// File: @openzeppelin/contracts/access/Ownable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/Context.sol";

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

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

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor() {
        _transferOwnership(_msgSender());
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }

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

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }

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

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

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC721/IERC721.sol)

pragma solidity ^0.8.0;

import "../../utils/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`.
     *
     * 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;

    /**
     * @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 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: Note that the caller is responsible to confirm that the recipient is capable of receiving ERC721
     * or else they may be permanently lost. Usage of {safeTransferFrom} prevents loss, though the caller must
     * understand this adds an external call which potentially creates a reentrancy vulnerability.
     *
     * 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 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 the account approved for `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function getApproved(uint256 tokenId) external view returns (address operator);

    /**
     * @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);
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
}

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



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/Math.sol";

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _SYMBOLS = "0123456789abcdef";
    uint8 private constant _ADDRESS_LENGTH = 20;

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = Math.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
    }
}

// File: @openzeppelin/contracts/utils/cryptography/ECDSA.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.0;

import "../Strings.sol";

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV // Deprecated in v4.8
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            /// @solidity memory-safe-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address, RecoverError) {
        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
        uint8 v = uint8((uint256(vs) >> 255) + 27);
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address, RecoverError) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n32", hash));
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n", Strings.toString(s.length), s));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", domainSeparator, structHash));
    }
}

// File: @openzeppelin/contracts/utils/introspection/IERC165.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

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

// File: @openzeppelin/contracts/utils/math/Math.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // 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(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }

            // 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].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            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 for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the 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.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // 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 preconditions 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 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator,
        Rounding rounding
    ) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10**64) {
                value /= 10**64;
                result += 64;
            }
            if (value >= 10**32) {
                value /= 10**32;
                result += 32;
            }
            if (value >= 10**16) {
                value /= 10**16;
                result += 16;
            }
            if (value >= 10**8) {
                value /= 10**8;
                result += 8;
            }
            if (value >= 10**4) {
                value /= 10**4;
                result += 4;
            }
            if (value >= 10**2) {
                value /= 10**2;
                result += 2;
            }
            if (value >= 10**1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10**result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result * 8) < value ? 1 : 0);
        }
    }
}

// File: src/IDataHolder.sol



//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

/// @title IVerified
/// @author @dievardump
interface IDataHolder {
	/// @notice returns the uniqid for an NFT
	/// @param collection the collection
	/// @param tokenId the id
	/// @return an uniq id
	function id(address collection, uint256 tokenId) external view returns (bytes32);

	/// @notice returns the data holder for the given format of a verified id
	/// @param verifiedId the verified token id
	/// @param format the format id
	function getVerifiedFormatHolder(uint256 verifiedId, uint256 format) external view returns (address);

	/// @notice returns the verified id linked to the token
	/// @param collection the collection
	/// @param tokenId the id
	/// @return the verified if
	function getOriginTokenVerifiedId(address collection, uint256 tokenId) external view returns (uint256);

	/// @notice inits verifiedId storage
	/// @param verifiedId the verified token id
	/// @param collection the collection
	/// @param tokenId the id
	/// @param format the format provided
	/// @param dataHolder the contact holding the data for this format
	function initVerifiedTokenData(
		uint256 verifiedId,
		address collection,
		uint256 tokenId,
		uint256 format,
		address dataHolder
	) external;

	/// @notice allows to add another format safely (throws if already exist)
	/// @param collection the collection
	/// @param tokenId the id
	/// @param format the format provided
	/// @param dataHolder the contact holding the data for this format
	function safeSetData(
		address collection,
		uint256 tokenId,
		uint256 format,
		address dataHolder
	) external;

	/// @notice allows to add another format (it overwrites existing data for this format)
	/// @param collection the collection
	/// @param tokenId the id
	/// @param format the format provided
	/// @param dataHolder the contact holding the data for this format
	function setData(
		address collection,
		uint256 tokenId,
		uint256 format,
		address dataHolder
	) external;
}

// File: src/IVerified.sol



//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

/// @title IVerified
/// @author @dievardump
interface IVerified {
	/// @notice Returns a `tokenId` extra data
	/// @param tokenId the toke id
	/// @return the extraData

	function extraData(uint256 tokenId) external view returns (uint256);

	/// @notice allows a minter to mint a token to `to` with `extraData`
	function mint(address to, uint24 extraData) external returns (uint256);

