PenguStrategy

{{
  "language": "Solidity",
  "sources": {
    "src/auction/PenguStrategy.sol": {
      "content": "// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import {IPenguStrategyToken} from "../IPenguStrategyToken.sol";
import {ISeaport} from "./interfaces/ISeaport.sol";
import {IERC721} from "@openzeppelin/contracts/token/ERC721/IERC721.sol";
import {AuctionHouse} from "./AuctionHouse.sol";
import {VillageNFT} from "./VillageNFT.sol";

contract PenguStrategy is AuctionHouse {
    IPenguStrategyToken public token;
    IERC721 public pudgies;
    VillageNFT public villageNft;
    ISeaport public constant SEAPORT = ISeaport(0x0000000000000068F116a894984e2DB1123eB395);

    uint256 public constant AUCTION_PRICE_MULTIPLIER = 4;

    event PudgyBought(uint256 indexed pudgyId, uint256 price);

    constructor(address _token, address _pudgies, address _owner) {
        token = IPenguStrategyToken(_token);
        pudgies = IERC721(_pudgies);

        // Deploy the Village NFT contract
        villageNft = new VillageNFT(_pudgies, _token, address(this), _owner);

        // Note: Deployer must call token.configure(...) after deployment
    }

    function buyPudgy(ISeaport.Order calldata order, uint256 maxPrice) external payable nonReentrant {
        // Validate it's a Pudgy Penguins NFT
        require(
            order.parameters.offer.length > 0 && order.parameters.offer[0].token == address(pudgies)
                && order.parameters.offer[0].itemType == ISeaport.ItemType.ERC721,
            "Not a Pudgy"
        );

        // Calculate total ETH needed (sum all consideration items that are ETH)
        uint256 actualPrice = 0;
        for (uint256 i = 0; i < order.parameters.consideration.length; i++) {
            if (order.parameters.consideration[i].itemType == ISeaport.ItemType.NATIVE) {
                actualPrice += order.parameters.consideration[i].startAmount;
            }
        }

        // Slippage protection
        require(actualPrice <= maxPrice, "Price exceeds maximum");

        uint256 balance = address(this).balance;
        if (balance < actualPrice) {
            uint256 needed = actualPrice - balance;
            token.useSurplus(needed);
        }

        // Fulfill the order on Seaport v1.6
        bool fulfilled = SEAPORT.fulfillOrder{value: actualPrice}(order, bytes32(0));
        require(fulfilled, "Order not fulfilled");

        // Verify we received the NFT
        uint256 tokenId = order.parameters.offer[0].identifierOrCriteria;
        require(pudgies.ownerOf(tokenId) == address(this), "Not owner");

        emit PudgyBought(tokenId, actualPrice);

        // If auction is active, add to existing auction (village mode)
        // Otherwise, start new auction
        if (auction.active) {
            _addPudgyToActiveAuction(tokenId, actualPrice);
        } else {
            // Start new auction
            _startNewAuction(tokenId, actualPrice);
        }
    }

    function _startNewAuction(uint256 pudgyId, uint256 actualPrice) internal {
        _prepareAuction(pudgyId);

        uint256[] memory pudgyIds = new uint256[](1);
        pudgyIds[0] = pudgyId;

        uint256 auctionId = _nextAuctionId++;

        auction = Auction({
            active: true,
            auctionId: auctionId,
            pudgyIds: pudgyIds,
            startTime: block.timestamp,
            startPrice: 0,
            costBasis: actualPrice,
            maxUnitPrice: actualPrice
        });

        // Calculate dynamic start price for village of 1
        uint256 startPrice = _calculateStartPrice(actualPrice, 1, actualPrice, 0);
        auction.startPrice = startPrice;
        emit AuctionStarted(auctionId, pudgyIds, startPrice);
    }

    function _addPudgyToActiveAuction(uint256 tokenId, uint256 actualPrice) internal {
        // Add pudgy to existing auction
        auction.pudgyIds.push(tokenId);

        // Update cost basis tracking
        auction.costBasis += actualPrice;
        if (actualPrice > auction.maxUnitPrice) {
            auction.maxUnitPrice = actualPrice;
        }

        // Calculate new start price for village, ensuring it never decreases
        uint256 villageSize = auction.pudgyIds.length;
        uint256 newStartPrice =
            _calculateStartPrice(auction.costBasis, villageSize, auction.maxUnitPrice, auction.startPrice);

        // Reset auction with new price
        auction.startPrice = newStartPrice;
        auction.startTime = block.timestamp;

        emit PudgyAddedToAuction(auction.auctionId, tokenId, newStartPrice);
    }

    receive() external payable {} // can receive ETH

    function _prepareAuction(uint256 pudgyId) internal view override {
        require(pudgies.ownerOf(pudgyId) == address(this), "Not owner");
    }

    function _calculateStartPrice(
        uint256 costBasis,
        uint256 villageSize,
        uint256 maxUnitPrice,
        uint256 previousStartPrice
    ) internal view override returns (uint256) {
        uint256 startPrice = previousStartPrice;

        // Price based on cumulative ETH deployed into this village
        uint256 cumulativePengust = token.previewMint(costBasis);
        uint256 cumulativePricing = cumulativePengust * AUCTION_PRICE_MULTIPLIER;
        if (cumulativePricing > startPrice) {
            startPrice = cumulativePricing;
        }

        if (maxUnitPrice > 0 && villageSize > 0) {
            // Ensure unit cost floor scales with the most expensive pengu inside the village
            uint256 unitPengust = token.previewMint(maxUnitPrice * villageSize);
            uint256 unitPricing = unitPengust * AUCTION_PRICE_MULTIPLIER;
            if (unitPricing > startPrice) {
                startPrice = unitPricing;
            }
        }

        return startPrice;
    }

    function _settleAuction(uint256[] memory pudgyIds, address buyer, uint256 price) internal override {
        // Lock tokens from buyer
        token.lock(price, buyer);

        // Transfer all pudgies to the village NFT contract
        for (uint256 i = 0; i < pudgyIds.length; i++) {
            pudgies.transferFrom(address(this), address(villageNft), pudgyIds[i]);
        }

