// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.8.20;
import "../lib/solmate/src/tokens/ERC721.sol";
import "../lib/openzeppelin-contracts/contracts/utils/Strings.sol";
error FixTokenId();
error NotEOA();
error TransferFailed();
error NotTokenOwner();
error NotTheBuildr();
/// @title buildr contract
/// @author 2bb.dev
/// @notice this contract spawns buildrs
contract BuildrBuild is ERC721 {
    using Strings for uint256;
    enum Web3District {
        Nomads,
        ContentMaestros,
        Founders,
        Investors,
        Devs
    }
    struct Outputs {
        uint256 tokenId;
        uint256 balance;
        Web3District district;
        uint256 order;
    }
    mapping(uint256 => uint256) private map;
    mapping(uint256 => Web3District) private buildrDistrict;
    mapping(uint256 => string) private buildrInfo;
    mapping(uint256 => mapping(Web3District => uint256)) private buildrBalance;
    Outputs[] public outputs;
    string public baseURI;
    uint256 private constant TOTAL_SUPPLY = 4024;
    uint256 private constant INFRA_COST = 0.005 ether;
    address private buildr;
    event Received(
        address indexed caller,
        uint256 indexed amount,
        string indexed message
    );
    event MapChange(
        uint256 indexed mapToken1,
        uint256 indexed mapToken2,
        uint256 indexed token2
    );
    modifier onlyEOA() {
        if (msg.sender != tx.origin) {
            revert NotEOA();
        }
        _;
    }
    constructor(
        string memory _name,
        string memory _symbol,
        string memory _baseURI
    ) ERC721(_name, _symbol) {
        baseURI = _baseURI;
        buildr = msg.sender;
    }
    receive() external payable {
        emit Received(msg.sender, msg.value, "Kudos");
    }
    fallback() external payable {
        emit Received(msg.sender, msg.value, "Fallback was called");
    }
    function mintBuildr(uint256 _tokenId) external payable onlyEOA {
        if (msg.value < INFRA_COST) {
            revert TransferFailed();
        }
        if (_tokenId > TOTAL_SUPPLY || _tokenId < 1) {
            revert FixTokenId();
        }
        _mint(msg.sender, _tokenId);
    }
    /// @notice destination token is burned
    /// _token1 -> _token2 => _token2 is burned afterwards
    function mapChange(uint256 _token1, uint256 _token2) external {
        if (
            ownerOf(_token1) != ownerOf(_token2) ||
            ownerOf(_token2) != msg.sender
        ) {
            revert NotTokenOwner();
        }
        uint256 tmp_token1 = mapView(_token1);
        uint256 tmp_token2 = mapView(_token2);
        resetBuildrInfo(_token2);
        _burn(_token2);
        map[_token1] = tmp_token2;
        map[_token2] = tmp_token1;
        emit MapChange(map[_token1], map[_token2], _token2);
    }
    function fundBuildr(
        uint256 _tokenId,
        Web3District _district
    ) external payable {
        if (_tokenId > TOTAL_SUPPLY || _tokenId < 1) {
            revert FixTokenId();
        }
        buildrBalance[_tokenId][_district] += msg.value;
    }
    function withdrawETH() external {
        uint256 balance = address(this).balance;
        (bool transferTx /*memory data*/, ) = buildr.call{value: balance}("");
        if (!transferTx) {
            revert TransferFailed();
        }
    }
    function editAllDetails_v2(
        Web3District _district,
        uint256 _tokenId,
        string calldata _ipfsCID
    ) external {
        if (ownerOf(_tokenId) != msg.sender) {
            revert NotTokenOwner();
        }
        editDistrict(_district, _tokenId);
        editBuildrDetail(_ipfsCID, _tokenId);
    }
    function editBuildrDistrict(
        Web3District _district,
        uint256 _tokenId
    ) external {
        if (ownerOf(_tokenId) != msg.sender) {
            revert NotTokenOwner();
        }
        editDistrict(_district, _tokenId);
    }
    function editBuildrInfo(
        string calldata _ipfsCID,
        uint256 _tokenId
    ) external {
        if (ownerOf(_tokenId) != msg.sender) {
            revert NotTokenOwner();
        }
        editBuildrDetail(_ipfsCID, _tokenId);
    }
    function changeBuildr(address _buildr) external {
        if (msg.sender != buildr) {
            revert NotTheBuildr();
        }
        buildr = _buildr;
    }
    function transferFrom(
