// SPDX-License-Identifier: LicenseRef-Uniteum

pragma solidity ^0.8.30;

import {IUnit, IMigratable, IERC20} from "./IUnit.sol";
import {CloneERC20, Prototype} from "./CloneERC20.sol";
import {Units, Term} from "./Units.sol";
import {SafeERC20} from "erc20/SafeERC20.sol";
import {Math} from "math/Math.sol";

/**
 * @title IUnit — A universal liquidity system based on symbolic units.
 * See {IUnit} for details.
 */
contract Unit is CloneERC20, IUnit {
    using Units for *;
    using SafeERC20 for IERC20;

    /// @notice The ERC-20 symbol for the central 1 token.
    string public constant ONE_SYMBOL = "1";

    /// @notice The ERC-20 symbol for the central 1 token.
    string public constant NAME_PREFIX = "Uniteum-0.7 ";

    /// @notice The total original supply of {1} minted.
    /// @dev The total supply of {1} will never exceed this value.
    uint256 public immutable ONE_MINTED;

    /// @notice The central 1 unit.
    Unit private immutable ONE = this;

    /// @inheritdoc IUnit
    IUnit public reciprocal;

    /// @inheritdoc IUnit
    IERC20 public anchor;

    /// @inheritdoc IUnit
    mapping(IUnit => uint256) public reserves;

    /// @inheritdoc IUnit
    function one() public view returns (IUnit) {
        return ONE;
    }

    /// @inheritdoc IUnit
    function invariant(uint256 u, uint256 v) public pure returns (uint256 w) {
        w = Math.sqrt(u * v);
    }

    /// @inheritdoc IUnit
    function invariant() public view notOne returns (uint256 u, uint256 v, uint256 w) {
        u = ONE.reserves(this);
        v = ONE.reserves(reciprocal);
        w = invariant(u, v);
    }

    /// @inheritdoc IUnit
    function invariant(IUnit V) public view returns (IUnit W, uint256 u, uint256 v, uint256 w) {
        if (address(V) == address(this)) {
            revert DuplicateUnits();
        } else if (address(V) == address(reciprocal)) {
            W = one();
            (u, v, w) = invariant();
        } else {
            (IUnit P,) = product(V);
            (W,) = P.sqrt();
            u = W.reserves(this);
            v = W.reserves(V);
            w = invariant(u, v);
        }
    }

    /// @inheritdoc IUnit
    function forgeQuote(int256 du, int256 dv) public view returns (int256 dw) {
        (uint256 u0, uint256 v0, uint256 w0) = invariant();

        uint256 u1 = add(this, u0, du);
        uint256 v1 = add(reciprocal, v0, dv);
        uint256 w1 = invariant(u1, v1);

        // forge-lint: disable-next-line(unsafe-typecast)
        dw = int256(w0) - int256(w1);
        // Double dw if no anchor tokens are involved to keep the invariant balanced.
        if (address(anchor) == address(0) && address(reciprocal.anchor()) == address(0)) {
            dw *= 2;
        }
    }

    /// @inheritdoc IUnit
    function forgeQuote(IUnit V, int256 du, int256 dv) public view returns (IUnit W, int256 dw) {
        if (address(V) == address(reciprocal)) {
            W = one();
            dw = forgeQuote(du, dv);
        } else {
            uint256 u0;
            uint256 v0;
            uint256 w0;
            (W, u0, v0, w0) = invariant(V);

            uint256 u1 = add(this, u0, -du);
            uint256 v1 = add(V, v0, -dv);
            uint256 w1 = invariant(u1, v1);

            // forge-lint: disable-next-line(unsafe-typecast)
            int256 floatingCount = int256(
                uint256(
                    ((address(anchor) == address(0)) ? 1 : 0) + ((address(reciprocal.anchor()) == address(0)) ? 1 : 0)
                )
            );
            // forge-lint: disable-next-line(unsafe-typecast)
            dw = floatingCount * (int256(w1) - int256(w0));
        }
    }

    /// @inheritdoc IUnit
    function forge(int256 du, int256 dv) external returns (int256 dw) {
        dw = forgeQuote(du, dv);
        ONE.__forge(msg.sender, this, reciprocal, du, dv, dw);
        emit Forge(msg.sender, this, du, dv, dw);
    }

    //// @inheritdoc IUnit
    function forge(IUnit V, int256 du, int256 dv) external returns (IUnit W, int256 dw) {
        multiply(V).sqrtResolve();
        (W, dw) = forgeQuote(V, du, dv);
        ONE.__forge(msg.sender, this, reciprocal, du, dv, dw);
        emit Forge(msg.sender, this, du, dv, dw);
    }