        // Mint village NFT to the buyer
        uint256 villageId = villageNft.settleVillage(buyer, pudgyIds);
        token.onVillageCreated(villageId, pudgyIds.length, buyer);
    }

    function onERC721Received(address, address, uint256, bytes calldata) external pure returns (bytes4) {
        return this.onERC721Received.selector;
    }
}
"
    },
    "src/IPenguStrategyToken.sol": {
      "content": "// SPDX-License-Identifier: MIT
pragma solidity ^0.8.30;

interface IPenguStrategyToken {
    // === ERC20 FUNCTIONS (inherited from ERC20) ===
    // Note: ERC20 functions not redeclared here to avoid conflicts

    // === CONSTANTS ===
    function MAX_SUPPLY() external view returns (uint256);
    function DEAD_ADDRESS() external view returns (address);
    function BUY_FEE_RATE() external view returns (uint128);
    function SELL_FEE_RATE() external view returns (uint128);
    function PROTOCOL_FEE_BPS() external view returns (uint256);

    // === STATE VARIABLES ===
    function protocolFeeRecipient() external view returns (address);
    function strategy() external view returns (address);
    function villageNft() external view returns (address);

    // === CORE FUNCTIONS ===
    function mint(address receiver, uint256 minTokensOut) external payable;
    function enableTransfers() external;
    function redeem(uint256 amount, address from, address receiver, uint256 minAmountOut) external;
    function lock(uint256 amount, address from) external;

    // === PREVIEW FUNCTIONS ===
    function previewMint(uint256 ethAmount) external view returns (uint256);
    function quoteMint(uint256 amount) external view returns (uint256);
    function previewRedeem(uint256 amount) external view returns (uint256);

    // === SUPPLY FUNCTIONS ===
    function lockedSupply() external view returns (uint256);
    function effectiveSupply() external view returns (uint256);
    function reserve() external view returns (uint256);
    function surplus() external view returns (uint256);
    function transfersEnabled() external view returns (bool);
    function transferController() external view returns (address);

    // === ADMIN FUNCTIONS ===
    function deployer() external view returns (address);
    function configure(address newStrategy, address newVillageNft, address newProtocolFeeRecipient) external;
    function start() external;

    // === STRATEGY FUNCTIONS ===
    function useSurplus(uint256 amount) external;

    // === VILLAGE FEE SYSTEM ===
    function villageFeePool() external view returns (uint256);
    function totalVillageWeight() external view returns (uint256);
    function villageRewardsIndex() external view returns (uint256);
    function villageWeight(uint256 villageId) external view returns (uint256);
    function pendingVillageFees(uint256 villageId) external view returns (uint256);
    function onVillageCreated(uint256 villageId, uint256 pudgyCount, address owner) external;
    function claimVillageFees(uint256 villageId, address recipient) external returns (uint256);
    function removeVillage(uint256 villageId, address recipient) external;
}
"
    },
    "src/auction/interfaces/ISeaport.sol": {
      "content": "// SPDX-License-Identifier: MIT
pragma solidity ^0.8.30;

interface ISeaport {
    enum OrderType {
        FULL_OPEN,
        PARTIAL_OPEN,
        FULL_RESTRICTED,
        PARTIAL_RESTRICTED,
        CONTRACT
    }

    enum ItemType {
        NATIVE,
        ERC20,
        ERC721,
        ERC1155,
        ERC721_WITH_CRITERIA,
        ERC1155_WITH_CRITERIA
    }

    struct OfferItem {
        ItemType itemType;
        address token;
        uint256 identifierOrCriteria;
        uint256 startAmount;
        uint256 endAmount;
    }

    struct ConsiderationItem {
        ItemType itemType;
        address token;
        uint256 identifierOrCriteria;
        uint256 startAmount;
        uint256 endAmount;
        address payable recipient;
    }

    struct OrderParameters {
        address offerer;
        address zone;
        OfferItem[] offer;
        ConsiderationItem[] consideration;
        OrderType orderType;
        uint256 startTime;
        uint256 endTime;
        bytes32 zoneHash;
        uint256 salt;
        bytes32 conduitKey;
        uint256 totalOriginalConsiderationItems;
    }

    struct Order {
        OrderParameters parameters;
        bytes signature;
    }

    struct AdvancedOrder {
        OrderParameters parameters;
        uint120 numerator;
        uint120 denominator;
        bytes signature;
        bytes extraData;
    }

    struct CriteriaResolver {
        uint256 orderIndex;
        uint256 side;
        uint256 index;
        uint256 identifier;
        bytes32[] criteriaProof;
    }

    struct FulfillmentComponent {
        uint256 orderIndex;
        uint256 itemIndex;
    }

    struct Fulfillment {
        FulfillmentComponent[] offerComponents;
        FulfillmentComponent[] considerationComponents;
    }

    struct OrderComponents {
        address offerer;
        address zone;
        OfferItem[] offer;
        ConsiderationItem[] consideration;
        OrderType orderType;
        uint256 startTime;
        uint256 endTime;
        bytes32 zoneHash;
        uint256 salt;
        bytes32 conduitKey;
        uint256 counter;
    }

    /**
     * @notice Fulfill an order offering an ERC721 token by supplying Ether (or
     *         the native token for the given chain) as consideration for the order.
     */
    function fulfillOrder(Order calldata order, bytes32 fulfillerConduitKey) external payable returns (bool fulfilled);

    /**
     * @notice Fulfill an advanced order
     */
    function fulfillAdvancedOrder(
        AdvancedOrder calldata advancedOrder,
        CriteriaResolver[] calldata criteriaResolvers,
        bytes32 fulfillerConduitKey,
        address recipient
    ) external payable returns (bool fulfilled);

    /**
     * @notice Fulfill available advanced orders
     */
    function fulfillAvailableAdvancedOrders(
        AdvancedOrder[] calldata advancedOrders,
        CriteriaResolver[] calldata criteriaResolvers,
        FulfillmentComponent[][] calldata offerFulfillments,
        FulfillmentComponent[][] calldata considerationFulfillments,
        bytes32 fulfillerConduitKey,
        address recipient,
        uint256 maximumFulfilled
    ) external payable returns (bool[] memory availableOrders, Fulfillment[] memory fulfillments);