        address from,
        address to,
        uint256 id
    ) public override {
        super.transferFrom(from, to, id);
        resetBuildrInfo(id);
    }
    function tokenURI(
        uint256 tokenId
    ) public view override returns (string memory) {
        return string(abi.encodePacked(baseURI, tokenId.toString(), ".json"));
    }
    function getBuildrInfo(
        uint256 _tokenId
    ) public view returns (string memory) {
        if (_tokenId > TOTAL_SUPPLY || _tokenId < 1) {
            revert FixTokenId();
        }
        return buildrInfo[_tokenId];
    }
    function getInfraCosts() public pure returns (uint256) {
        return INFRA_COST;
    }
    function getTokenMap(uint256 _tokenId) public view returns (uint256) {
        if (_tokenId > TOTAL_SUPPLY || _tokenId < 1) {
            revert FixTokenId();
        }
        return mapView(_tokenId);
    }
    function getFullMap(
        uint256 _start,
        uint256 _limit
    ) public view returns (Outputs[] memory) {
        if (_start < 1) {
            revert FixTokenId();
        }
        Outputs[] memory mapOutput = new Outputs[](_limit);
        for (uint256 i = 0; i < _limit; i++) {
            uint256 id = _start + i;
            if (id <= 4024) {
                mapOutput[i].tokenId = id;
                mapOutput[i].balance = getBuildrTotalBalance(id);
                mapOutput[i].district = buildrDistrict[id];
                mapOutput[i].order = mapView(id);
            }
        }
        return mapOutput;
    }
    function getFullMap_v2(
        uint256 _start,
        uint256 _limit
    ) public view returns (Outputs[] memory) {
        if (_start < 1) {
            revert FixTokenId();
        }
        Outputs[] memory mapOutput = new Outputs[](_limit);
        for (uint256 i = 0; i < _limit; i++) {
            uint256 id = _start + i;
            if (id <= 4024) {
                mapOutput[i].district = buildrDistrict[id];
                mapOutput[i].balance = getBuildrDistrictBalance(
                    _start + i,
                    buildrDistrict[id]
                );
                mapOutput[i].tokenId = id;
            }
        }
        return mapOutput;
    }
    function getDistrictMap_v2(
        Web3District _district,
        uint256 _start,
        uint256 _limit
    ) public view returns (Outputs[] memory) {
        if (_start < 1) {
            revert FixTokenId();
        }
        Outputs[] memory mapOutput = new Outputs[](_limit);
        uint256 temp;
        for (uint256 i = 0; i < _limit; i++) {
            uint256 id = _start + i;
            if (
                (buildrDistrict[id] == _district) &&
                (_ownerOf[id] != address(0))
            ) {
                mapOutput[temp].tokenId = id;
                mapOutput[temp].balance = getBuildrDistrictBalance(
                    id,
                    _district
                );
                mapOutput[temp].district = buildrDistrict[id];
                temp++;
            }
        }
        return mapOutput;
    }
    function getUnassignedBuildrs(
        uint256 _start,
        uint256 _limit
    ) public view returns (Outputs[] memory) {
        if (_start < 1) {
            revert FixTokenId();
        }
        Outputs[] memory mapOutput = new Outputs[](_limit);
        uint256 temp;
        for (uint256 i = 0; i < _limit; i++) {
            uint256 id = _start + i;
            if (
                (buildrDistrict[id] == Web3District(0)) &&
                (_ownerOf[id] == address(0) && (id <= 4024))
            ) {
                mapOutput[temp].tokenId = id;
                mapOutput[temp].balance = getBuildrTotalBalance(id);
                temp++;
            }
        }
        return mapOutput;
    }
    function getDistrict(uint256 _tokenId) public view returns (Web3District) {
        if (_tokenId > TOTAL_SUPPLY || _tokenId < 1) {
            revert FixTokenId();
        }
        return buildrDistrict[_tokenId];
    }
    function getBuildrDistrictBalance(
        uint256 _tokenId,
        Web3District _district
    ) public view returns (uint256) {
        return buildrBalance[_tokenId][_district];
    }
    function getBuildrTotalBalance(
        uint256 _tokenId
    ) public view returns (uint256) {
        uint256 balance;