    /// @dev This function must be non-reentrant to thwart malicious anchor tokens.
    function __forge(address holder, IUnit U, IUnit V, int256 du, int256 dv, int256 dw) external nonReentrant {
        __forge(holder, U, du);
        __forge(holder, V, dv);
        __forge(holder, this, dw);
        emit Forge(msg.sender, this, du, dv, dw);
    }

    function __forge(address holder, IUnit V, int256 dv) internal {
        reserves[V] = add(V, reserves[V], dv);
        if (dv < 0) {
            // forge-lint: disable-next-line(unsafe-typecast)
            Unit(address(V)).__burn(holder, uint256(-dv));
        } else if (dv > 0) {
            // forge-lint: disable-next-line(unsafe-typecast)
            Unit(address(V)).__mint(holder, uint256(dv));
        }
    }

    /**
     * @notice Burn units of the holder.
     * @dev - Only Units with the same 1 can call this function.
     * @param holder The holder of the burned units.
     * @param units The number of units to burn.
     */
    function __burn(address holder, uint256 units) external onlyUnit {
        _burn(holder, units);
        // If this Unit wraps an external token, send wrapped tokens to the holder.
        if (address(anchor) != address(0)) {
            anchor.safeTransfer(holder, units);
        }
    }

    /**
     * @notice Mint units for the holder.
     * @dev - Only Units with the same 1 can call this function.
     * @param holder The recipient of the minted units.
     * @param units The number of units to mint.
     */
    function __mint(address holder, uint256 units) external onlyUnit {
        // If this Unit wraps an external token, get wrapped tokens from the holder.
        if (address(anchor) != address(0)) {
            anchor.safeTransferFrom(holder, address(this), units);
        }
        _mint(holder, units);
    }

    /**
     * @notice Safely computes an updated supply of tokens and reverts if the supply would be negative.
     * @param U The unit whose supply is being calculated. For errors only.
     * @param u0 The current supply of U.
     * @param du The change in the supply of U.
     * @return u1 The updated supply of U.
     */
    function add(IUnit U, uint256 u0, int256 du) private pure returns (uint256 u1) {
        // forge-lint: disable-next-line(unsafe-typecast)
        int256 u = int256(u0) + du;
        if (u < 0) {
            revert NegativeSupply(U, u);
        }
        // forge-lint: disable-next-line(unsafe-typecast)
        u1 = uint256(u);
    }

    /**
     * @dev Only one() can call this method.
     * @param canonical expression defining the unit.
     */
    function __initialize(string memory canonical) internal {
        _symbol = canonical;
        _name = string.concat(NAME_PREFIX, canonical);
        Term[] memory terms = canonical.parseTerms();
        if (terms.length == 1) {
            anchor = IERC20(terms[0].anchor());
        }
        terms = terms.reciprocal().sortAndMerge();
        (address reciprocalAddress,) = __clone(bytes(terms.symbol()));
        reciprocal = IUnit(reciprocalAddress);
    }

    /// @inheritdoc Prototype
    function __initialize(bytes memory initData) public virtual override onlyPrototype {
        __initialize(string(initData));
    }

    /// @inheritdoc IUnit
    function product(string memory expression) public view returns (IUnit unit, string memory canonical) {
        Term[] memory terms = symbol().parseTerms().product(expression.parseTerms().sortAndMerge());
        if (terms.length > 0) {
            terms = terms.sortAndMerge();
        }
        canonical = terms.symbol();
        if (terms.length == 0) {
            unit = one();
        } else {
            (address unitAddress,) = __predict(bytes(canonical));
            unit = IUnit(unitAddress);
        }
    }

    /// @inheritdoc IUnit
    function multiply(string memory expression) public returns (IUnit unit) {
        string memory canonical;
        (unit, canonical) = product(expression);
        if (address(unit).code.length == 0) {
            __clone(bytes(canonical));
        }
    }

    /// @inheritdoc IUnit
    function anchoredSymbol(IERC20 token) public pure returns (string memory s) {
        s = address(token).withExponent(Units.ONE_RATIONAL_8).symbol();
    }

    /// @inheritdoc IUnit
    function anchoredPredict(IERC20 token) external view returns (IUnit unit, string memory canonical) {
        (unit, canonical) = product(anchoredSymbol(token));
    }

    /// @inheritdoc IUnit
    function anchored(IERC20 token) external returns (IUnit unit) {
        unit = multiply(anchoredSymbol(token));
    }

    /// @dev Mapping of multipliers to their product units.
    mapping(IUnit => IUnit) private _products;

    /// @inheritdoc IUnit
    function product(IUnit multiplier) public view returns (IUnit unit, string memory canonical) {
        unit = _products[multiplier];
        if (address(unit) != address(0)) {
            canonical = unit.symbol();
        } else {
            (unit, canonical) = product(multiplier.symbol());
        }
    }

