// File: @openzeppelin/contracts/drafts/IERC20Permit.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on `{IERC20-approve}`, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over `owner`'s tokens,
     * given `owner`'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     */
    function permit(address owner, address spender, uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) external;

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) external view returns (uint256);

    /**
     * @dev Returns the domain separator used in the encoding of the signature for `permit`, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view returns (bytes32);
}

// File: @openzeppelin/contracts/introspection/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: @openzeppelin/contracts/introspection/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: @openzeppelin/contracts/math/SafeMath.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        uint256 c = a + b;
        if (c < a) return (false, 0);
        return (true, c);
    }

    /**
     * @dev Returns the substraction of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b > a) return (false, 0);
        return (true, a - b);
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool, 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 (true, 0);
        uint256 c = a * b;
        if (c / a != b) return (false, 0);
        return (true, c);
    }

    /**
     * @dev Returns the division of two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b == 0) return (false, 0);
        return (true, a / b);
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b == 0) return (false, 0);
        return (true, a % b);
    }

    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");
        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b <= a, "SafeMath: subtraction overflow");
        return a - b;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        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, reverting 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) {
        require(b > 0, "SafeMath: division by zero");
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0, "SafeMath: modulo by zero");
        return a % b;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {trySub}.
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        return a - b;
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryDiv}.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting with custom message when dividing by zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryMod}.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        return a % b;
    }
}

// File: @openzeppelin/contracts/token/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <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);
}

// File: @openzeppelin/contracts/token/ERC721/ERC721.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "../../utils/Context.sol";
import "./IERC721.sol";
import "./IERC721Metadata.sol";
import "./IERC721Enumerable.sol";
import "./IERC721Receiver.sol";
import "../../introspection/ERC165.sol";
import "../../math/SafeMath.sol";
import "../../utils/Address.sol";
import "../../utils/EnumerableSet.sol";
import "../../utils/EnumerableMap.sol";
import "../../utils/Strings.sol";

/**
 * @title ERC721 Non-Fungible Token Standard basic implementation
 * @dev see https://eips.ethereum.org/EIPS/eip-721
 */
contract ERC721 is Context, ERC165, IERC721, IERC721Metadata, IERC721Enumerable {
    using SafeMath for uint256;
    using Address for address;
    using EnumerableSet for EnumerableSet.UintSet;
    using EnumerableMap for EnumerableMap.UintToAddressMap;
    using Strings for uint256;

    // 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 holder address to their (enumerable) set of owned tokens
    mapping (address => EnumerableSet.UintSet) private _holderTokens;

    // Enumerable mapping from token ids to their owners
    EnumerableMap.UintToAddressMap private _tokenOwners;

    // 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;

    // Token name
    string private _name;

    // Token symbol
    string private _symbol;

    // Optional mapping for token URIs
    mapping (uint256 => string) private _tokenURIs;

    // Base URI
    string private _baseURI;

    /*
     *     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 ^ 0xe985e9c5 ^ 0x23b872dd ^ 0x42842e0e ^ 0xb88d4fde == 0x80ac58cd
     */
    bytes4 private constant _INTERFACE_ID_ERC721 = 0x80ac58cd;

    /*
     *     bytes4(keccak256('name()')) == 0x06fdde03
     *     bytes4(keccak256('symbol()')) == 0x95d89b41
     *     bytes4(keccak256('tokenURI(uint256)')) == 0xc87b56dd
     *
     *     => 0x06fdde03 ^ 0x95d89b41 ^ 0xc87b56dd == 0x5b5e139f
     */
    bytes4 private constant _INTERFACE_ID_ERC721_METADATA = 0x5b5e139f;

    /*
     *     bytes4(keccak256('totalSupply()')) == 0x18160ddd
     *     bytes4(keccak256('tokenOfOwnerByIndex(address,uint256)')) == 0x2f745c59
     *     bytes4(keccak256('tokenByIndex(uint256)')) == 0x4f6ccce7
     *
     *     => 0x18160ddd ^ 0x2f745c59 ^ 0x4f6ccce7 == 0x780e9d63
     */
    bytes4 private constant _INTERFACE_ID_ERC721_ENUMERABLE = 0x780e9d63;

    /**
     * @dev Initializes the contract by setting a `name` and a `symbol` to the token collection.
     */
    constructor (string memory name_, string memory symbol_) public {
        _name = name_;
        _symbol = symbol_;

        // register the supported interfaces to conform to ERC721 via ERC165
        _registerInterface(_INTERFACE_ID_ERC721);
        _registerInterface(_INTERFACE_ID_ERC721_METADATA);
        _registerInterface(_INTERFACE_ID_ERC721_ENUMERABLE);
    }

    /**
     * @dev See {IERC721-balanceOf}.
     */
    function balanceOf(address owner) public view virtual override returns (uint256) {
        require(owner != address(0), "ERC721: balance query for the zero address");
        return _holderTokens[owner].length();
    }

    /**
     * @dev See {IERC721-ownerOf}.
     */
    function ownerOf(uint256 tokenId) public view virtual override returns (address) {
        return _tokenOwners.get(tokenId, "ERC721: owner query for nonexistent token");
    }

    /**
     * @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 _tokenURI = _tokenURIs[tokenId];
        string memory base = baseURI();

        // If there is no base URI, return the token URI.
        if (bytes(base).length == 0) {
            return _tokenURI;
        }
        // If both are set, concatenate the baseURI and tokenURI (via abi.encodePacked).
        if (bytes(_tokenURI).length > 0) {
            return string(abi.encodePacked(base, _tokenURI));
        }
        // If there is a baseURI but no tokenURI, concatenate the tokenID to the baseURI.
        return string(abi.encodePacked(base, tokenId.toString()));
    }

    /**
    * @dev Returns the base URI set via {_setBaseURI}. This will be
    * automatically added as a prefix in {tokenURI} to each token's URI, or
    * to the token ID if no specific URI is set for that token ID.
    */
    function baseURI() public view virtual returns (string memory) {
        return _baseURI;
    }

    /**
     * @dev See {IERC721Enumerable-tokenOfOwnerByIndex}.
     */
    function tokenOfOwnerByIndex(address owner, uint256 index) public view virtual override returns (uint256) {
        return _holderTokens[owner].at(index);
    }

    /**
     * @dev See {IERC721Enumerable-totalSupply}.
     */
    function totalSupply() public view virtual override returns (uint256) {
        // _tokenOwners are indexed by tokenIds, so .length() returns the number of tokenIds
        return _tokenOwners.length();
    }

    /**
     * @dev See {IERC721Enumerable-tokenByIndex}.
     */
    function tokenByIndex(uint256 index) public view virtual override returns (uint256) {
        (uint256 tokenId, ) = _tokenOwners.at(index);
        return tokenId;
    }

    /**
     * @dev See {IERC721-approve}.
     */
    function approve(address to, uint256 tokenId) public virtual override {
        address owner = ERC721.ownerOf(tokenId);
        require(to != owner, "ERC721: approval to current owner");

        require(_msgSender() == owner || ERC721.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: approved query for 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: transfer caller is 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: transfer caller is 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: 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`),
     * and stop existing when they are burned (`_burn`).
     */
    function _exists(uint256 tokenId) internal view virtual returns (bool) {
        return _tokenOwners.contains(tokenId);
    }

    /**
     * @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: operator query for nonexistent token");
        address owner = ERC721.ownerOf(tokenId);
        return (spender == owner || getApproved(tokenId) == spender || ERC721.isApprovedForAll(owner, spender));
    }

    /**
     * @dev Safely mints `tokenId` and transfers it to `to`.
     *
     * Requirements:
     d*
     * - `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: transfer to 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: mint to the zero address");
        require(!_exists(tokenId), "ERC721: token already minted");

        _beforeTokenTransfer(address(0), to, tokenId);

        _holderTokens[to].add(tokenId);

        _tokenOwners.set(tokenId, to);

        emit Transfer(address(0), to, tokenId);
    }

    /**
     * @dev Destroys `tokenId`.
     * The approval is cleared when the token is burned.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     *
     * Emits a {Transfer} event.
     */
    function _burn(uint256 tokenId) internal virtual {
        address owner = ERC721.ownerOf(tokenId); // internal owner

        _beforeTokenTransfer(owner, address(0), tokenId);

        // Clear approvals
        _approve(address(0), tokenId);

        // Clear metadata (if any)
        if (bytes(_tokenURIs[tokenId]).length != 0) {
            delete _tokenURIs[tokenId];
        }

        _holderTokens[owner].remove(tokenId);

        _tokenOwners.remove(tokenId);

        emit Transfer(owner, address(0), 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(ERC721.ownerOf(tokenId) == from, "ERC721: transfer of token that is not own"); // internal owner
        require(to != address(0), "ERC721: transfer to the zero address");

        _beforeTokenTransfer(from, to, tokenId);

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

        _holderTokens[from].remove(tokenId);
        _holderTokens[to].add(tokenId);

        _tokenOwners.set(tokenId, to);

        emit Transfer(from, to, tokenId);
    }

    /**
     * @dev Sets `_tokenURI` as the tokenURI of `tokenId`.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function _setTokenURI(uint256 tokenId, string memory _tokenURI) internal virtual {
        require(_exists(tokenId), "ERC721Metadata: URI set of nonexistent token");
        _tokenURIs[tokenId] = _tokenURI;
    }

    /**
     * @dev Internal function to set the base URI for all token IDs. It is
     * automatically added as a prefix to the value returned in {tokenURI},
     * or to the token ID if {tokenURI} is empty.
     */
    function _setBaseURI(string memory baseURI_) internal virtual {
        _baseURI = baseURI_;
    }

    /**
     * @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()) {
            return true;
        }
        bytes memory returndata = to.functionCall(abi.encodeWithSelector(
            IERC721Receiver(to).onERC721Received.selector,
            _msgSender(),
            from,
            tokenId,
            _data
        ), "ERC721: transfer to non ERC721Receiver implementer");
        bytes4 retval = abi.decode(returndata, (bytes4));
        return (retval == _ERC721_RECEIVED);
    }

    /**
     * @dev Approve `to` to operate on `tokenId`
     *
     * Emits an {Approval} event.
     */
    function _approve(address to, uint256 tokenId) internal virtual {
        _tokenApprovals[tokenId] = to;
        emit Approval(ERC721.ownerOf(tokenId), to, tokenId); // internal owner
    }

    /**
     * @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` cannot be the zero address.
     * - `to` cannot be the zero address.
     *
     * 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 { }
}

// File: @openzeppelin/contracts/token/ERC721/IERC721.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.2 <0.8.0;

import "../../introspection/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: @openzeppelin/contracts/token/ERC721/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: @openzeppelin/contracts/token/ERC721/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: @openzeppelin/contracts/token/ERC721/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: @openzeppelin/contracts/utils/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: @openzeppelin/contracts/utils/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: @openzeppelin/contracts/utils/EnumerableMap.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Library for managing an enumerable variant of Solidity's
 * https://solidity.readthedocs.io/en/latest/types.html#mapping-types[`mapping`]
 * type.
 *
 * Maps have the following properties:
 *
 * - Entries are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Entries are enumerated in O(n). No guarantees are made on the ordering.
 *
 * ```
 * contract Example {
 *     // Add the library methods
 *     using EnumerableMap for EnumerableMap.UintToAddressMap;
 *
 *     // Declare a set state variable
 *     EnumerableMap.UintToAddressMap private myMap;
 * }
 * ```
 *
 * As of v3.0.0, only maps of type `uint256 -> address` (`UintToAddressMap`) are
 * supported.
 */
library EnumerableMap {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Map type with
    // bytes32 keys and values.
    // The Map implementation uses private functions, and user-facing
    // implementations (such as Uint256ToAddressMap) are just wrappers around
    // the underlying Map.
    // This means that we can only create new EnumerableMaps for types that fit
    // in bytes32.

    struct MapEntry {
        bytes32 _key;
        bytes32 _value;
    }

    struct Map {
        // Storage of map keys and values
        MapEntry[] _entries;

        // Position of the entry defined by a key in the `entries` array, plus 1
        // because index 0 means a key is not in the map.
        mapping (bytes32 => uint256) _indexes;
    }

    /**
     * @dev Adds a key-value pair to a map, or updates the value for an existing
     * key. O(1).
     *
     * Returns true if the key was added to the map, that is if it was not
     * already present.
     */
    function _set(Map storage map, bytes32 key, bytes32 value) private returns (bool) {
        // We read and store the key's index to prevent multiple reads from the same storage slot
        uint256 keyIndex = map._indexes[key];

        if (keyIndex == 0) { // Equivalent to !contains(map, key)
            map._entries.push(MapEntry({ _key: key, _value: value }));
            // The entry is stored at length-1, but we add 1 to all indexes
            // and use 0 as a sentinel value
            map._indexes[key] = map._entries.length;
            return true;
        } else {
            map._entries[keyIndex - 1]._value = value;
            return false;
        }
    }

    /**
     * @dev Removes a key-value pair from a map. O(1).
     *
     * Returns true if the key was removed from the map, that is if it was present.
     */
    function _remove(Map storage map, bytes32 key) private returns (bool) {
        // We read and store the key's index to prevent multiple reads from the same storage slot
        uint256 keyIndex = map._indexes[key];

        if (keyIndex != 0) { // Equivalent to contains(map, key)
            // To delete a key-value pair from the _entries array in O(1), we swap the entry to delete with the last one
            // in the array, and then remove the last entry (sometimes called as 'swap and pop').
            // This modifies the order of the array, as noted in {at}.

            uint256 toDeleteIndex = keyIndex - 1;
            uint256 lastIndex = map._entries.length - 1;

            // When the entry to delete is the last one, the swap operation is unnecessary. However, since this occurs
            // so rarely, we still do the swap anyway to avoid the gas cost of adding an 'if' statement.

