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// SPDX-License-Identifier: -
// License: https://license.sonic.market/LICENSE.pdf

pragma solidity ^0.8.20;

import {Ownable2Step, Ownable} from "@openzeppelin/contracts/access/Ownable2Step.sol";
import {SafeCast} from "@openzeppelin/contracts/utils/math/SafeCast.sol";

import {IBookManager} from "./interfaces/IBookManager.sol";
import {ILocker} from "./interfaces/ILocker.sol";
import {IHooks} from "./interfaces/IHooks.sol";
import {BookId, BookIdLibrary} from "./libraries/BookId.sol";
import {Book} from "./libraries/Book.sol";
import {Currency, CurrencyLibrary} from "./libraries/Currency.sol";
import {FeePolicy, FeePolicyLibrary} from "./libraries/FeePolicy.sol";
import {Tick, TickLibrary} from "./libraries/Tick.sol";
import {OrderId, OrderIdLibrary} from "./libraries/OrderId.sol";
import {Lockers} from "./libraries/Lockers.sol";
import {CurrencyDelta} from "./libraries/CurrencyDelta.sol";
import {ERC721Permit} from "./libraries/ERC721Permit.sol";
import {Hooks} from "./libraries/Hooks.sol";

contract BookManager is IBookManager, Ownable2Step, ERC721Permit {
    using SafeCast for *;
    using BookIdLibrary for IBookManager.BookKey;
    using TickLibrary for Tick;
    using Book for Book.State;
    using OrderIdLibrary for OrderId;
    using CurrencyLibrary for Currency;
    using FeePolicyLibrary for FeePolicy;
    using Hooks for IHooks;

    string public override baseURI; // slot 10
    string public override contractURI;
    address public override defaultProvider;

    mapping(Currency currency => uint256) public override reservesOf;
    mapping(BookId id => Book.State) internal _books;
    mapping(address provider => bool) public override isWhitelisted;
    mapping(address provider => mapping(Currency currency => uint256 amount)) public override tokenOwed;

    constructor(
        address owner_,
        address defaultProvider_,
        string memory baseURI_,
        string memory contractURI_,
        string memory name_,
        string memory symbol_
    ) Ownable(owner_) ERC721Permit(name_, symbol_, "2") {
        _setDefaultProvider(defaultProvider_);
        baseURI = baseURI_;
        contractURI = contractURI_;
    }

    modifier onlyByLocker() {
        _checkLocker(msg.sender);
        _;
    }

    function checkAuthorized(address owner, address spender, uint256 tokenId) external view {
        _checkAuthorized(owner, spender, tokenId);
    }

    function _checkLocker(address caller) internal view {
        address locker = Lockers.getCurrentLocker();
        IHooks hook = Lockers.getCurrentHook();
        if (caller == locker) return;
        if (caller == address(hook)) return;
        revert LockedBy(locker, address(hook));
    }

    function getBookKey(BookId id) external view returns (BookKey memory) {
        return _books[id].key;
    }

    function getOrder(OrderId id) external view returns (OrderInfo memory) {
        (BookId bookId, Tick tick, uint40 orderIndex) = id.decode();
        Book.State storage book = _books[bookId];
        Book.Order memory order = book.getOrder(tick, orderIndex);
        uint64 claimable = book.calculateClaimableUnit(tick, orderIndex);
        unchecked {
            return OrderInfo({provider: order.provider, open: order.pending - claimable, claimable: claimable});
        }
    }

    function open(BookKey calldata key, bytes calldata hookData) external onlyByLocker {
        // @dev Also, the book opener should set unit size at least circulatingTotalSupply / type(uint64).max to avoid overflow.
        //      But it is not checked here because it is not possible to check it without knowing circulatingTotalSupply.
        if (key.unitSize == 0) revert InvalidUnitSize();

        FeePolicy makerPolicy = key.makerPolicy;
        FeePolicy takerPolicy = key.takerPolicy;
        if (!(makerPolicy.isValid() && takerPolicy.isValid())) revert InvalidFeePolicy();
        unchecked {
            if (makerPolicy.rate() + takerPolicy.rate() < 0) revert InvalidFeePolicy();
        }
        if (makerPolicy.rate() < 0 || takerPolicy.rate() < 0) {
            if (makerPolicy.usesQuote() != takerPolicy.usesQuote()) revert InvalidFeePolicy();
        }
        IHooks hooks = key.hooks;
        if (!hooks.isValidHookAddress()) revert Hooks.HookAddressNotValid(address(hooks));

        hooks.beforeOpen(key, hookData);

        BookId id = key.toId();
        _books[id].open(key);

        emit Open(id, key.base, key.quote, key.unitSize, makerPolicy, takerPolicy, hooks);

        hooks.afterOpen(key, hookData);
    }

    function lock(address locker, bytes calldata data) external returns (bytes memory result) {
        // Add the locker to the stack
        Lockers.push(locker, msg.sender);

        // The locker does everything in this callback, including paying what they owe via calls to settle
        result = ILocker(locker).lockAcquired(msg.sender, data);

        // Remove the locker from the stack
        Lockers.pop();

        (uint128 length, uint128 nonzeroDeltaCount) = Lockers.lockData();
        // @dev The locker must settle all currency balances to zero.
        if (length == 0 && nonzeroDeltaCount != 0) revert CurrencyNotSettled();
    }

    function getCurrencyDelta(address locker, Currency currency) external view returns (int256) {
        return CurrencyDelta.get(locker, currency);
    }

    function getLock(uint256 i) external view returns (address, address) {
        return (Lockers.getLocker(i), Lockers.getLockCaller(i));
    }

    function getLockData() external view returns (uint128, uint128) {
        return Lockers.lockData();
    }

    function getDepth(BookId id, Tick tick) external view returns (uint64) {
        return _books[id].depth(tick);
    }

    function getHighest(BookId id) external view returns (Tick) {
        return _books[id].highest();
    }

    function maxLessThan(BookId id, Tick tick) external view returns (Tick) {
        return _books[id].maxLessThan(tick);
    }

    function isOpened(BookId id) external view returns (bool) {
        return _books[id].isOpened();
    }

    function isEmpty(BookId id) external view returns (bool) {
        return _books[id].isEmpty();
    }

    function encodeBookKey(BookKey calldata key) external pure returns (BookId) {
        return key.toId();
    }

    function make(MakeParams calldata params, bytes calldata hookData)
        external
        onlyByLocker
        returns (OrderId id, uint256 quoteAmount)
    {
        if (params.provider != address(0) && !isWhitelisted[params.provider]) revert InvalidProvider(params.provider);
        params.tick.validateTick();
        BookId bookId = params.key.toId();
        Book.State storage book = _books[bookId];
        book.checkOpened();

        params.key.hooks.beforeMake(params, hookData);

        uint40 orderIndex = book.make(params.tick, params.unit, params.provider);
        id = OrderIdLibrary.encode(bookId, params.tick, orderIndex);
        int256 quoteDelta;
        unchecked {
            // @dev uint64 * uint64 < type(uint256).max
            quoteAmount = uint256(params.unit) * params.key.unitSize;

            // @dev 0 < uint64 * uint64 + rate * uint64 * uint64 < type(int256).max
            quoteDelta = int256(quoteAmount);
            if (params.key.makerPolicy.usesQuote()) {
                quoteDelta += params.key.makerPolicy.calculateFee(quoteAmount, false);
                quoteAmount = uint256(quoteDelta);
            }
        }

        _accountDelta(params.key.quote, -quoteDelta);

        _mint(msg.sender, OrderId.unwrap(id));

        emit Make(bookId, msg.sender, params.tick, orderIndex, params.unit, params.provider);

        params.key.hooks.afterMake(params, id, hookData);
    }

    function take(TakeParams calldata params, bytes calldata hookData)
        external
        onlyByLocker
        returns (uint256 quoteAmount, uint256 baseAmount)
    {
        params.tick.validateTick();
        BookId bookId = params.key.toId();
        Book.State storage book = _books[bookId];
        book.checkOpened();

        params.key.hooks.beforeTake(params, hookData);

        uint64 takenUnit = book.take(params.tick, params.maxUnit);
        unchecked {
            quoteAmount = uint256(takenUnit) * params.key.unitSize;
        }
        baseAmount = params.tick.quoteToBase(quoteAmount, true);

        int256 quoteDelta = int256(quoteAmount);
        int256 baseDelta = baseAmount.toInt256();
        if (params.key.takerPolicy.usesQuote()) {
            quoteDelta -= params.key.takerPolicy.calculateFee(quoteAmount, false);
            quoteAmount = uint256(quoteDelta);
        } else {
            baseDelta += params.key.takerPolicy.calculateFee(baseAmount, false);
            baseAmount = uint256(baseDelta);
        }
        _accountDelta(params.key.quote, quoteDelta);
        _accountDelta(params.key.base, -baseDelta);

        emit Take(bookId, msg.sender, params.tick, takenUnit);

        params.key.hooks.afterTake(params, takenUnit, hookData);
    }

    function cancel(CancelParams calldata params, bytes calldata hookData)
        external
        onlyByLocker
        returns (uint256 canceledAmount)
    {
        _checkAuthorized(_ownerOf(OrderId.unwrap(params.id)), msg.sender, OrderId.unwrap(params.id));

        Book.State storage book = _books[params.id.getBookId()];
        BookKey memory key = book.key;

        key.hooks.beforeCancel(params, hookData);

        (uint64 canceledUnit, uint64 pendingUnit) = book.cancel(params.id, params.toUnit);

        unchecked {
            canceledAmount = uint256(canceledUnit) * key.unitSize;
            if (key.makerPolicy.usesQuote()) {
                int256 quoteFee = key.makerPolicy.calculateFee(canceledAmount, true);
                canceledAmount = uint256(int256(canceledAmount) + quoteFee);
            }
        }

        if (pendingUnit == 0) _burn(OrderId.unwrap(params.id));

        _accountDelta(key.quote, int256(canceledAmount));

        emit Cancel(params.id, canceledUnit);

        key.hooks.afterCancel(params, canceledUnit, hookData);
    }

    function claim(OrderId id, bytes calldata hookData) external onlyByLocker returns (uint256 claimedAmount) {
        _checkAuthorized(_ownerOf(OrderId.unwrap(id)), msg.sender, OrderId.unwrap(id));

        Tick tick;
        uint40 orderIndex;
        Book.State storage book;
        {
            BookId bookId;
            (bookId, tick, orderIndex) = id.decode();
            book = _books[bookId];
        }
        IBookManager.BookKey memory key = book.key;

        key.hooks.beforeClaim(id, hookData);

        uint64 claimedUnit = book.claim(tick, orderIndex);

        int256 quoteFee;
        int256 baseFee;
        {
            uint256 claimedInQuote;
            unchecked {
                claimedInQuote = uint256(claimedUnit) * key.unitSize;
            }
            claimedAmount = tick.quoteToBase(claimedInQuote, false);

            FeePolicy makerPolicy = key.makerPolicy;
            FeePolicy takerPolicy = key.takerPolicy;
            if (takerPolicy.usesQuote()) {
                quoteFee = takerPolicy.calculateFee(claimedInQuote, true);
            } else {
                baseFee = takerPolicy.calculateFee(claimedAmount, true);
            }

            if (makerPolicy.usesQuote()) {
                quoteFee += makerPolicy.calculateFee(claimedInQuote, true);
            } else {
                int256 makeFee = makerPolicy.calculateFee(claimedAmount, false);
                baseFee += makeFee;
                claimedAmount = makeFee > 0 ? claimedAmount - uint256(makeFee) : claimedAmount + uint256(-makeFee);
            }
        }

        Book.Order memory order = book.getOrder(tick, orderIndex);
        address provider = order.provider;
        if (provider == address(0)) provider = defaultProvider;
        if (quoteFee > 0) tokenOwed[provider][key.quote] += quoteFee.toUint256();
        if (baseFee > 0) tokenOwed[provider][key.base] += baseFee.toUint256();

        if (order.pending == 0) _burn(OrderId.unwrap(id));

        _accountDelta(key.base, claimedAmount.toInt256());

        emit Claim(id, claimedUnit);

        key.hooks.afterClaim(id, claimedUnit, hookData);
    }

    function collect(address recipient, Currency currency) external returns (uint256 amount) {
        amount = tokenOwed[msg.sender][currency];
        tokenOwed[msg.sender][currency] = 0;
        reservesOf[currency] -= amount;
        currency.transfer(recipient, amount);
        emit Collect(msg.sender, recipient, currency, amount);
    }

    function withdraw(Currency currency, address to, uint256 amount) external onlyByLocker {
        if (amount > 0) {
            _accountDelta(currency, -amount.toInt256());
            reservesOf[currency] -= amount;
            currency.transfer(to, amount);
        }
    }

    function settle(Currency currency) external payable onlyByLocker returns (uint256 paid) {
        uint256 reservesBefore = reservesOf[currency];
        reservesOf[currency] = currency.balanceOfSelf();
        paid = reservesOf[currency] - reservesBefore;
        // subtraction must be safe
        _accountDelta(currency, paid.toInt256());
    }

    function whitelist(address provider) external onlyOwner {
        isWhitelisted[provider] = true;
        emit Whitelist(provider);
    }

    function delist(address provider) external onlyOwner {
        isWhitelisted[provider] = false;
        emit Delist(provider);
    }

    function setDefaultProvider(address newDefaultProvider) external onlyOwner {
        _setDefaultProvider(newDefaultProvider);
    }

    function _setDefaultProvider(address newDefaultProvider) internal {
        defaultProvider = newDefaultProvider;
        emit SetDefaultProvider(newDefaultProvider);
    }

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

    function _accountDelta(Currency currency, int256 delta) internal {
        if (delta == 0) return;

        address locker = Lockers.getCurrentLocker();
        int256 next = CurrencyDelta.add(locker, currency, delta);

        if (next == 0) Lockers.decrementNonzeroDeltaCount();
        else if (next == delta) Lockers.incrementNonzeroDeltaCount();
    }

    function load(bytes32 slot) external view returns (bytes32 value) {
        assembly {
            value := sload(slot)
        }
    }

    function load(bytes32 startSlot, uint256 nSlot) external view returns (bytes memory value) {
        value = new bytes(32 * nSlot);

        assembly {
            for { let i := 0 } lt(i, nSlot) { i := add(i, 1) } {
                mstore(add(value, mul(add(i, 1), 32)), sload(add(startSlot, i)))
            }
        }
    }

    receive() external payable {}
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (access/Ownable.sol)

pragma solidity ^0.8.20;

import {Context} from "../utils/Context.sol";

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

    /**
     * @dev The caller account is not authorized to perform an operation.
     */
    error OwnableUnauthorizedAccount(address account);

    /**
     * @dev The owner is not a valid owner account. (eg. `address(0)`)
     */
    error OwnableInvalidOwner(address owner);

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

    /**
     * @dev Initializes the contract setting the address provided by the deployer as the initial owner.
     */
    constructor(address initialOwner) {
        if (initialOwner == address(0)) {
            revert OwnableInvalidOwner(address(0));
        }
        _transferOwnership(initialOwner);
    }

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

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

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        if (owner() != _msgSender()) {
            revert OwnableUnauthorizedAccount(_msgSender());
        }
    }

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

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        if (newOwner == address(0)) {
            revert OwnableInvalidOwner(address(0));
        }
        _transferOwnership(newOwner);
    }

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (access/Ownable2Step.sol)

pragma solidity ^0.8.20;

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

/**
 * @dev Contract module which provides access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * This extension of the {Ownable} contract includes a two-step mechanism to transfer
 * ownership, where the new owner must call {acceptOwnership} in order to replace the
 * old one. This can help prevent common mistakes, such as transfers of ownership to
 * incorrect accounts, or to contracts that are unable to interact with the
 * permission system.
 *
 * The initial owner is specified at deployment time in the constructor for `Ownable`. This
 * can later be changed with {transferOwnership} and {acceptOwnership}.
 *
 * This module is used through inheritance. It will make available all functions
 * from parent (Ownable).
 */
abstract contract Ownable2Step is Ownable {
    address private _pendingOwner;

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

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

    /**
     * @dev Starts the ownership transfer of the contract to a new account. Replaces the pending transfer if there is one.
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual override onlyOwner {
        _pendingOwner = newOwner;
        emit OwnershipTransferStarted(owner(), newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`) and deletes any pending owner.
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual override {
        delete _pendingOwner;
        super._transferOwnership(newOwner);
    }

    /**
     * @dev The new owner accepts the ownership transfer.
     */
    function acceptOwnership() public virtual {
        address sender = _msgSender();
        if (pendingOwner() != sender) {
            revert OwnableUnauthorizedAccount(sender);
        }
        _transferOwnership(sender);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/draft-IERC6093.sol)
pragma solidity ^0.8.20;

/**
 * @dev Standard ERC-20 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-20 tokens.
 */
interface IERC20Errors {
    /**
     * @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param balance Current balance for the interacting account.
     * @param needed Minimum amount required to perform a transfer.
     */
    error ERC20InsufficientBalance(address sender, uint256 balance, uint256 needed);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC20InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC20InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `spender`’s `allowance`. Used in transfers.
     * @param spender Address that may be allowed to operate on tokens without being their owner.
     * @param allowance Amount of tokens a `spender` is allowed to operate with.
     * @param needed Minimum amount required to perform a transfer.
     */
    error ERC20InsufficientAllowance(address spender, uint256 allowance, uint256 needed);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC20InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `spender` to be approved. Used in approvals.
     * @param spender Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC20InvalidSpender(address spender);
}

/**
 * @dev Standard ERC-721 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-721 tokens.
 */
interface IERC721Errors {
    /**
     * @dev Indicates that an address can't be an owner. For example, `address(0)` is a forbidden owner in ERC-20.
     * Used in balance queries.
     * @param owner Address of the current owner of a token.
     */
    error ERC721InvalidOwner(address owner);

    /**
     * @dev Indicates a `tokenId` whose `owner` is the zero address.
     * @param tokenId Identifier number of a token.
     */
    error ERC721NonexistentToken(uint256 tokenId);

    /**
     * @dev Indicates an error related to the ownership over a particular token. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param tokenId Identifier number of a token.
     * @param owner Address of the current owner of a token.
     */
    error ERC721IncorrectOwner(address sender, uint256 tokenId, address owner);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC721InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC721InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `operator`’s approval. Used in transfers.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     * @param tokenId Identifier number of a token.
     */
    error ERC721InsufficientApproval(address operator, uint256 tokenId);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC721InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `operator` to be approved. Used in approvals.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC721InvalidOperator(address operator);
}

/**
 * @dev Standard ERC-1155 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-1155 tokens.
 */
interface IERC1155Errors {
    /**
     * @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param balance Current balance for the interacting account.
     * @param needed Minimum amount required to perform a transfer.
     * @param tokenId Identifier number of a token.
     */
    error ERC1155InsufficientBalance(address sender, uint256 balance, uint256 needed, uint256 tokenId);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC1155InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC1155InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `operator`’s approval. Used in transfers.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     * @param owner Address of the current owner of a token.
     */
    error ERC1155MissingApprovalForAll(address operator, address owner);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC1155InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `operator` to be approved. Used in approvals.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC1155InvalidOperator(address operator);

    /**
     * @dev Indicates an array length mismatch between ids and values in a safeBatchTransferFrom operation.
     * Used in batch transfers.
     * @param idsLength Length of the array of token identifiers
     * @param valuesLength Length of the array of token amounts
     */
    error ERC1155InvalidArrayLength(uint256 idsLength, uint256 valuesLength);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC1271.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface of the ERC-1271 standard signature validation method for
 * contracts as defined in https://eips.ethereum.org/EIPS/eip-1271[ERC-1271].
 */
interface IERC1271 {
    /**
     * @dev Should return whether the signature provided is valid for the provided data
     * @param hash      Hash of the data to be signed
     * @param signature Signature byte array associated with _data
     */
    function isValidSignature(bytes32 hash, bytes memory signature) external view returns (bytes4 magicValue);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC5267.sol)

pragma solidity ^0.8.20;

interface IERC5267 {
    /**
     * @dev MAY be emitted to signal that the domain could have changed.
     */
    event EIP712DomainChanged();

    /**
     * @dev returns the fields and values that describe the domain separator used by this contract for EIP-712
     * signature.
     */
    function eip712Domain()
        external
        view
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        );
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface of the ERC-20 standard as defined in the ERC.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the value of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the value of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves a `value` amount of tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 value) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets a `value` amount of tokens as the allowance of `spender` over the
     * caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 value) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to` using the
     * allowance mechanism. `value` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(address from, address to, uint256 value) external returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC721/extensions/IERC721Metadata.sol)

pragma solidity ^0.8.20;

import {IERC721} from "../IERC721.sol";

/**
 * @title ERC-721 Non-Fungible Token Standard, optional metadata extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721Metadata is IERC721 {
    /**
     * @dev Returns the token collection name.
     */
    function name() external view returns (string memory);

    /**
     * @dev Returns the token collection symbol.
     */
    function symbol() external view returns (string memory);

    /**
     * @dev Returns the Uniform Resource Identifier (URI) for `tokenId` token.
     */
    function tokenURI(uint256 tokenId) external view returns (string memory);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC721/IERC721.sol)

pragma solidity ^0.8.20;

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);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC721/IERC721Receiver.sol)

pragma solidity ^0.8.20;

/**
 * @title ERC-721 token receiver interface
 * @dev Interface for any contract that wants to support safeTransfers
 * from ERC-721 asset contracts.
 */
interface IERC721Receiver {
    /**
     * @dev Whenever an {IERC721} `tokenId` token is transferred to this contract via {IERC721-safeTransferFrom}
     * by `operator` from `from`, this function is called.
     *
     * It must return its Solidity selector to confirm the token transfer.
     * If any other value is returned or the interface is not implemented by the recipient, the transfer will be
     * reverted.
     *
     * The selector can be obtained in Solidity with `IERC721Receiver.onERC721Received.selector`.
     */
    function onERC721Received(
        address operator,
        address from,
        uint256 tokenId,
        bytes calldata data
    ) external returns (bytes4);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.1) (utils/Context.sol)

pragma solidity ^0.8.20;

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

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

    function _contextSuffixLength() internal view virtual returns (uint256) {
        return 0;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.20;

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

    /**
     * @dev The signature derives the `address(0)`.
     */
    error ECDSAInvalidSignature();

    /**
     * @dev The signature has an invalid length.
     */
    error ECDSAInvalidSignatureLength(uint256 length);

    /**
     * @dev The signature has an S value that is in the upper half order.
     */
    error ECDSAInvalidSignatureS(bytes32 s);

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with `signature` or an error. This will not
     * return address(0) without also returning an error description. Errors are documented using an enum (error type)
     * and a bytes32 providing additional information about the error.
     *
     * If no error is returned, then the address can be used for verification purposes.
     *
     * The `ecrecover` EVM precompile allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {MessageHashUtils-toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError, bytes32) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            /// @solidity memory-safe-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength, bytes32(signature.length));
        }
    }

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

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[ERC-2098 short signatures]
     */
    function tryRecover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address, RecoverError, bytes32) {
        unchecked {
            bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
            // We do not check for an overflow here since the shift operation results in 0 or 1.
            uint8 v = uint8((uint256(vs) >> 255) + 27);
            return tryRecover(hash, v, r, s);
        }
    }