        for (uint256 i = 0; i < 5; i++) {
            Web3District district = Web3District(i);
            balance += buildrBalance[_tokenId][district];
        }
        return balance;
    }
    function totalSupply() public pure returns (uint256) {
        return TOTAL_SUPPLY;
    }
    function getBuildr() public view returns (address) {
        return buildr;
    }
    function resetBuildrInfo(uint256 _tokenId) private {
        delete buildrInfo[_tokenId];
        buildrDistrict[_tokenId] = Web3District.Nomads;
    }
    function editDistrict(Web3District _district, uint256 _tokenId) private {
        buildrDistrict[_tokenId] = _district;
    }
    function editBuildrDetail(
        string calldata _ipfsCID,
        uint256 _tokenId
    ) private {
        buildrInfo[_tokenId] = _ipfsCID;
    }
    function mapView(uint256 _tokenId) private view returns (uint256) {
        return map[_tokenId] == 0 ? _tokenId : map[_tokenId];
    }
}
// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;
/// @notice Modern, minimalist, and gas efficient ERC-721 implementation.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC721.sol)
abstract contract ERC721 {
    /*//////////////////////////////////////////////////////////////
                                 EVENTS
    //////////////////////////////////////////////////////////////*/
    event Transfer(address indexed from, address indexed to, uint256 indexed id);
    event Approval(address indexed owner, address indexed spender, uint256 indexed id);
    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);
    /*//////////////////////////////////////////////////////////////
                         METADATA STORAGE/LOGIC
    //////////////////////////////////////////////////////////////*/
    string public name;
    string public symbol;
    function tokenURI(uint256 id) public view virtual returns (string memory);
    /*//////////////////////////////////////////////////////////////
                      ERC721 BALANCE/OWNER STORAGE
    //////////////////////////////////////////////////////////////*/
    mapping(uint256 => address) internal _ownerOf;
    mapping(address => uint256) internal _balanceOf;
    function ownerOf(uint256 id) public view virtual returns (address owner) {
        require((owner = _ownerOf[id]) != address(0), "NOT_MINTED");
    }
    function balanceOf(address owner) public view virtual returns (uint256) {
        require(owner != address(0), "ZERO_ADDRESS");
        return _balanceOf[owner];
    }
    /*//////////////////////////////////////////////////////////////
                         ERC721 APPROVAL STORAGE
    //////////////////////////////////////////////////////////////*/
    mapping(uint256 => address) public getApproved;
    mapping(address => mapping(address => bool)) public isApprovedForAll;
    /*//////////////////////////////////////////////////////////////
                               CONSTRUCTOR
    //////////////////////////////////////////////////////////////*/
    constructor(string memory _name, string memory _symbol) {
        name = _name;
        symbol = _symbol;
    }
    /*//////////////////////////////////////////////////////////////
                              ERC721 LOGIC
    //////////////////////////////////////////////////////////////*/
    function approve(address spender, uint256 id) public virtual {
        address owner = _ownerOf[id];
        require(msg.sender == owner || isApprovedForAll[owner][msg.sender], "NOT_AUTHORIZED");
        getApproved[id] = spender;
        emit Approval(owner, spender, id);
    }
    function setApprovalForAll(address operator, bool approved) public virtual {
        isApprovedForAll[msg.sender][operator] = approved;
        emit ApprovalForAll(msg.sender, operator, approved);
    }
    function transferFrom(
        address from,
        address to,
        uint256 id
    ) public virtual {
        require(from == _ownerOf[id], "WRONG_FROM");
        require(to != address(0), "INVALID_RECIPIENT");
        require(
            msg.sender == from || isApprovedForAll[from][msg.sender] || msg.sender == getApproved[id],
            "NOT_AUTHORIZED"
        );
        // Underflow of the sender's balance is impossible because we check for
        // ownership above and the recipient's balance can't realistically overflow.