            MapEntry storage lastEntry = map._entries[lastIndex];

            // Move the last entry to the index where the entry to delete is
            map._entries[toDeleteIndex] = lastEntry;
            // Update the index for the moved entry
            map._indexes[lastEntry._key] = toDeleteIndex + 1; // All indexes are 1-based

            // Delete the slot where the moved entry was stored
            map._entries.pop();

            // Delete the index for the deleted slot
            delete map._indexes[key];

            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Returns true if the key is in the map. O(1).
     */
    function _contains(Map storage map, bytes32 key) private view returns (bool) {
        return map._indexes[key] != 0;
    }

    /**
     * @dev Returns the number of key-value pairs in the map. O(1).
     */
    function _length(Map storage map) private view returns (uint256) {
        return map._entries.length;
    }

   /**
    * @dev Returns the key-value pair stored at position `index` in the map. O(1).
    *
    * Note that there are no guarantees on the ordering of entries inside the
    * array, and it may change when more entries are added or removed.
    *
    * Requirements:
    *
    * - `index` must be strictly less than {length}.
    */
    function _at(Map storage map, uint256 index) private view returns (bytes32, bytes32) {
        require(map._entries.length > index, "EnumerableMap: index out of bounds");

        MapEntry storage entry = map._entries[index];
        return (entry._key, entry._value);
    }

    /**
     * @dev Tries to returns the value associated with `key`.  O(1).
     * Does not revert if `key` is not in the map.
     */
    function _tryGet(Map storage map, bytes32 key) private view returns (bool, bytes32) {
        uint256 keyIndex = map._indexes[key];
        if (keyIndex == 0) return (false, 0); // Equivalent to contains(map, key)
        return (true, map._entries[keyIndex - 1]._value); // All indexes are 1-based
    }

    /**
     * @dev Returns the value associated with `key`.  O(1).
     *
     * Requirements:
     *
     * - `key` must be in the map.
     */
    function _get(Map storage map, bytes32 key) private view returns (bytes32) {
        uint256 keyIndex = map._indexes[key];
        require(keyIndex != 0, "EnumerableMap: nonexistent key"); // Equivalent to contains(map, key)
        return map._entries[keyIndex - 1]._value; // All indexes are 1-based
    }

    /**
     * @dev Same as {_get}, with a custom error message when `key` is not in the map.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {_tryGet}.
     */
    function _get(Map storage map, bytes32 key, string memory errorMessage) private view returns (bytes32) {
        uint256 keyIndex = map._indexes[key];
        require(keyIndex != 0, errorMessage); // Equivalent to contains(map, key)
        return map._entries[keyIndex - 1]._value; // All indexes are 1-based
    }

    // UintToAddressMap

    struct UintToAddressMap {
        Map _inner;
    }

    /**
     * @dev Adds a key-value pair to a map, or updates the value for an existing
     * key. O(1).
     *
     * Returns true if the key was added to the map, that is if it was not
     * already present.
     */
    function set(UintToAddressMap storage map, uint256 key, address value) internal returns (bool) {
        return _set(map._inner, bytes32(key), bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the key was removed from the map, that is if it was present.
     */
    function remove(UintToAddressMap storage map, uint256 key) internal returns (bool) {
        return _remove(map._inner, bytes32(key));
    }

    /**
     * @dev Returns true if the key is in the map. O(1).
     */
    function contains(UintToAddressMap storage map, uint256 key) internal view returns (bool) {
        return _contains(map._inner, bytes32(key));
    }

    /**
     * @dev Returns the number of elements in the map. O(1).
     */
    function length(UintToAddressMap storage map) internal view returns (uint256) {
        return _length(map._inner);
    }

   /**
    * @dev Returns the element stored at position `index` in the set. O(1).
    * Note that there are no guarantees on the ordering of values inside the
    * array, and it may change when more values are added or removed.
    *
    * Requirements:
    *
    * - `index` must be strictly less than {length}.
    */
    function at(UintToAddressMap storage map, uint256 index) internal view returns (uint256, address) {
        (bytes32 key, bytes32 value) = _at(map._inner, index);
        return (uint256(key), address(uint160(uint256(value))));
    }

    /**
     * @dev Tries to returns the value associated with `key`.  O(1).
     * Does not revert if `key` is not in the map.
     *
     * _Available since v3.4._
     */
    function tryGet(UintToAddressMap storage map, uint256 key) internal view returns (bool, address) {
        (bool success, bytes32 value) = _tryGet(map._inner, bytes32(key));
        return (success, address(uint160(uint256(value))));
    }

    /**
     * @dev Returns the value associated with `key`.  O(1).
     *
     * Requirements:
     *
     * - `key` must be in the map.
     */
    function get(UintToAddressMap storage map, uint256 key) internal view returns (address) {
        return address(uint160(uint256(_get(map._inner, bytes32(key)))));
    }

    /**
     * @dev Same as {get}, with a custom error message when `key` is not in the map.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryGet}.
     */
    function get(UintToAddressMap storage map, uint256 key, string memory errorMessage) internal view returns (address) {
        return address(uint160(uint256(_get(map._inner, bytes32(key), errorMessage))));
    }
}

// File: @openzeppelin/contracts/utils/EnumerableSet.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Library for managing
 * https://en.wikipedia.org/wiki/Set_(abstract_data_type)[sets] of primitive
 * types.
 *
 * Sets have the following properties:
 *
 * - Elements are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Elements are enumerated in O(n). No guarantees are made on the ordering.
 *
 * ```
 * contract Example {
 *     // Add the library methods
 *     using EnumerableSet for EnumerableSet.AddressSet;
 *
 *     // Declare a set state variable
 *     EnumerableSet.AddressSet private mySet;
 * }
 * ```
 *
 * As of v3.3.0, sets of type `bytes32` (`Bytes32Set`), `address` (`AddressSet`)
 * and `uint256` (`UintSet`) are supported.
 */
library EnumerableSet {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Set type with
    // bytes32 values.
    // The Set implementation uses private functions, and user-facing
    // implementations (such as AddressSet) are just wrappers around the
    // underlying Set.
    // This means that we can only create new EnumerableSets for types that fit
    // in bytes32.

    struct Set {
        // Storage of set values
        bytes32[] _values;

        // Position of the value in the `values` array, plus 1 because index 0
        // means a value is not in the set.
        mapping (bytes32 => uint256) _indexes;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function _add(Set storage set, bytes32 value) private returns (bool) {
        if (!_contains(set, value)) {
            set._values.push(value);
            // The value is stored at length-1, but we add 1 to all indexes
            // and use 0 as a sentinel value
            set._indexes[value] = set._values.length;
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function _remove(Set storage set, bytes32 value) private returns (bool) {
        // We read and store the value's index to prevent multiple reads from the same storage slot
        uint256 valueIndex = set._indexes[value];

        if (valueIndex != 0) { // Equivalent to contains(set, value)
            // To delete an element from the _values array in O(1), we swap the element to delete with the last one in
            // the array, and then remove the last element (sometimes called as 'swap and pop').
            // This modifies the order of the array, as noted in {at}.

            uint256 toDeleteIndex = valueIndex - 1;
            uint256 lastIndex = set._values.length - 1;

            // When the value to delete is the last one, the swap operation is unnecessary. However, since this occurs
            // so rarely, we still do the swap anyway to avoid the gas cost of adding an 'if' statement.

            bytes32 lastvalue = set._values[lastIndex];

            // Move the last value to the index where the value to delete is
            set._values[toDeleteIndex] = lastvalue;
            // Update the index for the moved value
            set._indexes[lastvalue] = toDeleteIndex + 1; // All indexes are 1-based

            // Delete the slot where the moved value was stored
            set._values.pop();

            // Delete the index for the deleted slot
            delete set._indexes[value];

            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function _contains(Set storage set, bytes32 value) private view returns (bool) {
        return set._indexes[value] != 0;
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function _length(Set storage set) private view returns (uint256) {
        return set._values.length;
    }

   /**
    * @dev Returns the value stored at position `index` in the set. O(1).
    *
    * Note that there are no guarantees on the ordering of values inside the
    * array, and it may change when more values are added or removed.
    *
    * Requirements:
    *
    * - `index` must be strictly less than {length}.
    */
    function _at(Set storage set, uint256 index) private view returns (bytes32) {
        require(set._values.length > index, "EnumerableSet: index out of bounds");
        return set._values[index];
    }

    // Bytes32Set

    struct Bytes32Set {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _add(set._inner, value);
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _remove(set._inner, value);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(Bytes32Set storage set, bytes32 value) internal view returns (bool) {
        return _contains(set._inner, value);
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(Bytes32Set storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

   /**
    * @dev Returns the value stored at position `index` in the set. O(1).
    *
    * Note that there are no guarantees on the ordering of values inside the
    * array, and it may change when more values are added or removed.
    *
    * Requirements:
    *
    * - `index` must be strictly less than {length}.
    */
    function at(Bytes32Set storage set, uint256 index) internal view returns (bytes32) {
        return _at(set._inner, index);
    }

    // AddressSet

    struct AddressSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(AddressSet storage set, address value) internal returns (bool) {
        return _add(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(AddressSet storage set, address value) internal returns (bool) {
        return _remove(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(AddressSet storage set, address value) internal view returns (bool) {
        return _contains(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(AddressSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

   /**
    * @dev Returns the value stored at position `index` in the set. O(1).
    *
    * Note that there are no guarantees on the ordering of values inside the
    * array, and it may change when more values are added or removed.
    *
    * Requirements:
    *
    * - `index` must be strictly less than {length}.
    */
    function at(AddressSet storage set, uint256 index) internal view returns (address) {
        return address(uint160(uint256(_at(set._inner, index))));
    }


    // UintSet

    struct UintSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(UintSet storage set, uint256 value) internal returns (bool) {
        return _add(set._inner, bytes32(value));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(UintSet storage set, uint256 value) internal returns (bool) {
        return _remove(set._inner, bytes32(value));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(UintSet storage set, uint256 value) internal view returns (bool) {
        return _contains(set._inner, bytes32(value));
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function length(UintSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

   /**
    * @dev Returns the value stored at position `index` in the set. O(1).
    *
    * Note that there are no guarantees on the ordering of values inside the
    * array, and it may change when more values are added or removed.
    *
    * Requirements:
    *
    * - `index` must be strictly less than {length}.
    */
    function at(UintSet storage set, uint256 index) internal view returns (uint256) {
        return uint256(_at(set._inner, index));
    }
}

// File: @openzeppelin/contracts/utils/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: @uniswap/v3-core/contracts/interfaces/callback/IUniswapV3MintCallback.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Callback for IUniswapV3PoolActions#mint
/// @notice Any contract that calls IUniswapV3PoolActions#mint must implement this interface
interface IUniswapV3MintCallback {
    /// @notice Called to `msg.sender` after minting liquidity to a position from IUniswapV3Pool#mint.
    /// @dev In the implementation you must pay the pool tokens owed for the minted liquidity.
    /// The caller of this method must be checked to be a UniswapV3Pool deployed by the canonical UniswapV3Factory.
    /// @param amount0Owed The amount of token0 due to the pool for the minted liquidity
    /// @param amount1Owed The amount of token1 due to the pool for the minted liquidity
    /// @param data Any data passed through by the caller via the IUniswapV3PoolActions#mint call
    function uniswapV3MintCallback(
        uint256 amount0Owed,
        uint256 amount1Owed,
        bytes calldata data
    ) external;
}

// File: @uniswap/v3-core/contracts/interfaces/IUniswapV3Factory.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title The interface for the Uniswap V3 Factory
/// @notice The Uniswap V3 Factory facilitates creation of Uniswap V3 pools and control over the protocol fees
interface IUniswapV3Factory {
    /// @notice Emitted when the owner of the factory is changed
    /// @param oldOwner The owner before the owner was changed
    /// @param newOwner The owner after the owner was changed
    event OwnerChanged(address indexed oldOwner, address indexed newOwner);

    /// @notice Emitted when a pool is created
    /// @param token0 The first token of the pool by address sort order
    /// @param token1 The second token of the pool by address sort order
    /// @param fee The fee collected upon every swap in the pool, denominated in hundredths of a bip
    /// @param tickSpacing The minimum number of ticks between initialized ticks
    /// @param pool The address of the created pool
    event PoolCreated(
        address indexed token0,
        address indexed token1,
        uint24 indexed fee,
        int24 tickSpacing,
        address pool
    );

    /// @notice Emitted when a new fee amount is enabled for pool creation via the factory
    /// @param fee The enabled fee, denominated in hundredths of a bip
    /// @param tickSpacing The minimum number of ticks between initialized ticks for pools created with the given fee
    event FeeAmountEnabled(uint24 indexed fee, int24 indexed tickSpacing);

    /// @notice Returns the current owner of the factory
    /// @dev Can be changed by the current owner via setOwner
    /// @return The address of the factory owner
    function owner() external view returns (address);

    /// @notice Returns the tick spacing for a given fee amount, if enabled, or 0 if not enabled
    /// @dev A fee amount can never be removed, so this value should be hard coded or cached in the calling context
    /// @param fee The enabled fee, denominated in hundredths of a bip. Returns 0 in case of unenabled fee
    /// @return The tick spacing
    function feeAmountTickSpacing(uint24 fee) external view returns (int24);

    /// @notice Returns the pool address for a given pair of tokens and a fee, or address 0 if it does not exist
    /// @dev tokenA and tokenB may be passed in either token0/token1 or token1/token0 order
    /// @param tokenA The contract address of either token0 or token1
    /// @param tokenB The contract address of the other token
    /// @param fee The fee collected upon every swap in the pool, denominated in hundredths of a bip
    /// @return pool The pool address
    function getPool(
        address tokenA,
        address tokenB,
        uint24 fee
    ) external view returns (address pool);

    /// @notice Creates a pool for the given two tokens and fee
    /// @param tokenA One of the two tokens in the desired pool
    /// @param tokenB The other of the two tokens in the desired pool
    /// @param fee The desired fee for the pool
    /// @dev tokenA and tokenB may be passed in either order: token0/token1 or token1/token0. tickSpacing is retrieved
    /// from the fee. The call will revert if the pool already exists, the fee is invalid, or the token arguments
    /// are invalid.
    /// @return pool The address of the newly created pool
    function createPool(
        address tokenA,
        address tokenB,
        uint24 fee
    ) external returns (address pool);

    /// @notice Updates the owner of the factory
    /// @dev Must be called by the current owner
    /// @param _owner The new owner of the factory
    function setOwner(address _owner) external;

    /// @notice Enables a fee amount with the given tickSpacing
    /// @dev Fee amounts may never be removed once enabled
    /// @param fee The fee amount to enable, denominated in hundredths of a bip (i.e. 1e-6)
    /// @param tickSpacing The spacing between ticks to be enforced for all pools created with the given fee amount
    function enableFeeAmount(uint24 fee, int24 tickSpacing) external;
}

// File: @uniswap/v3-core/contracts/interfaces/IUniswapV3Pool.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

import './pool/IUniswapV3PoolImmutables.sol';
import './pool/IUniswapV3PoolState.sol';
import './pool/IUniswapV3PoolDerivedState.sol';
import './pool/IUniswapV3PoolActions.sol';
import './pool/IUniswapV3PoolOwnerActions.sol';
import './pool/IUniswapV3PoolEvents.sol';

/// @title The interface for a Uniswap V3 Pool
/// @notice A Uniswap pool facilitates swapping and automated market making between any two assets that strictly conform
/// to the ERC20 specification
/// @dev The pool interface is broken up into many smaller pieces
interface IUniswapV3Pool is
    IUniswapV3PoolImmutables,
    IUniswapV3PoolState,
    IUniswapV3PoolDerivedState,
    IUniswapV3PoolActions,
    IUniswapV3PoolOwnerActions,
    IUniswapV3PoolEvents
{

}

// File: @uniswap/v3-core/contracts/interfaces/pool/IUniswapV3PoolActions.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Permissionless pool actions
/// @notice Contains pool methods that can be called by anyone
interface IUniswapV3PoolActions {
    /// @notice Sets the initial price for the pool
    /// @dev Price is represented as a sqrt(amountToken1/amountToken0) Q64.96 value
    /// @param sqrtPriceX96 the initial sqrt price of the pool as a Q64.96
    function initialize(uint160 sqrtPriceX96) external;