    /**
     * @notice Match an arbitrary number of orders
     */
    function matchOrders(Order[] calldata orders, Fulfillment[] calldata fulfillments)
        external
        payable
        returns (Fulfillment[] memory);

    /**
     * @notice Match an arbitrary number of advanced orders
     */
    function matchAdvancedOrders(
        AdvancedOrder[] calldata advancedOrders,
        CriteriaResolver[] calldata criteriaResolvers,
        Fulfillment[] calldata fulfillments,
        address recipient
    ) external payable returns (Fulfillment[] memory);

    /**
     * @notice Cancel an arbitrary number of orders
     */
    function cancel(OrderComponents[] calldata orders) external returns (bool cancelled);

    /**
     * @notice Validate an arbitrary number of orders
     */
    function validate(Order[] calldata orders) external returns (bool validated);

    /**
     * @notice Retrieve the order hash for a given order
     */
    function getOrderHash(OrderComponents calldata order) external view returns (bytes32 orderHash);

    /**
     * @notice Retrieve the status of a given order
     */
    function getOrderStatus(bytes32 orderHash)
        external
        view
        returns (bool isValidated, bool isCancelled, uint256 totalFilled, uint256 totalSize);

    /**
     * @notice Retrieve the current counter for a given offerer
     */
    function getCounter(address offerer) external view returns (uint256 counter);

    /**
     * @notice Retrieve configuration information for this contract
     */
    function information()
        external
        view
        returns (string memory version, bytes32 domainSeparator, address conduitController);

    /**
     * @notice Retrieve the name of this contract
     */
    function name() external pure returns (string memory contractName);
}
"
    },
    "lib/openzeppelin-contracts/contracts/token/ERC721/IERC721.sol": {
      "content": "// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (token/ERC721/IERC721.sol)

pragma solidity >=0.6.2;

import {IERC165} from "../../utils/introspection/IERC165.sol";

/**
 * @dev Required interface of an ERC-721 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 ERC-721 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 ERC-721
     * 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 address zero.
     *
     * 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);
}
"
    },
    "src/auction/AuctionHouse.sol": {
      "content": "// SPDX-License-Identifier: MIT
pragma solidity ^0.8.30;

import {FixedPointMathLib} from "solady/utils/FixedPointMathLib.sol";
import {ReentrancyGuard} from "@openzeppelin/contracts/utils/ReentrancyGuard.sol";

abstract contract AuctionHouse is ReentrancyGuard {
    // 12-hour half-life: ln(2) / 43200 seconds ≈ 1.604e-5
    // Expressed in WAD: 1.604e-5 * 1e18 = 1.604e13
    uint256 public constant AUCTION_DECAY_RATE = 16040000000000; // 1.604e13 in WAD

    event AuctionStarted(uint256 indexed auctionId, uint256[] pudgyIds, uint256 startPrice);
    event AuctionSettled(uint256 indexed auctionId, uint256[] pudgyIds, address indexed buyer, uint256 price);
    event PudgyAddedToAuction(uint256 indexed auctionId, uint256 indexed pudgyId, uint256 newStartPrice);

    Auction public auction;

    uint256 public _nextAuctionId;

    struct Auction {
        bool active;
        uint256 auctionId;
        uint256[] pudgyIds;
        uint256 startTime;
        uint256 startPrice;
        uint256 costBasis;
        uint256 maxUnitPrice;
    }

    modifier whenAuctionActive() {
        _whenAuctionActive();
        _;
    }

    modifier whenAuctionNotActive() {
        _whenAuctionNotActive();
        _;
    }

    function _whenAuctionActive() internal view {
        require(auction.active, "Auction not active");
    }

    function _whenAuctionNotActive() internal view {
        require(!auction.active, "Auction already active");
    }

    function take(uint256 maxPrice) external whenAuctionActive nonReentrant {
        uint256 price = currentAuctionPrice();
        require(price <= maxPrice, "Price too high");

        auction.active = false;
        uint256[] memory pudgyIds = auction.pudgyIds;
        uint256 auctionId = auction.auctionId;
        _settleAuction(pudgyIds, msg.sender, price);
        emit AuctionSettled(auctionId, pudgyIds, msg.sender, price);
    }

    function currentAuction() external view returns (Auction memory) {
        return auction;
    }

    function isAuctionActive() external view returns (bool) {
        return auction.active;
    }

    function currentAuctionPrice() public view returns (uint256) {
        if (!auction.active) return 0;
        return _priceAt(block.timestamp - auction.startTime);
    }

    function _priceAt(uint256 t) internal view virtual returns (uint256 price) {
        // casting to int256 is safe because AUCTION_DECAY_RATE and t are uint256 values bounded by
        // reasonably small timestamps, so the product fits within int256 during auction lifetime.
        // forge-lint: disable-next-line(unsafe-typecast)
        int256 exp = -int256(AUCTION_DECAY_RATE) * int256(t);
        uint256 ratio = uint256(FixedPointMathLib.expWad(exp));

        if (ratio == 0) return 1;

        price = FixedPointMathLib.mulWadUp(auction.startPrice, ratio);
    }

    function _calculateStartPrice(
        uint256 costBasis,
        uint256 villageSize,
        uint256 maxUnitPrice,
        uint256 previousStartPrice
    ) internal view virtual returns (uint256);
    function _prepareAuction(uint256 pudgyId) internal virtual;
    function _settleAuction(uint256[] memory pudgyIds, address buyer, uint256 price) internal virtual;
}
"
    },
    "src/auction/VillageNFT.sol": {
      "content": "// SPDX-License-Identifier: MIT
pragma solidity ^0.8.30;

import {ERC721} from "solady/tokens/ERC721.sol";
import {LibString} from "solady/utils/LibString.sol";
import {IERC721} from "@openzeppelin/contracts/token/ERC721/IERC721.sol";
import {ReentrancyGuard} from "@openzeppelin/contracts/utils/ReentrancyGuard.sol";
import {IPenguStrategyToken} from "../IPenguStrategyToken.sol";

import {Ownable} from "solady/auth/Ownable.sol";

contract VillageNFT is ERC721, ReentrancyGuard, Ownable {
    IERC721 public immutable PUDGIES;
    IPenguStrategyToken public immutable TOKEN;
   address public immutable AUCTION_CONTRACT;

   uint256 private _nextVillageId;
    string private _baseTokenURI;

