != address(0)) {
                return ownership;
            }
        }

        revert("ERC721A: unable to determine the owner of token");
    }

    /**
     * @dev See {IERC721-ownerOf}.
     */
    function ownerOf(uint256 tokenId) public view override returns (address) {
        return ownershipOf(tokenId).addr;
    }

    /**
     * @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: URI query for 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 "";
    }

    /**
     * @dev See {IERC721-approve}.
     */
    function approve(address to, uint256 tokenId) public override {
        address owner = ERC721A.ownerOf(tokenId);
        require(to != owner, "ERC721A: approval to current owner");

        require(
            _msgSender() == owner || isApprovedForAll(owner, _msgSender()),
            "ERC721A: approve caller is not owner nor approved for all"
        );

        _approve(to, tokenId, owner);
    }

    /**
     * @dev See {IERC721-getApproved}.
     */
    function getApproved(uint256 tokenId)
        public
        view
        override
        returns (address)
    {
        require(
            _exists(tokenId),
            "ERC721A: approved query for nonexistent token"
        );

        return _tokenApprovals[tokenId];
    }

    /**
     * @dev See {IERC721-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved)
        public
        override
    {
        require(operator != _msgSender(), "ERC721A: 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 override {
        _transfer(from, to, tokenId);
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public override {
        safeTransferFrom(from, to, tokenId, "");
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId,
        bytes memory _data
    ) public override {
        _transfer(from, to, tokenId);
        require(
            _checkOnERC721Received(from, to, tokenId, _data),
            "ERC721A: transfer to 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`),
     */
    function _exists(uint256 tokenId) internal view returns (bool) {
        return tokenId < currentIndex;
    }

    function _safeMint(address to, uint256 quantity) internal {
        _safeMint(to, quantity, "");
    }

    /**
     * @dev Mints `quantity` tokens and transfers them to `to`.
     *
     * Requirements:
     *
     * - there must be `quantity` tokens remaining unminted in the total collection.
     * - `to` cannot be the zero address.
     * - `quantity` cannot be larger than the max batch size.
     *
     * Emits a {Transfer} event.
     */
    function _safeMint(
        address to,
        uint256 quantity,
        bytes memory _data
    ) internal {
        uint256 startTokenId = currentIndex;
        require(to != address(0), "ERC721A: mint to the zero address");
        // We know if the first token in the batch doesn't exist, the other ones don't as well, because of serial ordering.
        require(!_exists(startTokenId), "ERC721A: token already minted");
        require(quantity <= maxBatchSize, "ERC721A: quantity to mint too high");

        _beforeTokenTransfers(address(0), to, startTokenId, quantity);

        AddressData memory addressData = _addressData[to];
        _addressData[to] = AddressData(
            addressData.balance + uint128(quantity),
            addressData.numberMinted + uint128(quantity)
        );
        _ownerships[startTokenId] = TokenOwnership(to, uint64(block.timestamp));

        uint256 updatedIndex = startTokenId;

        for (uint256 i = 0; i < quantity; i++) {
            emit Transfer(address(0), to, updatedIndex);
            require(
                _checkOnERC721Received(address(0), to, updatedIndex, _data),
                "ERC721A: transfer to non ERC721Receiver implementer"
            );
            updatedIndex++;
        }

        currentIndex = updatedIndex;
        _afterTokenTransfers(address(0), to, startTokenId, quantity);
    }

    /**
     * @dev Transfers `tokenId` from `from` to `to`.
     *
     * 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
    ) private {
        TokenOwnership memory prevOwnership = ownershipOf(tokenId);

        bool isApprovedOrOwner = (_msgSender() == prevOwnership.addr ||
            getApproved(tokenId) == _msgSender() ||
            isApprovedForAll(prevOwnership.addr, _msgSender()));

        require(
            isApprovedOrOwner,
            "ERC721A: transfer caller is not owner nor approved"
        );

        require(
            prevOwnership.addr == from,
            "ERC721A: transfer from incorrect owner"
        );
        require(to != address(0), "ERC721A: transfer to the zero address");