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

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

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature, bytes32(0));
        }

        return (signer, RecoverError.NoError, bytes32(0));
    }

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

    /**
     * @dev Optionally reverts with the corresponding custom error according to the `error` argument provided.
     */
    function _throwError(RecoverError error, bytes32 errorArg) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert ECDSAInvalidSignature();
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert ECDSAInvalidSignatureLength(uint256(errorArg));
        } else if (error == RecoverError.InvalidSignatureS) {
            revert ECDSAInvalidSignatureS(errorArg);
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/cryptography/EIP712.sol)

pragma solidity ^0.8.20;

import {MessageHashUtils} from "./MessageHashUtils.sol";
import {ShortStrings, ShortString} from "../ShortStrings.sol";
import {IERC5267} from "../../interfaces/IERC5267.sol";

/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP-712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding scheme specified in the EIP requires a domain separator and a hash of the typed structured data, whose
 * encoding is very generic and therefore its implementation in Solidity is not feasible, thus this contract
 * does not implement the encoding itself. Protocols need to implement the type-specific encoding they need in order to
 * produce the hash of their typed data using a combination of `abi.encode` and `keccak256`.
 *
 * This contract implements the EIP-712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
 * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
 * ({_hashTypedDataV4}).
 *
 * The implementation of the domain separator was designed to be as efficient as possible while still properly updating
 * the chain id to protect against replay attacks on an eventual fork of the chain.
 *
 * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
 * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].
 *
 * NOTE: In the upgradeable version of this contract, the cached values will correspond to the address, and the domain
 * separator of the implementation contract. This will cause the {_domainSeparatorV4} function to always rebuild the
 * separator from the immutable values, which is cheaper than accessing a cached version in cold storage.
 *
 * @custom:oz-upgrades-unsafe-allow state-variable-immutable
 */
abstract contract EIP712 is IERC5267 {
    using ShortStrings for *;

    bytes32 private constant TYPE_HASH =
        keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)");

    // Cache the domain separator as an immutable value, but also store the chain id that it corresponds to, in order to
    // invalidate the cached domain separator if the chain id changes.
    bytes32 private immutable _cachedDomainSeparator;
    uint256 private immutable _cachedChainId;
    address private immutable _cachedThis;

    bytes32 private immutable _hashedName;
    bytes32 private immutable _hashedVersion;

    ShortString private immutable _name;
    ShortString private immutable _version;
    string private _nameFallback;
    string private _versionFallback;

    /**
     * @dev Initializes the domain separator and parameter caches.
     *
     * The meaning of `name` and `version` is specified in
     * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP-712]:
     *
     * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
     * - `version`: the current major version of the signing domain.
     *
     * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
     * contract upgrade].
     */
    constructor(string memory name, string memory version) {
        _name = name.toShortStringWithFallback(_nameFallback);
        _version = version.toShortStringWithFallback(_versionFallback);
        _hashedName = keccak256(bytes(name));
        _hashedVersion = keccak256(bytes(version));

        _cachedChainId = block.chainid;
        _cachedDomainSeparator = _buildDomainSeparator();
        _cachedThis = address(this);
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        if (address(this) == _cachedThis && block.chainid == _cachedChainId) {
            return _cachedDomainSeparator;
        } else {
            return _buildDomainSeparator();
        }
    }

    function _buildDomainSeparator() private view returns (bytes32) {
        return keccak256(abi.encode(TYPE_HASH, _hashedName, _hashedVersion, block.chainid, address(this)));
    }

    /**
     * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
     * function returns the hash of the fully encoded EIP712 message for this domain.
     *
     * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:
     *
     * ```solidity
     * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
     *     keccak256("Mail(address to,string contents)"),
     *     mailTo,
     *     keccak256(bytes(mailContents))
     * )));
     * address signer = ECDSA.recover(digest, signature);
     * ```
     */
    function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) {
        return MessageHashUtils.toTypedDataHash(_domainSeparatorV4(), structHash);
    }

    /**
     * @dev See {IERC-5267}.
     */
    function eip712Domain()
        public
        view
        virtual
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        )
    {
        return (
            hex"0f", // 01111
            _EIP712Name(),
            _EIP712Version(),
            block.chainid,
            address(this),
            bytes32(0),
            new uint256[](0)
        );
    }

    /**
     * @dev The name parameter for the EIP712 domain.
     *
     * NOTE: By default this function reads _name which is an immutable value.
     * It only reads from storage if necessary (in case the value is too large to fit in a ShortString).
     */
    // solhint-disable-next-line func-name-mixedcase
    function _EIP712Name() internal view returns (string memory) {
        return _name.toStringWithFallback(_nameFallback);
    }

    /**
     * @dev The version parameter for the EIP712 domain.
     *
     * NOTE: By default this function reads _version which is an immutable value.
     * It only reads from storage if necessary (in case the value is too large to fit in a ShortString).
     */
    // solhint-disable-next-line func-name-mixedcase
    function _EIP712Version() internal view returns (string memory) {
        return _version.toStringWithFallback(_versionFallback);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/cryptography/MessageHashUtils.sol)

pragma solidity ^0.8.20;

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

/**
 * @dev Signature message hash utilities for producing digests to be consumed by {ECDSA} recovery or signing.
 *
 * The library provides methods for generating a hash of a message that conforms to the
 * https://eips.ethereum.org/EIPS/eip-191[ERC-191] and https://eips.ethereum.org/EIPS/eip-712[EIP 712]
 * specifications.
 */
library MessageHashUtils {
    /**
     * @dev Returns the keccak256 digest of an ERC-191 signed data with version
     * `0x45` (`personal_sign` messages).
     *
     * The digest is calculated by prefixing a bytes32 `messageHash` with
     * `"\x19Ethereum Signed Message:\n32"` and hashing the result. It corresponds with the
     * hash signed when using the https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`] JSON-RPC method.
     *
     * NOTE: The `messageHash` parameter is intended to be the result of hashing a raw message with
     * keccak256, although any bytes32 value can be safely used because the final digest will
     * be re-hashed.
     *
     * See {ECDSA-recover}.
     */
    function toEthSignedMessageHash(bytes32 messageHash) internal pure returns (bytes32 digest) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, "\x19Ethereum Signed Message:\n32") // 32 is the bytes-length of messageHash
            mstore(0x1c, messageHash) // 0x1c (28) is the length of the prefix
            digest := keccak256(0x00, 0x3c) // 0x3c is the length of the prefix (0x1c) + messageHash (0x20)
        }
    }

    /**
     * @dev Returns the keccak256 digest of an ERC-191 signed data with version
     * `0x45` (`personal_sign` messages).
     *
     * The digest is calculated by prefixing an arbitrary `message` with
     * `"\x19Ethereum Signed Message:\n" + len(message)` and hashing the result. It corresponds with the
     * hash signed when using the https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`] JSON-RPC method.
     *
     * See {ECDSA-recover}.
     */
    function toEthSignedMessageHash(bytes memory message) internal pure returns (bytes32) {
        return
            keccak256(bytes.concat("\x19Ethereum Signed Message:\n", bytes(Strings.toString(message.length)), message));
    }

    /**
     * @dev Returns the keccak256 digest of an ERC-191 signed data with version
     * `0x00` (data with intended validator).
     *
     * The digest is calculated by prefixing an arbitrary `data` with `"\x19\x00"` and the intended
     * `validator` address. Then hashing the result.
     *
     * See {ECDSA-recover}.
     */
    function toDataWithIntendedValidatorHash(address validator, bytes memory data) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked(hex"19_00", validator, data));
    }

    /**
     * @dev Returns the keccak256 digest of an EIP-712 typed data (ERC-191 version `0x01`).
     *
     * The digest is calculated from a `domainSeparator` and a `structHash`, by prefixing them with
     * `\x19\x01` and hashing the result. It corresponds to the hash signed by the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`] JSON-RPC method as part of EIP-712.
     *
     * See {ECDSA-recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32 digest) {
        /// @solidity memory-safe-assembly
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, hex"19_01")
            mstore(add(ptr, 0x02), domainSeparator)
            mstore(add(ptr, 0x22), structHash)
            digest := keccak256(ptr, 0x42)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/introspection/ERC165.sol)

pragma solidity ^0.8.20;

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

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC-165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 */
abstract contract ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/introspection/IERC165.sol)

pragma solidity ^0.8.20;

/**
 * @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);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/Math.sol)

pragma solidity ^0.8.20;

import {Panic} from "../Panic.sol";
import {SafeCast} from "./SafeCast.sol";

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    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 success flag (no overflow).
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a + b;
            if (c < a) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, with an success flag (no overflow).
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            if (b > a) return (false, 0);
            return (true, a - b);
        }
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an success flag (no overflow).
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        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 success flag (no division by zero).
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            if (b == 0) return (false, 0);
            return (true, a / b);
        }
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a success flag (no division by zero).
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        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.
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }

        // The following calculation ensures accurate ceiling division without overflow.
        // Since a is non-zero, (a - 1) / b will not overflow.
        // The largest possible result occurs when (a - 1) / b is type(uint256).max,
        // but the largest value we can obtain is type(uint256).max - 1, which happens
        // when a = type(uint256).max and b = 1.
        unchecked {
            return a == 0 ? 0 : (a - 1) / b + 1;
        }
    }

    /**
     * @dev Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or
     * denominator == 0.
     *
     * 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 2²⁵⁶ and mod 2²⁵⁶ - 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 * 2²⁵⁶ + 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 2²⁵⁶. Also prevents denominator == 0.
            if (denominator <= prod1) {
                Panic.panic(denominator == 0 ? Panic.DIVISION_BY_ZERO : Panic.UNDER_OVERFLOW);
            }

            ///////////////////////////////////////////////
            // 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 2²⁵⁶ / 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 2²⁵⁶. Now that denominator is an odd number, it has an inverse modulo 2²⁵⁶ such
            // that denominator * inv ≡ 1 mod 2²⁵⁶. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv ≡ 1 mod 2⁴.
            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 2⁸
            inverse *= 2 - denominator * inverse; // inverse mod 2¹⁶
            inverse *= 2 - denominator * inverse; // inverse mod 2³²
            inverse *= 2 - denominator * inverse; // inverse mod 2⁶⁴
            inverse *= 2 - denominator * inverse; // inverse mod 2¹²⁸
            inverse *= 2 - denominator * inverse; // inverse mod 2²⁵⁶

            // 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 2²⁵⁶. Since the preconditions guarantee that the outcome is
            // less than 2²⁵⁶, 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;
        }
    }

    /**
     * @dev 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) {
        return mulDiv(x, y, denominator) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, denominator) > 0);
    }

    /**
     * @dev Calculate the modular multiplicative inverse of a number in Z/nZ.
     *
     * If n is a prime, then Z/nZ is a field. In that case all elements are inversible, expect 0.
     * If n is not a prime, then Z/nZ is not a field, and some elements might not be inversible.
     *
     * If the input value is not inversible, 0 is returned.
     *
     * NOTE: If you know for sure that n is (big) a prime, it may be cheaper to use Ferma's little theorem and get the
     * inverse using `Math.modExp(a, n - 2, n)`.
     */
    function invMod(uint256 a, uint256 n) internal pure returns (uint256) {
        unchecked {
            if (n == 0) return 0;

            // The inverse modulo is calculated using the Extended Euclidean Algorithm (iterative version)
            // Used to compute integers x and y such that: ax + ny = gcd(a, n).
            // When the gcd is 1, then the inverse of a modulo n exists and it's x.
            // ax + ny = 1
            // ax = 1 + (-y)n
            // ax ≡ 1 (mod n) # x is the inverse of a modulo n

            // If the remainder is 0 the gcd is n right away.
            uint256 remainder = a % n;
            uint256 gcd = n;

            // Therefore the initial coefficients are:
            // ax + ny = gcd(a, n) = n
            // 0a + 1n = n
            int256 x = 0;
            int256 y = 1;

            while (remainder != 0) {
                uint256 quotient = gcd / remainder;

                (gcd, remainder) = (
                    // The old remainder is the next gcd to try.
                    remainder,
                    // Compute the next remainder.
                    // Can't overflow given that (a % gcd) * (gcd // (a % gcd)) <= gcd
                    // where gcd is at most n (capped to type(uint256).max)
                    gcd - remainder * quotient
                );

                (x, y) = (
                    // Increment the coefficient of a.
                    y,
                    // Decrement the coefficient of n.
                    // Can overflow, but the result is casted to uint256 so that the
                    // next value of y is "wrapped around" to a value between 0 and n - 1.
                    x - y * int256(quotient)
                );
            }

            if (gcd != 1) return 0; // No inverse exists.
            return x < 0 ? (n - uint256(-x)) : uint256(x); // Wrap the result if it's negative.
        }
    }

    /**
     * @dev Returns the modular exponentiation of the specified base, exponent and modulus (b ** e % m)
     *
     * Requirements:
     * - modulus can't be zero
     * - underlying staticcall to precompile must succeed
     *
     * IMPORTANT: The result is only valid if the underlying call succeeds. When using this function, make
     * sure the chain you're using it on supports the precompiled contract for modular exponentiation
     * at address 0x05 as specified in https://eips.ethereum.org/EIPS/eip-198[EIP-198]. Otherwise,
     * the underlying function will succeed given the lack of a revert, but the result may be incorrectly
     * interpreted as 0.
     */
    function modExp(uint256 b, uint256 e, uint256 m) internal view returns (uint256) {
        (bool success, uint256 result) = tryModExp(b, e, m);
        if (!success) {
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }
        return result;
    }

    /**
     * @dev Returns the modular exponentiation of the specified base, exponent and modulus (b ** e % m).
     * It includes a success flag indicating if the operation succeeded. Operation will be marked has failed if trying
     * to operate modulo 0 or if the underlying precompile reverted.
     *
     * IMPORTANT: The result is only valid if the success flag is true. When using this function, make sure the chain
     * you're using it on supports the precompiled contract for modular exponentiation at address 0x05 as specified in
     * https://eips.ethereum.org/EIPS/eip-198[EIP-198]. Otherwise, the underlying function will succeed given the lack
     * of a revert, but the result may be incorrectly interpreted as 0.
     */
    function tryModExp(uint256 b, uint256 e, uint256 m) internal view returns (bool success, uint256 result) {
        if (m == 0) return (false, 0);
        /// @solidity memory-safe-assembly
        assembly {
            let ptr := mload(0x40)
            // | Offset    | Content    | Content (Hex)                                                      |
            // |-----------|------------|--------------------------------------------------------------------|
            // | 0x00:0x1f | size of b  | 0x0000000000000000000000000000000000000000000000000000000000000020 |
            // | 0x20:0x3f | size of e  | 0x0000000000000000000000000000000000000000000000000000000000000020 |
            // | 0x40:0x5f | size of m  | 0x0000000000000000000000000000000000000000000000000000000000000020 |
            // | 0x60:0x7f | value of b | 0x<.............................................................b> |
            // | 0x80:0x9f | value of e | 0x<.............................................................e> |
            // | 0xa0:0xbf | value of m | 0x<.............................................................m> |
            mstore(ptr, 0x20)
            mstore(add(ptr, 0x20), 0x20)
            mstore(add(ptr, 0x40), 0x20)
            mstore(add(ptr, 0x60), b)
            mstore(add(ptr, 0x80), e)
            mstore(add(ptr, 0xa0), m)

            // Given the result < m, it's guaranteed to fit in 32 bytes,
            // so we can use the memory scratch space located at offset 0.
            success := staticcall(gas(), 0x05, ptr, 0xc0, 0x00, 0x20)
            result := mload(0x00)
        }
    }

    /**
     * @dev Variant of {modExp} that supports inputs of arbitrary length.
     */
    function modExp(bytes memory b, bytes memory e, bytes memory m) internal view returns (bytes memory) {
        (bool success, bytes memory result) = tryModExp(b, e, m);
        if (!success) {
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }
        return result;
    }

    /**
     * @dev Variant of {tryModExp} that supports inputs of arbitrary length.
     */
    function tryModExp(
        bytes memory b,
        bytes memory e,
        bytes memory m
    ) internal view returns (bool success, bytes memory result) {
        if (_zeroBytes(m)) return (false, new bytes(0));

        uint256 mLen = m.length;

        // Encode call args in result and move the free memory pointer
        result = abi.encodePacked(b.length, e.length, mLen, b, e, m);

        /// @solidity memory-safe-assembly
        assembly {
            let dataPtr := add(result, 0x20)
            // Write result on top of args to avoid allocating extra memory.
            success := staticcall(gas(), 0x05, dataPtr, mload(result), dataPtr, mLen)
            // Overwrite the length.
            // result.length > returndatasize() is guaranteed because returndatasize() == m.length
            mstore(result, mLen)
            // Set the memory pointer after the returned data.
            mstore(0x40, add(dataPtr, mLen))
        }
    }

    /**
     * @dev Returns whether the provided byte array is zero.
     */
    function _zeroBytes(bytes memory byteArray) private pure returns (bool) {
        for (uint256 i = 0; i < byteArray.length; ++i) {
            if (byteArray[i] != 0) {
                return false;
            }
        }
        return true;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded
     * towards zero.
     *
     * This method is based on Newton's method for computing square roots; the algorithm is restricted to only
     * using integer operations.
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        unchecked {
            // Take care of easy edge cases when a == 0 or a == 1
            if (a <= 1) {
                return a;
            }

            // In this function, we use Newton's method to get a root of `f(x) := x² - a`. It involves building a
            // sequence x_n that converges toward sqrt(a). For each iteration x_n, we also define the error between
            // the current value as `ε_n = | x_n - sqrt(a) |`.
            //
            // For our first estimation, we consider `e` the smallest power of 2 which is bigger than the square root
            // of the target. (i.e. `2**(e-1) ≤ sqrt(a) < 2**e`). We know that `e ≤ 128` because `(2¹²⁸)² = 2²⁵⁶` is
            // bigger than any uint256.
            //
            // By noticing that
            // `2**(e-1) ≤ sqrt(a) < 2**e → (2**(e-1))² ≤ a < (2**e)² → 2**(2*e-2) ≤ a < 2**(2*e)`
            // we can deduce that `e - 1` is `log2(a) / 2`. We can thus compute `x_n = 2**(e-1)` using a method similar
            // to the msb function.
            uint256 aa = a;
            uint256 xn = 1;

            if (aa >= (1 << 128)) {
                aa >>= 128;
                xn <<= 64;
            }
            if (aa >= (1 << 64)) {
                aa >>= 64;
                xn <<= 32;
            }
            if (aa >= (1 << 32)) {
                aa >>= 32;
                xn <<= 16;
            }
            if (aa >= (1 << 16)) {
                aa >>= 16;
                xn <<= 8;
            }
            if (aa >= (1 << 8)) {
                aa >>= 8;
                xn <<= 4;
            }
            if (aa >= (1 << 4)) {
                aa >>= 4;
                xn <<= 2;
            }
            if (aa >= (1 << 2)) {
                xn <<= 1;
            }

            // We now have x_n such that `x_n = 2**(e-1) ≤ sqrt(a) < 2**e = 2 * x_n`. This implies ε_n ≤ 2**(e-1).
            //
            // We can refine our estimation by noticing that the middle of that interval minimizes the error.
            // If we move x_n to equal 2**(e-1) + 2**(e-2), then we reduce the error to ε_n ≤ 2**(e-2).
            // This is going to be our x_0 (and ε_0)
            xn = (3 * xn) >> 1; // ε_0 := | x_0 - sqrt(a) | ≤ 2**(e-2)

            // From here, Newton's method give us:
            // x_{n+1} = (x_n + a / x_n) / 2
            //
            // One should note that:
            // x_{n+1}² - a = ((x_n + a / x_n) / 2)² - a
            //              = ((x_n² + a) / (2 * x_n))² - a
            //              = (x_n⁴ + 2 * a * x_n² + a²) / (4 * x_n²) - a
            //              = (x_n⁴ + 2 * a * x_n² + a² - 4 * a * x_n²) / (4 * x_n²)
            //              = (x_n⁴ - 2 * a * x_n² + a²) / (4 * x_n²)
            //              = (x_n² - a)² / (2 * x_n)²
            //              = ((x_n² - a) / (2 * x_n))²
            //              ≥ 0
            // Which proves that for all n ≥ 1, sqrt(a) ≤ x_n
            //
            // This gives us the proof of quadratic convergence of the sequence:
            // ε_{n+1} = | x_{n+1} - sqrt(a) |
            //         = | (x_n + a / x_n) / 2 - sqrt(a) |
            //         = | (x_n² + a - 2*x_n*sqrt(a)) / (2 * x_n) |
            //         = | (x_n - sqrt(a))² / (2 * x_n) |
            //         = | ε_n² / (2 * x_n) |
            //         = ε_n² / | (2 * x_n) |
            //
            // For the first iteration, we have a special case where x_0 is known:
            // ε_1 = ε_0² / | (2 * x_0) |
            //     ≤ (2**(e-2))² / (2 * (2**(e-1) + 2**(e-2)))
            //     ≤ 2**(2*e-4) / (3 * 2**(e-1))
            //     ≤ 2**(e-3) / 3
            //     ≤ 2**(e-3-log2(3))
            //     ≤ 2**(e-4.5)
            //
            // For the following iterations, we use the fact that, 2**(e-1) ≤ sqrt(a) ≤ x_n:
            // ε_{n+1} = ε_n² / | (2 * x_n) |
            //         ≤ (2**(e-k))² / (2 * 2**(e-1))
            //         ≤ 2**(2*e-2*k) / 2**e
            //         ≤ 2**(e-2*k)
            xn = (xn + a / xn) >> 1; // ε_1 := | x_1 - sqrt(a) | ≤ 2**(e-4.5)  -- special case, see above
            xn = (xn + a / xn) >> 1; // ε_2 := | x_2 - sqrt(a) | ≤ 2**(e-9)    -- general case with k = 4.5
            xn = (xn + a / xn) >> 1; // ε_3 := | x_3 - sqrt(a) | ≤ 2**(e-18)   -- general case with k = 9
            xn = (xn + a / xn) >> 1; // ε_4 := | x_4 - sqrt(a) | ≤ 2**(e-36)   -- general case with k = 18
            xn = (xn + a / xn) >> 1; // ε_5 := | x_5 - sqrt(a) | ≤ 2**(e-72)   -- general case with k = 36
            xn = (xn + a / xn) >> 1; // ε_6 := | x_6 - sqrt(a) | ≤ 2**(e-144)  -- general case with k = 72

            // Because e ≤ 128 (as discussed during the first estimation phase), we know have reached a precision
            // ε_6 ≤ 2**(e-144) < 1. Given we're operating on integers, then we can ensure that xn is now either
            // sqrt(a) or sqrt(a) + 1.
            return xn - SafeCast.toUint(xn > a / xn);
        }
    }

    /**
     * @dev 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 + SafeCast.toUint(unsignedRoundsUp(rounding) && result * result < a);
        }
    }

    /**
     * @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;
        uint256 exp;
        unchecked {
            exp = 128 * SafeCast.toUint(value > (1 << 128) - 1);
            value >>= exp;
            result += exp;

            exp = 64 * SafeCast.toUint(value > (1 << 64) - 1);
            value >>= exp;
            result += exp;

            exp = 32 * SafeCast.toUint(value > (1 << 32) - 1);
            value >>= exp;
            result += exp;

            exp = 16 * SafeCast.toUint(value > (1 << 16) - 1);
            value >>= exp;
            result += exp;

            exp = 8 * SafeCast.toUint(value > (1 << 8) - 1);
            value >>= exp;
            result += exp;

            exp = 4 * SafeCast.toUint(value > (1 << 4) - 1);
            value >>= exp;
            result += exp;

            exp = 2 * SafeCast.toUint(value > (1 << 2) - 1);
            value >>= exp;
            result += exp;

            result += SafeCast.toUint(value > 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 + SafeCast.toUint(unsignedRoundsUp(rounding) && 1 << result < value);
        }
    }