    /// @inheritdoc IUnit
    function multiply(IUnit multiplier) public returns (IUnit unit) {
        unit = _products[multiplier];
        if (address(unit) == address(0)) {
            unit = multiply(multiplier.symbol());
            _products[multiplier] = unit;
        }
    }

    IUnit private _sqrt;

    /// @inheritdoc IUnit
    function sqrt() public view returns (IUnit unit, string memory canonical) {
        unit = _sqrt;
        if (address(unit) == address(0)) {
            Term[] memory terms = symbol().parseTerms().sqrt();
            canonical = terms.symbol();
            (address sqrtAddress,) = __predict(bytes(canonical));
            unit = IUnit(sqrtAddress);
        }
    }

    /// @inheritdoc IUnit
    function sqrtResolve() external returns (IUnit root) {
        if (_sqrt != IUnit(address(0))) {
            return _sqrt;
        }
        string memory sqrtSymbol;
        (root, sqrtSymbol) = sqrt();
        if (address(root).code.length == 0) {
            __clone(bytes(sqrtSymbol));
        }
        _sqrt = root;
    }

    modifier onlyUnit() {
        _onlyUnit();
        _;
    }

    function _onlyUnit() private view {
        // Revert if the caller does not have the same address as predicted by its hash.
        // Prevent malicious actors from calling protected functions.
        if ((msg.sender != PROTOTYPE) && (!Prototype(PROTOTYPE).isClone(msg.sender))) {
            revert Unauthorized();
        }
    }

    modifier onlyOne() {
        _onlyOne();
        _;
    }

    function _onlyOne() private view {
        if (this != one()) {
            revert FunctionNotCalledOnOne();
        }
    }

    modifier notOne() {
        _notOne();
        _;
    }

    function _notOne() private view {
        if (this == one()) {
            revert FunctionCalledOnOne();
        }
    }

    // The following reentrancy code was modified from openzeppelin.storage.ReentrancyGuardTransient
    // It uses transient boolean storage on {one()} to prevent reentrancy on all units during a transaction.
    // keccak256(abi.encode(uint256(keccak256("openzeppelin.storage.ReentrancyGuardTransient")) - 1)) & ~bytes32(uint256(0xff))
    bytes32 private constant REENTRANCY_GUARD_STORAGE =
        0x9b779b17422d0df92223018b32b4d1fa46e071723d6817e2486d003becc55f00;

    function tstore(bool value) internal {
        assembly ("memory-safe") {
            tstore(REENTRANCY_GUARD_STORAGE, value)
        }
    }

    function _reentrancyGuardEntered() internal view returns (bool value) {
        assembly ("memory-safe") {
            value := tload(REENTRANCY_GUARD_STORAGE)
        }
    }

    modifier nonReentrant() {
        _nonReentrantBefore();
        _;
        _nonReentrantAfter();
    }

    function _nonReentrantBefore() private {
        ONE.__nonReentrantBefore();
    }

    function _nonReentrantAfter() private {
        ONE.__nonReentrantAfter();
    }

    function __nonReentrantBefore() public onlyOne {
        if (_reentrancyGuardEntered()) {
            revert ReentryForbidden();
        }

        // Any calls to nonReentrant after this point will fail
        tstore(true);
    }

    function __nonReentrantAfter() public onlyOne {
        tstore(false);
    }

    /// @inheritdoc IMigratable
    IERC20 public immutable UPSTREAM;

    /// @inheritdoc IMigratable
    function migrate(uint256 units) external onlyOne {
        UPSTREAM.safeTransferFrom(msg.sender, address(this), units);
        // forge-lint: disable-next-line(unsafe-typecast)
        __forge(msg.sender, ONE, int256(units));
        emit Migrate(msg.sender, units);
    }

    /// @inheritdoc IMigratable
    function unmigrate(uint256 units) external onlyOne {
        // forge-lint: disable-next-line(unsafe-typecast)
        __forge(msg.sender, ONE, -int256(units));
        UPSTREAM.safeTransferFrom(address(this), msg.sender, units);
        emit Unmigrate(msg.sender, units);
    }

    constructor(IERC20 upstream) CloneERC20(ONE_SYMBOL, ONE_SYMBOL) {
        reciprocal = this;
        _sqrt = this;
        _symbol = ONE_SYMBOL;
        _name = string.concat(NAME_PREFIX, ONE_SYMBOL);
        UPSTREAM = upstream;
        emit UnitCreate(this, anchor, bytes32(0), _symbol);
    }
}

// SPDX-License-Identifier: LicenseRef-Uniteum

pragma solidity ^0.8.30;

import {IERC20Metadata, IERC20} from "ierc20/IERC20Metadata.sol";
import {IMigratable} from "./IMigratable.sol";