    /// @notice Adds liquidity for the given recipient/tickLower/tickUpper position
    /// @dev The caller of this method receives a callback in the form of IUniswapV3MintCallback#uniswapV3MintCallback
    /// in which they must pay any token0 or token1 owed for the liquidity. The amount of token0/token1 due depends
    /// on tickLower, tickUpper, the amount of liquidity, and the current price.
    /// @param recipient The address for which the liquidity will be created
    /// @param tickLower The lower tick of the position in which to add liquidity
    /// @param tickUpper The upper tick of the position in which to add liquidity
    /// @param amount The amount of liquidity to mint
    /// @param data Any data that should be passed through to the callback
    /// @return amount0 The amount of token0 that was paid to mint the given amount of liquidity. Matches the value in the callback
    /// @return amount1 The amount of token1 that was paid to mint the given amount of liquidity. Matches the value in the callback
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        bytes calldata data
    ) external returns (uint256 amount0, uint256 amount1);

    /// @notice Collects tokens owed to a position
    /// @dev Does not recompute fees earned, which must be done either via mint or burn of any amount of liquidity.
    /// Collect must be called by the position owner. To withdraw only token0 or only token1, amount0Requested or
    /// amount1Requested may be set to zero. To withdraw all tokens owed, caller may pass any value greater than the
    /// actual tokens owed, e.g. type(uint128).max. Tokens owed may be from accumulated swap fees or burned liquidity.
    /// @param recipient The address which should receive the fees collected
    /// @param tickLower The lower tick of the position for which to collect fees
    /// @param tickUpper The upper tick of the position for which to collect fees
    /// @param amount0Requested How much token0 should be withdrawn from the fees owed
    /// @param amount1Requested How much token1 should be withdrawn from the fees owed
    /// @return amount0 The amount of fees collected in token0
    /// @return amount1 The amount of fees collected in token1
    function collect(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external returns (uint128 amount0, uint128 amount1);

    /// @notice Burn liquidity from the sender and account tokens owed for the liquidity to the position
    /// @dev Can be used to trigger a recalculation of fees owed to a position by calling with an amount of 0
    /// @dev Fees must be collected separately via a call to #collect
    /// @param tickLower The lower tick of the position for which to burn liquidity
    /// @param tickUpper The upper tick of the position for which to burn liquidity
    /// @param amount How much liquidity to burn
    /// @return amount0 The amount of token0 sent to the recipient
    /// @return amount1 The amount of token1 sent to the recipient
    function burn(
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) external returns (uint256 amount0, uint256 amount1);

    /// @notice Swap token0 for token1, or token1 for token0
    /// @dev The caller of this method receives a callback in the form of IUniswapV3SwapCallback#uniswapV3SwapCallback
    /// @param recipient The address to receive the output of the swap
    /// @param zeroForOne The direction of the swap, true for token0 to token1, false for token1 to token0
    /// @param amountSpecified The amount of the swap, which implicitly configures the swap as exact input (positive), or exact output (negative)
    /// @param sqrtPriceLimitX96 The Q64.96 sqrt price limit. If zero for one, the price cannot be less than this
    /// value after the swap. If one for zero, the price cannot be greater than this value after the swap
    /// @param data Any data to be passed through to the callback
    /// @return amount0 The delta of the balance of token0 of the pool, exact when negative, minimum when positive
    /// @return amount1 The delta of the balance of token1 of the pool, exact when negative, minimum when positive
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        bytes calldata data
    ) external returns (int256 amount0, int256 amount1);

    /// @notice Receive token0 and/or token1 and pay it back, plus a fee, in the callback
    /// @dev The caller of this method receives a callback in the form of IUniswapV3FlashCallback#uniswapV3FlashCallback
    /// @dev Can be used to donate underlying tokens pro-rata to currently in-range liquidity providers by calling
    /// with 0 amount{0,1} and sending the donation amount(s) from the callback
    /// @param recipient The address which will receive the token0 and token1 amounts
    /// @param amount0 The amount of token0 to send
    /// @param amount1 The amount of token1 to send
    /// @param data Any data to be passed through to the callback
    function flash(
        address recipient,
        uint256 amount0,
        uint256 amount1,
        bytes calldata data
    ) external;

    /// @notice Increase the maximum number of price and liquidity observations that this pool will store
    /// @dev This method is no-op if the pool already has an observationCardinalityNext greater than or equal to
    /// the input observationCardinalityNext.
    /// @param observationCardinalityNext The desired minimum number of observations for the pool to store
    function increaseObservationCardinalityNext(uint16 observationCardinalityNext) external;
}

// File: @uniswap/v3-core/contracts/interfaces/pool/IUniswapV3PoolDerivedState.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Pool state that is not stored
/// @notice Contains view functions to provide information about the pool that is computed rather than stored on the
/// blockchain. The functions here may have variable gas costs.
interface IUniswapV3PoolDerivedState {
    /// @notice Returns the cumulative tick and liquidity as of each timestamp `secondsAgo` from the current block timestamp
    /// @dev To get a time weighted average tick or liquidity-in-range, you must call this with two values, one representing
    /// the beginning of the period and another for the end of the period. E.g., to get the last hour time-weighted average tick,
    /// you must call it with secondsAgos = [3600, 0].
    /// @dev The time weighted average tick represents the geometric time weighted average price of the pool, in
    /// log base sqrt(1.0001) of token1 / token0. The TickMath library can be used to go from a tick value to a ratio.
    /// @param secondsAgos From how long ago each cumulative tick and liquidity value should be returned
    /// @return tickCumulatives Cumulative tick values as of each `secondsAgos` from the current block timestamp
    /// @return secondsPerLiquidityCumulativeX128s Cumulative seconds per liquidity-in-range value as of each `secondsAgos` from the current block
    /// timestamp
    function observe(uint32[] calldata secondsAgos)
        external
        view
        returns (int56[] memory tickCumulatives, uint160[] memory secondsPerLiquidityCumulativeX128s);

    /// @notice Returns a snapshot of the tick cumulative, seconds per liquidity and seconds inside a tick range
    /// @dev Snapshots must only be compared to other snapshots, taken over a period for which a position existed.
    /// I.e., snapshots cannot be compared if a position is not held for the entire period between when the first
    /// snapshot is taken and the second snapshot is taken.
    /// @param tickLower The lower tick of the range
    /// @param tickUpper The upper tick of the range
    /// @return tickCumulativeInside The snapshot of the tick accumulator for the range
    /// @return secondsPerLiquidityInsideX128 The snapshot of seconds per liquidity for the range
    /// @return secondsInside The snapshot of seconds per liquidity for the range
    function snapshotCumulativesInside(int24 tickLower, int24 tickUpper)
        external
        view
        returns (
            int56 tickCumulativeInside,
            uint160 secondsPerLiquidityInsideX128,
            uint32 secondsInside
        );
}

// File: @uniswap/v3-core/contracts/interfaces/pool/IUniswapV3PoolEvents.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Events emitted by a pool
/// @notice Contains all events emitted by the pool
interface IUniswapV3PoolEvents {
    /// @notice Emitted exactly once by a pool when #initialize is first called on the pool
    /// @dev Mint/Burn/Swap cannot be emitted by the pool before Initialize
    /// @param sqrtPriceX96 The initial sqrt price of the pool, as a Q64.96
    /// @param tick The initial tick of the pool, i.e. log base 1.0001 of the starting price of the pool
    event Initialize(uint160 sqrtPriceX96, int24 tick);

    /// @notice Emitted when liquidity is minted for a given position
    /// @param sender The address that minted the liquidity
    /// @param owner The owner of the position and recipient of any minted liquidity
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param amount The amount of liquidity minted to the position range
    /// @param amount0 How much token0 was required for the minted liquidity
    /// @param amount1 How much token1 was required for the minted liquidity
    event Mint(
        address sender,
        address indexed owner,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        uint128 amount,
        uint256 amount0,
        uint256 amount1
    );

    /// @notice Emitted when fees are collected by the owner of a position
    /// @dev Collect events may be emitted with zero amount0 and amount1 when the caller chooses not to collect fees
    /// @param owner The owner of the position for which fees are collected
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param amount0 The amount of token0 fees collected
    /// @param amount1 The amount of token1 fees collected
    event Collect(
        address indexed owner,
        address recipient,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        uint128 amount0,
        uint128 amount1
    );

    /// @notice Emitted when a position's liquidity is removed
    /// @dev Does not withdraw any fees earned by the liquidity position, which must be withdrawn via #collect
    /// @param owner The owner of the position for which liquidity is removed
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param amount The amount of liquidity to remove
    /// @param amount0 The amount of token0 withdrawn
    /// @param amount1 The amount of token1 withdrawn
    event Burn(
        address indexed owner,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        uint128 amount,
        uint256 amount0,
        uint256 amount1
    );

    /// @notice Emitted by the pool for any swaps between token0 and token1
    /// @param sender The address that initiated the swap call, and that received the callback
    /// @param recipient The address that received the output of the swap
    /// @param amount0 The delta of the token0 balance of the pool
    /// @param amount1 The delta of the token1 balance of the pool
    /// @param sqrtPriceX96 The sqrt(price) of the pool after the swap, as a Q64.96
    /// @param liquidity The liquidity of the pool after the swap
    /// @param tick The log base 1.0001 of price of the pool after the swap
    event Swap(
        address indexed sender,
        address indexed recipient,
        int256 amount0,
        int256 amount1,
        uint160 sqrtPriceX96,
        uint128 liquidity,
        int24 tick
    );

    /// @notice Emitted by the pool for any flashes of token0/token1
    /// @param sender The address that initiated the swap call, and that received the callback
    /// @param recipient The address that received the tokens from flash
    /// @param amount0 The amount of token0 that was flashed
    /// @param amount1 The amount of token1 that was flashed
    /// @param paid0 The amount of token0 paid for the flash, which can exceed the amount0 plus the fee
    /// @param paid1 The amount of token1 paid for the flash, which can exceed the amount1 plus the fee
    event Flash(
        address indexed sender,
        address indexed recipient,
        uint256 amount0,
        uint256 amount1,
        uint256 paid0,
        uint256 paid1
    );

    /// @notice Emitted by the pool for increases to the number of observations that can be stored
    /// @dev observationCardinalityNext is not the observation cardinality until an observation is written at the index
    /// just before a mint/swap/burn.
    /// @param observationCardinalityNextOld The previous value of the next observation cardinality
    /// @param observationCardinalityNextNew The updated value of the next observation cardinality
    event IncreaseObservationCardinalityNext(
        uint16 observationCardinalityNextOld,
        uint16 observationCardinalityNextNew
    );

    /// @notice Emitted when the protocol fee is changed by the pool
    /// @param feeProtocol0Old The previous value of the token0 protocol fee
    /// @param feeProtocol1Old The previous value of the token1 protocol fee
    /// @param feeProtocol0New The updated value of the token0 protocol fee
    /// @param feeProtocol1New The updated value of the token1 protocol fee
    event SetFeeProtocol(uint8 feeProtocol0Old, uint8 feeProtocol1Old, uint8 feeProtocol0New, uint8 feeProtocol1New);

    /// @notice Emitted when the collected protocol fees are withdrawn by the factory owner
    /// @param sender The address that collects the protocol fees
    /// @param recipient The address that receives the collected protocol fees
    /// @param amount0 The amount of token0 protocol fees that is withdrawn
    /// @param amount0 The amount of token1 protocol fees that is withdrawn
    event CollectProtocol(address indexed sender, address indexed recipient, uint128 amount0, uint128 amount1);
}

// File: @uniswap/v3-core/contracts/interfaces/pool/IUniswapV3PoolImmutables.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Pool state that never changes
/// @notice These parameters are fixed for a pool forever, i.e., the methods will always return the same values
interface IUniswapV3PoolImmutables {
    /// @notice The contract that deployed the pool, which must adhere to the IUniswapV3Factory interface
    /// @return The contract address
    function factory() external view returns (address);

    /// @notice The first of the two tokens of the pool, sorted by address
    /// @return The token contract address
    function token0() external view returns (address);

    /// @notice The second of the two tokens of the pool, sorted by address
    /// @return The token contract address
    function token1() external view returns (address);

    /// @notice The pool's fee in hundredths of a bip, i.e. 1e-6
    /// @return The fee
    function fee() external view returns (uint24);

    /// @notice The pool tick spacing
    /// @dev Ticks can only be used at multiples of this value, minimum of 1 and always positive
    /// e.g.: a tickSpacing of 3 means ticks can be initialized every 3rd tick, i.e., ..., -6, -3, 0, 3, 6, ...
    /// This value is an int24 to avoid casting even though it is always positive.
    /// @return The tick spacing
    function tickSpacing() external view returns (int24);

    /// @notice The maximum amount of position liquidity that can use any tick in the range
    /// @dev This parameter is enforced per tick to prevent liquidity from overflowing a uint128 at any point, and
    /// also prevents out-of-range liquidity from being used to prevent adding in-range liquidity to a pool
    /// @return The max amount of liquidity per tick
    function maxLiquidityPerTick() external view returns (uint128);
}

// File: @uniswap/v3-core/contracts/interfaces/pool/IUniswapV3PoolOwnerActions.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Permissioned pool actions
/// @notice Contains pool methods that may only be called by the factory owner
interface IUniswapV3PoolOwnerActions {
    /// @notice Set the denominator of the protocol's % share of the fees
    /// @param feeProtocol0 new protocol fee for token0 of the pool
    /// @param feeProtocol1 new protocol fee for token1 of the pool
    function setFeeProtocol(uint8 feeProtocol0, uint8 feeProtocol1) external;

    /// @notice Collect the protocol fee accrued to the pool
    /// @param recipient The address to which collected protocol fees should be sent
    /// @param amount0Requested The maximum amount of token0 to send, can be 0 to collect fees in only token1
    /// @param amount1Requested The maximum amount of token1 to send, can be 0 to collect fees in only token0
    /// @return amount0 The protocol fee collected in token0
    /// @return amount1 The protocol fee collected in token1
    function collectProtocol(
        address recipient,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external returns (uint128 amount0, uint128 amount1);
}

// File: @uniswap/v3-core/contracts/interfaces/pool/IUniswapV3PoolState.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Pool state that can change
/// @notice These methods compose the pool's state, and can change with any frequency including multiple times
/// per transaction
interface IUniswapV3PoolState {
    /// @notice The 0th storage slot in the pool stores many values, and is exposed as a single method to save gas
    /// when accessed externally.
    /// @return sqrtPriceX96 The current price of the pool as a sqrt(token1/token0) Q64.96 value
    /// tick The current tick of the pool, i.e. according to the last tick transition that was run.
    /// This value may not always be equal to SqrtTickMath.getTickAtSqrtRatio(sqrtPriceX96) if the price is on a tick
    /// boundary.
    /// observationIndex The index of the last oracle observation that was written,
    /// observationCardinality The current maximum number of observations stored in the pool,
    /// observationCardinalityNext The next maximum number of observations, to be updated when the observation.
    /// feeProtocol The protocol fee for both tokens of the pool.
    /// Encoded as two 4 bit values, where the protocol fee of token1 is shifted 4 bits and the protocol fee of token0
    /// is the lower 4 bits. Used as the denominator of a fraction of the swap fee, e.g. 4 means 1/4th of the swap fee.
    /// unlocked Whether the pool is currently locked to reentrancy
    function slot0()
        external
        view
        returns (
            uint160 sqrtPriceX96,
            int24 tick,
            uint16 observationIndex,
            uint16 observationCardinality,
            uint16 observationCardinalityNext,
            uint8 feeProtocol,
            bool unlocked
        );