    /**
     * @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 + SafeCast.toUint(unsignedRoundsUp(rounding) && 10 ** result < value);
        }
    }

    /**
     * @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;
        uint256 isGt;
        unchecked {
            isGt = SafeCast.toUint(value > (1 << 128) - 1);
            value >>= isGt * 128;
            result += isGt * 16;

            isGt = SafeCast.toUint(value > (1 << 64) - 1);
            value >>= isGt * 64;
            result += isGt * 8;

            isGt = SafeCast.toUint(value > (1 << 32) - 1);
            value >>= isGt * 32;
            result += isGt * 4;

            isGt = SafeCast.toUint(value > (1 << 16) - 1);
            value >>= isGt * 16;
            result += isGt * 2;

            result += SafeCast.toUint(value > (1 << 8) - 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 + SafeCast.toUint(unsignedRoundsUp(rounding) && 1 << (result << 3) < value);
        }
    }

    /**
     * @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/SafeCast.sol)
// This file was procedurally generated from scripts/generate/templates/SafeCast.js.

pragma solidity ^0.8.20;

/**
 * @dev Wrappers over Solidity's uintXX/intXX/bool casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such an operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeCast {
    /**
     * @dev Value doesn't fit in an uint of `bits` size.
     */
    error SafeCastOverflowedUintDowncast(uint8 bits, uint256 value);

    /**
     * @dev An int value doesn't fit in an uint of `bits` size.
     */
    error SafeCastOverflowedIntToUint(int256 value);

    /**
     * @dev Value doesn't fit in an int of `bits` size.
     */
    error SafeCastOverflowedIntDowncast(uint8 bits, int256 value);

    /**
     * @dev An uint value doesn't fit in an int of `bits` size.
     */
    error SafeCastOverflowedUintToInt(uint256 value);

    /**
     * @dev Returns the downcasted uint248 from uint256, reverting on
     * overflow (when the input is greater than largest uint248).
     *
     * Counterpart to Solidity's `uint248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     */
    function toUint248(uint256 value) internal pure returns (uint248) {
        if (value > type(uint248).max) {
            revert SafeCastOverflowedUintDowncast(248, value);
        }
        return uint248(value);
    }

    /**
     * @dev Returns the downcasted uint240 from uint256, reverting on
     * overflow (when the input is greater than largest uint240).
     *
     * Counterpart to Solidity's `uint240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     */
    function toUint240(uint256 value) internal pure returns (uint240) {
        if (value > type(uint240).max) {
            revert SafeCastOverflowedUintDowncast(240, value);
        }
        return uint240(value);
    }

    /**
     * @dev Returns the downcasted uint232 from uint256, reverting on
     * overflow (when the input is greater than largest uint232).
     *
     * Counterpart to Solidity's `uint232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     */
    function toUint232(uint256 value) internal pure returns (uint232) {
        if (value > type(uint232).max) {
            revert SafeCastOverflowedUintDowncast(232, value);
        }
        return uint232(value);
    }

    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        if (value > type(uint224).max) {
            revert SafeCastOverflowedUintDowncast(224, value);
        }
        return uint224(value);
    }

    /**
     * @dev Returns the downcasted uint216 from uint256, reverting on
     * overflow (when the input is greater than largest uint216).
     *
     * Counterpart to Solidity's `uint216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     */
    function toUint216(uint256 value) internal pure returns (uint216) {
        if (value > type(uint216).max) {
            revert SafeCastOverflowedUintDowncast(216, value);
        }
        return uint216(value);
    }

    /**
     * @dev Returns the downcasted uint208 from uint256, reverting on
     * overflow (when the input is greater than largest uint208).
     *
     * Counterpart to Solidity's `uint208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     */
    function toUint208(uint256 value) internal pure returns (uint208) {
        if (value > type(uint208).max) {
            revert SafeCastOverflowedUintDowncast(208, value);
        }
        return uint208(value);
    }

    /**
     * @dev Returns the downcasted uint200 from uint256, reverting on
     * overflow (when the input is greater than largest uint200).
     *
     * Counterpart to Solidity's `uint200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     */
    function toUint200(uint256 value) internal pure returns (uint200) {
        if (value > type(uint200).max) {
            revert SafeCastOverflowedUintDowncast(200, value);
        }
        return uint200(value);
    }

    /**
     * @dev Returns the downcasted uint192 from uint256, reverting on
     * overflow (when the input is greater than largest uint192).
     *
     * Counterpart to Solidity's `uint192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     */
    function toUint192(uint256 value) internal pure returns (uint192) {
        if (value > type(uint192).max) {
            revert SafeCastOverflowedUintDowncast(192, value);
        }
        return uint192(value);
    }

    /**
     * @dev Returns the downcasted uint184 from uint256, reverting on
     * overflow (when the input is greater than largest uint184).
     *
     * Counterpart to Solidity's `uint184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     */
    function toUint184(uint256 value) internal pure returns (uint184) {
        if (value > type(uint184).max) {
            revert SafeCastOverflowedUintDowncast(184, value);
        }
        return uint184(value);
    }

    /**
     * @dev Returns the downcasted uint176 from uint256, reverting on
     * overflow (when the input is greater than largest uint176).
     *
     * Counterpart to Solidity's `uint176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     */
    function toUint176(uint256 value) internal pure returns (uint176) {
        if (value > type(uint176).max) {
            revert SafeCastOverflowedUintDowncast(176, value);
        }
        return uint176(value);
    }

    /**
     * @dev Returns the downcasted uint168 from uint256, reverting on
     * overflow (when the input is greater than largest uint168).
     *
     * Counterpart to Solidity's `uint168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     */
    function toUint168(uint256 value) internal pure returns (uint168) {
        if (value > type(uint168).max) {
            revert SafeCastOverflowedUintDowncast(168, value);
        }
        return uint168(value);
    }

    /**
     * @dev Returns the downcasted uint160 from uint256, reverting on
     * overflow (when the input is greater than largest uint160).
     *
     * Counterpart to Solidity's `uint160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     */
    function toUint160(uint256 value) internal pure returns (uint160) {
        if (value > type(uint160).max) {
            revert SafeCastOverflowedUintDowncast(160, value);
        }
        return uint160(value);
    }

    /**
     * @dev Returns the downcasted uint152 from uint256, reverting on
     * overflow (when the input is greater than largest uint152).
     *
     * Counterpart to Solidity's `uint152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     */
    function toUint152(uint256 value) internal pure returns (uint152) {
        if (value > type(uint152).max) {
            revert SafeCastOverflowedUintDowncast(152, value);
        }
        return uint152(value);
    }

    /**
     * @dev Returns the downcasted uint144 from uint256, reverting on
     * overflow (when the input is greater than largest uint144).
     *
     * Counterpart to Solidity's `uint144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     */
    function toUint144(uint256 value) internal pure returns (uint144) {
        if (value > type(uint144).max) {
            revert SafeCastOverflowedUintDowncast(144, value);
        }
        return uint144(value);
    }

    /**
     * @dev Returns the downcasted uint136 from uint256, reverting on
     * overflow (when the input is greater than largest uint136).
     *
     * Counterpart to Solidity's `uint136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     */
    function toUint136(uint256 value) internal pure returns (uint136) {
        if (value > type(uint136).max) {
            revert SafeCastOverflowedUintDowncast(136, value);
        }
        return uint136(value);
    }

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        if (value > type(uint128).max) {
            revert SafeCastOverflowedUintDowncast(128, value);
        }
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint120 from uint256, reverting on
     * overflow (when the input is greater than largest uint120).
     *
     * Counterpart to Solidity's `uint120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     */
    function toUint120(uint256 value) internal pure returns (uint120) {
        if (value > type(uint120).max) {
            revert SafeCastOverflowedUintDowncast(120, value);
        }
        return uint120(value);
    }

    /**
     * @dev Returns the downcasted uint112 from uint256, reverting on
     * overflow (when the input is greater than largest uint112).
     *
     * Counterpart to Solidity's `uint112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     */
    function toUint112(uint256 value) internal pure returns (uint112) {
        if (value > type(uint112).max) {
            revert SafeCastOverflowedUintDowncast(112, value);
        }
        return uint112(value);
    }

    /**
     * @dev Returns the downcasted uint104 from uint256, reverting on
     * overflow (when the input is greater than largest uint104).
     *
     * Counterpart to Solidity's `uint104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     */
    function toUint104(uint256 value) internal pure returns (uint104) {
        if (value > type(uint104).max) {
            revert SafeCastOverflowedUintDowncast(104, value);
        }
        return uint104(value);
    }

    /**
     * @dev Returns the downcasted uint96 from uint256, reverting on
     * overflow (when the input is greater than largest uint96).
     *
     * Counterpart to Solidity's `uint96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        if (value > type(uint96).max) {
            revert SafeCastOverflowedUintDowncast(96, value);
        }
        return uint96(value);
    }

    /**
     * @dev Returns the downcasted uint88 from uint256, reverting on
     * overflow (when the input is greater than largest uint88).
     *
     * Counterpart to Solidity's `uint88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     */
    function toUint88(uint256 value) internal pure returns (uint88) {
        if (value > type(uint88).max) {
            revert SafeCastOverflowedUintDowncast(88, value);
        }
        return uint88(value);
    }

    /**
     * @dev Returns the downcasted uint80 from uint256, reverting on
     * overflow (when the input is greater than largest uint80).
     *
     * Counterpart to Solidity's `uint80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     */
    function toUint80(uint256 value) internal pure returns (uint80) {
        if (value > type(uint80).max) {
            revert SafeCastOverflowedUintDowncast(80, value);
        }
        return uint80(value);
    }

    /**
     * @dev Returns the downcasted uint72 from uint256, reverting on
     * overflow (when the input is greater than largest uint72).
     *
     * Counterpart to Solidity's `uint72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     */
    function toUint72(uint256 value) internal pure returns (uint72) {
        if (value > type(uint72).max) {
            revert SafeCastOverflowedUintDowncast(72, value);
        }
        return uint72(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        if (value > type(uint64).max) {
            revert SafeCastOverflowedUintDowncast(64, value);
        }
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint56 from uint256, reverting on
     * overflow (when the input is greater than largest uint56).
     *
     * Counterpart to Solidity's `uint56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     */
    function toUint56(uint256 value) internal pure returns (uint56) {
        if (value > type(uint56).max) {
            revert SafeCastOverflowedUintDowncast(56, value);
        }
        return uint56(value);
    }

    /**
     * @dev Returns the downcasted uint48 from uint256, reverting on
     * overflow (when the input is greater than largest uint48).
     *
     * Counterpart to Solidity's `uint48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     */
    function toUint48(uint256 value) internal pure returns (uint48) {
        if (value > type(uint48).max) {
            revert SafeCastOverflowedUintDowncast(48, value);
        }
        return uint48(value);
    }

    /**
     * @dev Returns the downcasted uint40 from uint256, reverting on
     * overflow (when the input is greater than largest uint40).
     *
     * Counterpart to Solidity's `uint40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     */
    function toUint40(uint256 value) internal pure returns (uint40) {
        if (value > type(uint40).max) {
            revert SafeCastOverflowedUintDowncast(40, value);
        }
        return uint40(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        if (value > type(uint32).max) {
            revert SafeCastOverflowedUintDowncast(32, value);
        }
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint24 from uint256, reverting on
     * overflow (when the input is greater than largest uint24).
     *
     * Counterpart to Solidity's `uint24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     */
    function toUint24(uint256 value) internal pure returns (uint24) {
        if (value > type(uint24).max) {
            revert SafeCastOverflowedUintDowncast(24, value);
        }
        return uint24(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        if (value > type(uint16).max) {
            revert SafeCastOverflowedUintDowncast(16, value);
        }
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        if (value > type(uint8).max) {
            revert SafeCastOverflowedUintDowncast(8, value);
        }
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        if (value < 0) {
            revert SafeCastOverflowedIntToUint(value);
        }
        return uint256(value);
    }

    /**
     * @dev Returns the downcasted int248 from int256, reverting on
     * overflow (when the input is less than smallest int248 or
     * greater than largest int248).
     *
     * Counterpart to Solidity's `int248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     */
    function toInt248(int256 value) internal pure returns (int248 downcasted) {
        downcasted = int248(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(248, value);
        }
    }

    /**
     * @dev Returns the downcasted int240 from int256, reverting on
     * overflow (when the input is less than smallest int240 or
     * greater than largest int240).
     *
     * Counterpart to Solidity's `int240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     */
    function toInt240(int256 value) internal pure returns (int240 downcasted) {
        downcasted = int240(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(240, value);
        }
    }

    /**
     * @dev Returns the downcasted int232 from int256, reverting on
     * overflow (when the input is less than smallest int232 or
     * greater than largest int232).
     *
     * Counterpart to Solidity's `int232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     */
    function toInt232(int256 value) internal pure returns (int232 downcasted) {
        downcasted = int232(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(232, value);
        }
    }

    /**
     * @dev Returns the downcasted int224 from int256, reverting on
     * overflow (when the input is less than smallest int224 or
     * greater than largest int224).
     *
     * Counterpart to Solidity's `int224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toInt224(int256 value) internal pure returns (int224 downcasted) {
        downcasted = int224(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(224, value);
        }
    }

    /**
     * @dev Returns the downcasted int216 from int256, reverting on
     * overflow (when the input is less than smallest int216 or
     * greater than largest int216).
     *
     * Counterpart to Solidity's `int216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     */
    function toInt216(int256 value) internal pure returns (int216 downcasted) {
        downcasted = int216(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(216, value);
        }
    }

    /**
     * @dev Returns the downcasted int208 from int256, reverting on
     * overflow (when the input is less than smallest int208 or
     * greater than largest int208).
     *
     * Counterpart to Solidity's `int208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     */
    function toInt208(int256 value) internal pure returns (int208 downcasted) {
        downcasted = int208(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(208, value);
        }
    }

    /**
     * @dev Returns the downcasted int200 from int256, reverting on
     * overflow (when the input is less than smallest int200 or
     * greater than largest int200).
     *
     * Counterpart to Solidity's `int200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     */
    function toInt200(int256 value) internal pure returns (int200 downcasted) {
        downcasted = int200(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(200, value);
        }
    }

    /**
     * @dev Returns the downcasted int192 from int256, reverting on
     * overflow (when the input is less than smallest int192 or
     * greater than largest int192).
     *
     * Counterpart to Solidity's `int192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     */
    function toInt192(int256 value) internal pure returns (int192 downcasted) {
        downcasted = int192(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(192, value);
        }
    }

    /**
     * @dev Returns the downcasted int184 from int256, reverting on
     * overflow (when the input is less than smallest int184 or
     * greater than largest int184).
     *
     * Counterpart to Solidity's `int184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     */
    function toInt184(int256 value) internal pure returns (int184 downcasted) {
        downcasted = int184(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(184, value);
        }
    }

    /**
     * @dev Returns the downcasted int176 from int256, reverting on
     * overflow (when the input is less than smallest int176 or
     * greater than largest int176).
     *
     * Counterpart to Solidity's `int176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     */
    function toInt176(int256 value) internal pure returns (int176 downcasted) {
        downcasted = int176(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(176, value);
        }
    }

    /**
     * @dev Returns the downcasted int168 from int256, reverting on
     * overflow (when the input is less than smallest int168 or
     * greater than largest int168).
     *
     * Counterpart to Solidity's `int168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     */
    function toInt168(int256 value) internal pure returns (int168 downcasted) {
        downcasted = int168(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(168, value);
        }
    }

    /**
     * @dev Returns the downcasted int160 from int256, reverting on
     * overflow (when the input is less than smallest int160 or
     * greater than largest int160).
     *
     * Counterpart to Solidity's `int160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     */
    function toInt160(int256 value) internal pure returns (int160 downcasted) {
        downcasted = int160(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(160, value);
        }
    }

    /**
     * @dev Returns the downcasted int152 from int256, reverting on
     * overflow (when the input is less than smallest int152 or
     * greater than largest int152).
     *
     * Counterpart to Solidity's `int152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     */
    function toInt152(int256 value) internal pure returns (int152 downcasted) {
        downcasted = int152(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(152, value);
        }
    }

    /**
     * @dev Returns the downcasted int144 from int256, reverting on
     * overflow (when the input is less than smallest int144 or
     * greater than largest int144).
     *
     * Counterpart to Solidity's `int144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     */
    function toInt144(int256 value) internal pure returns (int144 downcasted) {
        downcasted = int144(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(144, value);
        }
    }

    /**
     * @dev Returns the downcasted int136 from int256, reverting on
     * overflow (when the input is less than smallest int136 or
     * greater than largest int136).
     *
     * Counterpart to Solidity's `int136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     */
    function toInt136(int256 value) internal pure returns (int136 downcasted) {
        downcasted = int136(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(136, value);
        }
    }

    /**
     * @dev Returns the downcasted int128 from int256, reverting on
     * overflow (when the input is less than smallest int128 or
     * greater than largest int128).
     *
     * Counterpart to Solidity's `int128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toInt128(int256 value) internal pure returns (int128 downcasted) {
        downcasted = int128(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(128, value);
        }
    }

    /**
     * @dev Returns the downcasted int120 from int256, reverting on
     * overflow (when the input is less than smallest int120 or
     * greater than largest int120).
     *
     * Counterpart to Solidity's `int120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     */
    function toInt120(int256 value) internal pure returns (int120 downcasted) {
        downcasted = int120(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(120, value);
        }
    }

    /**
     * @dev Returns the downcasted int112 from int256, reverting on
     * overflow (when the input is less than smallest int112 or
     * greater than largest int112).
     *
     * Counterpart to Solidity's `int112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     */
    function toInt112(int256 value) internal pure returns (int112 downcasted) {
        downcasted = int112(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(112, value);
        }
    }

    /**
     * @dev Returns the downcasted int104 from int256, reverting on
     * overflow (when the input is less than smallest int104 or
     * greater than largest int104).
     *
     * Counterpart to Solidity's `int104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     */
    function toInt104(int256 value) internal pure returns (int104 downcasted) {
        downcasted = int104(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(104, value);
        }
    }

    /**
     * @dev Returns the downcasted int96 from int256, reverting on
     * overflow (when the input is less than smallest int96 or
     * greater than largest int96).
     *
     * Counterpart to Solidity's `int96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toInt96(int256 value) internal pure returns (int96 downcasted) {
        downcasted = int96(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(96, value);
        }
    }

    /**
     * @dev Returns the downcasted int88 from int256, reverting on
     * overflow (when the input is less than smallest int88 or
     * greater than largest int88).
     *
     * Counterpart to Solidity's `int88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     */
    function toInt88(int256 value) internal pure returns (int88 downcasted) {
        downcasted = int88(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(88, value);
        }
    }

    /**
     * @dev Returns the downcasted int80 from int256, reverting on
     * overflow (when the input is less than smallest int80 or
     * greater than largest int80).
     *
     * Counterpart to Solidity's `int80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     */
    function toInt80(int256 value) internal pure returns (int80 downcasted) {
        downcasted = int80(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(80, value);
        }
    }

    /**
     * @dev Returns the downcasted int72 from int256, reverting on
     * overflow (when the input is less than smallest int72 or
     * greater than largest int72).
     *
     * Counterpart to Solidity's `int72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     */
    function toInt72(int256 value) internal pure returns (int72 downcasted) {
        downcasted = int72(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(72, value);
        }
    }

    /**
     * @dev Returns the downcasted int64 from int256, reverting on
     * overflow (when the input is less than smallest int64 or
     * greater than largest int64).
     *
     * Counterpart to Solidity's `int64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toInt64(int256 value) internal pure returns (int64 downcasted) {
        downcasted = int64(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(64, value);
        }
    }

    /**
     * @dev Returns the downcasted int56 from int256, reverting on
     * overflow (when the input is less than smallest int56 or
     * greater than largest int56).
     *
     * Counterpart to Solidity's `int56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     */
    function toInt56(int256 value) internal pure returns (int56 downcasted) {
        downcasted = int56(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(56, value);
        }
    }

    /**
     * @dev Returns the downcasted int48 from int256, reverting on
     * overflow (when the input is less than smallest int48 or
     * greater than largest int48).
     *
     * Counterpart to Solidity's `int48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     */
    function toInt48(int256 value) internal pure returns (int48 downcasted) {
        downcasted = int48(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(48, value);
        }
    }

    /**
     * @dev Returns the downcasted int40 from int256, reverting on
     * overflow (when the input is less than smallest int40 or
     * greater than largest int40).
     *
     * Counterpart to Solidity's `int40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     */
    function toInt40(int256 value) internal pure returns (int40 downcasted) {
        downcasted = int40(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(40, value);
        }
    }

    /**
     * @dev Returns the downcasted int32 from int256, reverting on
     * overflow (when the input is less than smallest int32 or
     * greater than largest int32).
     *
     * Counterpart to Solidity's `int32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toInt32(int256 value) internal pure returns (int32 downcasted) {
        downcasted = int32(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(32, value);
        }
    }

    /**
     * @dev Returns the downcasted int24 from int256, reverting on
     * overflow (when the input is less than smallest int24 or
     * greater than largest int24).
     *
     * Counterpart to Solidity's `int24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     */
    function toInt24(int256 value) internal pure returns (int24 downcasted) {
        downcasted = int24(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(24, value);
        }
    }

    /**
     * @dev Returns the downcasted int16 from int256, reverting on
     * overflow (when the input is less than smallest int16 or
     * greater than largest int16).
     *
     * Counterpart to Solidity's `int16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toInt16(int256 value) internal pure returns (int16 downcasted) {
        downcasted = int16(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(16, value);
        }
    }

    /**
     * @dev Returns the downcasted int8 from int256, reverting on
     * overflow (when the input is less than smallest int8 or
     * greater than largest int8).
     *
     * Counterpart to Solidity's `int8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     */
    function toInt8(int256 value) internal pure returns (int8 downcasted) {
        downcasted = int8(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(8, value);
        }
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        if (value > uint256(type(int256).max)) {
            revert SafeCastOverflowedUintToInt(value);
        }
        return int256(value);
    }

    /**
     * @dev Cast a boolean (false or true) to a uint256 (0 or 1) with no jump.
     */
    function toUint(bool b) internal pure returns (uint256 u) {
        /// @solidity memory-safe-assembly
        assembly {
            u := iszero(iszero(b))
        }
    }
}

// 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 {
            // Formula from the "Bit Twiddling Hacks" by Sean Eron Anderson.
            // Since `n` is a signed integer, the generated bytecode will use the SAR opcode to perform the right shift,
            // taking advantage of the most significant (or "sign" bit) in two's complement representation.
            // This opcode adds new most significant bits set to the value of the previous most significant bit. As a result,
            // the mask will either be `bytes(0)` (if n is positive) or `~bytes32(0)` (if n is negative).
            int256 mask = n >> 255;

            // A `bytes(0)` mask leaves the input unchanged, while a `~bytes32(0)` mask complements it.
            return uint256((n + mask) ^ mask);
        }
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.20;