/**
 * @title IUnit — A universal liquidity system based on symbolic units.
 * @notice A Unit (U) is an ERC-20 token with built-in liquidity via reciprocal minting/burning.
 * The identity unit {one()} aka {1} is the universal liquidity token around which a unit and its reciprocal pivot.
 * Units support a {forge} operation that mints/burns combinations of 1, U, and 1/U to maintain a constant product invariant.
 * If a unit goes up in price, its reciprocal goes down, and vice versa.
 * Some units are anchored to external ERC-20 tokens, to integrate the system with the broader ERC-20 ecosystem.
 *
 * A Unit symbolically represents a unit of measure, such as a a physical dimension, abstract quantity, linked ERC-20 token, or compound units.
 * It supports rational powers of base units and algebraic composition such as product and reciprocal.
 * A base unit has two varieties: anchored or unanchored.
 *
 * An anchored unit is a 1:1 custodial owner of an external ERC-20 token
 *   Its symbol is the Ethereum address of the external token.
 *   Examples: 0xdAC17F958D2ee523a2206206994597C13D831ec7 (USDT), 0x1f9840a85d5af5bf1d1762f925bdaddc4201f984 (UNI)
 *
 * An unanchored base unit has no associated external token.
 *   Its symbol is an unbroken sequence of the following characters: 'a'-'z', 'A'-'Z', '0'-'9', '_', '-', '.'
 *   Symbols are case sensitive and are limited to 30 characters.
 *   Examples: kg, KG, kG, Kg, m, s, MSFT, USD, _, -, ., example.com, QmFzZTY0IGVuY29kZWQgdW5pdA
 *   Note: unanchored base units have no inherent connection to real world entities.
 *         MSFT IS NOT inherently connected to Microsoft stock.
 *         kg IS NOT inherently connected to the concept of a kilogram.
 *
 * A pure power unit, aka term, is a base unit raised to a power using a combination of '^' and '1/' notation
 *   Division in exponents uses ':' instead of '/' to simplify parsing
 *   Powers can be rational fractions represented using ':' for division in the exponent
 *     Examples: kg^2, 1/s, 1/m^2, 1/T^1:4, 1/0xdAC17F958D2ee523a2206206994597C13D831ec7^3:7
 *   Operations within terms:
 *     ^ power
 *     : divide
 * Compound units are products of pure power units separated by '*' or '/'
 *   Examples: kg*m/s^2, MSFT/USD, 1/foo^2:5/bar^7:9
 *   Operations combining terms:
 *     * multiply
 *     / divide
 *
 * @dev Version scope (v1)
 * - Value constraints exist between a Unit and its reciprocal, and between an anchored token and its anchor.
 * - Powers/exponentials (e.g., constraining value across A and A^k like power perpetuals) are
 *   not enforced; this may be future work.
 *
 * @dev Safety
 * - Anchored units are custodial: underlying tokens are held by this contract.
 * - This system uses no price oracles or off-chain dependencies.
 *
 * @dev Reentrancy Protection
 * All state-changing functions use a transient reentrancy guard stored on the "1" unit
 * per EIP-1153. This protects against malicious anchor token callbacks.
 * @custom:security Uses transient storage; requires EVM version Cancun or later
 *
 * @dev Internal Function Naming Convention
 * Functions prefixed with __ are restricted to calls from other Units in the same system (same ONE).
 * These are used for cross-unit operations during forge.
 */
interface IUnit is IERC20Metadata, IMigratable {
    /**
     * @notice Compute the constant product invariant for a reciprocal pair.
     * The implied price for the unit is w/u, and w/v for its reciprocal.
     * @param u Total supply of a unit.
     * @param v Total supply of its reciprocal.
     * @return w sqrt(u * v).
     */
    function invariant(uint256 u, uint256 v) external view returns (uint256 w);

    /**
     * @notice Return the constant product invariant for a reciprocal pair.
     * @return u Total supply of the unit.
     * @return v Total supply of its reciprocal.
     * @return w sqrt(u * v).
     */
    function invariant() external view returns (uint256 u, uint256 v, uint256 w);

    /**
     * @notice Return the constant product invariant for a pair.
     * @param V The invariant pair for this unit.
     * @return W Product of this unit and V.
     * @return u Total supply of the unit.
     * @return v Total supply of its reciprocal.
     * @return w sqrt(u * v).
     */
    function invariant(IUnit V) external view returns (IUnit W, uint256 u, uint256 v, uint256 w);

    /**
     * @notice Return the amount of a reserve unit where this unit is the liquidity provider.
     * @param V One of the reserve units associated with this unit.
     * @return v The reserve amount.
     */
    function reserves(IUnit V) external view returns (uint256 v);