    /// @notice The fee growth as a Q128.128 fees of token0 collected per unit of liquidity for the entire life of the pool
    /// @dev This value can overflow the uint256
    function feeGrowthGlobal0X128() external view returns (uint256);

    /// @notice The fee growth as a Q128.128 fees of token1 collected per unit of liquidity for the entire life of the pool
    /// @dev This value can overflow the uint256
    function feeGrowthGlobal1X128() external view returns (uint256);

    /// @notice The amounts of token0 and token1 that are owed to the protocol
    /// @dev Protocol fees will never exceed uint128 max in either token
    function protocolFees() external view returns (uint128 token0, uint128 token1);

    /// @notice The currently in range liquidity available to the pool
    /// @dev This value has no relationship to the total liquidity across all ticks
    function liquidity() external view returns (uint128);

    /// @notice Look up information about a specific tick in the pool
    /// @param tick The tick to look up
    /// @return liquidityGross the total amount of position liquidity that uses the pool either as tick lower or
    /// tick upper,
    /// liquidityNet how much liquidity changes when the pool price crosses the tick,
    /// feeGrowthOutside0X128 the fee growth on the other side of the tick from the current tick in token0,
    /// feeGrowthOutside1X128 the fee growth on the other side of the tick from the current tick in token1,
    /// tickCumulativeOutside the cumulative tick value on the other side of the tick from the current tick
    /// secondsPerLiquidityOutsideX128 the seconds spent per liquidity on the other side of the tick from the current tick,
    /// secondsOutside the seconds spent on the other side of the tick from the current tick,
    /// initialized Set to true if the tick is initialized, i.e. liquidityGross is greater than 0, otherwise equal to false.
    /// Outside values can only be used if the tick is initialized, i.e. if liquidityGross is greater than 0.
    /// In addition, these values are only relative and must be used only in comparison to previous snapshots for
    /// a specific position.
    function ticks(int24 tick)
        external
        view
        returns (
            uint128 liquidityGross,
            int128 liquidityNet,
            uint256 feeGrowthOutside0X128,
            uint256 feeGrowthOutside1X128,
            int56 tickCumulativeOutside,
            uint160 secondsPerLiquidityOutsideX128,
            uint32 secondsOutside,
            bool initialized
        );

    /// @notice Returns 256 packed tick initialized boolean values. See TickBitmap for more information
    function tickBitmap(int16 wordPosition) external view returns (uint256);

    /// @notice Returns the information about a position by the position's key
    /// @param key The position's key is a hash of a preimage composed by the owner, tickLower and tickUpper
    /// @return _liquidity The amount of liquidity in the position,
    /// Returns feeGrowthInside0LastX128 fee growth of token0 inside the tick range as of the last mint/burn/poke,
    /// Returns feeGrowthInside1LastX128 fee growth of token1 inside the tick range as of the last mint/burn/poke,
    /// Returns tokensOwed0 the computed amount of token0 owed to the position as of the last mint/burn/poke,
    /// Returns tokensOwed1 the computed amount of token1 owed to the position as of the last mint/burn/poke
    function positions(bytes32 key)
        external
        view
        returns (
            uint128 _liquidity,
            uint256 feeGrowthInside0LastX128,
            uint256 feeGrowthInside1LastX128,
            uint128 tokensOwed0,
            uint128 tokensOwed1
        );

    /// @notice Returns data about a specific observation index
    /// @param index The element of the observations array to fetch
    /// @dev You most likely want to use #observe() instead of this method to get an observation as of some amount of time
    /// ago, rather than at a specific index in the array.
    /// @return blockTimestamp The timestamp of the observation,
    /// Returns tickCumulative the tick multiplied by seconds elapsed for the life of the pool as of the observation timestamp,
    /// Returns secondsPerLiquidityCumulativeX128 the seconds per in range liquidity for the life of the pool as of the observation timestamp,
    /// Returns initialized whether the observation has been initialized and the values are safe to use
    function observations(uint256 index)
        external
        view
        returns (
            uint32 blockTimestamp,
            int56 tickCumulative,
            uint160 secondsPerLiquidityCumulativeX128,
            bool initialized
        );
}

// File: @uniswap/v3-core/contracts/libraries/FixedPoint128.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.4.0;

/// @title FixedPoint128
/// @notice A library for handling binary fixed point numbers, see https://en.wikipedia.org/wiki/Q_(number_format)
library FixedPoint128 {
    uint256 internal constant Q128 = 0x100000000000000000000000000000000;
}

// File: @uniswap/v3-core/contracts/libraries/FixedPoint96.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.4.0;

/// @title FixedPoint96
/// @notice A library for handling binary fixed point numbers, see https://en.wikipedia.org/wiki/Q_(number_format)
/// @dev Used in SqrtPriceMath.sol
library FixedPoint96 {
    uint8 internal constant RESOLUTION = 96;
    uint256 internal constant Q96 = 0x1000000000000000000000000;
}

// File: @uniswap/v3-core/contracts/libraries/FullMath.sol



// SPDX-License-Identifier: MIT
pragma solidity >=0.4.0 <0.8.0;

/// @title Contains 512-bit math functions
/// @notice Facilitates multiplication and division that can have overflow of an intermediate value without any loss of precision
/// @dev Handles "phantom overflow" i.e., allows multiplication and division where an intermediate value overflows 256 bits
library FullMath {
    /// @notice Calculates floor(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
    /// @param a The multiplicand
    /// @param b The multiplier
    /// @param denominator The divisor
    /// @return result The 256-bit result
    /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv
    function mulDiv(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        // 512-bit multiply [prod1 prod0] = a * b
        // Compute the product mod 2**256 and mod 2**256 - 1
        // then use the Chinese Remainder Theorem to reconstruct
        // the 512 bit result. The result is stored in two 256
        // variables such that product = prod1 * 2**256 + prod0
        uint256 prod0; // Least significant 256 bits of the product
        uint256 prod1; // Most significant 256 bits of the product
        assembly {
            let mm := mulmod(a, b, not(0))
            prod0 := mul(a, b)
            prod1 := sub(sub(mm, prod0), lt(mm, prod0))
        }

        // Handle non-overflow cases, 256 by 256 division
        if (prod1 == 0) {
            require(denominator > 0);
            assembly {
                result := div(prod0, denominator)
            }
            return result;
        }

        // Make sure the result is less than 2**256.
        // Also prevents denominator == 0
        require(denominator > prod1);

        ///////////////////////////////////////////////
        // 512 by 256 division.
        ///////////////////////////////////////////////

        // Make division exact by subtracting the remainder from [prod1 prod0]
        // Compute remainder using mulmod
        uint256 remainder;
        assembly {
            remainder := mulmod(a, b, denominator)
        }
        // Subtract 256 bit number from 512 bit number
        assembly {
            prod1 := sub(prod1, gt(remainder, prod0))
            prod0 := sub(prod0, remainder)
        }

        // Factor powers of two out of denominator
        // Compute largest power of two divisor of denominator.
        // Always >= 1.
        uint256 twos = -denominator & denominator;
        // Divide denominator by power of two
        assembly {
            denominator := div(denominator, twos)
        }

        // Divide [prod1 prod0] by the factors of two
        assembly {
            prod0 := div(prod0, twos)
        }
        // Shift in bits from prod1 into prod0. For this we need
        // to flip `twos` such that it is 2**256 / twos.
        // If twos is zero, then it becomes one
        assembly {
            twos := add(div(sub(0, twos), twos), 1)
        }
        prod0 |= prod1 * twos;

        // Invert denominator mod 2**256
        // Now that denominator is an odd number, it has an inverse
        // modulo 2**256 such that denominator * inv = 1 mod 2**256.
        // Compute the inverse by starting with a seed that is correct
        // correct for four bits. That is, denominator * inv = 1 mod 2**4
        uint256 inv = (3 * denominator) ^ 2;
        // Now use Newton-Raphson iteration to improve the precision.
        // Thanks to Hensel's lifting lemma, this also works in modular
        // arithmetic, doubling the correct bits in each step.
        inv *= 2 - denominator * inv; // inverse mod 2**8
        inv *= 2 - denominator * inv; // inverse mod 2**16
        inv *= 2 - denominator * inv; // inverse mod 2**32
        inv *= 2 - denominator * inv; // inverse mod 2**64
        inv *= 2 - denominator * inv; // inverse mod 2**128
        inv *= 2 - denominator * inv; // inverse mod 2**256

        // Because the division is now exact we can divide by multiplying
        // with the modular inverse of denominator. This will give us the
        // correct result modulo 2**256. Since the precoditions guarantee
        // that the outcome is less than 2**256, this is the final result.
        // We don't need to compute the high bits of the result and prod1
        // is no longer required.
        result = prod0 * inv;
        return result;
    }

    /// @notice Calculates ceil(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
    /// @param a The multiplicand
    /// @param b The multiplier
    /// @param denominator The divisor
    /// @return result The 256-bit result
    function mulDivRoundingUp(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        result = mulDiv(a, b, denominator);
        if (mulmod(a, b, denominator) > 0) {
            require(result < type(uint256).max);
            result++;
        }
    }
}

// File: @uniswap/v3-core/contracts/libraries/TickMath.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0 <0.8.0;

/// @title Math library for computing sqrt prices from ticks and vice versa
/// @notice Computes sqrt price for ticks of size 1.0001, i.e. sqrt(1.0001^tick) as fixed point Q64.96 numbers. Supports
/// prices between 2**-128 and 2**128
library TickMath {
    /// @dev The minimum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**-128
    int24 internal constant MIN_TICK = -887272;
    /// @dev The maximum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**128
    int24 internal constant MAX_TICK = -MIN_TICK;

    /// @dev The minimum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MIN_TICK)
    uint160 internal constant MIN_SQRT_RATIO = 4295128739;
    /// @dev The maximum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MAX_TICK)
    uint160 internal constant MAX_SQRT_RATIO = 1461446703485210103287273052203988822378723970342;

    /// @notice Calculates sqrt(1.0001^tick) * 2^96
    /// @dev Throws if |tick| > max tick
    /// @param tick The input tick for the above formula
    /// @return sqrtPriceX96 A Fixed point Q64.96 number representing the sqrt of the ratio of the two assets (token1/token0)
    /// at the given tick
    function getSqrtRatioAtTick(int24 tick) internal pure returns (uint160 sqrtPriceX96) {
        uint256 absTick = tick < 0 ? uint256(-int256(tick)) : uint256(int256(tick));
        require(absTick <= uint256(MAX_TICK), 'T');

        uint256 ratio = absTick & 0x1 != 0 ? 0xfffcb933bd6fad37aa2d162d1a594001 : 0x100000000000000000000000000000000;
        if (absTick & 0x2 != 0) ratio = (ratio * 0xfff97272373d413259a46990580e213a) >> 128;
        if (absTick & 0x4 != 0) ratio = (ratio * 0xfff2e50f5f656932ef12357cf3c7fdcc) >> 128;
        if (absTick & 0x8 != 0) ratio = (ratio * 0xffe5caca7e10e4e61c3624eaa0941cd0) >> 128;
        if (absTick & 0x10 != 0) ratio = (ratio * 0xffcb9843d60f6159c9db58835c926644) >> 128;
        if (absTick & 0x20 != 0) ratio = (ratio * 0xff973b41fa98c081472e6896dfb254c0) >> 128;
        if (absTick & 0x40 != 0) ratio = (ratio * 0xff2ea16466c96a3843ec78b326b52861) >> 128;
        if (absTick & 0x80 != 0) ratio = (ratio * 0xfe5dee046a99a2a811c461f1969c3053) >> 128;
        if (absTick & 0x100 != 0) ratio = (ratio * 0xfcbe86c7900a88aedcffc83b479aa3a4) >> 128;
        if (absTick & 0x200 != 0) ratio = (ratio * 0xf987a7253ac413176f2b074cf7815e54) >> 128;
        if (absTick & 0x400 != 0) ratio = (ratio * 0xf3392b0822b70005940c7a398e4b70f3) >> 128;
        if (absTick & 0x800 != 0) ratio = (ratio * 0xe7159475a2c29b7443b29c7fa6e889d9) >> 128;
        if (absTick & 0x1000 != 0) ratio = (ratio * 0xd097f3bdfd2022b8845ad8f792aa5825) >> 128;
        if (absTick & 0x2000 != 0) ratio = (ratio * 0xa9f746462d870fdf8a65dc1f90e061e5) >> 128;
        if (absTick & 0x4000 != 0) ratio = (ratio * 0x70d869a156d2a1b890bb3df62baf32f7) >> 128;
        if (absTick & 0x8000 != 0) ratio = (ratio * 0x31be135f97d08fd981231505542fcfa6) >> 128;
        if (absTick & 0x10000 != 0) ratio = (ratio * 0x9aa508b5b7a84e1c677de54f3e99bc9) >> 128;
        if (absTick & 0x20000 != 0) ratio = (ratio * 0x5d6af8dedb81196699c329225ee604) >> 128;
        if (absTick & 0x40000 != 0) ratio = (ratio * 0x2216e584f5fa1ea926041bedfe98) >> 128;
        if (absTick & 0x80000 != 0) ratio = (ratio * 0x48a170391f7dc42444e8fa2) >> 128;

        if (tick > 0) ratio = type(uint256).max / ratio;

        // this divides by 1<<32 rounding up to go from a Q128.128 to a Q128.96.
        // we then downcast because we know the result always fits within 160 bits due to our tick input constraint
        // we round up in the division so getTickAtSqrtRatio of the output price is always consistent
        sqrtPriceX96 = uint160((ratio >> 32) + (ratio % (1 << 32) == 0 ? 0 : 1));
    }

    /// @notice Calculates the greatest tick value such that getRatioAtTick(tick) <= ratio
    /// @dev Throws in case sqrtPriceX96 < MIN_SQRT_RATIO, as MIN_SQRT_RATIO is the lowest value getRatioAtTick may
    /// ever return.
    /// @param sqrtPriceX96 The sqrt ratio for which to compute the tick as a Q64.96
    /// @return tick The greatest tick for which the ratio is less than or equal to the input ratio
    function getTickAtSqrtRatio(uint160 sqrtPriceX96) internal pure returns (int24 tick) {
        // second inequality must be < because the price can never reach the price at the max tick
        require(sqrtPriceX96 >= MIN_SQRT_RATIO && sqrtPriceX96 < MAX_SQRT_RATIO, 'R');
        uint256 ratio = uint256(sqrtPriceX96) << 32;

        uint256 r = ratio;
        uint256 msb = 0;

        assembly {
            let f := shl(7, gt(r, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(6, gt(r, 0xFFFFFFFFFFFFFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(5, gt(r, 0xFFFFFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(4, gt(r, 0xFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(3, gt(r, 0xFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(2, gt(r, 0xF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(1, gt(r, 0x3))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := gt(r, 0x1)
            msb := or(msb, f)
        }

        if (msb >= 128) r = ratio >> (msb - 127);
        else r = ratio << (127 - msb);

        int256 log_2 = (int256(msb) - 128) << 64;