        unchecked {
            _balanceOf[from]--;
            _balanceOf[to]++;
        }
        _ownerOf[id] = to;
        delete getApproved[id];
        emit Transfer(from, to, id);
    }
    function safeTransferFrom(
        address from,
        address to,
        uint256 id
    ) public virtual {
        transferFrom(from, to, id);
        require(
            to.code.length == 0 ||
                ERC721TokenReceiver(to).onERC721Received(msg.sender, from, id, "") ==
                ERC721TokenReceiver.onERC721Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }
    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        bytes calldata data
    ) public virtual {
        transferFrom(from, to, id);
        require(
            to.code.length == 0 ||
                ERC721TokenReceiver(to).onERC721Received(msg.sender, from, id, data) ==
                ERC721TokenReceiver.onERC721Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }
    /*//////////////////////////////////////////////////////////////
                              ERC165 LOGIC
    //////////////////////////////////////////////////////////////*/
    function supportsInterface(bytes4 interfaceId) public view virtual returns (bool) {
        return
            interfaceId == 0x01ffc9a7 || // ERC165 Interface ID for ERC165
            interfaceId == 0x80ac58cd || // ERC165 Interface ID for ERC721
            interfaceId == 0x5b5e139f; // ERC165 Interface ID for ERC721Metadata
    }
    /*//////////////////////////////////////////////////////////////
                        INTERNAL MINT/BURN LOGIC
    //////////////////////////////////////////////////////////////*/
    function _mint(address to, uint256 id) internal virtual {
        require(to != address(0), "INVALID_RECIPIENT");
        require(_ownerOf[id] == address(0), "ALREADY_MINTED");
        // Counter overflow is incredibly unrealistic.
        unchecked {
            _balanceOf[to]++;
        }
        _ownerOf[id] = to;
        emit Transfer(address(0), to, id);
    }
    function _burn(uint256 id) internal virtual {
        address owner = _ownerOf[id];
        require(owner != address(0), "NOT_MINTED");
        // Ownership check above ensures no underflow.
        unchecked {
            _balanceOf[owner]--;
        }
        delete _ownerOf[id];
        delete getApproved[id];
        emit Transfer(owner, address(0), id);
    }
    /*//////////////////////////////////////////////////////////////
                        INTERNAL SAFE MINT LOGIC
    //////////////////////////////////////////////////////////////*/
    function _safeMint(address to, uint256 id) internal virtual {
        _mint(to, id);
        require(
            to.code.length == 0 ||
                ERC721TokenReceiver(to).onERC721Received(msg.sender, address(0), id, "") ==
                ERC721TokenReceiver.onERC721Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }
    function _safeMint(
        address to,
        uint256 id,
        bytes memory data
    ) internal virtual {
        _mint(to, id);
        require(
            to.code.length == 0 ||
                ERC721TokenReceiver(to).onERC721Received(msg.sender, address(0), id, data) ==
                ERC721TokenReceiver.onERC721Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }
}
/// @notice A generic interface for a contract which properly accepts ERC721 tokens.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC721.sol)
abstract contract ERC721TokenReceiver {
    function onERC721Received(
        address,
        address,
        uint256,
        bytes calldata
    ) external virtual returns (bytes4) {
        return ERC721TokenReceiver.onERC721Received.selector;
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/Strings.sol)
pragma solidity ^0.8.20;
import {Math} from "./math/Math.sol";
import {SignedMath} from "./math/SignedMath.sol";
/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant HEX_DIGITS = "0123456789abcdef";
    uint8 private constant ADDRESS_LENGTH = 20;
    /**
     * @dev The `value` string doesn't fit in the specified `length`.