    /**
     * @notice Compute the change of the caller's 1 balance that would result from forging this unit.
     *
     * @dev Invariant solver for the forge operation.
     * Given signed changes to the caller's balances of the unit `du` and its reciprocal `dv`,
     * this function computes the signed change to 1 `dw` required to preserve the
     * constant-product relationship across the triad (U, 1/U, 1).
     *
     * Sign convention:
     *  - Positive values mint units to the caller.
     *  - Negative values burn units from the caller.
     *
     * @param V Other unit.
     * @param du Signed change of the caller's unit balance.
     * @param dv Signed change of the caller's reciprocal balance.
     * @return W Product of this unit and V.
     * @return dw Signed change of caller's 1 balance.
     */
    function forgeQuote(IUnit V, int256 du, int256 dv) external view returns (IUnit W, int256 dw);

    /**
     * @notice Compute the change of the caller's 1 balance that would result from forging this unit.
     *
     * @dev Invariant solver for the forge operation.
     * Given signed changes to the caller's balances of the unit `du` and its reciprocal `dv`,
     * this function computes the signed change to 1 `dw` required to preserve the
     * constant-product relationship across the triad (U, 1/U, 1).
     *
     * Sign convention:
     *  - Positive values mint units to the caller.
     *  - Negative values burn units from the caller.
     *
     * @param du Signed change of the caller's unit balance.
     * @param dv Signed change of the caller's reciprocal balance.
     * @return dw Signed change of caller's 1 balance.
     */
    function forgeQuote(int256 du, int256 dv) external view returns (int256 dw);

    /**
     * @notice Mint/burn combinations of this unit, its reciprocal and 1.
     * @dev
     * Uses {forgeQuote} to compute the necessary deltas to maintain the invariant,
     * then mints/burns the corresponding amounts of du, dv, and dw for the caller.
     * To mint an anchored unit, even if it participates as the reciprocal,
     * the caller must approve transferring the anchor token to the unit:
     *     u.anchor().approve(address(u)), uint256(du));
     *
     * @param V Other unit.
     * @param du Signed delta of the unit U.
     * @param dv Signed delta of the unit 1/U.
     * @return W Product of this unit and V.
     * @return dw Signed delta of 1 minted/burned for the caller.
     */
    function forge(IUnit V, int256 du, int256 dv) external returns (IUnit W, int256 dw);

    /**
     * @notice Mint/burn combinations of this unit, its reciprocal and 1.
     * @dev
     * Uses {forgeQuote} to compute the necessary deltas to maintain the invariant,
     * then mints/burns the corresponding amounts of du, dv, and dw for the caller.
     * To mint an anchored unit, even if it participates as the reciprocal,
     * the caller must approve transferring the anchor token to the unit:
     *     u.anchor().approve(address(u)), uint256(du));
     *
     * @param du Signed delta of the unit U.
     * @param dv Signed delta of the unit 1/U.
     * @return dw Signed delta of 1 minted/burned for the caller.
     */
    function forge(int256 du, int256 dv) external returns (int256 dw);

    /**
     * @notice Predict the address of the IUnit resulting from multiplying by a symbolic expression.
     * @dev View-only; does not create the unit. Use {multiply} to create if needed.
     * @param expression a string representation of the unit.
     * @return unit the IUnit for the given expression.
     * @return symbol the canonical form of the string representation of the unit.
     */
    function product(string memory expression) external view returns (IUnit unit, string memory symbol);

    /**
     * @notice Create a new unit if it does not exist, or return existing unit.
     * @dev Creates the unit by multiplying this unit with the expression.
     * @param expression a string representation of the unit to multiply by.
     * @return unit the IUnit with the resulting symbol.
     */
    function multiply(string memory expression) external returns (IUnit unit);

    /**
     * @notice Predict the unit resulting from multiplying this unit by another unit.
     * @dev View-only; uses cached product mapping when available, otherwise computes from symbols.
     * Does not create the unit. Use {multiply} to create if needed.
     * @param multiplier The right-hand unit operand.
     * @return unit The IUnit representing the product.
     * @return symbol the canonical form of the string representation of the unit.
     */
    function product(IUnit multiplier) external view returns (IUnit unit, string memory symbol);

    /**
     * @notice Create or return the product of this unit with another unit.
     * @dev Creates the product unit if it doesn't exist, caches the mapping for future calls.
     * @param multiplier The right-hand unit operand.
     * @return product The new or existing IUnit representing the product.
     */
    function multiply(IUnit multiplier) external returns (IUnit product);