        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(63, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(62, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(61, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(60, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(59, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(58, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(57, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(56, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(55, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(54, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(53, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(52, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(51, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(50, f))
        }

        int256 log_sqrt10001 = log_2 * 255738958999603826347141; // 128.128 number

        int24 tickLow = int24((log_sqrt10001 - 3402992956809132418596140100660247210) >> 128);
        int24 tickHi = int24((log_sqrt10001 + 291339464771989622907027621153398088495) >> 128);

        tick = tickLow == tickHi ? tickLow : getSqrtRatioAtTick(tickHi) <= sqrtPriceX96 ? tickHi : tickLow;
    }
}

// File: @uniswap/v3-periphery/contracts/base/BlockTimestamp.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;

/// @title Function for getting block timestamp
/// @dev Base contract that is overridden for tests
abstract contract BlockTimestamp {
    /// @dev Method that exists purely to be overridden for tests
    /// @return The current block timestamp
    function _blockTimestamp() internal view virtual returns (uint256) {
        return block.timestamp;
    }
}

// File: @uniswap/v3-periphery/contracts/base/ERC721Permit.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;

import '@openzeppelin/contracts/token/ERC721/ERC721.sol';
import '@openzeppelin/contracts/utils/Address.sol';

import '../libraries/ChainId.sol';
import '../interfaces/external/IERC1271.sol';
import '../interfaces/IERC721Permit.sol';
import './BlockTimestamp.sol';

/// @title ERC721 with permit
/// @notice Nonfungible tokens that support an approve via signature, i.e. permit
abstract contract ERC721Permit is BlockTimestamp, ERC721, IERC721Permit {
    /// @dev Gets the current nonce for a token ID and then increments it, returning the original value
    function _getAndIncrementNonce(uint256 tokenId) internal virtual returns (uint256);

    /// @dev The hash of the name used in the permit signature verification
    bytes32 private immutable nameHash;

    /// @dev The hash of the version string used in the permit signature verification
    bytes32 private immutable versionHash;

    /// @notice Computes the nameHash and versionHash
    constructor(
        string memory name_,
        string memory symbol_,
        string memory version_
    ) ERC721(name_, symbol_) {
        nameHash = keccak256(bytes(name_));
        versionHash = keccak256(bytes(version_));
    }

    /// @inheritdoc IERC721Permit
    function DOMAIN_SEPARATOR() public view override returns (bytes32) {
        return
            keccak256(
                abi.encode(
                    // keccak256('EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)')
                    0x8b73c3c69bb8fe3d512ecc4cf759cc79239f7b179b0ffacaa9a75d522b39400f,
                    nameHash,
                    versionHash,
                    ChainId.get(),
                    address(this)
                )
            );
    }

    /// @inheritdoc IERC721Permit
    /// @dev Value is equal to keccak256("Permit(address spender,uint256 tokenId,uint256 nonce,uint256 deadline)");
    bytes32 public constant override PERMIT_TYPEHASH =
        0x49ecf333e5b8c95c40fdafc95c1ad136e8914a8fb55e9dc8bb01eaa83a2df9ad;

    /// @inheritdoc IERC721Permit
    function permit(
        address spender,
        uint256 tokenId,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external payable override {
        require(_blockTimestamp() <= deadline, 'Permit expired');

        bytes32 digest =
            keccak256(
                abi.encodePacked(
                    '\x19\x01',
                    DOMAIN_SEPARATOR(),
                    keccak256(abi.encode(PERMIT_TYPEHASH, spender, tokenId, _getAndIncrementNonce(tokenId), deadline))
                )
            );
        address owner = ownerOf(tokenId);
        require(spender != owner, 'ERC721Permit: approval to current owner');

        if (Address.isContract(owner)) {
            require(IERC1271(owner).isValidSignature(digest, abi.encodePacked(r, s, v)) == 0x1626ba7e, 'Unauthorized');
        } else {
            address recoveredAddress = ecrecover(digest, v, r, s);
            require(recoveredAddress != address(0), 'Invalid signature');
            require(recoveredAddress == owner, 'Unauthorized');
        }

        _approve(spender, tokenId);
    }
}

// File: @uniswap/v3-periphery/contracts/base/LiquidityManagement.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;
pragma abicoder v2;

import '@uniswap/v3-core/contracts/interfaces/IUniswapV3Factory.sol';
import '@uniswap/v3-core/contracts/interfaces/callback/IUniswapV3MintCallback.sol';
import '@uniswap/v3-core/contracts/libraries/TickMath.sol';

import '../libraries/PoolAddress.sol';
import '../libraries/CallbackValidation.sol';
import '../libraries/LiquidityAmounts.sol';

import './PeripheryPayments.sol';
import './PeripheryImmutableState.sol';

/// @title Liquidity management functions
/// @notice Internal functions for safely managing liquidity in Uniswap V3
abstract contract LiquidityManagement is IUniswapV3MintCallback, PeripheryImmutableState, PeripheryPayments {
    struct MintCallbackData {
        PoolAddress.PoolKey poolKey;
        address payer;
    }

    /// @inheritdoc IUniswapV3MintCallback
    function uniswapV3MintCallback(
        uint256 amount0Owed,
        uint256 amount1Owed,
        bytes calldata data
    ) external override {
        MintCallbackData memory decoded = abi.decode(data, (MintCallbackData));
        CallbackValidation.verifyCallback(factory, decoded.poolKey);

        if (amount0Owed > 0) pay(decoded.poolKey.token0, decoded.payer, msg.sender, amount0Owed);
        if (amount1Owed > 0) pay(decoded.poolKey.token1, decoded.payer, msg.sender, amount1Owed);
    }

    struct AddLiquidityParams {
        address token0;
        address token1;
        uint24 fee;
        address recipient;
        int24 tickLower;
        int24 tickUpper;
        uint256 amount0Desired;
        uint256 amount1Desired;
        uint256 amount0Min;
        uint256 amount1Min;
    }

    /// @notice Add liquidity to an initialized pool
    function addLiquidity(AddLiquidityParams memory params)
        internal
        returns (
            uint128 liquidity,
            uint256 amount0,
            uint256 amount1,
            IUniswapV3Pool pool
        )
    {
        PoolAddress.PoolKey memory poolKey =
            PoolAddress.PoolKey({token0: params.token0, token1: params.token1, fee: params.fee});

        pool = IUniswapV3Pool(PoolAddress.computeAddress(factory, poolKey));

        // compute the liquidity amount
        {
            (uint160 sqrtPriceX96, , , , , , ) = pool.slot0();
            uint160 sqrtRatioAX96 = TickMath.getSqrtRatioAtTick(params.tickLower);
            uint160 sqrtRatioBX96 = TickMath.getSqrtRatioAtTick(params.tickUpper);

            liquidity = LiquidityAmounts.getLiquidityForAmounts(
                sqrtPriceX96,
                sqrtRatioAX96,
                sqrtRatioBX96,
                params.amount0Desired,
                params.amount1Desired
            );
        }

        (amount0, amount1) = pool.mint(
            params.recipient,
            params.tickLower,
            params.tickUpper,
            liquidity,
            abi.encode(MintCallbackData({poolKey: poolKey, payer: msg.sender}))
        );

        require(amount0 >= params.amount0Min && amount1 >= params.amount1Min, 'Price slippage check');
    }
}

// File: @uniswap/v3-periphery/contracts/base/Multicall.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;
pragma abicoder v2;

import '../interfaces/IMulticall.sol';

/// @title Multicall
/// @notice Enables calling multiple methods in a single call to the contract
abstract contract Multicall is IMulticall {
    /// @inheritdoc IMulticall
    function multicall(bytes[] calldata data) public payable override returns (bytes[] memory results) {
        results = new bytes[](data.length);
        for (uint256 i = 0; i < data.length; i++) {
            (bool success, bytes memory result) = address(this).delegatecall(data[i]);

            if (!success) {
                // Next 5 lines from https://ethereum.stackexchange.com/a/83577
                if (result.length < 68) revert();
                assembly {
                    result := add(result, 0x04)
                }
                revert(abi.decode(result, (string)));
            }

            results[i] = result;
        }
    }
}

// File: @uniswap/v3-periphery/contracts/base/PeripheryImmutableState.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;

import '../interfaces/IPeripheryImmutableState.sol';

/// @title Immutable state
/// @notice Immutable state used by periphery contracts
abstract contract PeripheryImmutableState is IPeripheryImmutableState {
    /// @inheritdoc IPeripheryImmutableState
    address public immutable override factory;
    /// @inheritdoc IPeripheryImmutableState
    address public immutable override WETH9;

    constructor(address _factory, address _WETH9) {
        factory = _factory;
        WETH9 = _WETH9;
    }
}

// File: @uniswap/v3-periphery/contracts/base/PeripheryPayments.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.7.5;

import '@openzeppelin/contracts/token/ERC20/IERC20.sol';

import '../interfaces/IPeripheryPayments.sol';
import '../interfaces/external/IWETH9.sol';

import '../libraries/TransferHelper.sol';

import './PeripheryImmutableState.sol';

abstract contract PeripheryPayments is IPeripheryPayments, PeripheryImmutableState {
    receive() external payable {
        require(msg.sender == WETH9, 'Not WETH9');
    }

    /// @inheritdoc IPeripheryPayments
    function unwrapWETH9(uint256 amountMinimum, address recipient) public payable override {
        uint256 balanceWETH9 = IWETH9(WETH9).balanceOf(address(this));
        require(balanceWETH9 >= amountMinimum, 'Insufficient WETH9');

        if (balanceWETH9 > 0) {
            IWETH9(WETH9).withdraw(balanceWETH9);
            TransferHelper.safeTransferETH(recipient, balanceWETH9);
        }
    }

    /// @inheritdoc IPeripheryPayments
    function sweepToken(
        address token,
        uint256 amountMinimum,
        address recipient
    ) public payable override {
        uint256 balanceToken = IERC20(token).balanceOf(address(this));
        require(balanceToken >= amountMinimum, 'Insufficient token');

        if (balanceToken > 0) {
            TransferHelper.safeTransfer(token, recipient, balanceToken);
        }
    }

    /// @inheritdoc IPeripheryPayments
    function refundETH() external payable override {
        if (address(this).balance > 0) TransferHelper.safeTransferETH(msg.sender, address(this).balance);
    }

    /// @param token The token to pay
    /// @param payer The entity that must pay
    /// @param recipient The entity that will receive payment
    /// @param value The amount to pay
    function pay(
        address token,
        address payer,
        address recipient,
        uint256 value
    ) internal {
        if (token == WETH9 && address(this).balance >= value) {
            // pay with WETH9
            IWETH9(WETH9).deposit{value: value}(); // wrap only what is needed to pay
            IWETH9(WETH9).transfer(recipient, value);
        } else if (payer == address(this)) {
            // pay with tokens already in the contract (for the exact input multihop case)
            TransferHelper.safeTransfer(token, recipient, value);
        } else {
            // pull payment
            TransferHelper.safeTransferFrom(token, payer, recipient, value);
        }
    }
}

// File: @uniswap/v3-periphery/contracts/base/PeripheryValidation.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;

import './BlockTimestamp.sol';

abstract contract PeripheryValidation is BlockTimestamp {
    modifier checkDeadline(uint256 deadline) {
        require(_blockTimestamp() <= deadline, 'Transaction too old');
        _;
    }
}

// File: @uniswap/v3-periphery/contracts/base/PoolInitializer.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;

import '@uniswap/v3-core/contracts/interfaces/IUniswapV3Factory.sol';
import '@uniswap/v3-core/contracts/interfaces/IUniswapV3Pool.sol';

import './PeripheryImmutableState.sol';
import '../interfaces/IPoolInitializer.sol';

/// @title Creates and initializes V3 Pools
abstract contract PoolInitializer is IPoolInitializer, PeripheryImmutableState {
    /// @inheritdoc IPoolInitializer
    function createAndInitializePoolIfNecessary(
        address token0,
        address token1,
        uint24 fee,
        uint160 sqrtPriceX96
    ) external payable override returns (address pool) {
        require(token0 < token1);
        pool = IUniswapV3Factory(factory).getPool(token0, token1, fee);

        if (pool == address(0)) {
            pool = IUniswapV3Factory(factory).createPool(token0, token1, fee);
            IUniswapV3Pool(pool).initialize(sqrtPriceX96);
        } else {
            (uint160 sqrtPriceX96Existing, , , , , , ) = IUniswapV3Pool(pool).slot0();
            if (sqrtPriceX96Existing == 0) {
                IUniswapV3Pool(pool).initialize(sqrtPriceX96);
            }
        }
    }
}

// File: @uniswap/v3-periphery/contracts/base/SelfPermit.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

import '@openzeppelin/contracts/token/ERC20/IERC20.sol';
import '@openzeppelin/contracts/drafts/IERC20Permit.sol';

import '../interfaces/ISelfPermit.sol';
import '../interfaces/external/IERC20PermitAllowed.sol';

/// @title Self Permit
/// @notice Functionality to call permit on any EIP-2612-compliant token for use in the route
/// @dev These functions are expected to be embedded in multicalls to allow EOAs to approve a contract and call a function
/// that requires an approval in a single transaction.
abstract contract SelfPermit is ISelfPermit {
    /// @inheritdoc ISelfPermit
    function selfPermit(
        address token,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public payable override {
        IERC20Permit(token).permit(msg.sender, address(this), value, deadline, v, r, s);
    }

    /// @inheritdoc ISelfPermit
    function selfPermitIfNecessary(
        address token,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external payable override {
        if (IERC20(token).allowance(msg.sender, address(this)) < value) selfPermit(token, value, deadline, v, r, s);
    }

    /// @inheritdoc ISelfPermit
    function selfPermitAllowed(
        address token,
        uint256 nonce,
        uint256 expiry,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public payable override {
        IERC20PermitAllowed(token).permit(msg.sender, address(this), nonce, expiry, true, v, r, s);
    }

    /// @inheritdoc ISelfPermit
    function selfPermitAllowedIfNecessary(
        address token,
        uint256 nonce,
        uint256 expiry,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external payable override {
        if (IERC20(token).allowance(msg.sender, address(this)) < type(uint256).max)
            selfPermitAllowed(token, nonce, expiry, v, r, s);
    }
}