	/// @notice allows a token owner OR a minter to set the extra data for a token (here the index of dataHolder)
	function setExtraData(uint256 tokenId, uint24 index) external;
}

// File: src/SSTORE2/SSTORE2.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

import "./utils/Bytecode.sol";

/**
  @title A key-value storage with auto-generated keys for storing chunks of data with a lower write & read cost.
  @author Agustin Aguilar <aa@horizon.io>

  Readme: https://github.com/0xsequence/sstore2#readme
*/
library SSTORE2 {
	error WriteError();

	/**
    @notice Stores `_data` and returns `pointer` as key for later retrieval
    @dev The pointer is a contract address with `_data` as code
    @param _data to be written
    @return pointer Pointer to the written `_data`
  */
	function write(bytes memory _data) internal returns (address pointer) {
		// Append 00 to _data so contract can't be called
		// Build init code
		bytes memory code = Bytecode.creationCodeFor(abi.encodePacked(hex"00", _data));

		// Deploy contract using create
		assembly {
			pointer := create(0, add(code, 32), mload(code))
		}

		// Address MUST be non-zero
		if (pointer == address(0)) revert WriteError();
	}

	/**
    @notice Reads the contents of the `_pointer` code as data, skips the first byte
    @dev The function is intended for reading pointers generated by `write`
    @param _pointer to be read
    @return data read from `_pointer` contract
  */
	function read(address _pointer) internal view returns (bytes memory) {
		return Bytecode.codeAt(_pointer, 1, type(uint256).max);
	}

	/**
    @notice Reads the contents of the `_pointer` code as data, skips the first byte
    @dev The function is intended for reading pointers generated by `write`
    @param _pointer to be read
    @param _start number of bytes to skip
    @return data read from `_pointer` contract
  */
	function read(address _pointer, uint256 _start) internal view returns (bytes memory) {
		return Bytecode.codeAt(_pointer, _start + 1, type(uint256).max);
	}

	/**
    @notice Reads the contents of the `_pointer` code as data, skips the first byte
    @dev The function is intended for reading pointers generated by `write`
    @param _pointer to be read
    @param _start number of bytes to skip
    @param _end index before which to end extraction
    @return data read from `_pointer` contract
  */
	function read(
		address _pointer,
		uint256 _start,
		uint256 _end
	) internal view returns (bytes memory) {
		return Bytecode.codeAt(_pointer, _start + 1, _end + 1);
	}
}

// File: src/SSTORE2/utils/Bytecode.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

library Bytecode {
	error InvalidCodeAtRange(uint256 _size, uint256 _start, uint256 _end);

	/**
    @notice Generate a creation code that results on a contract with `_code` as bytecode
    @param _code The returning value of the resulting `creationCode`
    @return creationCode (constructor) for new contract
  */
	function creationCodeFor(bytes memory _code) internal pure returns (bytes memory) {
		/*
      0x00    0x63         0x63XXXXXX  PUSH4 _code.length  size
      0x01    0x80         0x80        DUP1                size size
      0x02    0x60         0x600e      PUSH1 14            14 size size
      0x03    0x60         0x6000      PUSH1 00            0 14 size size
      0x04    0x39         0x39        CODECOPY            size
      0x05    0x60         0x6000      PUSH1 00            0 size
      0x06    0xf3         0xf3        RETURN
      <CODE>
    */

		return abi.encodePacked(hex"63", uint32(_code.length), hex"80_60_0E_60_00_39_60_00_F3", _code);
	}

	/**
    @notice Returns the size of the code on a given address
    @param _addr Address that may or may not contain code
    @return size of the code on the given `_addr`
  */
	function codeSize(address _addr) internal view returns (uint256 size) {
		assembly {
			size := extcodesize(_addr)
		}
	}

	/**
    @notice Returns the code of a given address
    @dev It will fail if `_end < _start`
    @param _addr Address that may or may not contain code
    @param _start number of bytes of code to skip on read
    @param _end index before which to end extraction
    @return oCode read from `_addr` deployed bytecode