    /**
     * @notice Predict the address of an anchored unit.
     * @param token to be anchored to.
     * @return unit the IUnit anchored to the given token.
     * @return symbol the canonical form of the string representation of the unit.
     */
    function anchoredPredict(IERC20 token) external view returns (IUnit unit, string memory symbol);

    /**
     * @notice Create an anchored unit if it does not exist.
     * @param token to be anchored to.
     * @return unit the IUnit anchored to the given token.
     */
    function anchored(IERC20 token) external returns (IUnit unit);

    /**
     * @notice Return the symbol for an anchored token.
     *   Example: 0xdAC17F958D2ee523a2206206994597C13D831ec7 (USDT)
     * @param token to be anchored to.
     * @return symbol the canonical form of the string representation of the unit.
     */
    function anchoredSymbol(IERC20 token) external pure returns (string memory symbol);

    /**
     * @notice The identity unit "1".
     * @dev Also the implementation and deployer for all other units, which are clones.
     */
    function one() external view returns (IUnit);

    /**
     * @return The IUnit representing the reciprocal of this unit.
     */
    function reciprocal() external view returns (IUnit);

    /**
     * @return root The IUnit representing the sqrt of this unit.
     * @return symbol the canonical form of the string representation of the unit.
     * Symbol is only returned if the root is not known to be deployed.
     */
    function sqrt() external view returns (IUnit root, string memory symbol);

    /**
     * @notice Ensure the sqrt of this unit is deployed.
     */
    function sqrtResolve() external returns (IUnit root);

    /**
     * @return The external token, if any, anchored to this unit.
     */
    function anchor() external view returns (IERC20);

    /**
     * @dev Revert when called with duplicate units.
     */
    error DuplicateUnits();

    /**
     * @dev Revert when called on 1.
     */
    error FunctionCalledOnOne();

    /**
     * @dev Revert when called on anything but 1.
     */
    error FunctionNotCalledOnOne();

    /**
     * @dev Revert when a negative supply would result from an operation.
     * @param unit The unit that would have negative supply.
     * @param supply The calculated negative supply value.
     */
    error NegativeSupply(IUnit unit, int256 supply);

    /**
     * @dev Reentrant calls are forbidden.
     */
    error ReentryForbidden();

    /**
     * @notice Emit on unit creation.
     * @param unit The created unit.
     * @param hash used to compute the address of the unit.
     * @param symbol The symbol of the the unit.
     */
    event UnitCreate(IUnit indexed unit, IERC20 indexed anchor, bytes32 indexed hash, string symbol);

    /**
     * @notice Emit when a holder calls forge.
     * @param holder The address whose balances were updated.
     * @param unit   The unit doing the forge.
     * @param du     signed change to the holder's balance of the unit.
     * @param dv     signed change to the holder's balance of the reciprocal unit.
     * @param dw     signed change to the holder's balance of 1.
     */
    event Forge(address indexed holder, IUnit indexed unit, int256 du, int256 dv, int256 dw);

    /**
     * @notice Emitted when tokens are migrated into the system.
     * @param user The address migrating tokens.
     * @param amount Amount of tokens migrated.
     */
    event Migrate(address indexed user, uint256 amount);

    /**
     * @notice Emitted when tokens are unmigrated from the system.
     * @param user The address unmigrating tokens.
     * @param amount Amount of tokens unmigrated.
     */
    event Unmigrate(address indexed user, uint256 amount);
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.30;

import {Prototype} from "./Prototype.sol";
import {ERC20} from "erc20/ERC20.sol";

/**
 * @title CloneERC20
 * @notice ERC-20 base contract with support for minimal proxy cloning (EIP-1167).
 * @dev
 * Combines OpenZeppelin's ERC20 standard implementation with the Prototype
 * cloning pattern, enabling gas-efficient deployment of multiple ERC-20 tokens
 * that share the same implementation logic but maintain isolated storage.
 *
 * **Key Design Pattern:**
 * Standard ERC-20 implementations store name and symbol as immutables set during
 * construction. This prevents cloning because minimal proxies (EIP-1167) delegate
 * all logic via DELEGATECALL and cannot have their own constructor parameters.
 *
 * CloneERC20 solves this by:
 * 1. Storing name and symbol in regular storage variables (_name, _symbol)
 * 2. Overriding name() and symbol() accessors to read from storage
 * 3. Allowing these values to be set during __initialize() on each clone
 *
 * **Usage Pattern:**
 * ```solidity
 * // 1. Deploy prototype
 * MyToken prototype = new MyToken("PROTO", "PROTO");
 *
 * // 2. Create clones with custom metadata
 * bytes memory initData = abi.encode(creator, "Token A", "TKA");
 * (address tokenA, ) = prototype.__clone(initData);
 *
 * initData = abi.encode(creator, "Token B", "TKB");
 * (address tokenB, ) = prototype.__clone(initData);
 *
 * // 3. Each clone has its own name/symbol but shares logic
 * assert(MyToken(tokenA).name() == "Token A");
 * assert(MyToken(tokenB).name() == "Token B");
 * ```
 *
 * **Storage Layout:**
 * Each clone maintains its own:
 * - _name: Token name (settable during initialization)
 * - _symbol: Token symbol (settable during initialization)
 * - _balances: Mapping of account balances (ERC20 inherited)
 * - _allowances: Mapping of allowances (ERC20 inherited)
 * - _totalSupply: Total token supply (ERC20 inherited)
 *
 * **Why Empty String Constructor:**
 * The ERC20 base constructor is passed empty strings because:
 * - Those values would only affect the prototype contract itself
 * - Clones override name() and symbol() to read from their own storage
 * - This prevents confusion between prototype metadata and clone metadata
 *
 * **Inheritance Chain:**
 * CloneERC20 → ERC20 (OpenZeppelin) + Prototype (factory pattern)
 *
 * @author Paul Reinholdtsen (reinholdtsen.eth)
 */
abstract contract CloneERC20 is ERC20, Prototype {
    // ============ Constructor ============