/**
 * @dev Helper library for emitting standardized panic codes.
 *
 * ```solidity
 * contract Example {
 *      using Panic for uint256;
 *
 *      // Use any of the declared internal constants
 *      function foo() { Panic.GENERIC.panic(); }
 *
 *      // Alternatively
 *      function foo() { Panic.panic(Panic.GENERIC); }
 * }
 * ```
 *
 * Follows the list from https://github.com/ethereum/solidity/blob/v0.8.24/libsolutil/ErrorCodes.h[libsolutil].
 */
// slither-disable-next-line unused-state
library Panic {
    /// @dev generic / unspecified error
    uint256 internal constant GENERIC = 0x00;
    /// @dev used by the assert() builtin
    uint256 internal constant ASSERT = 0x01;
    /// @dev arithmetic underflow or overflow
    uint256 internal constant UNDER_OVERFLOW = 0x11;
    /// @dev division or modulo by zero
    uint256 internal constant DIVISION_BY_ZERO = 0x12;
    /// @dev enum conversion error
    uint256 internal constant ENUM_CONVERSION_ERROR = 0x21;
    /// @dev invalid encoding in storage
    uint256 internal constant STORAGE_ENCODING_ERROR = 0x22;
    /// @dev empty array pop
    uint256 internal constant EMPTY_ARRAY_POP = 0x31;
    /// @dev array out of bounds access
    uint256 internal constant ARRAY_OUT_OF_BOUNDS = 0x32;
    /// @dev resource error (too large allocation or too large array)
    uint256 internal constant RESOURCE_ERROR = 0x41;
    /// @dev calling invalid internal function
    uint256 internal constant INVALID_INTERNAL_FUNCTION = 0x51;

    /// @dev Reverts with a panic code. Recommended to use with
    /// the internal constants with predefined codes.
    function panic(uint256 code) internal pure {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, 0x4e487b71)
            mstore(0x20, code)
            revert(0x1c, 0x24)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/ShortStrings.sol)

pragma solidity ^0.8.20;

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

// | string  | 0xAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA   |
// | length  | 0x                                                              BB |
type ShortString is bytes32;

/**
 * @dev This library provides functions to convert short memory strings
 * into a `ShortString` type that can be used as an immutable variable.
 *
 * Strings of arbitrary length can be optimized using this library if
 * they are short enough (up to 31 bytes) by packing them with their
 * length (1 byte) in a single EVM word (32 bytes). Additionally, a
 * fallback mechanism can be used for every other case.
 *
 * Usage example:
 *
 * ```solidity
 * contract Named {
 *     using ShortStrings for *;
 *
 *     ShortString private immutable _name;
 *     string private _nameFallback;
 *
 *     constructor(string memory contractName) {
 *         _name = contractName.toShortStringWithFallback(_nameFallback);
 *     }
 *
 *     function name() external view returns (string memory) {
 *         return _name.toStringWithFallback(_nameFallback);
 *     }
 * }
 * ```
 */
library ShortStrings {
    // Used as an identifier for strings longer than 31 bytes.
    bytes32 private constant FALLBACK_SENTINEL = 0x00000000000000000000000000000000000000000000000000000000000000FF;

    error StringTooLong(string str);
    error InvalidShortString();

    /**
     * @dev Encode a string of at most 31 chars into a `ShortString`.
     *
     * This will trigger a `StringTooLong` error is the input string is too long.
     */
    function toShortString(string memory str) internal pure returns (ShortString) {
        bytes memory bstr = bytes(str);
        if (bstr.length > 31) {
            revert StringTooLong(str);
        }
        return ShortString.wrap(bytes32(uint256(bytes32(bstr)) | bstr.length));
    }

    /**
     * @dev Decode a `ShortString` back to a "normal" string.
     */
    function toString(ShortString sstr) internal pure returns (string memory) {
        uint256 len = byteLength(sstr);
        // using `new string(len)` would work locally but is not memory safe.
        string memory str = new string(32);
        /// @solidity memory-safe-assembly
        assembly {
            mstore(str, len)
            mstore(add(str, 0x20), sstr)
        }
        return str;
    }

    /**
     * @dev Return the length of a `ShortString`.
     */
    function byteLength(ShortString sstr) internal pure returns (uint256) {
        uint256 result = uint256(ShortString.unwrap(sstr)) & 0xFF;
        if (result > 31) {
            revert InvalidShortString();
        }
        return result;
    }

    /**
     * @dev Encode a string into a `ShortString`, or write it to storage if it is too long.
     */
    function toShortStringWithFallback(string memory value, string storage store) internal returns (ShortString) {
        if (bytes(value).length < 32) {
            return toShortString(value);
        } else {
            StorageSlot.getStringSlot(store).value = value;
            return ShortString.wrap(FALLBACK_SENTINEL);
        }
    }

    /**
     * @dev Decode a string that was encoded to `ShortString` or written to storage using {setWithFallback}.
     */
    function toStringWithFallback(ShortString value, string storage store) internal pure returns (string memory) {
        if (ShortString.unwrap(value) != FALLBACK_SENTINEL) {
            return toString(value);
        } else {
            return store;
        }
    }

    /**
     * @dev Return the length of a string that was encoded to `ShortString` or written to storage using
     * {setWithFallback}.
     *
     * WARNING: This will return the "byte length" of the string. This may not reflect the actual length in terms of
     * actual characters as the UTF-8 encoding of a single character can span over multiple bytes.
     */
    function byteLengthWithFallback(ShortString value, string storage store) internal view returns (uint256) {
        if (ShortString.unwrap(value) != FALLBACK_SENTINEL) {
            return byteLength(value);
        } else {
            return bytes(store).length;
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/StorageSlot.sol)
// This file was procedurally generated from scripts/generate/templates/StorageSlot.js.

pragma solidity ^0.8.24;