    // Maps village token ID to array of pudgy IDs
    mapping(uint256 => uint256[]) public villagePudgies;

    event VillageMinted(uint256 indexed villageId, address indexed owner, uint256[] pudgyIds);
    event VillageDisassembled(uint256 indexed villageId, address indexed owner, uint256[] pudgyIds);

    modifier onlyAuction() {
        _onlyAuction();
        _;
    }

    function _onlyAuction() internal view {
        require(msg.sender == AUCTION_CONTRACT, "Only auction contract");
    }

    constructor(address _pudgies, address _token, address _auctionContract, address _owner) {
        PUDGIES = IERC721(_pudgies);
        TOKEN = IPenguStrategyToken(_token);
        AUCTION_CONTRACT = _auctionContract;
        _initializeOwner(_owner);
    }

    function name() public pure override returns (string memory) {
        return "Pudgy Village";
    }

    function symbol() public pure override returns (string memory) {
        return "VILLAGE";
    }

    function tokenURI(uint256 villageId) public view override returns (string memory) {
        require(_ownerOf(villageId) != address(0), "TokenDoesNotExist");
        string memory base = _baseTokenURI;
        return bytes(base).length == 0
            ? ""
            : string.concat(base, LibString.toString(villageId));
    }

    function baseURI() external view returns (string memory) {
       return _baseTokenURI;
   }

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

    /// @notice Mint a new village NFT containing the specified pudgies
    /// @param to The address to mint the village to
    /// @param pudgyIds Array of pudgy penguin token IDs to include in the village
    /// @return villageId The ID of the newly minted village NFT
    function settleVillage(address to, uint256[] calldata pudgyIds) external onlyAuction returns (uint256 villageId) {
        require(pudgyIds.length > 0, "Empty village");

        // Verify this contract owns all the pudgies
        for (uint256 i = 0; i < pudgyIds.length; i++) {
            require(PUDGIES.ownerOf(pudgyIds[i]) == address(this), "Village does not own pudgy");
        }

        villageId = _nextVillageId++;

        // Store pudgy IDs in the village
        villagePudgies[villageId] = pudgyIds;

        // Mint the village NFT
        _mint(to, villageId);

        emit VillageMinted(villageId, to, pudgyIds);
    }

    /// @notice Claim accumulated protocol fees for a given village
    /// @param villageId The village whose fees to claim
    function claimFees(uint256 villageId) external nonReentrant {
        address owner = ownerOf(villageId);
        require(msg.sender == owner, "Not village owner");
        TOKEN.claimVillageFees(villageId, owner);
    }

    /// @notice Disassemble a village, returning all pudgies to the owner and burning the village NFT
    /// @param villageId The ID of the village to disassemble
    function genocide(uint256 villageId) external nonReentrant {
        address owner = ownerOf(villageId);
        require(msg.sender == owner, "Not village owner");

        uint256[] memory pudgyIds = villagePudgies[villageId];
        require(pudgyIds.length > 0, "Village already disassembled");

        // Claim outstanding fees and remove village weight from the strategy token
        TOKEN.removeVillage(villageId, owner);

        // Transfer all pudgies to the owner
        for (uint256 i = 0; i < pudgyIds.length; i++) {
            PUDGIES.safeTransferFrom(address(this), owner, pudgyIds[i]);
        }

        // Clear the village data
        delete villagePudgies[villageId];

        // Burn the village NFT
        _burn(villageId);

        emit VillageDisassembled(villageId, owner, pudgyIds);
    }

    /// @notice Get the pudgy IDs contained in a village
    /// @param villageId The ID of the village
    /// @return Array of pudgy penguin token IDs
    function getVillagePudgies(uint256 villageId) external view returns (uint256[] memory) {
        return villagePudgies[villageId];
    }

    /// @notice Get the size (number of pudgies) in a village
    /// @param villageId The ID of the village
    /// @return Number of pudgies in the village
    function getVillageSize(uint256 villageId) external view returns (uint256) {
        return villagePudgies[villageId].length;
    }

    /// @notice Required for receiving ERC721 tokens
    function onERC721Received(address, address, uint256, bytes calldata) external pure returns (bytes4) {
        return this.onERC721Received.selector;
    }
}
"
    },
    "lib/openzeppelin-contracts/contracts/utils/introspection/IERC165.sol": {
      "content": "// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (utils/introspection/IERC165.sol)

pragma solidity >=0.4.16;

/**
 * @dev Interface of the ERC-165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[ERC].
 *
 * 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[ERC 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);
}
"
    },
    "lib/solady/src/utils/FixedPointMathLib.sol": {
      "content": "// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/FixedPointMathLib.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/FixedPointMathLib.sol)
library FixedPointMathLib {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The operation failed, as the output exceeds the maximum value of uint256.
    error ExpOverflow();

    /// @dev The operation failed, as the output exceeds the maximum value of uint256.
    error FactorialOverflow();

    /// @dev The operation failed, due to an overflow.
    error RPowOverflow();

    /// @dev The mantissa is too big to fit.
    error MantissaOverflow();

    /// @dev The operation failed, due to an multiplication overflow.
    error MulWadFailed();

    /// @dev The operation failed, due to an multiplication overflow.
    error SMulWadFailed();

    /// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
    error DivWadFailed();

    /// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
    error SDivWadFailed();

    /// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
    error MulDivFailed();

    /// @dev The division failed, as the denominator is zero.
    error DivFailed();

    /// @dev The full precision multiply-divide operation failed, either due
    /// to the result being larger than 256 bits, or a division by a zero.
    error FullMulDivFailed();

    /// @dev The output is undefined, as the input is less-than-or-equal to zero.
    error LnWadUndefined();