    /**
     * @notice Initializes the prototype implementation with name and symbol.
     * @dev
     * **Important:** These parameters only affect the prototype contract itself,
     * NOT the clones. Each clone sets its own _name and _symbol during __initialize().
     *
     * The ERC20 base constructor receives empty strings ("", "") because:
     * 1. We override name() and symbol() to read from storage instead
     * 2. The prototype's metadata is rarely used (clones are what matter)
     * 3. This keeps the pattern consistent across prototype and clones
     *
     * **For derived contracts:**
     * Pass descriptive metadata for the prototype (often "PROTO" or similar)
     * to distinguish it from actual clone instances.
     *
     * @param name_ Name for the prototype implementation.
     * @param symbol_ Symbol for the prototype implementation.
     */
    constructor(string memory name_, string memory symbol_) ERC20("", "") {
        _name = name_;
        _symbol = symbol_;
    }

    // ============ ERC-20 Metadata Overrides ============

    /**
     * @notice Returns the name of the token.
     * @dev Overrides ERC20.name() to read from storage instead of immutables.
     *
     *      **On the prototype:** Returns the name set in constructor.
     *      **On clones:** Returns the name set during __initialize().
     *
     *      This allows each clone to have distinct metadata while sharing
     *      the same implementation logic.
     *
     * @return The token name.
     */
    function name() public view virtual override(ERC20) returns (string memory) {
        return _name;
    }

    /**
     * @notice Returns the symbol of the token.
     * @dev Overrides ERC20.symbol() to read from storage instead of immutables.
     *
     *      **On the prototype:** Returns the symbol set in constructor.
     *      **On clones:** Returns the symbol set during __initialize().
     *
     *      This allows each clone to have distinct metadata while sharing
     *      the same implementation logic.
     *
     * @return The token symbol.
     */
    function symbol() public view virtual override(ERC20) returns (string memory) {
        return _symbol;
    }
}

// SPDX-License-Identifier: LicenseRef-Uniteum

pragma solidity ^0.8.30;

import {Term} from "./Term.sol";
import {Rationals, Rational, Rational8} from "./Rationals.sol";
import {Strings} from "strings/Strings.sol";

/**
 * @title Units
 * @dev Library for unit term operations.
 * Base unit terms are packed into uint:
 * The last two bytes (30, 31) are a rational exponent.
 * Symbolic terms have the first 30 bytes as the base symbol.
 * Address terms have the first byte = 1, and the next 20 bytes are an address.
 * +0......0|1.........................20|21................29|30...........31+
 * | Symbol                                                   |    Exponent   |
 * |----------------------------------------------------------| ± num / den   |
 * | Type=1 | Address [1..20]            | Reserved           |  int8 | uint8 |
 * +255................................96|95................16|15....8|7.....0+
 * Example 1: meter^2:3
 * |6d 6574657200000000000000000000000000000000 000000000000000000 02 03|
 * |  |                                        |                  |  |  |
 * |01 c02aaa39b223fe8d0a0e5c4f27ead9083c756cc2 000000000000000000 ff 01|
 * Example 2: [address of WETH]^-1
 */
library Units {
    using Units for *;
    using Rationals for *;
    using Strings for *;