// File: @uniswap/v3-periphery/contracts/interfaces/external/IERC1271.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Interface for verifying contract-based account signatures
/// @notice Interface that verifies provided signature for the data
/// @dev Interface defined by EIP-1271
interface IERC1271 {
    /// @notice Returns whether the provided signature is valid for the provided data
    /// @dev MUST return the bytes4 magic value 0x1626ba7e when function passes.
    /// MUST NOT modify state (using STATICCALL for solc < 0.5, view modifier for solc > 0.5).
    /// MUST allow external calls.
    /// @param hash Hash of the data to be signed
    /// @param signature Signature byte array associated with _data
    /// @return magicValue The bytes4 magic value 0x1626ba7e
    function isValidSignature(bytes32 hash, bytes memory signature) external view returns (bytes4 magicValue);
}

// File: @uniswap/v3-periphery/contracts/interfaces/external/IERC20PermitAllowed.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Interface for permit
/// @notice Interface used by DAI/CHAI for permit
interface IERC20PermitAllowed {
    /// @notice Approve the spender to spend some tokens via the holder signature
    /// @dev This is the permit interface used by DAI and CHAI
    /// @param holder The address of the token holder, the token owner
    /// @param spender The address of the token spender
    /// @param nonce The holder's nonce, increases at each call to permit
    /// @param expiry The timestamp at which the permit is no longer valid
    /// @param allowed Boolean that sets approval amount, true for type(uint256).max and false for 0
    /// @param v Must produce valid secp256k1 signature from the holder along with `r` and `s`
    /// @param r Must produce valid secp256k1 signature from the holder along with `v` and `s`
    /// @param s Must produce valid secp256k1 signature from the holder along with `r` and `v`
    function permit(
        address holder,
        address spender,
        uint256 nonce,
        uint256 expiry,
        bool allowed,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;
}

// File: @uniswap/v3-periphery/contracts/interfaces/external/IWETH9.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;

import '@openzeppelin/contracts/token/ERC20/IERC20.sol';

/// @title Interface for WETH9
interface IWETH9 is IERC20 {
    /// @notice Deposit ether to get wrapped ether
    function deposit() external payable;

    /// @notice Withdraw wrapped ether to get ether
    function withdraw(uint256) external;
}

// File: @uniswap/v3-periphery/contracts/interfaces/IERC721Permit.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.7.5;

import '@openzeppelin/contracts/token/ERC721/IERC721.sol';

/// @title ERC721 with permit
/// @notice Extension to ERC721 that includes a permit function for signature based approvals
interface IERC721Permit is IERC721 {
    /// @notice The permit typehash used in the permit signature
    /// @return The typehash for the permit
    function PERMIT_TYPEHASH() external pure returns (bytes32);

    /// @notice The domain separator used in the permit signature
    /// @return The domain seperator used in encoding of permit signature
    function DOMAIN_SEPARATOR() external view returns (bytes32);

    /// @notice Approve of a specific token ID for spending by spender via signature
    /// @param spender The account that is being approved
    /// @param tokenId The ID of the token that is being approved for spending
    /// @param deadline The deadline timestamp by which the call must be mined for the approve to work
    /// @param v Must produce valid secp256k1 signature from the holder along with `r` and `s`
    /// @param r Must produce valid secp256k1 signature from the holder along with `v` and `s`
    /// @param s Must produce valid secp256k1 signature from the holder along with `r` and `v`
    function permit(
        address spender,
        uint256 tokenId,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external payable;
}

// File: @uniswap/v3-periphery/contracts/interfaces/IMulticall.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.7.5;
pragma abicoder v2;

/// @title Multicall interface
/// @notice Enables calling multiple methods in a single call to the contract
interface IMulticall {
    /// @notice Call multiple functions in the current contract and return the data from all of them if they all succeed
    /// @dev The `msg.value` should not be trusted for any method callable from multicall.
    /// @param data The encoded function data for each of the calls to make to this contract
    /// @return results The results from each of the calls passed in via data
    function multicall(bytes[] calldata data) external payable returns (bytes[] memory results);
}

// File: @uniswap/v3-periphery/contracts/interfaces/INonfungiblePositionManager.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.7.5;
pragma abicoder v2;

import '@openzeppelin/contracts/token/ERC721/IERC721Metadata.sol';
import '@openzeppelin/contracts/token/ERC721/IERC721Enumerable.sol';

import './IPoolInitializer.sol';
import './IERC721Permit.sol';
import './IPeripheryPayments.sol';
import './IPeripheryImmutableState.sol';
import '../libraries/PoolAddress.sol';

/// @title Non-fungible token for positions
/// @notice Wraps Uniswap V3 positions in a non-fungible token interface which allows for them to be transferred
/// and authorized.
interface INonfungiblePositionManager is
    IPoolInitializer,
    IPeripheryPayments,
    IPeripheryImmutableState,
    IERC721Metadata,
    IERC721Enumerable,
    IERC721Permit
{
    /// @notice Emitted when liquidity is increased for a position NFT
    /// @dev Also emitted when a token is minted
    /// @param tokenId The ID of the token for which liquidity was increased
    /// @param liquidity The amount by which liquidity for the NFT position was increased
    /// @param amount0 The amount of token0 that was paid for the increase in liquidity
    /// @param amount1 The amount of token1 that was paid for the increase in liquidity
    event IncreaseLiquidity(uint256 indexed tokenId, uint128 liquidity, uint256 amount0, uint256 amount1);
    /// @notice Emitted when liquidity is decreased for a position NFT
    /// @param tokenId The ID of the token for which liquidity was decreased
    /// @param liquidity The amount by which liquidity for the NFT position was decreased
    /// @param amount0 The amount of token0 that was accounted for the decrease in liquidity
    /// @param amount1 The amount of token1 that was accounted for the decrease in liquidity
    event DecreaseLiquidity(uint256 indexed tokenId, uint128 liquidity, uint256 amount0, uint256 amount1);
    /// @notice Emitted when tokens are collected for a position NFT
    /// @dev The amounts reported may not be exactly equivalent to the amounts transferred, due to rounding behavior
    /// @param tokenId The ID of the token for which underlying tokens were collected
    /// @param recipient The address of the account that received the collected tokens
    /// @param amount0 The amount of token0 owed to the position that was collected
    /// @param amount1 The amount of token1 owed to the position that was collected
    event Collect(uint256 indexed tokenId, address recipient, uint256 amount0, uint256 amount1);

    /// @notice Returns the position information associated with a given token ID.
    /// @dev Throws if the token ID is not valid.
    /// @param tokenId The ID of the token that represents the position
    /// @return nonce The nonce for permits
    /// @return operator The address that is approved for spending
    /// @return token0 The address of the token0 for a specific pool
    /// @return token1 The address of the token1 for a specific pool
    /// @return fee The fee associated with the pool
    /// @return tickLower The lower end of the tick range for the position
    /// @return tickUpper The higher end of the tick range for the position
    /// @return liquidity The liquidity of the position
    /// @return feeGrowthInside0LastX128 The fee growth of token0 as of the last action on the individual position
    /// @return feeGrowthInside1LastX128 The fee growth of token1 as of the last action on the individual position
    /// @return tokensOwed0 The uncollected amount of token0 owed to the position as of the last computation
    /// @return tokensOwed1 The uncollected amount of token1 owed to the position as of the last computation
    function positions(uint256 tokenId)
        external
        view
        returns (
            uint96 nonce,
            address operator,
            address token0,
            address token1,
            uint24 fee,
            int24 tickLower,
            int24 tickUpper,
            uint128 liquidity,
            uint256 feeGrowthInside0LastX128,
            uint256 feeGrowthInside1LastX128,
            uint128 tokensOwed0,
            uint128 tokensOwed1
        );

    struct MintParams {
        address token0;
        address token1;
        uint24 fee;
        int24 tickLower;
        int24 tickUpper;
        uint256 amount0Desired;
        uint256 amount1Desired;
        uint256 amount0Min;
        uint256 amount1Min;
        address recipient;
        uint256 deadline;
    }

    /// @notice Creates a new position wrapped in a NFT
    /// @dev Call this when the pool does exist and is initialized. Note that if the pool is created but not initialized
    /// a method does not exist, i.e. the pool is assumed to be initialized.
    /// @param params The params necessary to mint a position, encoded as `MintParams` in calldata
    /// @return tokenId The ID of the token that represents the minted position
    /// @return liquidity The amount of liquidity for this position
    /// @return amount0 The amount of token0
    /// @return amount1 The amount of token1
    function mint(MintParams calldata params)
        external
        payable
        returns (
            uint256 tokenId,
            uint128 liquidity,
            uint256 amount0,
            uint256 amount1
        );

    struct IncreaseLiquidityParams {
        uint256 tokenId;
        uint256 amount0Desired;
        uint256 amount1Desired;
        uint256 amount0Min;
        uint256 amount1Min;
        uint256 deadline;
    }

    /// @notice Increases the amount of liquidity in a position, with tokens paid by the `msg.sender`
    /// @param params tokenId The ID of the token for which liquidity is being increased,
    /// amount0Desired The desired amount of token0 to be spent,
    /// amount1Desired The desired amount of token1 to be spent,
    /// amount0Min The minimum amount of token0 to spend, which serves as a slippage check,
    /// amount1Min The minimum amount of token1 to spend, which serves as a slippage check,
    /// deadline The time by which the transaction must be included to effect the change
    /// @return liquidity The new liquidity amount as a result of the increase
    /// @return amount0 The amount of token0 to acheive resulting liquidity
    /// @return amount1 The amount of token1 to acheive resulting liquidity
    function increaseLiquidity(IncreaseLiquidityParams calldata params)
        external
        payable
        returns (
            uint128 liquidity,
            uint256 amount0,
            uint256 amount1
        );

    struct DecreaseLiquidityParams {
        uint256 tokenId;
        uint128 liquidity;
        uint256 amount0Min;
        uint256 amount1Min;
        uint256 deadline;
    }

    /// @notice Decreases the amount of liquidity in a position and accounts it to the position
    /// @param params tokenId The ID of the token for which liquidity is being decreased,
    /// amount The amount by which liquidity will be decreased,
    /// amount0Min The minimum amount of token0 that should be accounted for the burned liquidity,
    /// amount1Min The minimum amount of token1 that should be accounted for the burned liquidity,
    /// deadline The time by which the transaction must be included to effect the change
    /// @return amount0 The amount of token0 accounted to the position's tokens owed
    /// @return amount1 The amount of token1 accounted to the position's tokens owed
    function decreaseLiquidity(DecreaseLiquidityParams calldata params)
        external
        payable
        returns (uint256 amount0, uint256 amount1);

    struct CollectParams {
        uint256 tokenId;
        address recipient;
        uint128 amount0Max;
        uint128 amount1Max;
    }

    /// @notice Collects up to a maximum amount of fees owed to a specific position to the recipient
    /// @param params tokenId The ID of the NFT for which tokens are being collected,
    /// recipient The account that should receive the tokens,
    /// amount0Max The maximum amount of token0 to collect,
    /// amount1Max The maximum amount of token1 to collect
    /// @return amount0 The amount of fees collected in token0
    /// @return amount1 The amount of fees collected in token1
    function collect(CollectParams calldata params) external payable returns (uint256 amount0, uint256 amount1);

    /// @notice Burns a token ID, which deletes it from the NFT contract. The token must have 0 liquidity and all tokens
    /// must be collected first.
    /// @param tokenId The ID of the token that is being burned
    function burn(uint256 tokenId) external payable;
}

// File: @uniswap/v3-periphery/contracts/interfaces/INonfungibleTokenPositionDescriptor.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

import './INonfungiblePositionManager.sol';

/// @title Describes position NFT tokens via URI
interface INonfungibleTokenPositionDescriptor {
    /// @notice Produces the URI describing a particular token ID for a position manager
    /// @dev Note this URI may be a data: URI with the JSON contents directly inlined
    /// @param positionManager The position manager for which to describe the token
    /// @param tokenId The ID of the token for which to produce a description, which may not be valid
    /// @return The URI of the ERC721-compliant metadata
    function tokenURI(INonfungiblePositionManager positionManager, uint256 tokenId)
        external
        view
        returns (string memory);
}

// File: @uniswap/v3-periphery/contracts/interfaces/IPeripheryImmutableState.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Immutable state
/// @notice Functions that return immutable state of the router
interface IPeripheryImmutableState {
    /// @return Returns the address of the Uniswap V3 factory
    function factory() external view returns (address);

    /// @return Returns the address of WETH9
    function WETH9() external view returns (address);
}

// File: @uniswap/v3-periphery/contracts/interfaces/IPeripheryPayments.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.7.5;

/// @title Periphery Payments
/// @notice Functions to ease deposits and withdrawals of ETH
interface IPeripheryPayments {
    /// @notice Unwraps the contract's WETH9 balance and sends it to recipient as ETH.
    /// @dev The amountMinimum parameter prevents malicious contracts from stealing WETH9 from users.
    /// @param amountMinimum The minimum amount of WETH9 to unwrap
    /// @param recipient The address receiving ETH
    function unwrapWETH9(uint256 amountMinimum, address recipient) external payable;

    /// @notice Refunds any ETH balance held by this contract to the `msg.sender`
    /// @dev Useful for bundling with mint or increase liquidity that uses ether, or exact output swaps
    /// that use ether for the input amount
    function refundETH() external payable;

    /// @notice Transfers the full amount of a token held by this contract to recipient
    /// @dev The amountMinimum parameter prevents malicious contracts from stealing the token from users
    /// @param token The contract address of the token which will be transferred to `recipient`
    /// @param amountMinimum The minimum amount of token required for a transfer
    /// @param recipient The destination address of the token
    function sweepToken(
        address token,
        uint256 amountMinimum,
        address recipient
    ) external payable;
}

// File: @uniswap/v3-periphery/contracts/interfaces/IPoolInitializer.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.7.5;
pragma abicoder v2;

/// @title Creates and initializes V3 Pools
/// @notice Provides a method for creating and initializing a pool, if necessary, for bundling with other methods that
/// require the pool to exist.
interface IPoolInitializer {
    /// @notice Creates a new pool if it does not exist, then initializes if not initialized
    /// @dev This method can be bundled with others via IMulticall for the first action (e.g. mint) performed against a pool
    /// @param token0 The contract address of token0 of the pool
    /// @param token1 The contract address of token1 of the pool
    /// @param fee The fee amount of the v3 pool for the specified token pair
    /// @param sqrtPriceX96 The initial square root price of the pool as a Q64.96 value
    /// @return pool Returns the pool address based on the pair of tokens and fee, will return the newly created pool address if necessary
    function createAndInitializePoolIfNecessary(
        address token0,
        address token1,
        uint24 fee,
        uint160 sqrtPriceX96
    ) external payable returns (address pool);
}

// File: @uniswap/v3-periphery/contracts/interfaces/ISelfPermit.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.7.5;

/// @title Self Permit
/// @notice Functionality to call permit on any EIP-2612-compliant token for use in the route
interface ISelfPermit {
    /// @notice Permits this contract to spend a given token from `msg.sender`
    /// @dev The `owner` is always msg.sender and the `spender` is always address(this).
    /// @param token The address of the token spent
    /// @param value The amount that can be spent of token
    /// @param deadline A timestamp, the current blocktime must be less than or equal to this timestamp
    /// @param v Must produce valid secp256k1 signature from the holder along with `r` and `s`
    /// @param r Must produce valid secp256k1 signature from the holder along with `v` and `s`
    /// @param s Must produce valid secp256k1 signature from the holder along with `r` and `v`
    function selfPermit(
        address token,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external payable;