    /// @dev The input outside the acceptable domain.
    error OutOfDomain();

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The scalar of ETH and most ERC20s.
    uint256 internal constant WAD = 1e18;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*              SIMPLIFIED FIXED POINT OPERATIONS             */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Equivalent to `(x * y) / WAD` rounded down.
    function mulWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y == 0 || x <= type(uint256).max / y)`.
            if gt(x, div(not(0), y)) {
                if y {
                    mstore(0x00, 0xbac65e5b) // `MulWadFailed()`.
                    revert(0x1c, 0x04)
                }
            }
            z := div(mul(x, y), WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded down.
    function sMulWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require((x == 0 || z / x == y) && !(x == -1 && y == type(int256).min))`.
            if iszero(gt(or(iszero(x), eq(sdiv(z, x), y)), lt(not(x), eq(y, shl(255, 1))))) {
                mstore(0x00, 0xedcd4dd4) // `SMulWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := sdiv(z, WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded down, but without overflow checks.
    function rawMulWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := div(mul(x, y), WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded down, but without overflow checks.
    function rawSMulWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := sdiv(mul(x, y), WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded up.
    function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require(y == 0 || x <= type(uint256).max / y)`.
            if iszero(eq(div(z, y), x)) {
                if y {
                    mstore(0x00, 0xbac65e5b) // `MulWadFailed()`.
                    revert(0x1c, 0x04)
                }
            }
            z := add(iszero(iszero(mod(z, WAD))), div(z, WAD))
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded up, but without overflow checks.
    function rawMulWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := add(iszero(iszero(mod(mul(x, y), WAD))), div(mul(x, y), WAD))
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down.
    function divWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y != 0 && x <= type(uint256).max / WAD)`.
            if iszero(mul(y, lt(x, add(1, div(not(0), WAD))))) {
                mstore(0x00, 0x7c5f487d) // `DivWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := div(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down.
    function sDivWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, WAD)
            // Equivalent to `require(y != 0 && ((x * WAD) / WAD == x))`.
            if iszero(mul(y, eq(sdiv(z, WAD), x))) {
                mstore(0x00, 0x5c43740d) // `SDivWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := sdiv(z, y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down, but without overflow and divide by zero checks.
    function rawDivWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := div(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down, but without overflow and divide by zero checks.
    function rawSDivWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := sdiv(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded up.
    function divWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y != 0 && x <= type(uint256).max / WAD)`.
            if iszero(mul(y, lt(x, add(1, div(not(0), WAD))))) {
                mstore(0x00, 0x7c5f487d) // `DivWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(mul(x, WAD), y))), div(mul(x, WAD), y))
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded up, but without overflow and divide by zero checks.
    function rawDivWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := add(iszero(iszero(mod(mul(x, WAD), y))), div(mul(x, WAD), y))
        }
    }

    /// @dev Equivalent to `x` to the power of `y`.
    /// because `x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)`.
    /// Note: This function is an approximation.
    function powWad(int256 x, int256 y) internal pure returns (int256) {
        // Using `ln(x)` means `x` must be greater than 0.
        return expWad((lnWad(x) * y) / int256(WAD));
    }

    /// @dev Returns `exp(x)`, denominated in `WAD`.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
    /// Note: This function is an approximation. Monotonically increasing.
    function expWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            // When the result is less than 0.5 we return zero.
            // This happens when `x <= (log(1e-18) * 1e18) ~ -4.15e19`.
            if (x <= -41446531673892822313) return r;

            /// @solidity memory-safe-assembly
            assembly {
                // When the result is greater than `(2**255 - 1) / 1e18` we can not represent it as
                // an int. This happens when `x >= floor(log((2**255 - 1) / 1e18) * 1e18) ≈ 135`.
                if iszero(slt(x, 135305999368893231589)) {
                    mstore(0x00, 0xa37bfec9) // `ExpOverflow()`.
                    revert(0x1c, 0x04)
                }
            }

            // `x` is now in the range `(-42, 136) * 1e18`. Convert to `(-42, 136) * 2**96`
            // for more intermediate precision and a binary basis. This base conversion
            // is a multiplication by 1e18 / 2**96 = 5**18 / 2**78.
            x = (x << 78) / 5 ** 18;

            // Reduce range of x to (-½ ln 2, ½ ln 2) * 2**96 by factoring out powers
            // of two such that exp(x) = exp(x') * 2**k, where k is an integer.
            // Solving this gives k = round(x / log(2)) and x' = x - k * log(2).
            int256 k = ((x << 96) / 54916777467707473351141471128 + 2 ** 95) >> 96;
            x = x - k * 54916777467707473351141471128;

            // `k` is in the range `[-61, 195]`.

            // Evaluate using a (6, 7)-term rational approximation.
            // `p` is made monic, we'll multiply by a scale factor later.
            int256 y = x + 1346386616545796478920950773328;
            y = ((y * x) >> 96) + 57155421227552351082224309758442;
            int256 p = y + x - 94201549194550492254356042504812;
            p = ((p * y) >> 96) + 28719021644029726153956944680412240;
            p = p * x + (4385272521454847904659076985693276 << 96);

            // We leave `p` in `2**192` basis so we don't need to scale it back up for the division.
            int256 q = x - 2855989394907223263936484059900;
            q = ((q * x) >> 96) + 50020603652535783019961831881945;
            q = ((q * x) >> 96) - 533845033583426703283633433725380;
            q = ((q * x) >> 96) + 3604857256930695427073651918091429;
            q = ((q * x) >> 96) - 14423608567350463180887372962807573;
            q = ((q * x) >> 96) + 26449188498355588339934803723976023;

            /// @solidity memory-safe-assembly
            assembly {
                // Div in assembly because solidity adds a zero check despite the unchecked.
                // The q polynomial won't have zeros in the domain as all its roots are complex.
                // No scaling is necessary because p is already `2**96` too large.
                r := sdiv(p, q)
            }

            // r should be in the range `(0.09, 0.25) * 2**96`.