/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC-1967 implementation slot:
 * ```solidity
 * contract ERC1967 {
 *     // Define the slot. Alternatively, use the SlotDerivation library to derive the slot.
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(newImplementation.code.length > 0);
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * Since version 5.1, this library also support writing and reading value types to and from transient storage.
 *
 *  * Example using transient storage:
 * ```solidity
 * contract Lock {
 *     // Define the slot. Alternatively, use the SlotDerivation library to derive the slot.
 *     bytes32 internal constant _LOCK_SLOT = 0xf4678858b2b588224636b8522b729e7722d32fc491da849ed75b3fdf3c84f542;
 *
 *     modifier locked() {
 *         require(!_LOCK_SLOT.asBoolean().tload());
 *
 *         _LOCK_SLOT.asBoolean().tstore(true);
 *         _;
 *         _LOCK_SLOT.asBoolean().tstore(false);
 *     }
 * }
 * ```
 *
 * TIP: Consider using this library along with {SlotDerivation}.
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }

    struct BooleanSlot {
        bool value;
    }

    struct Bytes32Slot {
        bytes32 value;
    }

    struct Uint256Slot {
        uint256 value;
    }

    struct Int256Slot {
        int256 value;
    }

    struct StringSlot {
        string value;
    }

    struct BytesSlot {
        bytes value;
    }

    /**
     * @dev Returns an `AddressSlot` with member `value` located at `slot`.
     */
    function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BooleanSlot` with member `value` located at `slot`.
     */
    function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Bytes32Slot` with member `value` located at `slot`.
     */
    function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Uint256Slot` with member `value` located at `slot`.
     */
    function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Int256Slot` with member `value` located at `slot`.
     */
    function getInt256Slot(bytes32 slot) internal pure returns (Int256Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `StringSlot` with member `value` located at `slot`.
     */
    function getStringSlot(bytes32 slot) internal pure returns (StringSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `StringSlot` representation of the string storage pointer `store`.
     */
    function getStringSlot(string storage store) internal pure returns (StringSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := store.slot
        }
    }

    /**
     * @dev Returns an `BytesSlot` with member `value` located at `slot`.
     */
    function getBytesSlot(bytes32 slot) internal pure returns (BytesSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BytesSlot` representation of the bytes storage pointer `store`.
     */
    function getBytesSlot(bytes storage store) internal pure returns (BytesSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := store.slot
        }
    }

    /**
     * @dev UDVT that represent a slot holding a address.
     */
    type AddressSlotType is bytes32;

    /**
     * @dev Cast an arbitrary slot to a AddressSlotType.
     */
    function asAddress(bytes32 slot) internal pure returns (AddressSlotType) {
        return AddressSlotType.wrap(slot);
    }

    /**
     * @dev UDVT that represent a slot holding a bool.
     */
    type BooleanSlotType is bytes32;

    /**
     * @dev Cast an arbitrary slot to a BooleanSlotType.
     */
    function asBoolean(bytes32 slot) internal pure returns (BooleanSlotType) {
        return BooleanSlotType.wrap(slot);
    }

    /**
     * @dev UDVT that represent a slot holding a bytes32.
     */
    type Bytes32SlotType is bytes32;

    /**
     * @dev Cast an arbitrary slot to a Bytes32SlotType.
     */
    function asBytes32(bytes32 slot) internal pure returns (Bytes32SlotType) {
        return Bytes32SlotType.wrap(slot);
    }

    /**
     * @dev UDVT that represent a slot holding a uint256.
     */
    type Uint256SlotType is bytes32;

    /**
     * @dev Cast an arbitrary slot to a Uint256SlotType.
     */
    function asUint256(bytes32 slot) internal pure returns (Uint256SlotType) {
        return Uint256SlotType.wrap(slot);
    }

    /**
     * @dev UDVT that represent a slot holding a int256.
     */
    type Int256SlotType is bytes32;

    /**
     * @dev Cast an arbitrary slot to a Int256SlotType.
     */
    function asInt256(bytes32 slot) internal pure returns (Int256SlotType) {
        return Int256SlotType.wrap(slot);
    }

    /**
     * @dev Load the value held at location `slot` in transient storage.
     */
    function tload(AddressSlotType slot) internal view returns (address value) {
        /// @solidity memory-safe-assembly
        assembly {
            value := tload(slot)
        }
    }

    /**
     * @dev Store `value` at location `slot` in transient storage.
     */
    function tstore(AddressSlotType slot, address value) internal {
        /// @solidity memory-safe-assembly
        assembly {
            tstore(slot, value)
        }
    }

    /**
     * @dev Load the value held at location `slot` in transient storage.
     */
    function tload(BooleanSlotType slot) internal view returns (bool value) {
        /// @solidity memory-safe-assembly
        assembly {
            value := tload(slot)
        }
    }

    /**
     * @dev Store `value` at location `slot` in transient storage.
     */
    function tstore(BooleanSlotType slot, bool value) internal {
        /// @solidity memory-safe-assembly
        assembly {
            tstore(slot, value)
        }
    }

    /**
     * @dev Load the value held at location `slot` in transient storage.
     */
    function tload(Bytes32SlotType slot) internal view returns (bytes32 value) {
        /// @solidity memory-safe-assembly
        assembly {
            value := tload(slot)
        }
    }

    /**
     * @dev Store `value` at location `slot` in transient storage.
     */
    function tstore(Bytes32SlotType slot, bytes32 value) internal {
        /// @solidity memory-safe-assembly
        assembly {
            tstore(slot, value)
        }
    }

    /**
     * @dev Load the value held at location `slot` in transient storage.
     */
    function tload(Uint256SlotType slot) internal view returns (uint256 value) {
        /// @solidity memory-safe-assembly
        assembly {
            value := tload(slot)
        }
    }

    /**
     * @dev Store `value` at location `slot` in transient storage.
     */
    function tstore(Uint256SlotType slot, uint256 value) internal {
        /// @solidity memory-safe-assembly
        assembly {
            tstore(slot, value)
        }
    }

    /**
     * @dev Load the value held at location `slot` in transient storage.
     */
    function tload(Int256SlotType slot) internal view returns (int256 value) {
        /// @solidity memory-safe-assembly
        assembly {
            value := tload(slot)
        }
    }

    /**
     * @dev Store `value` at location `slot` in transient storage.
     */
    function tstore(Int256SlotType slot, int256 value) internal {
        /// @solidity memory-safe-assembly
        assembly {
            tstore(slot, value)
        }
    }
}

// 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

pragma solidity ^0.8.0;

import {IERC721Metadata} from "@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol";

import {BookId} from "../libraries/BookId.sol";
import {Currency} from "../libraries/Currency.sol";
import {OrderId} from "../libraries/OrderId.sol";
import {Tick} from "../libraries/Tick.sol";
import {FeePolicy} from "../libraries/FeePolicy.sol";
import {IERC721Permit} from "./IERC721Permit.sol";
import {IHooks} from "./IHooks.sol";

/**
 * @title IBookManager
 * @notice The interface for the BookManager contract
 */
interface IBookManager is IERC721Metadata, IERC721Permit {
    error InvalidUnitSize();
    error InvalidFeePolicy();
    error InvalidProvider(address provider);
    error LockedBy(address locker, address hook);
    error CurrencyNotSettled();

    /**
     * @notice Event emitted when a new book is opened
     * @param id The book id
     * @param base The base currency
     * @param quote The quote currency
     * @param unitSize The unit size of the book
     * @param makerPolicy The maker fee policy
     * @param takerPolicy The taker fee policy
     * @param hooks The hooks contract
     */
    event Open(
        BookId indexed id,
        Currency indexed base,
        Currency indexed quote,
        uint64 unitSize,
        FeePolicy makerPolicy,
        FeePolicy takerPolicy,
        IHooks hooks
    );

    /**
     * @notice Event emitted when a new order is made
     * @param bookId The book id
     * @param user The user address
     * @param tick The order tick
     * @param orderIndex The order index
     * @param unit The order unit
     * @param provider The provider address
     */
    event Make(
        BookId indexed bookId, address indexed user, Tick tick, uint256 orderIndex, uint64 unit, address provider
    );

    /**
     * @notice Event emitted when an order is taken
     * @param bookId The book id
     * @param user The user address
     * @param tick The order tick
     * @param unit The order unit
     */
    event Take(BookId indexed bookId, address indexed user, Tick tick, uint64 unit);

    /**
     * @notice Event emitted when an order is canceled
     * @param orderId The order id
     * @param unit The canceled unit
     */
    event Cancel(OrderId indexed orderId, uint64 unit);

    /**
     * @notice Event emitted when an order is claimed
     * @param orderId The order id
     * @param unit The claimed unit
     */
    event Claim(OrderId indexed orderId, uint64 unit);

    /**
     * @notice Event emitted when a provider is whitelisted
     * @param provider The provider address
     */
    event Whitelist(address indexed provider);

    /**
     * @notice Event emitted when a provider is delisted
     * @param provider The provider address
     */
    event Delist(address indexed provider);

    /**
     * @notice Event emitted when a provider collects fees
     * @param provider The provider address
     * @param recipient The recipient address
     * @param currency The currency
     * @param amount The collected amount
     */
    event Collect(address indexed provider, address indexed recipient, Currency indexed currency, uint256 amount);

    /**
     * @notice Event emitted when new default provider is set
     * @param newDefaultProvider The new default provider address
     */
    event SetDefaultProvider(address indexed newDefaultProvider);

    /**
     * @notice This structure represents a unique identifier for a book in the BookManager.
     * @param base The base currency of the book
     * @param unitSize The unit size of the book
     * @param quote The quote currency of the book
     * @param makerPolicy The maker fee policy of the book
     * @param hooks The hooks contract of the book
     * @param takerPolicy The taker fee policy of the book
     */
    struct BookKey {
        Currency base;
        uint64 unitSize;
        Currency quote;
        FeePolicy makerPolicy;
        IHooks hooks;
        FeePolicy takerPolicy;
    }

    /**
     * @notice Returns the base URI
     * @return The base URI
     */
    function baseURI() external view returns (string memory);

    /**
     * @notice Returns the contract URI
     * @return The contract URI
     */
    function contractURI() external view returns (string memory);

    /**
     * @notice Returns the default provider
     * @return The default provider
     */
    function defaultProvider() external view returns (address);

    /**
     * @notice Returns the total reserves of a given currency
     * @param currency The currency in question
     * @return The total reserves amount
     */
    function reservesOf(Currency currency) external view returns (uint256);

    /**
     * @notice Checks if a provider is whitelisted
     * @param provider The address of the provider
     * @return True if the provider is whitelisted, false otherwise
     */
    function isWhitelisted(address provider) external view returns (bool);

    /**
     * @notice Verifies if an owner has authorized a spender for a token
     * @param owner The address of the token owner
     * @param spender The address of the spender
     * @param tokenId The token ID
     */
    function checkAuthorized(address owner, address spender, uint256 tokenId) external view;

    /**
     * @notice Calculates the amount owed to a provider in a given currency
     * @param provider The provider's address
     * @param currency The currency in question
     * @return The owed amount
     */
    function tokenOwed(address provider, Currency currency) external view returns (uint256);

    /**
     * @notice Calculates the currency balance changes for a given locker
     * @param locker The address of the locker
     * @param currency The currency in question
     * @return The net change in currency balance
     */
    function getCurrencyDelta(address locker, Currency currency) external view returns (int256);

    /**
     * @notice Retrieves the book key for a given book ID
     * @param id The book ID
     * @return The book key
     */
    function getBookKey(BookId id) external view returns (BookKey memory);

    /**
     * @notice This structure represents a current status for an order in the BookManager.
     * @param provider The provider of the order
     * @param open The open unit of the order
     * @param claimable The claimable unit of the order
     */
    struct OrderInfo {
        address provider;
        uint64 open;
        uint64 claimable;
    }

    /**
     * @notice Provides information about an order
     * @param id The order ID
     * @return Order information including provider, open status, and claimable unit
     */
    function getOrder(OrderId id) external view returns (OrderInfo memory);

    /**
     * @notice Retrieves the locker and caller addresses for a given lock
     * @param i The index of the lock
     * @return locker The locker's address
     * @return lockCaller The caller's address
     */
    function getLock(uint256 i) external view returns (address locker, address lockCaller);

    /**
     * @notice Provides the lock data
     * @return The lock data including necessary numeric values
     */
    function getLockData() external view returns (uint128, uint128);

    /**
     * @notice Returns the depth of a given book ID and tick
     * @param id The book ID
     * @param tick The tick
     * @return The depth of the tick
     */
    function getDepth(BookId id, Tick tick) external view returns (uint64);

    /**
     * @notice Retrieves the highest tick for a given book ID
     * @param id The book ID
     * @return tick The highest tick
     */
    function getHighest(BookId id) external view returns (Tick tick);

    /**
     * @notice Finds the maximum tick less than a specified tick in a book
     * @dev Returns `Tick.wrap(type(int24).min)` if the specified tick is the lowest
     * @param id The book ID
     * @param tick The specified tick
     * @return The next lower tick
     */
    function maxLessThan(BookId id, Tick tick) external view returns (Tick);

    /**
     * @notice Checks if a book is opened
     * @param id The book ID
     * @return True if the book is opened, false otherwise
     */
    function isOpened(BookId id) external view returns (bool);

    /**
     * @notice Checks if a book is empty
     * @param id The book ID
     * @return True if the book is empty, false otherwise
     */
    function isEmpty(BookId id) external view returns (bool);

    /**
     * @notice Encodes a BookKey into a BookId
     * @param key The BookKey to encode
     * @return The encoded BookId
     */
    function encodeBookKey(BookKey calldata key) external pure returns (BookId);

    /**
     * @notice Loads a value from a specific storage slot
     * @param slot The storage slot
     * @return The value in the slot
     */
    function load(bytes32 slot) external view returns (bytes32);

    /**
     * @notice Loads a sequence of values starting from a specific slot
     * @param startSlot The starting slot
     * @param nSlot The number of slots to load
     * @return The sequence of values
     */
    function load(bytes32 startSlot, uint256 nSlot) external view returns (bytes memory);

    /**
     * @notice Opens a new book
     * @param key The book key
     * @param hookData The hook data
     */
    function open(BookKey calldata key, bytes calldata hookData) external;

    /**
     * @notice Locks a book manager function
     * @param locker The locker address
     * @param data The lock data
     * @return The lock return data
     */
    function lock(address locker, bytes calldata data) external returns (bytes memory);

    /**
     * @notice This structure represents the parameters for making an order.
     * @param key The book key for the order
     * @param tick The tick for the order
     * @param unit The unit for the order. Times key.unitSize to get actual bid amount.
     * @param provider The provider for the order. The limit order service provider address to collect fees.
     */
    struct MakeParams {
        BookKey key;
        Tick tick;
        uint64 unit;
        address provider;
    }

    /**
     * @notice Make a limit order
     * @param params The order parameters
     * @param hookData The hook data
     * @return id The order id. Returns 0 if the order is not settled
     * @return quoteAmount The amount of quote currency to be paid
     */
    function make(MakeParams calldata params, bytes calldata hookData)
        external
        returns (OrderId id, uint256 quoteAmount);

    /**
     * @notice This structure represents the parameters for taking orders in the specified tick.
     * @param key The book key for the order
     * @param tick The tick for the order
     * @param maxUnit The max unit to take
     */
    struct TakeParams {
        BookKey key;
        Tick tick;
        uint64 maxUnit;
    }

    /**
     * @notice Take a limit order at specific tick
     * @param params The order parameters
     * @param hookData The hook data
     * @return quoteAmount The amount of quote currency to be received
     * @return baseAmount The amount of base currency to be paid
     */
    function take(TakeParams calldata params, bytes calldata hookData)
        external
        returns (uint256 quoteAmount, uint256 baseAmount);

    /**
     * @notice This structure represents the parameters for canceling an order.
     * @param id The order id for the order
     * @param toUnit The remaining open unit for the order after cancellation. Must not exceed the current open unit.
     */
    struct CancelParams {
        OrderId id;
        uint64 toUnit;
    }

    /**
     * @notice Cancel a limit order
     * @param params The order parameters
     * @param hookData The hook data
     * @return canceledAmount The amount of quote currency canceled
     */
    function cancel(CancelParams calldata params, bytes calldata hookData) external returns (uint256 canceledAmount);

    /**
     * @notice Claims an order
     * @param id The order ID
     * @param hookData The hook data
     * @return claimedAmount The amount claimed
     */
    function claim(OrderId id, bytes calldata hookData) external returns (uint256 claimedAmount);

    /**
     * @notice Collects fees from a provider
     * @param recipient The recipient address
     * @param currency The currency
     * @return The collected amount
     */
    function collect(address recipient, Currency currency) external returns (uint256);

    /**
     * @notice Withdraws a currency
     * @param currency The currency
     * @param to The recipient address
     * @param amount The amount
     */
    function withdraw(Currency currency, address to, uint256 amount) external;

    /**
     * @notice Settles a currency
     * @param currency The currency
     * @return The settled amount
     */
    function settle(Currency currency) external payable returns (uint256);

    /**
     * @notice Whitelists a provider
     * @param provider The provider address
     */
    function whitelist(address provider) external;

    /**
     * @notice Delists a provider
     * @param provider The provider address
     */
    function delist(address provider) external;

    /**
     * @notice Sets the default provider
     * @param newDefaultProvider The new default provider address
     */
    function setDefaultProvider(address newDefaultProvider) external;
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import {IERC721} from "@openzeppelin/contracts/token/ERC721/IERC721.sol";

/**
 * @title IERC721Permit
 * @notice An interface for the ERC721 permit extension
 */
interface IERC721Permit is IERC721 {
    error InvalidSignature();
    error PermitExpired();

    /**
     * @notice The EIP-712 typehash for the permit struct used by the contract
     */
    function PERMIT_TYPEHASH() external pure returns (bytes32);

    /**
     * @notice The EIP-712 domain separator for this contract
     */
    function DOMAIN_SEPARATOR() external view returns (bytes32);

    /**
     * @notice Approve the spender to transfer the given tokenId
     * @param spender The address to approve
     * @param tokenId The tokenId to approve
     * @param deadline The deadline for the signature
     * @param v The recovery id of the signature
     * @param r The r value of the signature
     * @param s The s value of the signature
     */
    function permit(address spender, uint256 tokenId, uint256 deadline, uint8 v, bytes32 r, bytes32 s) external;

    /**
     * @notice Get the current nonce for a token
     * @param tokenId The tokenId to get the nonce for
     * @return The current nonce
     */
    function nonces(uint256 tokenId) external view returns (uint256);
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.20;

import {IBookManager} from "./IBookManager.sol";
import {OrderId} from "../libraries/OrderId.sol";

/**
 * @title IHooks
 * @notice Interface for the hooks contract
 */
interface IHooks {
    /**
     * @notice Hook called before opening a new book
     * @param sender The sender of the open transaction
     * @param key The key of the book being opened
     * @param hookData The data passed to the hook
     * @return Returns the function selector if the hook is successful
     */
    function beforeOpen(address sender, IBookManager.BookKey calldata key, bytes calldata hookData)
        external
        returns (bytes4);

    /**
     * @notice Hook called after opening a new book
     * @param sender The sender of the open transaction
     * @param key The key of the book being opened
     * @param hookData The data passed to the hook
     * @return Returns the function selector if the hook is successful
     */
    function afterOpen(address sender, IBookManager.BookKey calldata key, bytes calldata hookData)
        external
        returns (bytes4);

    /**
     * @notice Hook called before making a new order
     * @param sender The sender of the make transaction
     * @param params The parameters of the make transaction
     * @param hookData The data passed to the hook
     * @return Returns the function selector if the hook is successful
     */
    function beforeMake(address sender, IBookManager.MakeParams calldata params, bytes calldata hookData)
        external
        returns (bytes4);

    /**
     * @notice Hook called after making a new order
     * @param sender The sender of the make transaction
     * @param params The parameters of the make transaction
     * @param orderId The id of the order that was made
     * @param hookData The data passed to the hook
     * @return Returns the function selector if the hook is successful
     */
    function afterMake(
        address sender,
        IBookManager.MakeParams calldata params,
        OrderId orderId,
        bytes calldata hookData
    ) external returns (bytes4);

    /**
     * @notice Hook called before taking an order
     * @param sender The sender of the take transaction
     * @param params The parameters of the take transaction
     * @param hookData The data passed to the hook
     * @return Returns the function selector if the hook is successful
     */
    function beforeTake(address sender, IBookManager.TakeParams calldata params, bytes calldata hookData)
        external
        returns (bytes4);

    /**
     * @notice Hook called after taking an order
     * @param sender The sender of the take transaction
     * @param params The parameters of the take transaction
     * @param takenUnit The unit that was taken
     * @param hookData The data passed to the hook
     * @return Returns the function selector if the hook is successful
     */
    function afterTake(
        address sender,
        IBookManager.TakeParams calldata params,
        uint64 takenUnit,
        bytes calldata hookData
    ) external returns (bytes4);

    /**
     * @notice Hook called before canceling an order
     * @param sender The sender of the cancel transaction
     * @param params The parameters of the cancel transaction
     * @param hookData The data passed to the hook
     * @return Returns the function selector if the hook is successful
     */
    function beforeCancel(address sender, IBookManager.CancelParams calldata params, bytes calldata hookData)
        external
        returns (bytes4);

    /**
     * @notice Hook called after canceling an order
     * @param sender The sender of the cancel transaction
     * @param params The parameters of the cancel transaction
     * @param canceledUnit The unit that was canceled
     * @param hookData The data passed to the hook
     * @return Returns the function selector if the hook is successful
     */
    function afterCancel(
        address sender,
        IBookManager.CancelParams calldata params,
        uint64 canceledUnit,
        bytes calldata hookData
    ) external returns (bytes4);

    /**
     * @notice Hook called before claiming an order
     * @param sender The sender of the claim transaction
     * @param orderId The id of the order being claimed
     * @param hookData The data passed to the hook
     * @return Returns the function selector if the hook is successful
     */
    function beforeClaim(address sender, OrderId orderId, bytes calldata hookData) external returns (bytes4);

    /**
     * @notice Hook called after claiming an order
     * @param sender The sender of the claim transaction
     * @param orderId The id of the order being claimed
     * @param claimedUnit The unit that was claimed
     * @param hookData The data passed to the hook
     * @return Returns the function selector if the hook is successful
     */
    function afterClaim(address sender, OrderId orderId, uint64 claimedUnit, bytes calldata hookData)
        external
        returns (bytes4);
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 * @title ILocker
 * @notice Interface for the locker contract
 */
interface ILocker {
    /**
     * @notice Called by the book manager on `msg.sender` when a lock is acquired
     * @param data The data that was passed to the call to lock
     * @return Any data that you want to be returned from the lock call
     */
    function lockAcquired(address lockCaller, bytes calldata data) external returns (bytes memory);
}

// SPDX-License-Identifier: -
// License: https://license.sonic.market/LICENSE.pdf

pragma solidity ^0.8.20;

import {SafeCast} from "@openzeppelin/contracts/utils/math/SafeCast.sol";

import {IBookManager} from "../interfaces/IBookManager.sol";
import {SegmentedSegmentTree} from "./SegmentedSegmentTree.sol";
import {Tick, TickLibrary} from "./Tick.sol";
import {OrderId, OrderIdLibrary} from "./OrderId.sol";
import {TotalClaimableMap} from "./TotalClaimableMap.sol";
import {TickBitmap} from "./TickBitmap.sol";

library Book {
    using Book for State;
    using TickBitmap for mapping(uint256 => uint256);
    using SegmentedSegmentTree for SegmentedSegmentTree.Core;
    using TotalClaimableMap for mapping(uint24 => uint256);
    using TickLibrary for Tick;
    using OrderIdLibrary for OrderId;

    error ZeroUnit();
    error BookAlreadyOpened();
    error BookNotOpened();
    error QueueReplaceFailed();
    error CancelFailed(uint64 maxCancelableUnit);

    // @dev Due to the segment tree implementation, the maximum order size is 2 ** 15.
    uint40 internal constant MAX_ORDER = 2 ** 15; // 32768
    uint256 internal constant MAX_ORDER_M = 2 ** 15 - 1; // % 32768

    struct Order {
        address provider;
        uint64 pending; // @dev unfilled unit + filled(claimable) unit
    }

    struct Queue {
        SegmentedSegmentTree.Core tree;
        Order[] orders;
    }

    struct State {
        IBookManager.BookKey key;
        mapping(Tick tick => Queue) queues;
        mapping(uint256 => uint256) tickBitmap;
        // @dev Four values of totalClaimable are stored in one uint256
        mapping(uint24 groupIndex => uint256) totalClaimableOf;
    }

    function open(State storage self, IBookManager.BookKey calldata key) external {
        if (self.isOpened()) revert BookAlreadyOpened();
        self.key = key;
    }

    function isOpened(State storage self) internal view returns (bool) {
        return self.key.unitSize != 0;
    }