    Forked from: https://gist.github.com/KardanovIR/fe98661df9338c842b4a30306d507fbd
  */
	function codeAt(
		address _addr,
		uint256 _start,
		uint256 _end
	) internal view returns (bytes memory oCode) {
		uint256 csize = codeSize(_addr);
		if (csize == 0) return bytes("");

		if (_start > csize) return bytes("");
		if (_end < _start) revert InvalidCodeAtRange(csize, _start, _end);

		unchecked {
			uint256 reqSize = _end - _start;
			uint256 maxSize = csize - _start;

			uint256 size = maxSize < reqSize ? maxSize : reqSize;

			assembly {
				// allocate output byte array - this could also be done without assembly
				// by using o_code = new bytes(size)
				oCode := mload(0x40)
				// new "memory end" including padding
				mstore(0x40, add(oCode, and(add(add(size, 0x20), 0x1f), not(0x1f))))
				// store length in memory
				mstore(oCode, size)
				// actually retrieve the code, this needs assembly
				extcodecopy(_addr, add(oCode, 0x20), _start, size)
			}
		}
	}
}

// File: src/VerifiedMinter.sol



//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

import {ECDSA} from "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";
import {IERC721} from "@openzeppelin/contracts/token/ERC721/IERC721.sol";
import {Ownable} from "@openzeppelin/contracts/access/Ownable.sol";

import {SSTORE2} from "./SSTORE2/SSTORE2.sol";

import {IVerified} from "./IVerified.sol";
import {IDataHolder} from "./IDataHolder.sol";

/// @title VerifiedMinter
/// @author @dievardump
contract VerifiedMinter is Ownable {
	error InvalidValue();
	error InvalidSignature();
	error UnknownOwner();
	error InvalidVerifiedID();
	error TransferFundsError();

	address public immutable VERIFIED_NFTS;
	address public immutable VERIFIED_DATA_HOLDER;

	address public immutable FEE_RECIPIENT;

	uint256 public mintFee = 0.0048 ether;
	uint256 public addFormatFee = 0.0024 ether;

	address public signer;
	address public ownershipChecker;

	constructor(
		address nfts,
		address dataHolder,
		address newSigner,
		address newFeeRecipient
	) {
		VERIFIED_NFTS = nfts;
		VERIFIED_DATA_HOLDER = dataHolder;

		FEE_RECIPIENT = newFeeRecipient;

		signer = newSigner;
	}

	// =============================================================
	//                   				Getters
	// =============================================================

	/// @notice function that tries to hget an NFT owner address... might need to deploy a specific contract
	///         for this if there is a need for collections not implemneting ownerOf rightly
	/// @param collection the collection
	/// @param tokenId the token id
	function tryOwner(address collection, uint256 tokenId) public view returns (address to) {
		// if the contract is an ERC721 (or the CryptoKitty, not sure they support IERC721 or the Meta interface), check owner
		if (
			collection == 0x06012c8cf97BEaD5deAe237070F9587f8E7A266d ||
			IERC721(collection).supportsInterface(type(IERC721).interfaceId)
		) {
			to = IERC721(collection).ownerOf(tokenId);
		} else if (collection == 0xb47e3cd837dDF8e4c57F05d70Ab865de6e193BBB) {
			// else punks maybe?
			to = IOwnershipChecker(collection).punkIndexToAddress(tokenId);
		} else {
			address checker = ownershipChecker;

			// or maybe I added a contract to add custom ownership checks?
			if (checker != address(0)) {
				try IOwnershipChecker(checker).ownerOf(collection, tokenId) returns (address owner_) {
					to = owner_;
				} catch (bytes memory) {}
			} else {
				// try again with a simple ownerOf(), might probably work with 99% of contracts not using the right supportsInterface
				to = IERC721(collection).ownerOf(tokenId);
			}
		}
	}

	/// @notice verifies that the data have been signed by the backend
	/// @param collection the collection token
	/// @param tokenId the token id
	/// @param format the format for those data
	/// @param colors the colors for the output
	/// @param grid the grid (index in colors data)
	/// @param proof the backend signature
	function verify(
		address collection,
		uint256 tokenId,
		uint256 format,
		bytes calldata colors,
		bytes calldata grid,
		bytes calldata proof
	) public view returns (bytes memory) {
		// build the data, this is what will be saved on-chain
		bytes memory data = abi.encode(collection, tokenId, format, colors, grid);

		// verifies the data signature
		if (signer != ECDSA.recover(ECDSA.toEthSignedMessageHash(keccak256(data)), proof)) {
			revert InvalidSignature();
		}

		return data;
	}

	// =============================================================
	//                   				Interactions
	// =============================================================