            // We now need to multiply r by:
            // - The scale factor `s ≈ 6.031367120`.
            // - The `2**k` factor from the range reduction.
            // - The `1e18 / 2**96` factor for base conversion.
            // We do this all at once, with an intermediate result in `2**213`
            // basis, so the final right shift is always by a positive amount.
            r = int256(
                (uint256(r) * 3822833074963236453042738258902158003155416615667) >> uint256(195 - k)
            );
        }
    }

    /// @dev Returns `ln(x)`, denominated in `WAD`.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
    /// Note: This function is an approximation. Monotonically increasing.
    function lnWad(int256 x) internal pure returns (int256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            // We want to convert `x` from `10**18` fixed point to `2**96` fixed point.
            // We do this by multiplying by `2**96 / 10**18`. But since
            // `ln(x * C) = ln(x) + ln(C)`, we can simply do nothing here
            // and add `ln(2**96 / 10**18)` at the end.

            // Compute `k = log2(x) - 96`, `r = 159 - k = 255 - log2(x) = 255 ^ log2(x)`.
            r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            // We place the check here for more optimal stack operations.
            if iszero(sgt(x, 0)) {
                mstore(0x00, 0x1615e638) // `LnWadUndefined()`.
                revert(0x1c, 0x04)
            }
            // forgefmt: disable-next-item
            r := xor(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
                0xf8f9f9faf9fdfafbf9fdfcfdfafbfcfef9fafdfafcfcfbfefafafcfbffffffff))

            // Reduce range of x to (1, 2) * 2**96
            // ln(2^k * x) = k * ln(2) + ln(x)
            x := shr(159, shl(r, x))

            // Evaluate using a (8, 8)-term rational approximation.
            // `p` is made monic, we will multiply by a scale factor later.
            // forgefmt: disable-next-item
            let p := sub( // This heavily nested expression is to avoid stack-too-deep for via-ir.
                sar(96, mul(add(43456485725739037958740375743393,
                sar(96, mul(add(24828157081833163892658089445524,
                sar(96, mul(add(3273285459638523848632254066296,
                    x), x))), x))), x)), 11111509109440967052023855526967)
            p := sub(sar(96, mul(p, x)), 45023709667254063763336534515857)
            p := sub(sar(96, mul(p, x)), 14706773417378608786704636184526)
            p := sub(mul(p, x), shl(96, 795164235651350426258249787498))
            // We leave `p` in `2**192` basis so we don't need to scale it back up for the division.

            // `q` is monic by convention.
            let q := add(5573035233440673466300451813936, x)
            q := add(71694874799317883764090561454958, sar(96, mul(x, q)))
            q := add(283447036172924575727196451306956, sar(96, mul(x, q)))
            q := add(401686690394027663651624208769553, sar(96, mul(x, q)))
            q := add(204048457590392012362485061816622, sar(96, mul(x, q)))
            q := add(31853899698501571402653359427138, sar(96, mul(x, q)))
            q := add(909429971244387300277376558375, sar(96, mul(x, q)))

            // `p / q` is in the range `(0, 0.125) * 2**96`.

            // Finalization, we need to:
            // - Multiply by the scale factor `s = 5.549…`.
            // - Add `ln(2**96 / 10**18)`.
            // - Add `k * ln(2)`.
            // - Multiply by `10**18 / 2**96 = 5**18 >> 78`.

            // The q polynomial is known not to have zeros in the domain.
            // No scaling required because p is already `2**96` too large.
            p := sdiv(p, q)
            // Multiply by the scaling factor: `s * 5**18 * 2**96`, base is now `5**18 * 2**192`.
            p := mul(1677202110996718588342820967067443963516166, p)
            // Add `ln(2) * k * 5**18 * 2**192`.
            // forgefmt: disable-next-item
            p := add(mul(16597577552685614221487285958193947469193820559219878177908093499208371, sub(159, r)), p)
            // Add `ln(2**96 / 10**18) * 5**18 * 2**192`.
            p := add(600920179829731861736702779321621459595472258049074101567377883020018308, p)
            // Base conversion: mul `2**18 / 2**192`.
            r := sar(174, p)
        }
    }

    /// @dev Returns `W_0(x)`, denominated in `WAD`.
    /// See: https://en.wikipedia.org/wiki/Lambert_W_function
    /// a.k.a. Product log function. This is an approximation of the principal branch.
    /// Note: This function is an approximation. Monotonically increasing.
    function lambertW0Wad(int256 x) internal pure returns (int256 w) {
        // forgefmt: disable-next-item
        unchecked {
            if ((w = x) <= -367879441171442322) revert OutOfDomain(); // `x` less than `-1/e`.
            (int256 wad, int256 p) = (int256(WAD), x);
            uint256 c; // Whether we need to avoid catastrophic cancellation.
            uint256 i = 4; // Number of iterations.
            if (w <= 0x1ffffffffffff) {
                if (-0x4000000000000 <= w) {
                    i = 1; // Inputs near zero only take one step to converge.
                } else if (w <= -0x3ffffffffffffff) {
                    i = 32; // Inputs near `-1/e` take very long to converge.
                }
            } else if (uint256(w >> 63) == uint256(0)) {
                /// @solidity memory-safe-assembly
                assembly {
                    // Inline log2 for more performance, since the range is small.
                    let v := shr(49, w)
                    let l := shl(3, lt(0xff, v))
                    l := add(or(l, byte(and(0x1f, shr(shr(l, v), 0x8421084210842108cc6318c6db6d54be)),
                        0x0706060506020504060203020504030106050205030304010505030400000000)), 49)
                    w := sdiv(shl(l, 7), byte(sub(l, 31), 0x0303030303030303040506080c13))
                    c := gt(l, 60)
                    i := add(2, add(gt(l, 53), c))
                }
            } else {
                int256 ll = lnWad(w = lnWad(w));
                /// @solidity memory-safe-assembly
                assembly {
                    // `w = ln(x) - ln(ln(x)) + b * ln(ln(x)) / ln(x)`.
                    w := add(sdiv(mul(ll, 1023715080943847266), w), sub(w, ll))
                    i := add(3, iszero(shr(68, x)))
                    c := iszero(shr(143, x))
                }
                if (c == uint256(0)) {
                    do { // If `x` is big, use Newton's so that intermediate values won't overflow.
                        int256 e = expWad(w);
                        /// @solidity memory-safe-assembly
                        assembly {
                            let t := mul(w, div(e, wad))
                            w := sub(w, sdiv(sub(t, x), div(add(e, t), wad)))
                        }
                        if (p <= w) break;
                        p = w;
                    } while (--i != uint256(0));
                    /// @solidity memory-safe-assembly
                    assembly {
                        w := sub(w, sgt(w, 2))
                    }
                    return w;
                }
            }
            do { // Otherwise, use Halley's for faster convergence.
                int256 e = expWad(w);
                /// @solidity memory-safe-assembly
                assembly {
                    let t := add(w, wad)
                    let s := sub(mul(w, e), mul(x, wad))
                    w := sub(w, sdiv(mul(s, wad), sub(mul(e, t), sdiv(mul(add(t, wad), s), add(t, t)))))
                }
                if (p <= w) break;
                p = w;
            } while (--i != c);
            /// @solidity memory-safe-assembly
            assembly {
                w := sub(w, sgt(w, 2))
            }
            // For certain ranges of `x`, we'll use the quadratic-rate recursive formula of
            // R. Iacono and J.P. Boyd for the last iteration, to avoid catastrophic cancellation.
            if (c == uint256(0)) return w;
            int256 t = w | 1;
            /// @solidity memory-safe-assembly
            assembly {
                x := sdiv(mul(x, wad), t)
            }
            x = (t * (wad + lnWad(x)));
            /// @solidity memory-safe-assembly
            assembly {
                w := sdiv(x, add(wad, t))
            }
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  GENERAL NUMBER UTILITIES                  */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns `a * b == x * y`, with full precision.
    function fullMulEq(uint256 a, uint256 b, uint256 x, uint256 y)
        internal
        pure
        returns (bool result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            result := and(eq(mul(a, b), mul(x, y)), eq(mulmod(x, y, not(0)), mulmod(a, b, not(0))))
        }
    }