    function checkOpened(State storage self) internal view {
        if (!self.isOpened()) revert BookNotOpened();
    }

    function depth(State storage self, Tick tick) internal view returns (uint64) {
        return self.queues[tick].tree.total() - self.totalClaimableOf.get(tick);
    }

    function highest(State storage self) internal view returns (Tick) {
        return self.tickBitmap.highest();
    }

    function maxLessThan(State storage self, Tick tick) internal view returns (Tick) {
        return self.tickBitmap.maxLessThan(tick);
    }

    function isEmpty(State storage self) internal view returns (bool) {
        return self.tickBitmap.isEmpty();
    }

    function _getOrder(State storage self, Tick tick, uint40 index) private view returns (Order storage) {
        return self.queues[tick].orders[index];
    }

    function getOrder(State storage self, Tick tick, uint40 index) internal view returns (Order memory) {
        return _getOrder(self, tick, index);
    }

    function make(State storage self, Tick tick, uint64 unit, address provider) external returns (uint40 orderIndex) {
        if (unit == 0) revert ZeroUnit();
        if (!self.tickBitmap.has(tick)) self.tickBitmap.set(tick);

        Queue storage queue = self.queues[tick];
        // @dev Assume that orders.length cannot reach to type(uint40).max + 1.
        orderIndex = SafeCast.toUint40(queue.orders.length);

        if (orderIndex >= MAX_ORDER) {
            unchecked {
                uint40 staleOrderIndex = orderIndex - MAX_ORDER;
                uint64 stalePendingUnit = queue.orders[staleOrderIndex].pending;
                if (stalePendingUnit > 0) {
                    // If the order is not settled completely, we cannot replace it
                    uint64 claimable = calculateClaimableUnit(self, tick, staleOrderIndex);
                    if (claimable != stalePendingUnit) revert QueueReplaceFailed();
                }
            }

            // The stale order is settled completely, so remove it from the totalClaimableOf.
            // We can determine the stale order is claimable.
            uint64 staleOrderedUnit = queue.tree.get(orderIndex & MAX_ORDER_M);
            if (staleOrderedUnit > 0) self.totalClaimableOf.sub(tick, staleOrderedUnit);
        }

        queue.tree.update(orderIndex & MAX_ORDER_M, unit);

        queue.orders.push(Order({pending: unit, provider: provider}));
    }

    /**
     * @notice Take orders from the book
     * @param self The book state
     * @param maxTakeUnit The maximum unit to take
     * @return takenUnit The actual unit to take
     */
    function take(State storage self, Tick tick, uint64 maxTakeUnit) external returns (uint64 takenUnit) {
        uint64 currentDepth = depth(self, tick);
        if (currentDepth > maxTakeUnit) {
            takenUnit = maxTakeUnit;
        } else {
            takenUnit = currentDepth;
            self.tickBitmap.clear(tick);
        }

        self.totalClaimableOf.add(tick, takenUnit);
    }

    function cancel(State storage self, OrderId orderId, uint64 to)
        external
        returns (uint64 canceled, uint64 afterPending)
    {
        (, Tick tick, uint40 orderIndex) = orderId.decode();
        Queue storage queue = self.queues[tick];
        uint64 pendingUnit = queue.orders[orderIndex].pending;
        uint64 claimableUnit = calculateClaimableUnit(self, tick, orderIndex);
        afterPending = to + claimableUnit;
        unchecked {
            if (pendingUnit < afterPending) revert CancelFailed(pendingUnit - claimableUnit);
            canceled = pendingUnit - afterPending;

            self.queues[tick].tree.update(
                orderIndex & MAX_ORDER_M, self.queues[tick].tree.get(orderIndex & MAX_ORDER_M) - canceled
            );
        }
        queue.orders[orderIndex].pending = afterPending;

        if (depth(self, tick) == 0) {
            // clear() won't revert so we can cancel with to=0 even if the depth() is already zero
            // works even if bitmap is empty
            self.tickBitmap.clear(tick);
        }
    }

    function claim(State storage self, Tick tick, uint40 index) external returns (uint64 claimedUnit) {
        Order storage order = _getOrder(self, tick, index);

        claimedUnit = calculateClaimableUnit(self, tick, index);
        unchecked {
            order.pending -= claimedUnit;
        }
    }

    function calculateClaimableUnit(State storage self, Tick tick, uint40 index) public view returns (uint64) {
        uint64 orderUnit = self.getOrder(tick, index).pending;

        Queue storage queue = self.queues[tick];
        // @dev Book logic always considers replaced orders as claimable.
        unchecked {
            if (uint256(index) + MAX_ORDER < queue.orders.length) return orderUnit;
            uint64 totalClaimableUnit = self.totalClaimableOf.get(tick);
            uint64 rangeRight = _getClaimRangeRight(queue, index);
            if (rangeRight - orderUnit >= totalClaimableUnit) return 0;

            // -------- totalClaimable ---------|---
            // ------|----  orderUnit  ----|--------
            //   rangeLeft           rangeRight
            if (rangeRight <= totalClaimableUnit) return orderUnit;
            // -- totalClaimable --|----------------
            // ------|----  orderUnit  ----|--------
            //   rangeLeft           rangeRight
            else return totalClaimableUnit - (rangeRight - orderUnit);
        }
    }

    function _getClaimRangeRight(Queue storage queue, uint256 orderIndex) private view returns (uint64 rangeRight) {
        uint256 l = queue.orders.length & MAX_ORDER_M;
        uint256 r = (orderIndex + 1) & MAX_ORDER_M;
        rangeRight = (l < r) ? queue.tree.query(l, r) : queue.tree.total() - queue.tree.query(r, l);
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later

pragma solidity ^0.8.20;

import {IBookManager} from "../interfaces/IBookManager.sol";

type BookId is uint192;

library BookIdLibrary {
    function toId(IBookManager.BookKey memory bookKey) internal pure returns (BookId id) {
        bytes32 hash = keccak256(abi.encode(bookKey));
        assembly {
            id := and(hash, 0xffffffffffffffffffffffffffffffffffffffffffffffff)
        }
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later

pragma solidity ^0.8.20;

import {IERC20} from "@openzeppelin/contracts/token/ERC20/IERC20.sol";

type Currency is address;

/// @title CurrencyLibrary
/// @dev This library allows for transferring and holding native tokens and ERC20 tokens
library CurrencyLibrary {
    using CurrencyLibrary for Currency;

    /// @notice Thrown when a native transfer fails
    error NativeTransferFailed();

    /// @notice Thrown when an ERC20 transfer fails
    error ERC20TransferFailed();

    Currency public constant NATIVE = Currency.wrap(address(0));

    function transfer(Currency currency, address to, uint256 amount) internal {
        // implementation from
        // https://github.com/transmissions11/solmate/blob/e8f96f25d48fe702117ce76c79228ca4f20206cb/src/utils/SafeTransferLib.sol

        bool success;
        if (currency.isNative()) {
            assembly {
                // Transfer the ETH and store if it succeeded or not.
                success := call(gas(), to, amount, 0, 0, 0, 0)
            }

            if (!success) revert NativeTransferFailed();
        } else {
            assembly {
                // Get a pointer to some free memory.
                let freeMemoryPointer := mload(0x40)

                // Write the abi-encoded calldata into memory, beginning with the function selector.
                mstore(freeMemoryPointer, 0xa9059cbb00000000000000000000000000000000000000000000000000000000)
                mstore(add(freeMemoryPointer, 4), and(to, 0xffffffffffffffffffffffffffffffffffffffff)) // Append and mask the "to" argument.
                mstore(add(freeMemoryPointer, 36), amount) // Append the "amount" argument. Masking not required as it's a full 32 byte type.

                success :=
                    and(
                        // Set success to whether the call reverted, if not we check it either
                        // returned exactly 1 (can't just be non-zero data), or had no return data.
                        or(and(eq(mload(0), 1), gt(returndatasize(), 31)), iszero(returndatasize())),
                        // We use 68 because the length of our calldata totals up like so: 4 + 32 * 2.
                        // We use 0 and 32 to copy up to 32 bytes of return data into the scratch space.
                        // Counterintuitively, this call must be positioned second to the or() call in the
                        // surrounding and() call or else returndatasize() will be zero during the computation.
                        call(gas(), currency, 0, freeMemoryPointer, 68, 0, 32)
                    )
            }

            if (!success) revert ERC20TransferFailed();
        }
    }

    function balanceOfSelf(Currency currency) internal view returns (uint256) {
        if (currency.isNative()) return address(this).balance;
        else return IERC20(Currency.unwrap(currency)).balanceOf(address(this));
    }

    function equals(Currency currency, Currency other) internal pure returns (bool) {
        return Currency.unwrap(currency) == Currency.unwrap(other);
    }

    function isNative(Currency currency) internal pure returns (bool) {
        return Currency.unwrap(currency) == Currency.unwrap(NATIVE);
    }

    function toId(Currency currency) internal pure returns (uint256) {
        return uint160(Currency.unwrap(currency));
    }

    function fromId(uint256 id) internal pure returns (Currency) {
        return Currency.wrap(address(uint160(id)));
    }
}

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

import {Currency, CurrencyLibrary} from "./Currency.sol";

library CurrencyDelta {
    // uint256(keccak256("CurrencyDelta")) + 1
    uint256 internal constant CURRENCY_DELTA_SLOT = 0x95b400a0305233758f18c75aa62cbbb5d6882951dd55f1407390ee7b6924e26f;

    function get(address locker, Currency currency) internal view returns (int256 delta) {
        assembly {
            mstore(0x14, currency)
            mstore(0x00, locker)
            delta := tload(keccak256(0x0c, 0x28))
        }
    }

    function add(address locker, Currency currency, int256 delta) internal returns (int256 result) {
        assembly {
            mstore(0x14, currency)
            mstore(0x00, locker)
            let slot := keccak256(0x0c, 0x28)
            result := add(tload(slot), delta)
            tstore(slot, result)
        }
    }
}

// SPDX-License-Identifier: -
// License: https://license.sonic.market/LICENSE.pdf

pragma solidity ^0.8.0;

library DirtyUint64 {
    error DirtyUint64Error(uint256 errorCode);

    uint256 private constant _OVERFLOW_ERROR = 0;
    uint256 private constant _UNDERFLOW_ERROR = 1;

    function toDirtyUnsafe(uint64 cleanUint) internal pure returns (uint64 dirtyUint) {
        assembly {
            dirtyUint := add(cleanUint, 1)
        }
    }

    function toDirty(uint64 cleanUint) internal pure returns (uint64 dirtyUint) {
        assembly {
            dirtyUint := add(cleanUint, 1)
        }
        if (dirtyUint == 0) {
            revert DirtyUint64Error(_OVERFLOW_ERROR);
        }
    }

    function toClean(uint64 dirtyUint) internal pure returns (uint64 cleanUint) {
        assembly {
            cleanUint := sub(dirtyUint, gt(dirtyUint, 0))
        }
    }

    function addClean(uint64 current, uint64 cleanUint) internal pure returns (uint64) {
        assembly {
            current := add(add(current, iszero(current)), cleanUint)
        }
        if (current < cleanUint) {
            revert DirtyUint64Error(_OVERFLOW_ERROR);
        }
        return current;
    }

    function addDirty(uint64 current, uint64 dirtyUint) internal pure returns (uint64) {
        assembly {
            current := sub(add(add(current, iszero(current)), add(dirtyUint, iszero(dirtyUint))), 1)
        }
        if (current < dirtyUint) {
            revert DirtyUint64Error(_OVERFLOW_ERROR);
        }
        return current;
    }

    function subClean(uint64 current, uint64 cleanUint) internal pure returns (uint64 ret) {
        assembly {
            current := add(current, iszero(current))
            ret := sub(current, cleanUint)
        }
        if (current < ret || ret == 0) {
            revert DirtyUint64Error(_UNDERFLOW_ERROR);
        }
    }

    function subDirty(uint64 current, uint64 dirtyUint) internal pure returns (uint64 ret) {
        assembly {
            current := add(current, iszero(current))
            ret := sub(add(current, 1), add(dirtyUint, iszero(dirtyUint)))
        }
        if (current < ret || ret == 0) {
            revert DirtyUint64Error(_UNDERFLOW_ERROR);
        }
    }

    function sumPackedUnsafe(uint256 packed, uint256 from, uint256 to) internal pure returns (uint64 ret) {
        packed = packed >> (from << 6);
        unchecked {
            for (uint256 i = from; i < to; ++i) {
                assembly {
                    let element := and(packed, 0xffffffffffffffff)
                    ret := add(ret, add(element, iszero(element)))
                    packed := shr(64, packed)
                }
            }
        }
        assembly {
            ret := sub(ret, sub(to, from))
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC721/ERC721.sol)
// Modified by Sonic Market Team

pragma solidity ^0.8.20;

import {IERC721} from "@openzeppelin/contracts/token/ERC721/IERC721.sol";
import {IERC721Receiver} from "@openzeppelin/contracts/token/ERC721/IERC721Receiver.sol";
import {IERC721Metadata} from "@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol";
import {Context} from "@openzeppelin/contracts/utils/Context.sol";
import {Strings} from "@openzeppelin/contracts/utils/Strings.sol";
import {IERC165, ERC165} from "@openzeppelin/contracts/utils/introspection/ERC165.sol";
import {IERC721Errors} from "@openzeppelin/contracts/interfaces/draft-IERC6093.sol";

/**
 * @dev Implementation of https://eips.ethereum.org/EIPS/eip-721[ERC721] Non-Fungible Token Standard, including
 * the Metadata extension, but not including the Enumerable extension, which is available separately as
 * {ERC721Enumerable}.
 */
abstract contract ERC721 is Context, ERC165, IERC721, IERC721Metadata, IERC721Errors {
    using Strings for uint256;

    // Token name
    string private _name;

    // Token symbol
    string private _symbol;

    mapping(address owner => uint256) private _balances;

    mapping(uint256 tokenId => address) private _tokenApprovals;

    mapping(address owner => mapping(address operator => bool)) private _operatorApprovals;

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

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165, IERC165) returns (bool) {
        return interfaceId == type(IERC721).interfaceId || interfaceId == type(IERC721Metadata).interfaceId
            || super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC721-balanceOf}.
     */
    function balanceOf(address owner) public view virtual returns (uint256) {
        if (owner == address(0)) {
            revert ERC721InvalidOwner(address(0));
        }
        return _balances[owner];
    }

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

    /**
     * @dev See {IERC721Metadata-name}.
     */
    function name() public view virtual returns (string memory) {
        return _name;
    }

    /**
     * @dev See {IERC721Metadata-symbol}.
     */
    function symbol() public view virtual returns (string memory) {
        return _symbol;
    }

    /**
     * @dev See {IERC721Metadata-tokenURI}.
     */
    function tokenURI(uint256 tokenId) public view virtual returns (string memory) {
        _requireOwned(tokenId);

        string memory baseURI = _baseURI();
        return bytes(baseURI).length > 0 ? string.concat(baseURI, tokenId.toString()) : "";
    }

    /**
     * @dev Base URI for computing {tokenURI}. If set, the resulting URI for each
     * token will be the concatenation of the `baseURI` and the `tokenId`. Empty
     * by default, can be overridden in child contracts.
     */
    function _baseURI() internal view virtual returns (string memory) {
        return "";
    }

    /**
     * @dev See {IERC721-approve}.
     */
    function approve(address to, uint256 tokenId) public virtual {
        _approve(to, tokenId, _msgSender());
    }

    /**
     * @dev See {IERC721-getApproved}.
     */
    function getApproved(uint256 tokenId) public view virtual returns (address) {
        _requireOwned(tokenId);

        return _getApproved(tokenId);
    }

    /**
     * @dev See {IERC721-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved) public virtual {
        _setApprovalForAll(_msgSender(), operator, approved);
    }

    /**
     * @dev See {IERC721-isApprovedForAll}.
     */
    function isApprovedForAll(address owner, address operator) public view virtual returns (bool) {
        return _operatorApprovals[owner][operator];
    }

    /**
     * @dev See {IERC721-transferFrom}.
     */
    function transferFrom(address from, address to, uint256 tokenId) public virtual {
        if (to == address(0)) {
            revert ERC721InvalidReceiver(address(0));
        }
        // Setting an "auth" arguments enables the `_isAuthorized` check which verifies that the token exists
        // (from != 0). Therefore, it is not needed to verify that the return value is not 0 here.
        address previousOwner = _update(to, tokenId, _msgSender());
        if (previousOwner != from) {
            revert ERC721IncorrectOwner(from, tokenId, previousOwner);
        }
    }

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

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(address from, address to, uint256 tokenId, bytes memory data) public virtual {
        transferFrom(from, to, tokenId);
        _checkOnERC721Received(from, to, tokenId, data);
    }

    /**
     * @dev Returns the owner of the `tokenId`. Does NOT revert if token doesn't exist
     *
     * IMPORTANT: Any overrides to this function that add ownership of tokens not tracked by the
     * core ERC721 logic MUST be matched with the use of {_increaseBalance} to keep balances
     * consistent with ownership. The invariant to preserve is that for any address `a` the value returned by
     * `balanceOf(a)` must be equal to the number of tokens such that `_ownerOf(tokenId)` is `a`.
     */
    function _ownerOf(uint256 tokenId) internal view virtual returns (address);

    /**
     * @dev Returns the approved address for `tokenId`. Returns 0 if `tokenId` is not minted.
     */
    function _getApproved(uint256 tokenId) internal view virtual returns (address) {
        return _tokenApprovals[tokenId];
    }

    /**
     * @dev Returns whether `spender` is allowed to manage `owner`'s tokens, or `tokenId` in
     * particular (ignoring whether it is owned by `owner`).
     *
     * WARNING: This function assumes that `owner` is the actual owner of `tokenId` and does not verify this
     * assumption.
     */
    function _isAuthorized(address owner, address spender, uint256 tokenId) internal view virtual returns (bool) {
        return spender != address(0)
            && (owner == spender || isApprovedForAll(owner, spender) || _getApproved(tokenId) == spender);
    }

    /**
     * @dev Checks if `spender` can operate on `tokenId`, assuming the provided `owner` is the actual owner.
     * Reverts if `spender` does not have approval from the provided `owner` for the given token or for all its assets
     * the `spender` for the specific `tokenId`.
     *
     * WARNING: This function assumes that `owner` is the actual owner of `tokenId` and does not verify this
     * assumption.
     */
    function _checkAuthorized(address owner, address spender, uint256 tokenId) internal view virtual {
        if (!_isAuthorized(owner, spender, tokenId)) {
            if (owner == address(0)) {
                revert ERC721NonexistentToken(tokenId);
            } else {
                revert ERC721InsufficientApproval(spender, tokenId);
            }
        }
    }

    /**
     * @dev Unsafe write access to the balances, used by extensions that "mint" tokens using an {ownerOf} override.
     *
     * NOTE: the value is limited to type(uint128).max. This protect against _balance overflow. It is unrealistic that
     * a uint256 would ever overflow from increments when these increments are bounded to uint128 values.
     *
     * WARNING: Increasing an account's balance using this function tends to be paired with an override of the
     * {_ownerOf} function to resolve the ownership of the corresponding tokens so that balances and ownership
     * remain consistent with one another.
     */
    function _increaseBalance(address account, uint128 value) internal virtual {
        unchecked {
            _balances[account] += value;
        }
    }

    /**
     * @dev Transfers `tokenId` from its current owner to `to`, or alternatively mints (or burns) if the current owner
     * (or `to`) is the zero address. Returns the owner of the `tokenId` before the update.
     *
     * The `auth` argument is optional. If the value passed is non 0, then this function will check that
     * `auth` is either the owner of the token, or approved to operate on the token (by the owner).
     *
     * Emits a {Transfer} event.
     *
     * NOTE: If overriding this function in a way that tracks balances, see also {_increaseBalance}.
     */
    function _update(address to, uint256 tokenId, address auth) internal virtual returns (address) {
        address from = _ownerOf(tokenId);

        // Perform (optional) operator check
        if (auth != address(0)) {
            _checkAuthorized(from, auth, tokenId);
        }

        // Execute the update
        if (from != address(0)) {
            // Clear approval. No need to re-authorize or emit the Approval event
            _approve(address(0), tokenId, address(0), false);

            unchecked {
                _balances[from] -= 1;
            }
        }

        if (to != address(0)) {
            unchecked {
                _balances[to] += 1;
            }
        }

        // @dev MODIFIED: Define _setOwner
        _setOwner(tokenId, to);

        emit Transfer(from, to, tokenId);

        return from;
    }

    /**
     * @dev Mints `tokenId` and transfers it to `to`.
     *
     * WARNING: Usage of this method is discouraged, use {_safeMint} whenever possible
     *
     * Requirements:
     *
     * - `tokenId` must not exist.
     * - `to` cannot be the zero address.
     *
     * Emits a {Transfer} event.
     */
    function _mint(address to, uint256 tokenId) internal {
        if (to == address(0)) {
            revert ERC721InvalidReceiver(address(0));
        }
        address previousOwner = _update(to, tokenId, address(0));
        if (previousOwner != address(0)) {
            revert ERC721InvalidSender(address(0));
        }
    }

    /**
     * @dev Mints `tokenId`, transfers it to `to` and checks for `to` acceptance.
     *
     * Requirements:
     *
     * - `tokenId` must not exist.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeMint(address to, uint256 tokenId) internal {
        _safeMint(to, tokenId, "");
    }

    /**
     * @dev Same as {xref-ERC721-_safeMint-address-uint256-}[`_safeMint`], with an additional `data` parameter which is
     * forwarded in {IERC721Receiver-onERC721Received} to contract recipients.
     */
    function _safeMint(address to, uint256 tokenId, bytes memory data) internal virtual {
        _mint(to, tokenId);
        _checkOnERC721Received(address(0), to, tokenId, data);
    }

    /**
     * @dev Destroys `tokenId`.
     * The approval is cleared when the token is burned.
     * This is an internal function that does not check if the sender is authorized to operate on the token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     *
     * Emits a {Transfer} event.
     */
    function _burn(uint256 tokenId) internal {
        address previousOwner = _update(address(0), tokenId, address(0));
        if (previousOwner == address(0)) {
            revert ERC721NonexistentToken(tokenId);
        }
    }

    /**
     * @dev Transfers `tokenId` from `from` to `to`.
     *  As opposed to {transferFrom}, this imposes no restrictions on msg.sender.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     *
     * Emits a {Transfer} event.
     */
    function _transfer(address from, address to, uint256 tokenId) internal {
        if (to == address(0)) {
            revert ERC721InvalidReceiver(address(0));
        }
        address previousOwner = _update(to, tokenId, address(0));
        if (previousOwner == address(0)) {
            revert ERC721NonexistentToken(tokenId);
        } else if (previousOwner != from) {
            revert ERC721IncorrectOwner(from, tokenId, previousOwner);
        }
    }

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking that contract recipients
     * are aware of the ERC721 standard to prevent tokens from being forever locked.
     *
     * `data` is additional data, it has no specified format and it is sent in call to `to`.
     *
     * This internal function is like {safeTransferFrom} in the sense that it invokes
     * {IERC721Receiver-onERC721Received} on the receiver, and can be used to e.g.
     * implement alternative mechanisms to perform token transfer, such as signature-based.
     *
     * Requirements:
     *
     * - `tokenId` token must exist and be owned by `from`.
     * - `to` cannot be the zero address.
     * - `from` cannot be the zero address.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeTransfer(address from, address to, uint256 tokenId) internal {
        _safeTransfer(from, to, tokenId, "");
    }

    /**
     * @dev Same as {xref-ERC721-_safeTransfer-address-address-uint256-}[`_safeTransfer`], with an additional `data` parameter which is
     * forwarded in {IERC721Receiver-onERC721Received} to contract recipients.
     */
    function _safeTransfer(address from, address to, uint256 tokenId, bytes memory data) internal virtual {
        _transfer(from, to, tokenId);
        _checkOnERC721Received(from, to, tokenId, data);
    }

    /**
     * @dev Approve `to` to operate on `tokenId`
     *
     * The `auth` argument is optional. If the value passed is non 0, then this function will check that `auth` is
     * either the owner of the token, or approved to operate on all tokens held by this owner.
     *
     * Emits an {Approval} event.
     *
     * Overrides to this logic should be done to the variant with an additional `bool emitEvent` argument.
     */
    function _approve(address to, uint256 tokenId, address auth) internal {
        _approve(to, tokenId, auth, true);
    }

    /**
     * @dev Variant of `_approve` with an optional flag to enable or disable the {Approval} event. The event is not
     * emitted in the context of transfers.
     */
    function _approve(address to, uint256 tokenId, address auth, bool emitEvent) internal virtual {
        // Avoid reading the owner unless necessary
        if (emitEvent || auth != address(0)) {
            address owner = _requireOwned(tokenId);

            // We do not use _isAuthorized because single-token approvals should not be able to call approve
            if (auth != address(0) && owner != auth && !isApprovedForAll(owner, auth)) {
                revert ERC721InvalidApprover(auth);
            }

            if (emitEvent) {
                emit Approval(owner, to, tokenId);
            }
        }

        _tokenApprovals[tokenId] = to;
    }

    /**
     * @dev Approve `operator` to operate on all of `owner` tokens
     *
     * Requirements:
     * - operator can't be the address zero.
     *
     * Emits an {ApprovalForAll} event.
     */
    function _setApprovalForAll(address owner, address operator, bool approved) internal virtual {
        if (operator == address(0)) {
            revert ERC721InvalidOperator(operator);
        }
        _operatorApprovals[owner][operator] = approved;
        emit ApprovalForAll(owner, operator, approved);
    }

    /**
     * @dev Reverts if the `tokenId` doesn't have a current owner (it hasn't been minted, or it has been burned).
     * Returns the owner.
     *
     * Overrides to ownership logic should be done to {_ownerOf}.
     */
    function _requireOwned(uint256 tokenId) internal view returns (address) {
        address owner = _ownerOf(tokenId);
        if (owner == address(0)) {
            revert ERC721NonexistentToken(tokenId);
        }
        return owner;
    }

    /**
     * @dev Private function to invoke {IERC721Receiver-onERC721Received} on a target address. This will revert if the
     * recipient doesn't accept the token transfer. The call is not executed if the target address is not a contract.
     *
     * @param from address representing the previous owner of the given token ID
     * @param to target address that will receive the tokens
     * @param tokenId uint256 ID of the token to be transferred
     * @param data bytes optional data to send along with the call
     */
    function _checkOnERC721Received(address from, address to, uint256 tokenId, bytes memory data) private {
        if (to.code.length > 0) {
            try IERC721Receiver(to).onERC721Received(_msgSender(), from, tokenId, data) returns (bytes4 retval) {