        _beforeTokenTransfers(from, to, tokenId, 1);

        // Clear approvals from the previous owner
        _approve(address(0), tokenId, prevOwnership.addr);

        _addressData[from].balance -= 1;
        _addressData[to].balance += 1;
        _ownerships[tokenId] = TokenOwnership(to, uint64(block.timestamp));

        // If the ownership slot of tokenId+1 is not explicitly set, that means the transfer initiator owns it.
        // Set the slot of tokenId+1 explicitly in storage to maintain correctness for ownerOf(tokenId+1) calls.
        uint256 nextTokenId = tokenId + 1;
        if (_ownerships[nextTokenId].addr == address(0)) {
            if (_exists(nextTokenId)) {
                _ownerships[nextTokenId] = TokenOwnership(
                    prevOwnership.addr,
                    prevOwnership.startTimestamp
                );
            }
        }

        emit Transfer(from, to, tokenId);
        _afterTokenTransfers(from, to, tokenId, 1);
    }

    /**
     * @dev Approve `to` to operate on `tokenId`
     *
     * Emits a {Approval} event.
     */
    function _approve(
        address to,
        uint256 tokenId,
        address owner
    ) private {
        _tokenApprovals[tokenId] = to;
        emit Approval(owner, to, tokenId);
    }

    uint256 public nextOwnerToExplicitlySet = 0;

    /**
     * @dev Explicitly set `owners` to eliminate loops in future calls of ownerOf().
     */
    function _setOwnersExplicit(uint256 quantity) internal {
        uint256 oldNextOwnerToSet = nextOwnerToExplicitlySet;
        require(quantity > 0, "quantity must be nonzero");
        uint256 endIndex = oldNextOwnerToSet + quantity - 1;
        if (endIndex > collectionSize - 1) {
            endIndex = collectionSize - 1;
        }
        // We know if the last one in the group exists, all in the group exist, due to serial ordering.
        require(_exists(endIndex), "not enough minted yet for this cleanup");
        for (uint256 i = oldNextOwnerToSet; i <= endIndex; i++) {
            if (_ownerships[i].addr == address(0)) {
                TokenOwnership memory ownership = ownershipOf(i);
                _ownerships[i] = TokenOwnership(
                    ownership.addr,
                    ownership.startTimestamp
                );
            }
        }
        nextOwnerToExplicitlySet = endIndex + 1;
    }

    /**
     * @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(to).onERC721Received.selector;
            } catch (bytes memory reason) {
                if (reason.length == 0) {
                    revert(
                        "ERC721A: transfer to non ERC721Receiver implementer"
                    );
                } else {
                    assembly {
                        revert(add(32, reason), mload(reason))
                    }
                }
            }
        } else {
            return true;
        }
    }

    /**
     * @dev Hook that is called before a set of serially-ordered token ids are about to be transferred. This includes minting.
     *
     * startTokenId - the first token id to be transferred
     * quantity - the amount to be transferred
     *
     * 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`.
     */
    function _beforeTokenTransfers(
        address from,
        address to,
        uint256 startTokenId,
        uint256 quantity
    ) internal virtual {}

    /**
     * @dev Hook that is called after a set of serially-ordered token ids have been transferred. This includes
     * minting.
     *
     * startTokenId - the first token id to be transferred
     * quantity - the amount to be transferred
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero.
     * - `from` and `to` are never both zero.
     */
    function _afterTokenTransfers(
        address from,
        address to,
        uint256 startTokenId,
        uint256 quantity
    ) internal virtual {}
}

// File: IERC721.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.2 <0.8.0;

import "IERC165.sol";

/**
 * @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;
}

// File: IERC165.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

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

// File: IERC721Receiver.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <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);
}

// File: IERC721Metadata.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.2 <0.8.0;

import "IERC721.sol";