    /// @dev Calculates `floor(x * y / d)` with full precision.
    /// Throws if result overflows a uint256 or when `d` is zero.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/21/muldiv
    function fullMulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // 512-bit multiply `[p1 p0] = x * y`.
            // 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 = p1 * 2**256 + p0`.

            // Temporarily use `z` as `p0` to save gas.
            z := mul(x, y) // Lower 256 bits of `x * y`.
            for {} 1 {} {
                // If overflows.
                if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
                    let mm := mulmod(x, y, not(0))
                    let p1 := sub(mm, add(z, lt(mm, z))) // Upper 256 bits of `x * y`.

                    /*------------------- 512 by 256 division --------------------*/

                    // Make division exact by subtracting the remainder from `[p1 p0]`.
                    let r := mulmod(x, y, d) // Compute remainder using mulmod.
                    let t := and(d, sub(0, d)) // The least significant bit of `d`. `t >= 1`.
                    // Make sure `z` is less than `2**256`. Also prevents `d == 0`.
                    // Placing the check here seems to give more optimal stack operations.
                    if iszero(gt(d, p1)) {
                        mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
                        revert(0x1c, 0x04)
                    }
                    d := div(d, t) // Divide `d` by `t`, which is a power of two.
                    // Invert `d mod 2**256`
                    // Now that `d` is an odd number, it has an inverse
                    // modulo `2**256` such that `d * inv = 1 mod 2**256`.
                    // Compute the inverse by starting with a seed that is correct
                    // correct for four bits. That is, `d * inv = 1 mod 2**4`.
                    let inv := xor(2, mul(3, d))
                    // 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 := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**8
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**16
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**32
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**64
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**128
                    z :=
                        mul(
                            // Divide [p1 p0] by the factors of two.
                            // Shift in bits from `p1` into `p0`. For this we need
                            // to flip `t` such that it is `2**256 / t`.
                            or(mul(sub(p1, gt(r, z)), add(div(sub(0, t), t), 1)), div(sub(z, r), t)),
                            mul(sub(2, mul(d, inv)), inv) // inverse mod 2**256
                        )
                    break
                }
                z := div(z, d)
                break
            }
        }
    }

    /// @dev Calculates `floor(x * y / d)` with full precision.
    /// Behavior is undefined if `d` is zero or the final result cannot fit in 256 bits.
    /// Performs the full 512 bit calculation regardless.
    function fullMulDivUnchecked(uint256 x, uint256 y, uint256 d)
        internal
        pure
        returns (uint256 z)
    {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            let mm := mulmod(x, y, not(0))
            let p1 := sub(mm, add(z, lt(mm, z)))
            let t := and(d, sub(0, d))
            let r := mulmod(x, y, d)
            d := div(d, t)
            let inv := xor(2, mul(3, d))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            z :=
                mul(
                    or(mul(sub(p1, gt(r, z)), add(div(sub(0, t), t), 1)), div(sub(z, r), t)),
                    mul(sub(2, mul(d, inv)), inv)
                )
        }
    }

    /// @dev Calculates `floor(x * y / d)` with full precision, rounded up.
    /// Throws if result overflows a uint256 or when `d` is zero.
    /// Credit to Uniswap-v3-core under MIT license:
    /// https://github.com/Uniswap/v3-core/blob/main/contracts/libraries/FullMath.sol
    function fullMulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        z = fullMulDiv(x, y, d);
        /// @solidity memory-safe-assembly
        assembly {
            if mulmod(x, y, d) {
                z := add(z, 1)
                if iszero(z) {
                    mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
                    revert(0x1c, 0x04)
                }
            }
        }
    }