    /// @notice Permits this contract to spend a given token from `msg.sender`
    /// @dev The `owner` is always msg.sender and the `spender` is always address(this).
    /// Can be used instead of #selfPermit to prevent calls from failing due to a frontrun of a call to #selfPermit
    /// @param token The address of the token spent
    /// @param value The amount that can be spent of token
    /// @param deadline A timestamp, the current blocktime must be less than or equal to this timestamp
    /// @param v Must produce valid secp256k1 signature from the holder along with `r` and `s`
    /// @param r Must produce valid secp256k1 signature from the holder along with `v` and `s`
    /// @param s Must produce valid secp256k1 signature from the holder along with `r` and `v`
    function selfPermitIfNecessary(
        address token,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external payable;

    /// @notice Permits this contract to spend the sender's tokens for permit signatures that have the `allowed` parameter
    /// @dev The `owner` is always msg.sender and the `spender` is always address(this)
    /// @param token The address of the token spent
    /// @param nonce The current nonce of the owner
    /// @param expiry The timestamp at which the permit is no longer valid
    /// @param v Must produce valid secp256k1 signature from the holder along with `r` and `s`
    /// @param r Must produce valid secp256k1 signature from the holder along with `v` and `s`
    /// @param s Must produce valid secp256k1 signature from the holder along with `r` and `v`
    function selfPermitAllowed(
        address token,
        uint256 nonce,
        uint256 expiry,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external payable;

    /// @notice Permits this contract to spend the sender's tokens for permit signatures that have the `allowed` parameter
    /// @dev The `owner` is always msg.sender and the `spender` is always address(this)
    /// Can be used instead of #selfPermitAllowed to prevent calls from failing due to a frontrun of a call to #selfPermitAllowed.
    /// @param token The address of the token spent
    /// @param nonce The current nonce of the owner
    /// @param expiry The timestamp at which the permit is no longer valid
    /// @param v Must produce valid secp256k1 signature from the holder along with `r` and `s`
    /// @param r Must produce valid secp256k1 signature from the holder along with `v` and `s`
    /// @param s Must produce valid secp256k1 signature from the holder along with `r` and `v`
    function selfPermitAllowedIfNecessary(
        address token,
        uint256 nonce,
        uint256 expiry,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external payable;
}

// File: @uniswap/v3-periphery/contracts/libraries/CallbackValidation.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;

import '@uniswap/v3-core/contracts/interfaces/IUniswapV3Pool.sol';
import './PoolAddress.sol';

/// @notice Provides validation for callbacks from Uniswap V3 Pools
library CallbackValidation {
    /// @notice Returns the address of a valid Uniswap V3 Pool
    /// @param factory The contract address of the Uniswap V3 factory
    /// @param tokenA The contract address of either token0 or token1
    /// @param tokenB The contract address of the other token
    /// @param fee The fee collected upon every swap in the pool, denominated in hundredths of a bip
    /// @return pool The V3 pool contract address
    function verifyCallback(
        address factory,
        address tokenA,
        address tokenB,
        uint24 fee
    ) internal view returns (IUniswapV3Pool pool) {
        return verifyCallback(factory, PoolAddress.getPoolKey(tokenA, tokenB, fee));
    }

    /// @notice Returns the address of a valid Uniswap V3 Pool
    /// @param factory The contract address of the Uniswap V3 factory
    /// @param poolKey The identifying key of the V3 pool
    /// @return pool The V3 pool contract address
    function verifyCallback(address factory, PoolAddress.PoolKey memory poolKey)
        internal
        view
        returns (IUniswapV3Pool pool)
    {
        pool = IUniswapV3Pool(PoolAddress.computeAddress(factory, poolKey));
        require(msg.sender == address(pool));
    }
}

// File: @uniswap/v3-periphery/contracts/libraries/ChainId.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.7.0;

/// @title Function for getting the current chain ID
library ChainId {
    /// @dev Gets the current chain ID
    /// @return chainId The current chain ID
    function get() internal pure returns (uint256 chainId) {
        assembly {
            chainId := chainid()
        }
    }
}

// File: @uniswap/v3-periphery/contracts/libraries/LiquidityAmounts.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

import '@uniswap/v3-core/contracts/libraries/FullMath.sol';
import '@uniswap/v3-core/contracts/libraries/FixedPoint96.sol';

/// @title Liquidity amount functions
/// @notice Provides functions for computing liquidity amounts from token amounts and prices
library LiquidityAmounts {
    /// @notice Downcasts uint256 to uint128
    /// @param x The uint258 to be downcasted
    /// @return y The passed value, downcasted to uint128
    function toUint128(uint256 x) private pure returns (uint128 y) {
        require((y = uint128(x)) == x);
    }

    /// @notice Computes the amount of liquidity received for a given amount of token0 and price range
    /// @dev Calculates amount0 * (sqrt(upper) * sqrt(lower)) / (sqrt(upper) - sqrt(lower))
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param amount0 The amount0 being sent in
    /// @return liquidity The amount of returned liquidity
    function getLiquidityForAmount0(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 amount0
    ) internal pure returns (uint128 liquidity) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);
        uint256 intermediate = FullMath.mulDiv(sqrtRatioAX96, sqrtRatioBX96, FixedPoint96.Q96);
        return toUint128(FullMath.mulDiv(amount0, intermediate, sqrtRatioBX96 - sqrtRatioAX96));
    }

    /// @notice Computes the amount of liquidity received for a given amount of token1 and price range
    /// @dev Calculates amount1 / (sqrt(upper) - sqrt(lower)).
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param amount1 The amount1 being sent in
    /// @return liquidity The amount of returned liquidity
    function getLiquidityForAmount1(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 amount1
    ) internal pure returns (uint128 liquidity) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);
        return toUint128(FullMath.mulDiv(amount1, FixedPoint96.Q96, sqrtRatioBX96 - sqrtRatioAX96));
    }

    /// @notice Computes the maximum amount of liquidity received for a given amount of token0, token1, the current
    /// pool prices and the prices at the tick boundaries
    /// @param sqrtRatioX96 A sqrt price representing the current pool prices
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param amount0 The amount of token0 being sent in
    /// @param amount1 The amount of token1 being sent in
    /// @return liquidity The maximum amount of liquidity received
    function getLiquidityForAmounts(
        uint160 sqrtRatioX96,
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 amount0,
        uint256 amount1
    ) internal pure returns (uint128 liquidity) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        if (sqrtRatioX96 <= sqrtRatioAX96) {
            liquidity = getLiquidityForAmount0(sqrtRatioAX96, sqrtRatioBX96, amount0);
        } else if (sqrtRatioX96 < sqrtRatioBX96) {
            uint128 liquidity0 = getLiquidityForAmount0(sqrtRatioX96, sqrtRatioBX96, amount0);
            uint128 liquidity1 = getLiquidityForAmount1(sqrtRatioAX96, sqrtRatioX96, amount1);

            liquidity = liquidity0 < liquidity1 ? liquidity0 : liquidity1;
        } else {
            liquidity = getLiquidityForAmount1(sqrtRatioAX96, sqrtRatioBX96, amount1);
        }
    }

    /// @notice Computes the amount of token0 for a given amount of liquidity and a price range
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param liquidity The liquidity being valued
    /// @return amount0 The amount of token0
    function getAmount0ForLiquidity(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity
    ) internal pure returns (uint256 amount0) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        return
            FullMath.mulDiv(
                uint256(liquidity) << FixedPoint96.RESOLUTION,
                sqrtRatioBX96 - sqrtRatioAX96,
                sqrtRatioBX96
            ) / sqrtRatioAX96;
    }

    /// @notice Computes the amount of token1 for a given amount of liquidity and a price range
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param liquidity The liquidity being valued
    /// @return amount1 The amount of token1
    function getAmount1ForLiquidity(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity
    ) internal pure returns (uint256 amount1) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        return FullMath.mulDiv(liquidity, sqrtRatioBX96 - sqrtRatioAX96, FixedPoint96.Q96);
    }

    /// @notice Computes the token0 and token1 value for a given amount of liquidity, the current
    /// pool prices and the prices at the tick boundaries
    /// @param sqrtRatioX96 A sqrt price representing the current pool prices
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param liquidity The liquidity being valued
    /// @return amount0 The amount of token0
    /// @return amount1 The amount of token1
    function getAmountsForLiquidity(
        uint160 sqrtRatioX96,
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity
    ) internal pure returns (uint256 amount0, uint256 amount1) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        if (sqrtRatioX96 <= sqrtRatioAX96) {
            amount0 = getAmount0ForLiquidity(sqrtRatioAX96, sqrtRatioBX96, liquidity);
        } else if (sqrtRatioX96 < sqrtRatioBX96) {
            amount0 = getAmount0ForLiquidity(sqrtRatioX96, sqrtRatioBX96, liquidity);
            amount1 = getAmount1ForLiquidity(sqrtRatioAX96, sqrtRatioX96, liquidity);
        } else {
            amount1 = getAmount1ForLiquidity(sqrtRatioAX96, sqrtRatioBX96, liquidity);
        }
    }
}

// File: @uniswap/v3-periphery/contracts/libraries/PoolAddress.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Provides functions for deriving a pool address from the factory, tokens, and the fee
library PoolAddress {
    bytes32 internal constant POOL_INIT_CODE_HASH = 0xe34f199b19b2b4f47f68442619d555527d244f78a3297ea89325f843f87b8b54;

    /// @notice The identifying key of the pool
    struct PoolKey {
        address token0;
        address token1;
        uint24 fee;
    }

    /// @notice Returns PoolKey: the ordered tokens with the matched fee levels
    /// @param tokenA The first token of a pool, unsorted
    /// @param tokenB The second token of a pool, unsorted
    /// @param fee The fee level of the pool
    /// @return Poolkey The pool details with ordered token0 and token1 assignments
    function getPoolKey(
        address tokenA,
        address tokenB,
        uint24 fee
    ) internal pure returns (PoolKey memory) {
        if (tokenA > tokenB) (tokenA, tokenB) = (tokenB, tokenA);
        return PoolKey({token0: tokenA, token1: tokenB, fee: fee});
    }

    /// @notice Deterministically computes the pool address given the factory and PoolKey
    /// @param factory The Uniswap V3 factory contract address
    /// @param key The PoolKey
    /// @return pool The contract address of the V3 pool
    function computeAddress(address factory, PoolKey memory key) internal pure returns (address pool) {
        require(key.token0 < key.token1);
        pool = address(
            uint256(
                keccak256(
                    abi.encodePacked(
                        hex'ff',
                        factory,
                        keccak256(abi.encode(key.token0, key.token1, key.fee)),
                        POOL_INIT_CODE_HASH
                    )
                )
            )
        );
    }
}

// File: @uniswap/v3-periphery/contracts/libraries/PositionKey.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

library PositionKey {
    /// @dev Returns the key of the position in the core library
    function compute(
        address owner,
        int24 tickLower,
        int24 tickUpper
    ) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked(owner, tickLower, tickUpper));
    }
}

// File: @uniswap/v3-periphery/contracts/libraries/TransferHelper.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.6.0;

import '@openzeppelin/contracts/token/ERC20/IERC20.sol';

library TransferHelper {
    /// @notice Transfers tokens from the targeted address to the given destination
    /// @notice Errors with 'STF' if transfer fails
    /// @param token The contract address of the token to be transferred
    /// @param from The originating address from which the tokens will be transferred
    /// @param to The destination address of the transfer
    /// @param value The amount to be transferred
    function safeTransferFrom(
        address token,
        address from,
        address to,
        uint256 value
    ) internal {
        (bool success, bytes memory data) =
            token.call(abi.encodeWithSelector(IERC20.transferFrom.selector, from, to, value));
        require(success && (data.length == 0 || abi.decode(data, (bool))), 'STF');
    }

    /// @notice Transfers tokens from msg.sender to a recipient
    /// @dev Errors with ST if transfer fails
    /// @param token The contract address of the token which will be transferred
    /// @param to The recipient of the transfer
    /// @param value The value of the transfer
    function safeTransfer(
        address token,
        address to,
        uint256 value
    ) internal {
        (bool success, bytes memory data) = token.call(abi.encodeWithSelector(IERC20.transfer.selector, to, value));
        require(success && (data.length == 0 || abi.decode(data, (bool))), 'ST');
    }

    /// @notice Approves the stipulated contract to spend the given allowance in the given token
    /// @dev Errors with 'SA' if transfer fails
    /// @param token The contract address of the token to be approved
    /// @param to The target of the approval
    /// @param value The amount of the given token the target will be allowed to spend
    function safeApprove(
        address token,
        address to,
        uint256 value
    ) internal {
        (bool success, bytes memory data) = token.call(abi.encodeWithSelector(IERC20.approve.selector, to, value));
        require(success && (data.length == 0 || abi.decode(data, (bool))), 'SA');
    }

    /// @notice Transfers ETH to the recipient address
    /// @dev Fails with `STE`
    /// @param to The destination of the transfer
    /// @param value The value to be transferred
    function safeTransferETH(address to, uint256 value) internal {
        (bool success, ) = to.call{value: value}(new bytes(0));
        require(success, 'STE');
    }
}

// File: contracts/interfaces/INonfungiblePositionManager1EX.sol



// SPDX-License-Identifier: MIT
pragma solidity >=0.7.5;
pragma abicoder v2;

import "@uniswap/v3-periphery/contracts/interfaces/INonfungiblePositionManager.sol";

interface INonfungiblePositionManager1EX is INonfungiblePositionManager {
    /// @return Returns The address of the token descriptor contract, which handles generating token URIs for position tokens
    function tokenDescriptor() external view returns (address);

    /// @notice Set address of the token descriptor contract
    function setTokenDescriptor(address _tokenDescriptor) external;

    /// @notice Returns the address of the account that can change address of token descriptor contract
    function tokenDescriptorSetter() external returns (address);

    /// @notice Change tokenDescriptorSetter. Can only be called by the current owner
    function setTokenDescriptorSetter(address _tokenDescriptorSetter) external;
}

// File: contracts/NonfungiblePositionManager1EX.sol



// SPDX-License-Identifier: MIT
pragma solidity =0.7.6;
pragma abicoder v2;

import "@uniswap/v3-core/contracts/interfaces/IUniswapV3Pool.sol";
import "@uniswap/v3-core/contracts/libraries/FixedPoint128.sol";
import "@uniswap/v3-core/contracts/libraries/FullMath.sol";

import "@uniswap/v3-periphery/contracts/interfaces/INonfungibleTokenPositionDescriptor.sol";
import "@uniswap/v3-periphery/contracts/libraries/PositionKey.sol";
import "@uniswap/v3-periphery/contracts/libraries/PoolAddress.sol";
import "@uniswap/v3-periphery/contracts/base/LiquidityManagement.sol";
import "@uniswap/v3-periphery/contracts/base/PeripheryImmutableState.sol";
import "@uniswap/v3-periphery/contracts/base/Multicall.sol";
import "@uniswap/v3-periphery/contracts/base/ERC721Permit.sol";
import "@uniswap/v3-periphery/contracts/base/PeripheryValidation.sol";
import "@uniswap/v3-periphery/contracts/base/SelfPermit.sol";
import "@uniswap/v3-periphery/contracts/base/PoolInitializer.sol";

import "./interfaces/INonfungiblePositionManager1EX.sol";