	/// @notice allows to add another format to your verified id
	/// @param verifiedId the verified id to add a format to
	/// @param collection the collection token
	/// @param tokenId the token id
	/// @param format the format for those data
	/// @param colors the colors for the output
	/// @param grid the grid (index in colors data)
	/// @param proof the backend signature
	/// @param selectFormat if the format should be selected on the token
	function addFormat(
		uint256 verifiedId,
		address collection,
		uint256 tokenId,
		uint256 format,
		bytes calldata colors,
		bytes calldata grid,
		bytes calldata proof,
		bool selectFormat
	) external payable {
		// verifies sent value == the expected fee
		if (msg.value != addFormatFee) {
			revert InvalidValue();
		}

		bytes memory data = verify(collection, tokenId, format, colors, grid, proof);

		if (msg.value > 0) {
			(bool success, ) = FEE_RECIPIENT.call{value: msg.value}("");
			if (!success) {
				revert TransferFundsError();
			}
		}

		// we make sure dataHolder(collection, tokenId).verifiedId == verifiedId
		if (
			verifiedId == 0 ||
			verifiedId != IDataHolder(VERIFIED_DATA_HOLDER).getOriginTokenVerifiedId(collection, tokenId)
		) {
			revert InvalidVerifiedID();
		}

		// we save the data into a contract
		address dataHolder = SSTORE2.write(data);

		// we save the new format
		IDataHolder(VERIFIED_DATA_HOLDER).safeSetData(collection, tokenId, format, dataHolder);

		// and if we want to change format, let's change
		if (selectFormat) {
			IVerified(VERIFIED_NFTS).setExtraData(verifiedId, uint24(format));
		}
	}

	/// @notice allows to mint a new token with the given data
	/// @param collection the collection token
	/// @param tokenId the token id
	/// @param format the format for those data
	/// @param colors the colors for the output
	/// @param grid the grid (index in colors data)
	/// @param proof the backend signature
	function mint(
		address collection,
		uint256 tokenId,
		uint256 format,
		bytes calldata colors,
		bytes calldata grid,
		bytes calldata proof
	) external payable {
		if (msg.value != mintFee) {
			revert InvalidValue();
		}

		bytes memory data = verify(collection, tokenId, format, colors, grid, proof);

		_mint(collection, tokenId, format, data);

		if (msg.value > 0) {
			(bool success, ) = FEE_RECIPIENT.call{value: msg.value}("");
			if (!success) {
				revert TransferFundsError();
			}
		}
	}

	// =============================================================
	//                   				Gated Owner
	// =============================================================

	/// @notice allows owner to set the signer
	/// @param newSigner the new signer
	function setSigner(address newSigner) external onlyOwner {
		signer = newSigner;
	}

	/// @notice allows owner to set the ownership checker contract
	/// @param newOwnershipChecker the new checker
	function setOwnershipChecker(address newOwnershipChecker) external onlyOwner {
		ownershipChecker = newOwnershipChecker;
	}

	/// @notice allows owner to update the mint fee
	/// @param newMintFee the new mint fee
	function setMintFee(uint256 newMintFee) external onlyOwner {
		mintFee = newMintFee;
	}

	/// @notice allows owner to update the add format fee
	/// @param newAddFormatFee the new add format fee
	function setAddFormatFee(uint256 newAddFormatFee) external onlyOwner {
		addFormatFee = newAddFormatFee;
	}

	// =============================================================
	//                   				Internals
	// =============================================================

	function _mint(
		address collection,
		uint256 tokenId,
		uint256 format,
		bytes memory data
	) internal {
		address to = tryOwner(collection, tokenId);
		if (to == address(0)) {
			revert UnknownOwner();
		}

		// we mint the verified token to the current owner of the original token
		uint256 verifiedId = IVerified(VERIFIED_NFTS).mint(to, uint24(format));

		// we save the data into a contract
		address dataHolder = SSTORE2.write(data);

		// we link tokenId and
		IDataHolder(VERIFIED_DATA_HOLDER).initVerifiedTokenData(verifiedId, collection, tokenId, format, dataHolder);
	}
}

interface IOwnershipChecker {
	function punkIndexToAddress(uint256) external view returns (address);

	function ownerOf(address, uint256) external view returns (address);
}