    /// @dev Calculates `floor(x * y / 2 ** n)` with full precision.
    /// Throws if result overflows a uint256.
    /// Credit to Philogy under MIT license:
    /// https://github.com/SorellaLabs/angstrom/blob/main/contracts/src/libraries/X128MathLib.sol
    function fullMulDivN(uint256 x, uint256 y, uint8 n) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Temporarily use `z` as `p0` to save gas.
            z := mul(x, y) // Lower 256 bits of `x * y`. We'll call this `z`.
            for {} 1 {} {
                if iszero(or(iszero(x), eq(div(z, x), y))) {
                    let k := and(n, 0xff) // `n`, cleaned.
                    let mm := mulmod(x, y, not(0))
                    let p1 := sub(mm, add(z, lt(mm, z))) // Upper 256 bits of `x * y`.
                    //         |      p1     |      z     |
                    // Before: | p1_0 ¦ p1_1 | z_0  ¦ z_1 |
                    // Final:  |   0  ¦ p1_0 | p1_1 ¦ z_0 |
                    // Check that final `z` doesn't overflow by checking that p1_0 = 0.
                    if iszero(shr(k, p1)) {
                        z := add(shl(sub(256, k), p1), shr(k, z))
                        break
                    }
                    mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
                    revert(0x1c, 0x04)
                }
                z := shr(and(n, 0xff), z)
                break
            }
        }
    }

    /// @dev Returns `floor(x * y / d)`.
    /// Reverts if `x * y` overflows, or `d` is zero.
    function mulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require(d != 0 && (y == 0 || x <= type(uint256).max / y))`.
            if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
                mstore(0x00, 0xad251c27) // `MulDivFailed()`.
                revert(0x1c, 0x04)
            }
            z := div(z, d)
        }
    }

    /// @dev Returns `ceil(x * y / d)`.
    /// Reverts if `x * y` overflows, or `d` is zero.
    function mulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require(d != 0 && (y == 0 || x <= type(uint256).max / y))`.
            if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
                mstore(0x00, 0xad251c27) // `MulDivFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(z, d))), div(z, d))
        }
    }

    /// @dev Returns `x`, the modular multiplicative inverse of `a`, such that `(a * x) % n == 1`.
    function invMod(uint256 a, uint256 n) internal pure returns (uint256 x) {
        /// @solidity memory-safe-assembly
        assembly {
            let g := n
            let r := mod(a, n)
            for { let y := 1 } 1 {} {
                let q := div(g, r)
                let t := g
                g := r
                r := sub(t, mul(r, q))
                let u := x
                x := y
                y := sub(u, mul(y, q))
                if iszero(r) { break }
            }
            x := mul(eq(g, 1), add(x, mul(slt(x, 0), n)))
        }
    }

    /// @dev Returns `ceil(x / d)`.
    /// Reverts if `d` is zero.
    function divUp(uint256 x, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(d) {
                mstore(0x00, 0x65244e4e) // `DivFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(x, d))), div(x, d))
        }
    }

    /// @dev Returns `max(0, x - y)`. Alias for `saturatingSub`.
    function zeroFloorSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(gt(x, y), sub(x, y))
        }
    }

    /// @dev Returns `max(0, x - y)`.
    function saturatingSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(gt(x, y), sub(x, y))
        }
    }

    /// @dev Returns `min(2 ** 256 - 1, x + y)`.
    function saturatingAdd(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := or(sub(0, lt(add(x, y), x)), add(x, y))
        }
    }

    /// @dev Returns `min(2 ** 256 - 1, x * y)`.
    function saturatingMul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := or(sub(or(iszero(x), eq(div(mul(x, y), x), y)), 1), mul(x, y))
        }
    }

    /// @dev Returns `condition ? x : y`, without branching.
    function ternary(bool condition, uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), iszero(condition)))
        }
    }

    /// @dev Returns `condition ? x : y`, without branching.
    function ternary(bool condition, bytes32 x, bytes32 y) internal pure returns (bytes32 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), iszero(condition)))
        }
    }

    /// @dev Returns `condition ? x : y`, without branching.
    function ternary(bool condition, address x, address y) internal pure returns (address z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), iszero(condition)))
        }
    }

    /// @dev Returns `x != 0 ? x : y`, without branching.
    function coalesce(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := or(x, mul(y, iszero(x)))
        }
    }

    /// @dev Returns `x != bytes32(0) ? x : y`, without branching.
    function coalesce(bytes32 x, bytes32 y) internal pure returns (bytes32 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := or(x, mul(y, iszero(x)))
        }
    }

    /// @dev Returns `x != address(0) ? x : y`, without branching.
    function coalesce(address x, address y) internal pure returns (address z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := or(x, mul(y, iszero(shl(96, x))))
        }
    }

    /// @dev Exponentiate `x` to `y` by squaring, denominated in base `b`.
    /// Reverts if the computation overflows.
    function rpow(uint256 x, uint256 y, uint256 b) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(b, iszero(y)) // `0 ** 0 = 1`. Otherwise, `0 ** n = 0`.
            if x {
                z := xor(b, mul(xor(b, x), and(y, 1))) // `z = isEven(y) ? scale : x`
                let half := shr(1, b) // Divide `b` by 2.
                // Divide `y` by 2 every iteration.
                for { y := shr(1, y) } y { y := shr(1, y) } {
                    let xx := mul(x, x) // Store x squared.
                    let xxRound := add(xx, half) // Round to the nearest number.
                    // Revert if `xx + half` overflowed, or if `x ** 2` overflows.
                    if or(lt(xxRound, xx), shr(128, x)) {
                        mstore(0x00, 0x49f7642b) // `RPowOverflow()`.
                        revert(0x1c, 0x04)
                    }
                    x := div(xxRound, b) // Set `x` to scaled `xxRound`.
                    // If `y` is odd:
                    if and(y, 1) {
                        let zx := mul(z, x) // Compute `z * x`.
                        let zxRound := add(zx, half) // Round to the nearest number.
                        // If `z * x` overflowed or `zx + half` overflowed:
                        if or(xor(div(zx, x), z), lt(zxRound, zx)) {
                            // Revert if `x` is non-zero.
                            if x {
                                mstore(0x00, 0x49f7642b) // `RPowOverflow()`.
                                revert(0x1c, 0x04)
                            }
                        }
                        z := div(zxRound, b) // Return properly scaled `zxRound`.
                    }
                }
            }
        }
    }

    /// @dev Returns the square root of `x`, rounded down.
    function sqrt(uint256 x) internal pure returns (uint256 z) {
        /// @solidity memor