                if (retval != IERC721Receiver.onERC721Received.selector) {
                    revert ERC721InvalidReceiver(to);
                }
            } catch (bytes memory reason) {
                if (reason.length == 0) {
                    revert ERC721InvalidReceiver(to);
                } else {
                    /// @solidity memory-safe-assembly
                    assembly {
                        revert(add(32, reason), mload(reason))
                    }
                }
            }
        }
    }

    /**
     * @dev Override this function to set owner
     */
    function _setOwner(uint256 tokenId, address owner) internal virtual;
}

// SPDX-License-Identifier: GPL-2.0-or-later

pragma solidity ^0.8.0;

import {IERC1271} from "@openzeppelin/contracts/interfaces/IERC1271.sol";
import {IERC165} from "@openzeppelin/contracts/utils/introspection/IERC165.sol";
import {ECDSA} from "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";
import {EIP712} from "@openzeppelin/contracts/utils/cryptography/EIP712.sol";

import {ERC721} from "./ERC721.sol";
import {IERC721Permit} from "../interfaces/IERC721Permit.sol";

contract ERC721Permit is ERC721, IERC721Permit, EIP712 {
    // keccak256("Permit(address spender,uint256 tokenId,uint256 nonce,uint256 deadline)");
    bytes32 public constant override PERMIT_TYPEHASH =
        0x49ecf333e5b8c95c40fdafc95c1ad136e8914a8fb55e9dc8bb01eaa83a2df9ad;

    uint256 private constant _NONCE_MASK = uint256(0xffffffffffffffffffffffff) << 160;

    // @dev tokenId => (nonce << 160 | owner)
    mapping(uint256 => uint256) private _nonceAndOwner;

    constructor(string memory name_, string memory symbol_, string memory version_)
        ERC721(name_, symbol_)
        EIP712(name_, version_)
    {}

    function permit(address spender, uint256 tokenId, uint256 deadline, uint8 v, bytes32 r, bytes32 s)
        external
        override
    {
        if (block.timestamp > deadline) revert PermitExpired();

        bytes32 digest = _hashTypedDataV4(
            keccak256(abi.encode(PERMIT_TYPEHASH, spender, tokenId, _getAndIncrementNonce(tokenId), deadline))
        );

        address owner = ownerOf(tokenId);
        if (spender == owner) revert InvalidSignature();

        if (owner.code.length > 0) {
            if (IERC1271(owner).isValidSignature(digest, abi.encodePacked(r, s, v)) != 0x1626ba7e) {
                revert InvalidSignature();
            }
        } else {
            if (ECDSA.recover(digest, v, r, s) != owner) revert InvalidSignature();
        }

        _approve(spender, tokenId, owner, true);
    }

    function DOMAIN_SEPARATOR() public view override returns (bytes32) {
        return _domainSeparatorV4();
    }

    function supportsInterface(bytes4 interfaceId) public view virtual override(ERC721, IERC165) returns (bool) {
        return interfaceId == type(IERC721Permit).interfaceId || super.supportsInterface(interfaceId);
    }

    function nonces(uint256 id) external view returns (uint256) {
        return _nonceAndOwner[id] >> 160;
    }

    function _getAndIncrementNonce(uint256 tokenId) internal returns (uint256 nonce) {
        uint256 nonceAndOwner = _nonceAndOwner[tokenId];
        nonce = nonceAndOwner >> 160;
        _nonceAndOwner[tokenId] = nonceAndOwner + (1 << 160);
    }

    function _ownerOf(uint256 tokenId) internal view override returns (address) {
        return address(uint160(_nonceAndOwner[tokenId]));
    }

    function _setOwner(uint256 tokenId, address owner) internal override {
        _nonceAndOwner[tokenId] = (_nonceAndOwner[tokenId] & _NONCE_MASK) | uint256(uint160(owner));
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later

pragma solidity ^0.8.20;

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

type FeePolicy is uint24;

library FeePolicyLibrary {
    uint256 internal constant RATE_PRECISION = 10 ** 6;
    int256 internal constant MAX_FEE_RATE = 500000;
    int256 internal constant MIN_FEE_RATE = -500000;

    uint256 internal constant RATE_MASK = 0x7fffff; // 23 bits

    error InvalidFeePolicy();

    function encode(bool usesQuote_, int24 rate_) internal pure returns (FeePolicy feePolicy) {
        if (rate_ > MAX_FEE_RATE || rate_ < MIN_FEE_RATE) {
            revert InvalidFeePolicy();
        }

        uint256 mask = usesQuote_ ? 1 << 23 : 0;
        assembly {
            feePolicy := or(mask, add(and(rate_, 0xffffff), MAX_FEE_RATE))
        }
    }

    function isValid(FeePolicy self) internal pure returns (bool) {
        int24 r = rate(self);

        return !(r > MAX_FEE_RATE || r < MIN_FEE_RATE);
    }

    function usesQuote(FeePolicy self) internal pure returns (bool f) {
        assembly {
            f := shr(23, self)
        }
    }

    function rate(FeePolicy self) internal pure returns (int24 r) {
        assembly {
            r := sub(and(self, RATE_MASK), MAX_FEE_RATE)
        }
    }

    function calculateFee(FeePolicy self, uint256 amount, bool reverseRounding) internal pure returns (int256 fee) {
        int24 r = rate(self);

        bool positive = r > 0;
        uint256 absRate;
        unchecked {
            absRate = uint256(uint24(positive ? r : -r));
        }
        // @dev absFee must be less than type(int256).max
        uint256 absFee = Math.divide(amount * absRate, RATE_PRECISION, reverseRounding ? !positive : positive);
        fee = positive ? int256(absFee) : -int256(absFee);
    }

    function calculateOriginalAmount(FeePolicy self, uint256 amount, bool reverseFee)
        internal
        pure
        returns (uint256 originalAmount)
    {
        int24 r = rate(self);

        uint256 divider;
        assembly {
            if reverseFee { r := sub(0, r) }
            divider := add(RATE_PRECISION, r)
        }
        originalAmount = Math.divide(amount * RATE_PRECISION, divider, reverseFee);
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.20;

import {Lockers} from "./Lockers.sol";
import {IBookManager} from "../interfaces/IBookManager.sol";
import {IHooks} from "../interfaces/IHooks.sol";
import {OrderId} from "../libraries/OrderId.sol";

/// @author Sonic Market
/// @author Modified from Uniswap V4 (https://github.com/Uniswap/v4-core/blob/1f350fa95e862ba8c56c8ff7e146d47c9043465e)
/// @notice V4 decides whether to invoke specific hooks by inspecting the leading bits of the address that
/// the hooks contract is deployed to.
/// For example, a hooks contract deployed to address: 0x9000000000000000000000000000000000000000
/// has leading bits '1001' which would cause the 'before open' and 'after make' hooks to be used.
library Hooks {
    using Hooks for IHooks;

    uint256 internal constant BEFORE_OPEN_FLAG = 1 << 159;
    uint256 internal constant AFTER_OPEN_FLAG = 1 << 158;
    uint256 internal constant BEFORE_MAKE_FLAG = 1 << 157;
    uint256 internal constant AFTER_MAKE_FLAG = 1 << 156;
    uint256 internal constant BEFORE_TAKE_FLAG = 1 << 155;
    uint256 internal constant AFTER_TAKE_FLAG = 1 << 154;
    uint256 internal constant BEFORE_CANCEL_FLAG = 1 << 153;
    uint256 internal constant AFTER_CANCEL_FLAG = 1 << 152;
    uint256 internal constant BEFORE_CLAIM_FLAG = 1 << 151;
    uint256 internal constant AFTER_CLAIM_FLAG = 1 << 150;

    struct Permissions {
        bool beforeOpen;
        bool afterOpen;
        bool beforeMake;
        bool afterMake;
        bool beforeTake;
        bool afterTake;
        bool beforeCancel;
        bool afterCancel;
        bool beforeClaim;
        bool afterClaim;
    }

    /// @notice Thrown if the address will not lead to the specified hook calls being called
    /// @param hooks The address of the hooks contract
    error HookAddressNotValid(address hooks);

    /// @notice Hook did not return its selector
    error InvalidHookResponse();

    /// @notice thrown when a hook call fails
    error FailedHookCall();

    /// @notice Utility function intended to be used in hook constructors to ensure
    /// the deployed hooks address causes the intended hooks to be called
    /// @param permissions The hooks that are intended to be called
    /// @dev permissions param is memory as the function will be called from constructors
    function validateHookPermissions(IHooks self, Permissions memory permissions) internal pure {
        if (
            permissions.beforeOpen != self.hasPermission(BEFORE_OPEN_FLAG)
                || permissions.afterOpen != self.hasPermission(AFTER_OPEN_FLAG)
                || permissions.beforeMake != self.hasPermission(BEFORE_MAKE_FLAG)
                || permissions.afterMake != self.hasPermission(AFTER_MAKE_FLAG)
                || permissions.beforeTake != self.hasPermission(BEFORE_TAKE_FLAG)
                || permissions.afterTake != self.hasPermission(AFTER_TAKE_FLAG)
                || permissions.beforeCancel != self.hasPermission(BEFORE_CANCEL_FLAG)
                || permissions.afterCancel != self.hasPermission(AFTER_CANCEL_FLAG)
                || permissions.beforeClaim != self.hasPermission(BEFORE_CLAIM_FLAG)
                || permissions.afterClaim != self.hasPermission(AFTER_CLAIM_FLAG)
        ) {
            revert HookAddressNotValid(address(self));
        }
    }

    /// @notice Ensures that the hook address includes at least one hook flag or is the 0 address
    /// @param hook The hook to verify
    function isValidHookAddress(IHooks hook) internal pure returns (bool) {
        // If a hook contract is set, it must have at least 1 flag set
        return address(hook) == address(0) || uint160(address(hook)) >= AFTER_CLAIM_FLAG;
    }

    /// @notice performs a hook call using the given calldata on the given hook
    /// @return expectedSelector The selector that the hook is expected to return
    /// @return selector The selector that the hook actually returned
    function _callHook(IHooks self, bytes memory data) private returns (bytes4 expectedSelector, bytes4 selector) {
        bool set = Lockers.setCurrentHook(self);

        assembly {
            expectedSelector := mload(add(data, 0x20))
        }

        (bool success, bytes memory result) = address(self).call(data);
        if (!success) _revert(result);

        selector = abi.decode(result, (bytes4));

        // We only want to clear the current hook if it was set in setCurrentHook in this execution frame.
        if (set) Lockers.clearCurrentHook();
    }

    /// @notice performs a hook call using the given calldata on the given hook
    function callHook(IHooks self, bytes memory data) internal {
        (bytes4 expectedSelector, bytes4 selector) = _callHook(self, data);

        if (selector != expectedSelector) revert InvalidHookResponse();
    }

    /// @notice calls beforeOpen hook if permissioned and validates return value
    function beforeOpen(IHooks self, IBookManager.BookKey memory key, bytes calldata hookData) internal {
        if (self.hasPermission(BEFORE_OPEN_FLAG)) {
            self.callHook(abi.encodeWithSelector(IHooks.beforeOpen.selector, msg.sender, key, hookData));
        }
    }

    /// @notice calls afterOpen hook if permissioned and validates return value
    function afterOpen(IHooks self, IBookManager.BookKey memory key, bytes calldata hookData) internal {
        if (self.hasPermission(AFTER_OPEN_FLAG)) {
            self.callHook(abi.encodeWithSelector(IHooks.afterOpen.selector, msg.sender, key, hookData));
        }
    }

    /// @notice calls beforeMake hook if permissioned and validates return value
    function beforeMake(IHooks self, IBookManager.MakeParams memory params, bytes calldata hookData) internal {
        if (self.hasPermission(BEFORE_MAKE_FLAG)) {
            self.callHook(abi.encodeWithSelector(IHooks.beforeMake.selector, msg.sender, params, hookData));
        }
    }

    /// @notice calls afterMake hook if permissioned and validates return value
    function afterMake(IHooks self, IBookManager.MakeParams memory params, OrderId orderId, bytes calldata hookData)
        internal
    {
        if (self.hasPermission(AFTER_MAKE_FLAG)) {
            self.callHook(abi.encodeWithSelector(IHooks.afterMake.selector, msg.sender, params, orderId, hookData));
        }
    }

    /// @notice calls beforeTake hook if permissioned and validates return value
    function beforeTake(IHooks self, IBookManager.TakeParams memory params, bytes calldata hookData) internal {
        if (self.hasPermission(BEFORE_TAKE_FLAG)) {
            self.callHook(abi.encodeWithSelector(IHooks.beforeTake.selector, msg.sender, params, hookData));
        }
    }

    /// @notice calls afterTake hook if permissioned and validates return value
    function afterTake(IHooks self, IBookManager.TakeParams memory params, uint64 takenAmount, bytes calldata hookData)
        internal
    {
        if (self.hasPermission(AFTER_TAKE_FLAG)) {
            self.callHook(abi.encodeWithSelector(IHooks.afterTake.selector, msg.sender, params, takenAmount, hookData));
        }
    }

    /// @notice calls beforeCancel hook if permissioned and validates return value
    function beforeCancel(IHooks self, IBookManager.CancelParams calldata params, bytes calldata hookData) internal {
        if (self.hasPermission(BEFORE_CANCEL_FLAG)) {
            self.callHook(abi.encodeWithSelector(IHooks.beforeCancel.selector, msg.sender, params, hookData));
        }
    }

    /// @notice calls afterCancel hook if permissioned and validates return value
    function afterCancel(
        IHooks self,
        IBookManager.CancelParams calldata params,
        uint64 canceledAmount,
        bytes calldata hookData
    ) internal {
        if (self.hasPermission(AFTER_CANCEL_FLAG)) {
            self.callHook(
                abi.encodeWithSelector(IHooks.afterCancel.selector, msg.sender, params, canceledAmount, hookData)
            );
        }
    }

    /// @notice calls beforeClaim hook if permissioned and validates return value
    function beforeClaim(IHooks self, OrderId orderId, bytes calldata hookData) internal {
        if (self.hasPermission(BEFORE_CLAIM_FLAG)) {
            self.callHook(abi.encodeWithSelector(IHooks.beforeClaim.selector, msg.sender, orderId, hookData));
        }
    }

    /// @notice calls afterClaim hook if permissioned and validates return value
    function afterClaim(IHooks self, OrderId orderId, uint64 claimedAmount, bytes calldata hookData) internal {
        if (self.hasPermission(AFTER_CLAIM_FLAG)) {
            self.callHook(
                abi.encodeWithSelector(IHooks.afterClaim.selector, msg.sender, orderId, claimedAmount, hookData)
            );
        }
    }

    function hasPermission(IHooks self, uint256 flag) internal pure returns (bool) {
        return uint256(uint160(address(self))) & flag != 0;
    }

    /// @notice bubble up revert if present. Else throw FailedHookCall
    function _revert(bytes memory result) private pure {
        if (result.length == 0) revert FailedHookCall();
        assembly {
            revert(add(0x20, result), mload(result))
        }
    }
}

// SPDX-License-Identifier: BUSL-1.1

pragma solidity ^0.8.23;

import {IHooks} from "../interfaces/IHooks.sol";

/// @author Sonic Market
/// @author Modified from Uniswap V4 (https://github.com/Uniswap/v4-core/tree/98680ebc1a654120e995d53a5b10ec6fe153066f)
/// @notice Contains data about pool lockers.

/// @dev This library manages a custom storage implementation for a queue
///      that tracks current lockers. The "sentinel" storage slot for this data structure,
///      always passed in as IPoolManager.LockData storage self, stores not just the current
///      length of the queue but also the global count of non-zero deltas across all lockers.
///      The values of the data structure start at OFFSET, and each value is a locker address.
library Lockers {
    /// struct LockData {
    ///     /// @notice The current number of active lockers
    ///     uint128 length;
    ///     /// @notice The total number of nonzero deltas over all active + completed lockers
    ///     uint128 nonzeroDeltaCount;
    /// }
    // uint256(keccak256("LockData")) + 1
    uint256 internal constant LOCK_DATA_SLOT = 0x760a9a962ae3d184e99c0483cf5684fb3170f47116ca4f445c50209da4f4f907;

    // uint256(keccak256("Lockers")) + 1
    uint256 internal constant LOCKERS_SLOT = 0x722b431450ce53c44434ec138439e45a0639fe031b803ee019b776fae5cfa2b1;

    // The number of slots per item in the lockers array
    uint256 internal constant LOCKER_STRUCT_SIZE = 2;

    // uint256(keccak256("HookAddress")) + 1
    uint256 internal constant HOOK_ADDRESS_SLOT = 0xfcac7593714b88fec0c578a53e9f3f6e4b47eb26c9dcaa7eff23a3ac156be422;

    uint256 internal constant NONZERO_DELTA_COUNT_OFFSET = 2 ** 128;

    uint256 internal constant LENGTH_MASK = (1 << 128) - 1;

    /// @dev Pushes a locker onto the end of the queue, and updates the sentinel storage slot.
    function push(address locker, address lockCaller) internal {
        assembly {
            let data := tload(LOCK_DATA_SLOT)
            let l := and(data, LENGTH_MASK)

            // LOCKERS_SLOT + l * LOCKER_STRUCT_SIZE
            let indexToWrite := add(LOCKERS_SLOT, mul(l, LOCKER_STRUCT_SIZE))

            // in the next storage slot, write the locker and lockCaller
            tstore(indexToWrite, locker)
            tstore(add(indexToWrite, 1), lockCaller)

            // increase the length
            tstore(LOCK_DATA_SLOT, add(data, 1))
        }
    }

    function lockData() internal view returns (uint128 l, uint128 nonzeroDeltaCount) {
        assembly {
            let data := tload(LOCK_DATA_SLOT)
            l := and(data, LENGTH_MASK)
            nonzeroDeltaCount := shr(128, data)
        }
    }

    function length() internal view returns (uint128 l) {
        assembly {
            l := and(tload(LOCK_DATA_SLOT), LENGTH_MASK)
        }
    }

    /// @dev Pops a locker off the end of the queue. Note that no storage gets cleared.
    function pop() internal {
        assembly {
            let data := tload(LOCK_DATA_SLOT)
            let l := and(data, LENGTH_MASK)
            if iszero(l) {
                mstore(0x00, 0xf1c77ed0) // LockersPopFailed()
                revert(0x1c, 0x04)
            }

            // LOCKERS_SLOT + (l - 1) * LOCKER_STRUCT_SIZE
            let indexToWrite := add(LOCKERS_SLOT, mul(sub(l, 1), LOCKER_STRUCT_SIZE))

            // in the next storage slot, delete the locker and lockCaller
            tstore(indexToWrite, 0)
            tstore(add(indexToWrite, 1), 0)

            // decrease the length
            tstore(LOCK_DATA_SLOT, sub(data, 1))
        }
    }

    function getLocker(uint256 i) internal view returns (address locker) {
        assembly {
            // LOCKERS_SLOT + (i * LOCKER_STRUCT_SIZE)
            locker := tload(add(LOCKERS_SLOT, mul(i, LOCKER_STRUCT_SIZE)))
        }
    }

    function getLockCaller(uint256 i) internal view returns (address locker) {
        assembly {
            // LOCKERS_SLOT + (i * LOCKER_STRUCT_SIZE + 1)
            locker := tload(add(LOCKERS_SLOT, add(mul(i, LOCKER_STRUCT_SIZE), 1)))
        }
    }

    function getCurrentLocker() internal view returns (address) {
        unchecked {
            uint256 l = length();
            return l > 0 ? getLocker(l - 1) : address(0);
        }
    }

    function getCurrentLockCaller() internal view returns (address) {
        unchecked {
            uint256 l = length();
            return l > 0 ? getLockCaller(l - 1) : address(0);
        }
    }

    function incrementNonzeroDeltaCount() internal {
        assembly {
            tstore(LOCK_DATA_SLOT, add(tload(LOCK_DATA_SLOT), NONZERO_DELTA_COUNT_OFFSET))
        }
    }

    function decrementNonzeroDeltaCount() internal {
        assembly {
            tstore(LOCK_DATA_SLOT, sub(tload(LOCK_DATA_SLOT), NONZERO_DELTA_COUNT_OFFSET))
        }
    }

    function getCurrentHook() internal view returns (IHooks currentHook) {
        return IHooks(getHook(length()));
    }

    function getHook(uint256 i) internal view returns (address hook) {
        assembly {
            hook := tload(add(HOOK_ADDRESS_SLOT, i))
        }
    }

    function setCurrentHook(IHooks currentHook) internal returns (bool set) {
        // Set the hook address for the current locker if the address is 0.
        // If the address is nonzero, a hook has already been set for this lock, and is not allowed to be updated or cleared at the end of the call.
        if (address(getCurrentHook()) == address(0)) {
            uint256 l = length();
            assembly {
                tstore(add(HOOK_ADDRESS_SLOT, l), currentHook)
            }
            return true;
        }
    }

    function clearCurrentHook() internal {
        uint256 l = length();
        assembly {
            tstore(add(HOOK_ADDRESS_SLOT, l), 0)
        }
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later

pragma solidity ^0.8.0;

library Math {
    function divide(uint256 a, uint256 b, bool roundingUp) internal pure returns (uint256 ret) {
        // In the OrderBook contract code, b is never zero.
        assembly {
            ret := add(div(a, b), and(gt(mod(a, b), 0), roundingUp))
        }
    }

    /// @dev Returns `ln(x)`, denominated in `WAD`.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
    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)
            // Base conversion: mul `2**96 / (5**18 * 2**192)`.
            r := sdiv(p, 302231454903657293676544000000000000000000)
        }
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later

pragma solidity ^0.8.0;

import {Tick} from "./Tick.sol";
import {BookId} from "./BookId.sol";

type OrderId is uint256;

library OrderIdLibrary {
    /**
     * @dev Encode the order id.
     * @param bookId The book id.
     * @param tick The tick.
     * @param index The index.
     * @return id The order id.
     */
    function encode(BookId bookId, Tick tick, uint40 index) internal pure returns (OrderId id) {
        // @dev If we just use tick at the assembly code, the code will convert tick into bytes32.
        //      e.g. When index == -2, the shifted value( shl(40, tick) ) will be
        //      0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe0000000000 instead of 0xfffffffe0000000000
        //      Therefore, we have to safely cast tick into uint256 first.
        uint256 _tick = uint256(uint24(Tick.unwrap(tick)));
        assembly {
            id := add(index, add(shl(40, _tick), shl(64, bookId)))
        }
    }

    function decode(OrderId id) internal pure returns (BookId bookId, Tick tick, uint40 index) {
        assembly {
            bookId := shr(64, id)
            tick := and(shr(40, id), 0xffffff)
            index := and(id, 0xffffffffff)
        }
    }

    function getBookId(OrderId id) internal pure returns (BookId bookId) {
        assembly {
            bookId := shr(64, id)
        }
    }

    function getTick(OrderId id) internal pure returns (Tick tick) {
        assembly {
            tick := and(shr(40, id), 0xffffff)
        }
    }

    function getIndex(OrderId id) internal pure returns (uint40 index) {
        assembly {
            index := and(id, 0xffffffffff)
        }
    }
}

// SPDX-License-Identifier: -
// License: https://license.sonic.market/LICENSE.pdf

pragma solidity ^0.8.0;

library PackedUint256 {
    error PackedUint256Error(uint256 errorCode);

    uint256 private constant _UINT8_INDEX_ERROR = 0;
    uint256 private constant _UINT16_INDEX_ERROR = 1;
    uint256 private constant _UINT32_INDEX_ERROR = 2;
    uint256 private constant _UINT64_INDEX_ERROR = 3;

    uint256 private constant _MAX_UINT64 = type(uint64).max;
    uint256 private constant _MAX_UINT32 = type(uint32).max;
    uint256 private constant _MAX_UINT16 = type(uint16).max;
    uint256 private constant _MAX_UINT8 = type(uint8).max;

    function get8Unsafe(uint256 packed, uint256 index) internal pure returns (uint8 ret) {
        assembly {
            ret := and(shr(shl(3, index), packed), 0xff)
        }
    }

    function get8(uint256 packed, uint256 index) internal pure returns (uint8 ret) {
        if (index > 31) {
            revert PackedUint256Error(_UINT8_INDEX_ERROR);
        }
        assembly {
            ret := and(shr(shl(3, index), packed), 0xff)
        }
    }

    function get16Unsafe(uint256 packed, uint256 index) internal pure returns (uint16 ret) {
        assembly {
            ret := and(shr(shl(4, index), packed), 0xffff)
        }
    }

    function get16(uint256 packed, uint256 index) internal pure returns (uint16 ret) {
        if (index > 15) {
            revert PackedUint256Error(_UINT16_INDEX_ERROR);
        }
        assembly {
            ret := and(shr(shl(4, index), packed), 0xffff)
        }
    }

    function get32Unsafe(uint256 packed, uint256 index) internal pure returns (uint32 ret) {
        assembly {
            ret := and(shr(shl(5, index), packed), 0xffffffff)
        }
    }

    function get32(uint256 packed, uint256 index) internal pure returns (uint32 ret) {
        if (index > 7) {
            revert PackedUint256Error(_UINT32_INDEX_ERROR);
        }
        assembly {
            ret := and(shr(shl(5, index), packed), 0xffffffff)
        }
    }

    function get64Unsafe(uint256 packed, uint256 index) internal pure returns (uint64 ret) {
        assembly {
            ret := and(shr(shl(6, index), packed), 0xffffffffffffffff)
        }
    }

    function get64(uint256 packed, uint256 index) internal pure returns (uint64 ret) {
        if (index > 3) {
            revert PackedUint256Error(_UINT64_INDEX_ERROR);
        }
        assembly {
            ret := and(shr(shl(6, index), packed), 0xffffffffffffffff)
        }
    }

    function add8Unsafe(uint256 packed, uint256 index, uint8 value) internal pure returns (uint256 ret) {
        assembly {
            ret := add(packed, shl(shl(3, index), and(value, 0xff)))
        }
    }

    function add8(uint256 packed, uint256 index, uint8 value) internal pure returns (uint256 ret) {
        if (index > 31) {
            revert PackedUint256Error(_UINT8_INDEX_ERROR);
        }
        uint8 current = get8Unsafe(packed, index);
        current += value;
        ret = update8Unsafe(packed, index, current);
    }

    function add16Unsafe(uint256 packed, uint256 index, uint16 value) internal pure returns (uint256 ret) {
        assembly {
            ret := add(packed, shl(shl(4, index), and(value, 0xffff)))
        }
    }

    function add16(uint256 packed, uint256 index, uint16 value) internal pure returns (uint256 ret) {
        if (index > 15) {
            revert PackedUint256Error(_UINT16_INDEX_ERROR);
        }
        uint16 current = get16Unsafe(packed, index);
        current += value;
        ret = update16Unsafe(packed, index, current);
    }

    function add32Unsafe(uint256 packed, uint256 index, uint32 value) internal pure returns (uint256 ret) {
        assembly {
            ret := add(packed, shl(shl(5, index), and(value, 0xffffffff)))
        }
    }

    function add32(uint256 packed, uint256 index, uint32 value) internal pure returns (uint256 ret) {
        if (index > 7) {
            revert PackedUint256Error(_UINT32_INDEX_ERROR);
        }
        uint32 current = get32Unsafe(packed, index);
        current += value;
        ret = update32Unsafe(packed, index, current);
    }

    function add64Unsafe(uint256 packed, uint256 index, uint64 value) internal pure returns (uint256 ret) {
        assembly {
            ret := add(packed, shl(shl(6, index), and(value, 0xffffffffffffffff)))
        }
    }

    function add64(uint256 packed, uint256 index, uint64 value) internal pure returns (uint256 ret) {
        if (index > 3) {
            revert PackedUint256Error(_UINT64_INDEX_ERROR);
        }
        uint64 current = get64Unsafe(packed, index);
        current += value;
        ret = update64Unsafe(packed, index, current);
    }

    function sub8Unsafe(uint256 packed, uint256 index, uint8 value) internal pure returns (uint256 ret) {
        assembly {
            ret := sub(packed, shl(shl(3, index), and(value, 0xff)))
        }
    }

    function sub8(uint256 packed, uint256 index, uint8 value) internal pure returns (uint256 ret) {
        if (index > 31) {
            revert PackedUint256Error(_UINT8_INDEX_ERROR);
        }
        uint8 current = get8Unsafe(packed, index);
        current -= value;
        ret = update8Unsafe(packed, index, current);
    }

    function sub16Unsafe(uint256 packed, uint256 index, uint16 value) internal pure returns (uint256 ret) {
        assembly {
            ret := sub(packed, shl(shl(4, index), and(value, 0xffff)))
        }
    }

    function sub16(uint256 packed, uint256 index, uint16 value) internal pure returns (uint256 ret) {
        if (index > 15) {
            revert PackedUint256Error(_UINT16_INDEX_ERROR);
        }
        uint16 current = get16Unsafe(packed, index);
        current -= value;
        ret = update16Unsafe(packed, index, current);
    }

    function sub32Unsafe(uint256 packed, uint256 index, uint32 value) internal pure returns (uint256 ret) {
        assembly {
            ret := sub(packed, shl(shl(5, index), and(value, 0xffffffff)))
        }
    }

    function sub32(uint256 packed, uint256 index, uint32 value) internal pure returns (uint256 ret) {
        if (index > 7) {
            revert PackedUint256Error(_UINT32_INDEX_ERROR);
        }
        uint32 current = get32Unsafe(packed, index);