/**
 * @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);
}

// File: IERC721Enumerable.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.2 <0.8.0;

import "IERC721.sol";

/**
 * @title ERC-721 Non-Fungible Token Standard, optional enumeration extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721Enumerable is IERC721 {

    /**
     * @dev Returns the total amount of tokens stored by the contract.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns a token ID owned by `owner` at a given `index` of its token list.
     * Use along with {balanceOf} to enumerate all of ``owner``'s tokens.
     */
    function tokenOfOwnerByIndex(address owner, uint256 index) external view returns (uint256 tokenId);

    /**
     * @dev Returns a token ID at a given `index` of all the tokens stored by the contract.
     * Use along with {totalSupply} to enumerate all tokens.
     */
    function tokenByIndex(uint256 index) external view returns (uint256);
}

// File: Address.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.2 <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;
        // solhint-disable-next-line no-inline-assembly
        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");

        // solhint-disable-next-line avoid-low-level-calls, avoid-call-value
        (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");

        // solhint-disable-next-line avoid-low-level-calls
        (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");

        // solhint-disable-next-line avoid-low-level-calls
        (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");

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

    function _verifyCallResult(bool success, bytes memory returndata, string memory errorMessage) private 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

                // solhint-disable-next-line no-inline-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

// File: Context.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <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 GSN 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 payable) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes memory) {
        this; // silence state mutability warning without generating bytecode - see https://github.com/ethereum/solidity/issues/2691
        return msg.data;
    }
}

// File: Strings.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev String operations.
 */
library Strings {
    /**
     * @dev Converts a `uint256` to its ASCII `string` 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);
        uint256 index = digits - 1;
        temp = value;
        while (temp != 0) {
            buffer[index--] = bytes1(uint8(48 + temp % 10));
            temp /= 10;
        }
        return string(buffer);
    }
}

// File: ERC165.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "IERC165.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts may inherit from this and call {_registerInterface} to declare
 * their support of an interface.
 */
abstract 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) public view virtual override 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 virtual {
        require(interfaceId != 0xffffffff, "ERC165: invalid interface id");
        _supportedInterfaces[interfaceId] = true;
    }
}

// File: Ownable.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "Context.sol";
/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract Ownable is Context {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor () internal {
        address msgSender = _msgSender();
        _owner = msgSender;
        emit OwnershipTransferred(address(0), msgSender);
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
        _;
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        emit OwnershipTransferred(_owner, address(0));
        _owner = address(0);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        emit OwnershipTransferred(_owner, newOwner);
        _owner = newOwner;
    }
}

// File: ReentrancyGuard.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuard {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;

    uint256 private _status;

    constructor () internal {
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and make it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        // On the first call to nonReentrant, _notEntered will be true
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;

        _;

        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_ENTERED;
    }
}

// File: MerkleProof.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev These functions deal with verification of Merkle trees (hash trees),
 */
library MerkleProof {
    /**
     * @dev Returns true if a `leaf` can be proved to be a part of a Merkle tree
     * defined by `root`. For this, a `proof` must be provided, containing
     * sibling hashes on the branch from the leaf to the root of the tree. Each
     * pair of leaves and each pair of pre-images are assumed to be sorted.
     */
    function verify(bytes32[] memory proof, bytes32 root, bytes32 leaf) internal pure returns (bool) {
        bytes32 computedHash = leaf;

        for (uint256 i = 0; i < proof.length; i++) {
            bytes32 proofElement = proof[i];

            if (computedHash <= proofElement) {
                // Hash(current computed hash + current element of the proof)
                computedHash = keccak256(abi.encodePacked(computedHash, proofElement));
            } else {
                // Hash(current element of the proof + current computed hash)
                computedHash = keccak256(abi.encodePacked(proofElement, computedHash));
            }
        }

        // Check if the computed hash (root) is equal to the provided root
        return computedHash == root;
    }
}