     */
    error StringsInsufficientHexLength(uint256 value, uint256 length);
    /**
     * @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), HEX_DIGITS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }
    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toStringSigned(int256 value) internal pure returns (string memory) {
        return string.concat(value < 0 ? "-" : "", toString(SignedMath.abs(value)));
    }
    /**
     * @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) {
        uint256 localValue = value;
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = HEX_DIGITS[localValue & 0xf];
            localValue >>= 4;
        }
        if (localValue != 0) {
            revert StringsInsufficientHexLength(value, length);
        }
        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);
    }
    /**
     * @dev Returns true if the two strings are equal.
     */
    function equal(string memory a, string memory b) internal pure returns (bool) {
        return bytes(a).length == bytes(b).length && keccak256(bytes(a)) == keccak256(bytes(b));
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/Math.sol)
pragma solidity ^0.8.20;
/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    /**
     * @dev Muldiv operation overflow.
     */
    error MathOverflowedMulDiv();
    enum Rounding {
        Floor, // Toward negative infinity
        Ceil, // Toward positive infinity
        Trunc, // Toward zero
        Expand // Away from zero
    }
    /**
     * @dev Returns the addition of two unsigned integers, with an overflow flag.
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            uint256 c = a + b;
            if (c < a) return (false, 0);
            return (true, c);
        }
    }
    /**
     * @dev Returns the subtraction of two unsigned integers, with an overflow flag.
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            if (b > a) return (false, 0);
            return (true, a - b);
        }
    }
    /**
     * @dev Returns the multiplication of two unsigned integers, with an overflow flag.
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            // 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.
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            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.
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            if (b == 0) return (false, 0);
            return (true, a % b);
        }
    }
    /**
     * @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 towards infinity instead
     * of rounding towards zero.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        if (b == 0) {
            // Guarantee the same behavior as in a regular Solidity division.
            return a / b;
        }
        // (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 = x * y; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }
            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return prod0 / denominator;
            }
            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            if (denominator <= prod1) {
                revert MathOverflowedMulDiv();
            }
            ///////////////////////////////////////////////
            // 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.
            uint256 twos = denominator & (0 - denominator);
            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 (unsignedRoundsUp(rounding) && 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
     * towards zero.
     *
     * 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 + (unsignedRoundsUp(rounding) && result * result < a ? 1 : 0);
        }
    }
    /**
     * @dev Return the log in base 2 of a positive value rounded towards zero.
     * 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 + (unsignedRoundsUp(rounding) && 1 << result < value ? 1 : 0);
        }
    }
    /**
     * @dev Return the log in base 10 of a positive value rounded towards zero.
     * 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 + (unsignedRoundsUp(rounding) && 10 ** result < value ? 1 : 0);
        }
    }
    /**
     * @dev Return the log in base 256 of a positive value rounded towards zero.
     * 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 256, 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 + (unsignedRoundsUp(rounding) && 1 << (result << 3) < value ? 1 : 0);
        }
    }
    /**
     * @dev Returns whether a provided rounding mode is considered rounding up for unsigned integers.
     */
    function unsignedRoundsUp(Rounding rounding) internal pure returns (bool) {
        return uint8(rounding) % 2 == 1;
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/SignedMath.sol)
pragma solidity ^0.8.20;
/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a > b ? a : b;
    }
    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }
    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }
    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}