/// @title NFT positions
/// @notice Wraps 1EX positions in the ERC721 non-fungible token interface
contract NonfungiblePositionManager1EX is
    INonfungiblePositionManager1EX,
    Multicall,
    ERC721Permit,
    PeripheryImmutableState,
    PoolInitializer,
    LiquidityManagement,
    PeripheryValidation,
    SelfPermit
{
    // details about the 1EX position
    struct Position {
        // the nonce for permits
        uint96 nonce;
        // the address that is approved for spending this token
        address operator;
        // the ID of the pool with which this token is connected
        uint80 poolId;
        // the tick range of the position
        int24 tickLower;
        int24 tickUpper;
        // the liquidity of the position
        uint128 liquidity;
        // the fee growth of the aggregate position as of the last action on the individual position
        uint256 feeGrowthInside0LastX128;
        uint256 feeGrowthInside1LastX128;
        // how many uncollected tokens are owed to the position, as of the last computation
        uint128 tokensOwed0;
        uint128 tokensOwed1;
    }

    /// @dev IDs of pools assigned by this contract
    mapping(address => uint80) private _poolIds;

    /// @dev Pool keys by pool ID, to save on SSTOREs for position data
    mapping(uint80 => PoolAddress.PoolKey) private _poolIdToPoolKey;

    /// @dev The token ID position data
    mapping(uint256 => Position) private _positions;

    /// @dev The ID of the next token that will be minted. Skips 0
    uint176 private _nextId = 1;
    /// @dev The ID of the next pool that is used for the first time. Skips 0
    uint80 private _nextPoolId = 1;

    /// @inheritdoc INonfungiblePositionManager1EX
    address public override tokenDescriptorSetter;

    /// @inheritdoc INonfungiblePositionManager1EX
    address public override tokenDescriptor;

    constructor(
        address _factory,
        address _WNative,
        address _tokenDescriptor
    )
        ERC721Permit("1EX Positions NFT", "1EX-POS", "1")
        PeripheryImmutableState(_factory, _WNative)
    {
        tokenDescriptor = _tokenDescriptor;
        tokenDescriptorSetter = msg.sender;
    }

    /// @inheritdoc INonfungiblePositionManager
    function positions(uint256 tokenId)
        external
        view
        override
        returns (
            uint96 nonce,
            address operator,
            address token0,
            address token1,
            uint24 fee,
            int24 tickLower,
            int24 tickUpper,
            uint128 liquidity,
            uint256 feeGrowthInside0LastX128,
            uint256 feeGrowthInside1LastX128,
            uint128 tokensOwed0,
            uint128 tokensOwed1
        )
    {
        Position memory position = _positions[tokenId];
        require(position.poolId != 0, "Invalid token ID");
        PoolAddress.PoolKey memory poolKey = _poolIdToPoolKey[position.poolId];
        return (
            position.nonce,
            position.operator,
            poolKey.token0,
            poolKey.token1,
            poolKey.fee,
            position.tickLower,
            position.tickUpper,
            position.liquidity,
            position.feeGrowthInside0LastX128,
            position.feeGrowthInside1LastX128,
            position.tokensOwed0,
            position.tokensOwed1
        );
    }

    /// @dev Caches a pool key
    function cachePoolKey(address pool, PoolAddress.PoolKey memory poolKey)
        private
        returns (uint80 poolId)
    {
        poolId = _poolIds[pool];
        if (poolId == 0) {
            _poolIds[pool] = (poolId = _nextPoolId++);
            _poolIdToPoolKey[poolId] = poolKey;
        }
    }

    /// @inheritdoc INonfungiblePositionManager
    function mint(MintParams calldata params)
        external
        payable
        override
        checkDeadline(params.deadline)
        returns (
            uint256 tokenId,
            uint128 liquidity,
            uint256 amount0,
            uint256 amount1
        )
    {
        IUniswapV3Pool pool;
        (liquidity, amount0, amount1, pool) = addLiquidity(
            AddLiquidityParams({
                token0: params.token0,
                token1: params.token1,
                fee: params.fee,
                recipient: address(this),
                tickLower: params.tickLower,
                tickUpper: params.tickUpper,
                amount0Desired: params.amount0Desired,
                amount1Desired: params.amount1Desired,
                amount0Min: params.amount0Min,
                amount1Min: params.amount1Min
            })
        );

        _mint(params.recipient, (tokenId = _nextId++));

        bytes32 positionKey = PositionKey.compute(
            address(this),
            params.tickLower,
            params.tickUpper
        );
        (
            ,
            uint256 feeGrowthInside0LastX128,
            uint256 feeGrowthInside1LastX128,
            ,

        ) = pool.positions(positionKey);

        // idempotent set
        uint80 poolId = cachePoolKey(
            address(pool),
            PoolAddress.PoolKey({
                token0: params.token0,
                token1: params.token1,
                fee: params.fee
            })
        );

        _positions[tokenId] = Position({
            nonce: 0,
            operator: address(0),
            poolId: poolId,
            tickLower: params.tickLower,
            tickUpper: params.tickUpper,
            liquidity: liquidity,
            feeGrowthInside0LastX128: feeGrowthInside0LastX128,
            feeGrowthInside1LastX128: feeGrowthInside1LastX128,
            tokensOwed0: 0,
            tokensOwed1: 0
        });

        emit IncreaseLiquidity(tokenId, liquidity, amount0, amount1);
    }

    modifier isAuthorizedForToken(uint256 tokenId) {
        require(_isApprovedOrOwner(msg.sender, tokenId), "Not approved");
        _;
    }

    function tokenURI(uint256 tokenId)
        public
        view
        override(ERC721, IERC721Metadata)
        returns (string memory)
    {
        require(_exists(tokenId));
        return
            INonfungibleTokenPositionDescriptor(tokenDescriptor).tokenURI(
                this,
                tokenId
            );
    }

    // save bytecode by removing implementation of unused method
    function baseURI() public pure override returns (string memory) {}

    /// @inheritdoc INonfungiblePositionManager
    function increaseLiquidity(IncreaseLiquidityParams calldata params)
        external
        payable
        override
        checkDeadline(params.deadline)
        returns (
            uint128 liquidity,
            uint256 amount0,
            uint256 amount1
        )
    {
        Position storage position = _positions[params.tokenId];

        PoolAddress.PoolKey memory poolKey = _poolIdToPoolKey[position.poolId];

        IUniswapV3Pool pool;
        (liquidity, amount0, amount1, pool) = addLiquidity(
            AddLiquidityParams({
                token0: poolKey.token0,
                token1: poolKey.token1,
                fee: poolKey.fee,
                tickLower: position.tickLower,
                tickUpper: position.tickUpper,
                amount0Desired: params.amount0Desired,
                amount1Desired: params.amount1Desired,
                amount0Min: params.amount0Min,
                amount1Min: params.amount1Min,
                recipient: address(this)
            })
        );

        bytes32 positionKey = PositionKey.compute(
            address(this),
            position.tickLower,
            position.tickUpper
        );

        // this is now updated to the current transaction
        (
            ,
            uint256 feeGrowthInside0LastX128,
            uint256 feeGrowthInside1LastX128,
            ,

        ) = pool.positions(positionKey);

        position.tokensOwed0 += uint128(
            FullMath.mulDiv(
                feeGrowthInside0LastX128 - position.feeGrowthInside0LastX128,
                position.liquidity,
                FixedPoint128.Q128
            )
        );
        position.tokensOwed1 += uint128(
            FullMath.mulDiv(
                feeGrowthInside1LastX128 - position.feeGrowthInside1LastX128,
                position.liquidity,
                FixedPoint128.Q128
            )
        );

        position.feeGrowthInside0LastX128 = feeGrowthInside0LastX128;
        position.feeGrowthInside1LastX128 = feeGrowthInside1LastX128;
        position.liquidity += liquidity;

        emit IncreaseLiquidity(params.tokenId, liquidity, amount0, amount1);
    }

    /// @inheritdoc INonfungiblePositionManager
    function decreaseLiquidity(DecreaseLiquidityParams calldata params)
        external
        payable
        override
        isAuthorizedForToken(params.tokenId)
        checkDeadline(params.deadline)
        returns (uint256 amount0, uint256 amount1)
    {
        require(params.liquidity > 0);
        Position storage position = _positions[params.tokenId];

        uint128 positionLiquidity = position.liquidity;
        require(positionLiquidity >= params.liquidity);

        PoolAddress.PoolKey memory poolKey = _poolIdToPoolKey[position.poolId];
        IUniswapV3Pool pool = IUniswapV3Pool(
            PoolAddress.computeAddress(factory, poolKey)
        );
        (amount0, amount1) = pool.burn(
            position.tickLower,
            position.tickUpper,
            params.liquidity
        );

        require(
            amount0 >= params.amount0Min && amount1 >= params.amount1Min,
            "Price slippage check"
        );

        bytes32 positionKey = PositionKey.compute(
            address(this),
            position.tickLower,
            position.tickUpper
        );
        // this is now updated to the current transaction
        (
            ,
            uint256 feeGrowthInside0LastX128,
            uint256 feeGrowthInside1LastX128,
            ,

        ) = pool.positions(positionKey);

        position.tokensOwed0 +=
            uint128(amount0) +
            uint128(
                FullMath.mulDiv(
                    feeGrowthInside0LastX128 - position.feeGrowthInside0LastX128,
                    positionLiquidity,
                    FixedPoint128.Q128
                )
            );
        position.tokensOwed1 +=
            uint128(amount1) +
            uint128(
                FullMath.mulDiv(
                    feeGrowthInside1LastX128 - position.feeGrowthInside1LastX128,
                    positionLiquidity,
                    FixedPoint128.Q128
                )
            );

        position.feeGrowthInside0LastX128 = feeGrowthInside0LastX128;
        position.feeGrowthInside1LastX128 = feeGrowthInside1LastX128;
        // subtraction is safe because we checked positionLiquidity is gte params.liquidity
        position.liquidity = positionLiquidity - params.liquidity;

        emit DecreaseLiquidity(params.tokenId, params.liquidity, amount0, amount1);
    }

    /// @inheritdoc INonfungiblePositionManager
    function collect(CollectParams calldata params)
        external
        payable
        override
        isAuthorizedForToken(params.tokenId)
        returns (uint256 amount0, uint256 amount1)
    {
        require(params.amount0Max > 0 || params.amount1Max > 0);
        // allow collecting to the nft position manager address with address 0
        address recipient = params.recipient == address(0)
            ? address(this)
            : params.recipient;

        Position storage position = _positions[params.tokenId];

        PoolAddress.PoolKey memory poolKey = _poolIdToPoolKey[position.poolId];

        IUniswapV3Pool pool = IUniswapV3Pool(
            PoolAddress.computeAddress(factory, poolKey)
        );

        (uint128 tokensOwed0, uint128 tokensOwed1) = (
            position.tokensOwed0,
            position.tokensOwed1
        );

        // trigger an update of the position fees owed and fee growth snapshots if it has any liquidity
        if (position.liquidity > 0) {
            pool.burn(position.tickLower, position.tickUpper, 0);
            (
                ,
                uint256 feeGrowthInside0LastX128,
                uint256 feeGrowthInside1LastX128,
                ,

            ) = pool.positions(
                    PositionKey.compute(
                        address(this),
                        position.tickLower,
                        position.tickUpper
                    )
                );

            tokensOwed0 += uint128(
                FullMath.mulDiv(
                    feeGrowthInside0LastX128 - position.feeGrowthInside0LastX128,
                    position.liquidity,
                    FixedPoint128.Q128
                )
            );
            tokensOwed1 += uint128(
                FullMath.mulDiv(
                    feeGrowthInside1LastX128 - position.feeGrowthInside1LastX128,
                    position.liquidity,
                    FixedPoint128.Q128
                )
            );

            position.feeGrowthInside0LastX128 = feeGrowthInside0LastX128;
            position.feeGrowthInside1LastX128 = feeGrowthInside1LastX128;
        }

        // compute the arguments to give to the pool#collect method
        (uint128 amount0Collect, uint128 amount1Collect) = (
            params.amount0Max > tokensOwed0 ? tokensOwed0 : params.amount0Max,
            params.amount1Max > tokensOwed1 ? tokensOwed1 : params.amount1Max
        );

        // the actual amounts collected are returned
        (amount0, amount1) = pool.collect(
            recipient,
            position.tickLower,
            position.tickUpper,
            amount0Collect,
            amount1Collect
        );

        // sometimes there will be a few less wei than expected due to rounding down in core, but we just subtract the full amount expected
        // instead of the actual amount so we can burn the token
        (position.tokensOwed0, position.tokensOwed1) = (
            tokensOwed0 - amount0Collect,
            tokensOwed1 - amount1Collect
        );

        emit Collect(params.tokenId, recipient, amount0Collect, amount1Collect);
    }

    /// @inheritdoc INonfungiblePositionManager
    function burn(uint256 tokenId)
        external
        payable
        override
        isAuthorizedForToken(tokenId)
    {
        Position storage position = _positions[tokenId];
        require(
            position.liquidity == 0 &&
                position.tokensOwed0 == 0 &&
                position.tokensOwed1 == 0,
            "Not cleared"
        );
        delete _positions[tokenId];
        _burn(tokenId);
    }

    function _getAndIncrementNonce(uint256 tokenId)
        internal
        override
        returns (uint256)
    {
        return uint256(_positions[tokenId].nonce++);
    }

    /// @inheritdoc IERC721
    function getApproved(uint256 tokenId)
        public
        view
        override(ERC721, IERC721)
        returns (address)
    {
        require(_exists(tokenId), "ERC721: approved query for nonexistent token");

        return _positions[tokenId].operator;
    }

    /// @dev Overrides _approve to use the operator in the position, which is packed with the position permit nonce
    function _approve(address to, uint256 tokenId) internal override(ERC721) {
        _positions[tokenId].operator = to;
        emit Approval(ownerOf(tokenId), to, tokenId);
    }

    //// @inheritdoc INonfungiblePositionManager1EX
    function setTokenDescriptorSetter(address _tokenDescriptorSetter)
        external
        override
    {
        require(msg.sender == tokenDescriptorSetter, "Only token descriptor setter");
        require(_tokenDescriptorSetter != address(0), "Zero address is not allowed");

        tokenDescriptorSetter = _tokenDescriptorSetter;
    }

    /// @inheritdoc INonfungiblePositionManager1EX
    function setTokenDescriptor(address _tokenDescriptor) external override {
        require(msg.sender == tokenDescriptorSetter, "Only token descriptor setter");

        tokenDescriptor = _tokenDescriptor;
    }
}