        current -= value;
        ret = update32Unsafe(packed, index, current);
    }

    function sub64Unsafe(uint256 packed, uint256 index, uint64 value) internal pure returns (uint256 ret) {
        assembly {
            ret := sub(packed, shl(shl(6, index), and(value, 0xffffffffffffffff)))
        }
    }

    function sub64(uint256 packed, uint256 index, uint64 value) internal pure returns (uint256 ret) {
        if (index > 3) {
            revert PackedUint256Error(_UINT64_INDEX_ERROR);
        }
        uint64 current = get64Unsafe(packed, index);
        current -= value;
        ret = update64Unsafe(packed, index, current);
    }

    function update8Unsafe(uint256 packed, uint256 index, uint8 value) internal pure returns (uint256 ret) {
        unchecked {
            index = index << 3;
            packed = packed - (packed & (_MAX_UINT8 << index));
        }
        assembly {
            ret := add(packed, shl(index, and(value, 0xff)))
        }
    }

    function update8(uint256 packed, uint256 index, uint8 value) internal pure returns (uint256 ret) {
        if (index > 31) {
            revert PackedUint256Error(_UINT8_INDEX_ERROR);
        }
        unchecked {
            index = index << 3;
            packed = packed - (packed & (_MAX_UINT8 << index));
        }
        assembly {
            ret := add(packed, shl(index, and(value, 0xff)))
        }
    }

    function update16Unsafe(uint256 packed, uint256 index, uint16 value) internal pure returns (uint256 ret) {
        unchecked {
            index = index << 4;
            packed = packed - (packed & (_MAX_UINT16 << index));
        }
        assembly {
            ret := add(packed, shl(index, and(value, 0xffff)))
        }
    }

    function update16(uint256 packed, uint256 index, uint16 value) internal pure returns (uint256 ret) {
        if (index > 15) {
            revert PackedUint256Error(_UINT16_INDEX_ERROR);
        }
        unchecked {
            index = index << 4;
            packed = packed - (packed & (_MAX_UINT16 << index));
        }
        assembly {
            ret := add(packed, shl(index, and(value, 0xffff)))
        }
    }

    function update32Unsafe(uint256 packed, uint256 index, uint32 value) internal pure returns (uint256 ret) {
        unchecked {
            index = index << 5;
            packed = packed - (packed & (_MAX_UINT32 << index));
        }
        assembly {
            ret := add(packed, shl(index, and(value, 0xffffffff)))
        }
    }

    function update32(uint256 packed, uint256 index, uint32 value) internal pure returns (uint256 ret) {
        if (index > 7) {
            revert PackedUint256Error(_UINT32_INDEX_ERROR);
        }
        unchecked {
            index = index << 5;
            packed = packed - (packed & (_MAX_UINT32 << index));
        }
        assembly {
            ret := add(packed, shl(index, and(value, 0xffffffff)))
        }
    }

    function update64Unsafe(uint256 packed, uint256 index, uint64 value) internal pure returns (uint256 ret) {
        unchecked {
            index = index << 6;
            packed = packed - (packed & (_MAX_UINT64 << index));
        }
        assembly {
            ret := add(packed, shl(index, and(value, 0xffffffffffffffff)))
        }
    }

    function update64(uint256 packed, uint256 index, uint64 value) internal pure returns (uint256 ret) {
        if (index > 3) {
            revert PackedUint256Error(_UINT64_INDEX_ERROR);
        }
        unchecked {
            index = index << 6;
            packed = packed - (packed & (_MAX_UINT64 << index));
        }
        assembly {
            ret := add(packed, shl(index, and(value, 0xffffffffffffffff)))
        }
    }

    function total32(uint256 packed) internal pure returns (uint256) {
        unchecked {
            uint256 ret = _MAX_UINT32 & packed;
            for (uint256 i = 0; i < 7; ++i) {
                packed = packed >> 32;
                ret += _MAX_UINT32 & packed;
            }
            return ret;
        }
    }

    function total64(uint256 packed) internal pure returns (uint256) {
        unchecked {
            uint256 ret = _MAX_UINT64 & packed;
            for (uint256 i = 0; i < 3; ++i) {
                packed = packed >> 64;
                ret += _MAX_UINT64 & packed;
            }
            return ret;
        }
    }

    function sum32(uint256 packed, uint256 from, uint256 to) internal pure returns (uint256) {
        unchecked {
            packed = packed >> (from << 5);
            uint256 ret = 0;
            for (uint256 i = from; i < to; ++i) {
                ret += _MAX_UINT32 & packed;
                packed = packed >> 32;
            }
            return ret;
        }
    }

    function sum64(uint256 packed, uint256 from, uint256 to) internal pure returns (uint256) {
        unchecked {
            packed = packed >> (from << 6);
            uint256 ret = 0;
            for (uint256 i = from; i < to; ++i) {
                ret += _MAX_UINT64 & packed;
                packed = packed >> 64;
            }
            return ret;
        }
    }
}

// SPDX-License-Identifier: -
// License: https://license.sonic.market/LICENSE.pdf

pragma solidity ^0.8.0;

import "./PackedUint256.sol";
import "./DirtyUint64.sol";

/**
 * 🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲
 *
 *                   Segmented Segment Tree
 *                          by Sonic Market
 *
 * ____________/\\\_______________/\\\\\____________/\\\____
 *  __________/\\\\\___________/\\\\////___________/\\\\\____
 *   ________/\\\/\\\________/\\\///______________/\\\/\\\____
 *    ______/\\\/\/\\\______/\\\\\\\\\\\_________/\\\/\/\\\____
 *     ____/\\\/__\/\\\_____/\\\\///////\\\_____/\\\/__\/\\\____
 *      __/\\\\\\\\\\\\\\\\_\/\\\______\//\\\__/\\\\\\\\\\\\\\\\_
 *       _\///////////\\\//__\//\\\______/\\\__\///////////\\\//__
 *        ___________\/\\\_____\///\\\\\\\\\/_____________\/\\\____
 *         ___________\///________\/////////_______________\///_____
 *
 *           4 Layers of 64-bit nodes, hence 464
 *
 * 🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲
 */
library SegmentedSegmentTree {
    using PackedUint256 for uint256;
    using DirtyUint64 for uint64;

    error SegmentedSegmentTreeError(uint256 errorCode);

    uint256 private constant _INDEX_ERROR = 0;
    uint256 private constant _OVERFLOW_ERROR = 1;

    //    uint8 private constant _R = 2; // There are `2` root node groups
    //    uint8 private constant _C = 4; // There are `4` children (each child is a node group of its own) for each node
    uint8 private constant _L = 4; // There are `4` layers of node groups
    uint256 private constant _P = 4; // uint256 / uint64 = `4`
    uint256 private constant _P_M = 3; // % 4 = & `3`
    uint256 private constant _P_P = 2; // 2 ** `2` = 4
    uint256 private constant _N_P = 4; // C * P = 2 ** `4`
    uint256 private constant _MAX_NODES = 2 ** 15; // (R * P) * ((C * P) ** (L - 1)) = `32768`
    uint256 private constant _MAX_NODES_P_MINUS_ONE = 14; // MAX_NODES / R = 2 ** `14`

    struct Core {
        mapping(uint256 => uint256)[_L] layers;
    }

    struct LayerIndex {
        uint256 group;
        uint256 node;
    }

    function get(Core storage core, uint256 index) internal view returns (uint64 ret) {
        if (index >= _MAX_NODES) {
            revert SegmentedSegmentTreeError(_INDEX_ERROR);
        }
        unchecked {
            ret = core.layers[_L - 1][index >> _P_P].get64(index & _P_M).toClean();
        }
    }

    function total(Core storage core) internal view returns (uint64) {
        return DirtyUint64.sumPackedUnsafe(core.layers[0][0], 0, _P)
            + DirtyUint64.sumPackedUnsafe(core.layers[0][1], 0, _P);
    }

    function query(Core storage core, uint256 left, uint256 right) internal view returns (uint64 sum) {
        if (left == right) {
            return 0;
        }
        // right should be greater than left
        if (left >= right) {
            revert SegmentedSegmentTreeError(_INDEX_ERROR);
        }
        if (right > _MAX_NODES) {
            revert SegmentedSegmentTreeError(_INDEX_ERROR);
        }

        LayerIndex[] memory leftIndices = _getLayerIndices(left);
        LayerIndex[] memory rightIndices = _getLayerIndices(right);
        uint256 ret;
        uint256 deficit;

        unchecked {
            uint256 leftNodeIndex;
            uint256 rightNodeIndex;
            for (uint256 l = _L - 1;; --l) {
                LayerIndex memory leftIndex = leftIndices[l];
                LayerIndex memory rightIndex = rightIndices[l];
                leftNodeIndex += leftIndex.node;
                rightNodeIndex += rightIndex.node;

                if (rightIndex.group == leftIndex.group) {
                    ret += DirtyUint64.sumPackedUnsafe(core.layers[l][leftIndex.group], leftNodeIndex, rightNodeIndex);
                    break;
                }

                if (rightIndex.group - leftIndex.group < 4) {
                    ret += DirtyUint64.sumPackedUnsafe(core.layers[l][leftIndex.group], leftNodeIndex, _P);

                    ret += DirtyUint64.sumPackedUnsafe(core.layers[l][rightIndex.group], 0, rightNodeIndex);

                    for (uint256 group = leftIndex.group + 1; group < rightIndex.group; group++) {
                        ret += DirtyUint64.sumPackedUnsafe(core.layers[l][group], 0, _P);
                    }
                    break;
                }

                if (leftIndex.group % 4 == 0) {
                    deficit += DirtyUint64.sumPackedUnsafe(core.layers[l][leftIndex.group], 0, leftNodeIndex);
                    leftNodeIndex = 0;
                } else if (leftIndex.group % 4 == 1) {
                    deficit += DirtyUint64.sumPackedUnsafe(core.layers[l][leftIndex.group - 1], 0, _P);
                    deficit += DirtyUint64.sumPackedUnsafe(core.layers[l][leftIndex.group], 0, leftNodeIndex);
                    leftNodeIndex = 0;
                } else if (leftIndex.group % 4 == 2) {
                    ret += DirtyUint64.sumPackedUnsafe(core.layers[l][leftIndex.group], leftNodeIndex, _P);
                    ret += DirtyUint64.sumPackedUnsafe(core.layers[l][leftIndex.group + 1], 0, _P);
                    leftNodeIndex = 1;
                } else {
                    ret += DirtyUint64.sumPackedUnsafe(core.layers[l][leftIndex.group], leftNodeIndex, _P);
                    leftNodeIndex = 1;
                }

                if (rightIndex.group % 4 == 0) {
                    ret += DirtyUint64.sumPackedUnsafe(core.layers[l][rightIndex.group], 0, rightNodeIndex);
                    rightNodeIndex = 0;
                } else if (rightIndex.group % 4 == 1) {
                    ret += DirtyUint64.sumPackedUnsafe(core.layers[l][rightIndex.group - 1], 0, _P);
                    ret += DirtyUint64.sumPackedUnsafe(core.layers[l][rightIndex.group], 0, rightNodeIndex);
                    rightNodeIndex = 0;
                } else if (rightIndex.group % 4 == 2) {
                    deficit += DirtyUint64.sumPackedUnsafe(core.layers[l][rightIndex.group], rightNodeIndex, _P);
                    deficit += DirtyUint64.sumPackedUnsafe(core.layers[l][rightIndex.group + 1], 0, _P);
                    rightNodeIndex = 1;
                } else {
                    deficit += DirtyUint64.sumPackedUnsafe(core.layers[l][rightIndex.group], rightNodeIndex, _P);
                    rightNodeIndex = 1;
                }
            }
            ret -= deficit;
        }
        sum = uint64(ret);
    }

    function update(Core storage core, uint256 index, uint64 value) internal returns (uint64 replaced) {
        if (index >= _MAX_NODES) {
            revert SegmentedSegmentTreeError(_INDEX_ERROR);
        }
        LayerIndex[] memory indices = _getLayerIndices(index);
        unchecked {
            LayerIndex memory bottomIndex = indices[_L - 1];
            replaced = core.layers[_L - 1][bottomIndex.group].get64Unsafe(bottomIndex.node).toClean();
            if (replaced >= value) {
                uint64 diff = replaced - value;
                for (uint256 l = 0; l < _L; ++l) {
                    LayerIndex memory layerIndex = indices[l];
                    uint256 node = core.layers[l][layerIndex.group];
                    core.layers[l][layerIndex.group] =
                        node.update64(layerIndex.node, node.get64(layerIndex.node).subClean(diff));
                }
            } else {
                uint64 diff = value - replaced;
                if (total(core) > type(uint64).max - diff) revert SegmentedSegmentTreeError(_OVERFLOW_ERROR);
                for (uint256 l = 0; l < _L; ++l) {
                    LayerIndex memory layerIndex = indices[l];
                    uint256 node = core.layers[l][layerIndex.group];
                    core.layers[l][layerIndex.group] =
                        node.update64(layerIndex.node, node.get64(layerIndex.node).addClean(diff));
                }
            }
        }
    }

    function _getLayerIndices(uint256 index) private pure returns (LayerIndex[] memory) {
        unchecked {
            LayerIndex[] memory indices = new LayerIndex[](_L);
            uint256 shifter = _MAX_NODES_P_MINUS_ONE;
            for (uint256 l = 0; l < _L; ++l) {
                indices[l] = LayerIndex({group: index >> shifter, node: (index >> (shifter - _P_P)) & _P_M});
                shifter = shifter - _N_P;
            }
            return indices;
        }
    }
}

/*
 * Segmented Segment Tree is a Segment Tree
 * that has been compressed so that `C` nodes
 * are compressed into a single uint256.
 *
 * Each node in a non-leaf node group is the sum of the
 * total sum of each child node group that it represents.
 * Each non-leaf node represents `E` node groups.
 *
 * A node group consists of `S` uint256.
 *
 * By expressing the index in `N` notation,
 * we can find the index in each respective layer
 *
 * S: Size of each node group
 * C: Compression Coefficient
 * E: Expansion Coefficient
 * L: Number of Layers
 * N: Notation, S * C * E
 *
 * `E` will not be considered for this version of the implementation. (E = 2)
 */

// SPDX-License-Identifier: GPL-2.0-or-later

pragma solidity ^0.8.0;

library SignificantBit {
    // http://supertech.csail.mit.edu/papers/debruijn.pdf
    uint256 internal constant DEBRUIJN_SEQ = 0x818283848586878898A8B8C8D8E8F929395969799A9B9D9E9FAAEB6BEDEEFF;
    bytes internal constant DEBRUIJN_INDEX =
        hex"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";

    /**
     * @notice Finds the index of the least significant bit.
     * @param x The value to compute the least significant bit for. Must be a non-zero value.
     * @return ret The index of the least significant bit.
     */
    function leastSignificantBit(uint256 x) internal pure returns (uint8) {
        require(x > 0);
        uint256 index;
        assembly {
            index := shr(248, mul(and(x, add(not(x), 1)), DEBRUIJN_SEQ))
        }
        return uint8(DEBRUIJN_INDEX[index]); // can optimize with CODECOPY opcode
    }

    function mostSignificantBit(uint256 x) internal pure returns (uint8 msb) {
        require(x > 0);
        assembly {
            let f := shl(7, gt(x, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
            msb := or(msb, f)
            x := shr(f, x)
            f := shl(6, gt(x, 0xFFFFFFFFFFFFFFFF))
            msb := or(msb, f)
            x := shr(f, x)
            f := shl(5, gt(x, 0xFFFFFFFF))
            msb := or(msb, f)
            x := shr(f, x)
            f := shl(4, gt(x, 0xFFFF))
            msb := or(msb, f)
            x := shr(f, x)
            f := shl(3, gt(x, 0xFF))
            msb := or(msb, f)
            x := shr(f, x)
            f := shl(2, gt(x, 0xF))
            msb := or(msb, f)
            x := shr(f, x)
            f := shl(1, gt(x, 0x3))
            msb := or(msb, f)
            x := shr(f, x)
            f := gt(x, 0x1)
            msb := or(msb, f)
        }
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later

pragma solidity ^0.8.20;

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

type Tick is int24;

library TickLibrary {
    using Math for *;
    using TickLibrary for Tick;

    error InvalidTick();
    error InvalidPrice();
    error TickOverflow();

    int24 internal constant MAX_TICK = 2 ** 19 - 1;
    int24 internal constant MIN_TICK = -MAX_TICK;

    uint256 internal constant MIN_PRICE = 1350587;
    uint256 internal constant MAX_PRICE = 4647684107270898330752324302845848816923571339324334;

    uint256 private constant _R0 = 0xfff97272373d413259a46990;
    uint256 private constant _R1 = 0xfff2e50f5f656932ef12357c;
    uint256 private constant _R2 = 0xffe5caca7e10e4e61c3624ea;
    uint256 private constant _R3 = 0xffcb9843d60f6159c9db5883;
    uint256 private constant _R4 = 0xff973b41fa98c081472e6896;
    uint256 private constant _R5 = 0xff2ea16466c96a3843ec78b3;
    uint256 private constant _R6 = 0xfe5dee046a99a2a811c461f1;
    uint256 private constant _R7 = 0xfcbe86c7900a88aedcffc83b;
    uint256 private constant _R8 = 0xf987a7253ac413176f2b074c;
    uint256 private constant _R9 = 0xf3392b0822b70005940c7a39;
    uint256 private constant _R10 = 0xe7159475a2c29b7443b29c7f;
    uint256 private constant _R11 = 0xd097f3bdfd2022b8845ad8f7;
    uint256 private constant _R12 = 0xa9f746462d870fdf8a65dc1f;
    uint256 private constant _R13 = 0x70d869a156d2a1b890bb3df6;
    uint256 private constant _R14 = 0x31be135f97d08fd981231505;
    uint256 private constant _R15 = 0x9aa508b5b7a84e1c677de54;
    uint256 private constant _R16 = 0x5d6af8dedb81196699c329;
    uint256 private constant _R17 = 0x2216e584f5fa1ea92604;
    uint256 private constant _R18 = 0x48a170391f7dc42;
    uint256 private constant _R19 = 0x149b34;

    function validateTick(Tick tick) internal pure {
        if (Tick.unwrap(tick) > MAX_TICK || Tick.unwrap(tick) < MIN_TICK) revert InvalidTick();
    }

    modifier validatePrice(uint256 price) {
        if (price > MAX_PRICE || price < MIN_PRICE) revert InvalidPrice();
        _;
    }

    function fromPrice(uint256 price) internal pure validatePrice(price) returns (Tick) {
        unchecked {
            int24 tick = int24((int256(price).lnWad() * 42951820407860) / 2 ** 128);
            if (toPrice(Tick.wrap(tick)) > price) return Tick.wrap(tick - 1);
            return Tick.wrap(tick);
        }
    }

    function toPrice(Tick tick) internal pure returns (uint256 price) {
        validateTick(tick);
        int24 tickValue = Tick.unwrap(tick);
        uint256 absTick = uint24(tickValue < 0 ? -tickValue : tickValue);

        unchecked {
            if (absTick & 0x1 != 0) price = _R0;
            else price = 1 << 96;
            if (absTick & 0x2 != 0) price = (price * _R1) >> 96;
            if (absTick & 0x4 != 0) price = (price * _R2) >> 96;
            if (absTick & 0x8 != 0) price = (price * _R3) >> 96;
            if (absTick & 0x10 != 0) price = (price * _R4) >> 96;
            if (absTick & 0x20 != 0) price = (price * _R5) >> 96;
            if (absTick & 0x40 != 0) price = (price * _R6) >> 96;
            if (absTick & 0x80 != 0) price = (price * _R7) >> 96;
            if (absTick & 0x100 != 0) price = (price * _R8) >> 96;
            if (absTick & 0x200 != 0) price = (price * _R9) >> 96;
            if (absTick & 0x400 != 0) price = (price * _R10) >> 96;
            if (absTick & 0x800 != 0) price = (price * _R11) >> 96;
            if (absTick & 0x1000 != 0) price = (price * _R12) >> 96;
            if (absTick & 0x2000 != 0) price = (price * _R13) >> 96;
            if (absTick & 0x4000 != 0) price = (price * _R14) >> 96;
            if (absTick & 0x8000 != 0) price = (price * _R15) >> 96;
            if (absTick & 0x10000 != 0) price = (price * _R16) >> 96;
            if (absTick & 0x20000 != 0) price = (price * _R17) >> 96;
            if (absTick & 0x40000 != 0) price = (price * _R18) >> 96;
        }
        if (tickValue > 0) price = 0x1000000000000000000000000000000000000000000000000 / price;
    }

    function gt(Tick a, Tick b) internal pure returns (bool) {
        return Tick.unwrap(a) > Tick.unwrap(b);
    }

    function baseToQuote(Tick tick, uint256 base, bool roundingUp) internal pure returns (uint256) {
        return Math.divide((base * tick.toPrice()), 1 << 96, roundingUp);
    }

    function quoteToBase(Tick tick, uint256 quote, bool roundingUp) internal pure returns (uint256) {
        // @dev quote = unit(uint64) * unitSize(uint64) < 2^96
        //      We don't need to check overflow here
        return Math.divide(quote << 96, tick.toPrice(), roundingUp);
    }
}

// SPDX-License-Identifier: -
// License: https://license.sonic.market/LICENSE.pdf

pragma solidity ^0.8.0;

import {SignificantBit} from "./SignificantBit.sol";
import {Tick} from "./Tick.sol";

library TickBitmap {
    using SignificantBit for uint256;

    error EmptyError();
    error AlreadyExistsError();

    uint256 public constant B0_BITMAP_KEY = uint256(keccak256("TickBitmap")) + 1;
    uint256 public constant MAX_UINT_256_MINUS_1 = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe;

    function has(mapping(uint256 => uint256) storage self, Tick tick) internal view returns (bool) {
        (uint256 b0b1, uint256 b2) = _split(tick);
        uint256 mask = 1 << b2;
        return self[b0b1] & mask == mask;
    }

    function isEmpty(mapping(uint256 => uint256) storage self) internal view returns (bool) {
        return self[B0_BITMAP_KEY] == 0;
    }

    function _split(Tick tick) private pure returns (uint256 b0b1, uint256 b2) {
        assembly {
            let value := add(not(tick), 0x800000)
            b0b1 := shr(8, and(value, 0xffff00))
            b2 := and(value, 0xff)
        }
    }

    function highest(mapping(uint256 => uint256) storage self) internal view returns (Tick) {
        if (isEmpty(self)) revert EmptyError();

        uint256 b0 = self[B0_BITMAP_KEY].leastSignificantBit();
        uint256 b0b1 = (b0 << 8) | (self[~b0].leastSignificantBit());
        uint256 b2 = self[b0b1].leastSignificantBit();
        return _toTick((b0b1 << 8) | b2);
    }

    function set(mapping(uint256 => uint256) storage self, Tick tick) internal {
        (uint256 b0b1, uint256 b2) = _split(tick);
        uint256 mask = 1 << b2;
        uint256 b2Bitmap = self[b0b1];
        if (b2Bitmap & mask > 0) revert AlreadyExistsError();

        self[b0b1] = b2Bitmap | mask;
        if (b2Bitmap == 0) {
            mask = 1 << (b0b1 & 0xff);
            uint256 b1BitmapKey = ~(b0b1 >> 8);
            uint256 b1Bitmap = self[b1BitmapKey];
            self[b1BitmapKey] = b1Bitmap | mask;

            if (b1Bitmap == 0) self[B0_BITMAP_KEY] = self[B0_BITMAP_KEY] | (1 << ~b1BitmapKey);
        }
    }

    function clear(mapping(uint256 => uint256) storage self, Tick tick) internal {
        (uint256 b0b1, uint256 b2) = _split(tick);
        uint256 mask = 1 << b2;
        uint256 b2Bitmap = self[b0b1];

        self[b0b1] = b2Bitmap & (~mask);
        if (b2Bitmap == mask) {
            mask = 1 << (b0b1 & 0xff);
            uint256 b1BitmapKey = ~(b0b1 >> 8);
            uint256 b1Bitmap = self[b1BitmapKey];

            self[b1BitmapKey] = b1Bitmap & (~mask);
            if (mask == b1Bitmap) {
                mask = 1 << (~b1BitmapKey);
                self[B0_BITMAP_KEY] = self[B0_BITMAP_KEY] & (~mask);
            }
        }
    }

    function maxLessThan(mapping(uint256 => uint256) storage self, Tick tick) internal view returns (Tick) {
        (uint256 b0b1, uint256 b2) = _split(tick);
        uint256 b2Bitmap = (MAX_UINT_256_MINUS_1 << b2) & self[b0b1];
        if (b2Bitmap == 0) {
            uint256 b0 = b0b1 >> 8;
            uint256 b1Bitmap = (MAX_UINT_256_MINUS_1 << (b0b1 & 0xff)) & self[~b0];
            if (b1Bitmap == 0) {
                uint256 b0Bitmap = (MAX_UINT_256_MINUS_1 << b0) & self[B0_BITMAP_KEY];
                if (b0Bitmap == 0) return Tick.wrap(type(int24).min);
                b0 = b0Bitmap.leastSignificantBit();
                b1Bitmap = self[~b0];
            }
            b0b1 = (b0 << 8) | b1Bitmap.leastSignificantBit();
            b2Bitmap = self[b0b1];
        }
        b2 = b2Bitmap.leastSignificantBit();
        return _toTick((b0b1 << 8) | b2);
    }

    function _toTick(uint256 raw) private pure returns (Tick t) {
        assembly {
            t := and(not(sub(raw, 0x800000)), 0xffffff)
        }
    }
}

// SPDX-License-Identifier: -
// License: https://license.sonic.market/LICENSE.pdf

pragma solidity ^0.8.20;

import {DirtyUint64} from "./DirtyUint64.sol";
import {PackedUint256} from "./PackedUint256.sol";
import {Tick} from "./Tick.sol";

library TotalClaimableMap {
    using DirtyUint64 for uint64;
    using PackedUint256 for uint256;

    // @dev n should be less than type(uint64).max due to the dirty storage logic.
    function add(mapping(uint24 => uint256) storage self, Tick tick, uint64 n) internal {
        (uint24 groupIndex, uint8 elementIndex) = _splitTick(tick);
        uint256 group = self[groupIndex];
        // @notice Be aware of dirty storage add logic
        self[groupIndex] = group.update64Unsafe(
            elementIndex, // elementIndex < 4
            group.get64Unsafe(elementIndex).addClean(n)
        );
    }

    function sub(mapping(uint24 => uint256) storage self, Tick tick, uint64 n) internal {
        (uint24 groupIndex, uint8 elementIndex) = _splitTick(tick);
        self[groupIndex] = self[groupIndex].sub64Unsafe(elementIndex, n);
    }

    function get(mapping(uint24 => uint256) storage self, Tick tick) internal view returns (uint64) {
        (uint24 groupIndex, uint8 elementIndex) = _splitTick(tick);
        return self[groupIndex].get64Unsafe(elementIndex).toClean();
    }

    function _splitTick(Tick tick) internal pure returns (uint24 groupIndex, uint8 elementIndex) {
        uint256 casted = uint24(Tick.unwrap(tick));
        assembly {
            groupIndex := shr(2, casted) // div 4
            elementIndex := and(casted, 3) // mod 4
        }
    }
}

{
  "evmVersion": "cancun",
  "optimizer": {
    "enabled": true,
    "runs": 1000
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "metadata": {
    "useLiteralContent": true
  },
  "libraries": {
    "src/libraries/Book.sol": {
      "Book": "0x5489922f8312c812fbb7184ebf70b9dbfaeed9d4"
    }
  }
}

• No Contract Security Audit Submitted- Submit Audit Here

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nalType":"address","name":"provider","type":"address"}],"name":"Delist","type":"event"},{"anonymous":false,"inputs":[],"name":"EIP712DomainChanged","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"BookId","name":"bookId","type":"uint192"},{"indexed":true,"internalType":"address","name":"user","type":"address"},{"indexed":false,"internalType":"Tick","name":"tick","type":"int24"},{"indexed":false,"internalType":"uint256","name":"orderIndex","type":"uint256"},{"indexed":false,"internalType":"uint64","name":"unit","type":"uint64"},{"indexed":false,"internalType":"address","name":"provider","type":"address"}],"name":"Make","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"BookId","name":"id","type":"uint192"},{"indexed":true,"internalType":"Currency","name":"base","type":"address"},{"indexed":true,"internalType":"Currency","name":"quote","type":"address"},{"indexed":false,"internalType":"uint64","name":"unitSize","type":"uint64"},{"indexed":false,"internalType":"FeePolicy","name":"makerPolicy","type":"uint24"},{"indexed":false,"internalType":"FeePolicy","name":"takerPolicy","type":"uint24"},{"indexed":false,"internalType":"contract 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

-----Decoded View---------------
Arg [0] : owner_ (address): 0x4587dd6356d7293E5f10db4D853332BD5b218C0B
Arg [1] : defaultProvider_ (address): 0xcC92364b6B886158e71Fd4e4Da5C682D33d1491e
Arg [2] : baseURI_ (string): https://sonic.market/api/nft/chains/146/orders/
Arg [3] : contractURI_ (string): https://sonic.market/api/contract/chains/146
Arg [4] : name_ (string): Sonic Market Orderbook Maker Order
Arg [5] : symbol_ (string): SONIC-MARKET-ORDER

-----Encoded View---------------
17 Constructor Arguments found :
Arg [0] : 0000000000000000000000004587dd6356d7293e5f10db4d853332bd5b218c0b
Arg [1] : 000000000000000000000000cc92364b6b886158e71fd4e4da5c682d33d1491e
Arg [2] : 00000000000000000000000000000000000000000000000000000000000000c0
Arg [3] : 0000000000000000000000000000000000000000000000000000000000000120
Arg [4] : 0000000000000000000000000000000000000000000000000000000000000180
Arg [5] : 00000000000000000000000000000000000000000000000000000000000001e0
Arg [6] : 000000000000000000000000000000000000000000000000000000000000002f
Arg [7] : 68747470733a2f2f736f6e69632e6d61726b65742f6170692f6e66742f636861
Arg [8] : 696e732f3134362f6f72646572732f0000000000000000000000000000000000
Arg [9] : 000000000000000000000000000000000000000000000000000000000000002c
Arg [10] : 68747470733a2f2f736f6e69632e6d61726b65742f6170692f636f6e74726163
Arg [11] : 742f636861696e732f3134360000000000000000000000000000000000000000
Arg [12] : 0000000000000000000000000000000000000000000000000000000000000022
Arg [13] : 536f6e6963204d61726b6574204f72646572626f6f6b204d616b6572204f7264
Arg [14] : 6572000000000000000000000000000000000000000000000000000000000000
Arg [15] : 0000000000000000000000000000000000000000000000000000000000000012
Arg [16] : 534f4e49432d4d41524b45542d4f524445520000000000000000000000000000