    /// @dev Bitmap indicating valid symbol characters: 0-9, A-Z, a-z, _, -, .
    uint256 constant SYMBOL_CHAR_BITS = 0x7fffffe87fffffe03ff600000000000;
    /// @dev The term for 1^0. The ascii code for "1" is 0x31.
    /// @dev Shift amount for term type byte: 248 bits (31 bytes) = 0xf8
    uint256 constant ONE_TERM = 0x31 << 0xf8;
    /// @dev A term with this type is an encoded address reference with an exponent.
    uint256 constant ANCHOR_TERM_TYPE = 1;
    /// @dev Shift amount for anchor address: 20 bytes (address) + 9 bytes (reserved) = 88 bits = 0x58
    uint256 constant ANCHOR_SHIFT = 0x58;
    string constant ONE_SYMBOL = "1";
    bytes1 constant DIVIDE_SYMBOL = "/";
    bytes1 constant MULTIPLY_SYMBOL = "*";
    bytes1 constant POWER_SYMBOL = "^";
    bytes1 constant POWER_DIV = ":";
    Rational8 constant ZERO_RATIONAL_8 = Rational8.wrap(1);
    Rational8 constant ONE_RATIONAL_8 = Rational8.wrap(0x101);
    uint256 constant EXPONENT_MASK = 0xffff;
    uint256 constant MAX_SYMBOL_SIZE = 30;

    // Errors
    error BaseSymbolTooBig();
    error ExponentTooBig();
    error InvalidAddressTerm(Term term);
    error BadHexCharacter(uint8 char);
    error UnexpectedCharacter(bytes1 char);
    error UnexpectedEndOfInput();

    /// @dev Extracts the base part from a term (clears the exponent byte)
    function base(Term term) internal pure returns (Term base_) {
        base_ = Term.wrap(term.raw() & ~uint256(EXPONENT_MASK));
    }

    function raw(Term term) internal pure returns (uint256) {
        return Term.unwrap(term);
    }

    /// @dev Extracts the exponent from a term (int8 stored in lowest byte)
    function exponent(Term term) internal pure returns (Rational8) {
        return Rational8.wrap(int16(uint16(term.raw())));
    }

    /// @dev Returns whether the char is one of 0-9, A-Z, a-z, _, -, .
    function isSymbolChar(bytes1 char) internal pure returns (bool) {
        return (SYMBOL_CHAR_BITS >> uint8(char)) & 1 != 0;
    }

    function termType(Term term) internal pure returns (uint8 termType_) {
        termType_ = uint8(term.raw() >> 0xf8);
    }

    function isBase(Term term) internal pure returns (bool) {
        return term.exponent().raw() == ONE_RATIONAL_8.raw();
    }

    /**
     * @notice Return the external token address represented by the term.
     * @dev Return address(0) if the term is not an external token term.
     */
    function anchor(Term term) internal pure returns (address token) {
        if (term.termType() == ANCHOR_TERM_TYPE && term.isBase()) {
            // forge-lint: disable-next-line(unsafe-typecast)
            token = address(uint160(term.raw() >> ANCHOR_SHIFT));
        }
    }

    /**
     * @notice Return the external token address represented by the terms.
     * @dev Return address(0) if the term is not an external token term.
     */
    function anchor(Term[] memory terms) internal pure returns (address token) {
        if (terms.length == 1) {
            token = terms[0].anchor();
        }
    }

    function parts(Term term)
        internal
        pure
        returns (
            uint256 bits,
            bool isBase_,
            uint8 termType_,
            address tokenAddress_,
            bytes30 symbol_,
            int8 numerator_,
            uint8 denominator_
        )
    {
        bits = term.raw();
        // forge-lint: disable-next-line(unsafe-typecast)
        termType_ = uint8(bits >> 0xf8);
        // forge-lint: disable-next-line(unsafe-typecast)
        numerator_ = int8(uint8(bits >> 8));
        // forge-lint: disable-next-line(unsafe-typecast)
        denominator_ = uint8(bits);
        isBase_ = numerator_ == 1 && denominator_ == 1;
        if (termType_ != ANCHOR_TERM_TYPE) {
            // forge-lint: disable-next-line(unsafe-typecast)
            symbol_ = bytes30(uint240(bits >> 16));
        } else {
            // forge-lint: disable-next-line(unsafe-typecast)
            tokenAddress_ = address(uint160(bits >> ANCHOR_SHIFT));
        }
    }

    /**
     * @dev Reverts if the term is not valid
     *      - has non-symbol characters before the zero padding
     *      - has an exponent numerator = -128
     */
    function mustBeValidTerm(Term term) internal pure {
        (uint256 c,, uint8 t,, bytes30 s, int8 n, uint8 d) = term.parts();
        if (n == -128) {
            revert ExponentTooBig();
        }
        if (d == 0) {
            revert Rationals.ZeroDenominator();
        }

        if (t == ANCHOR_TERM_TYPE) {
            if (0 != ((c >> 16) << 23 * 8)) {
                revert InvalidAddressTerm(term);
            }
        } else {
            uint256 i;
            unchecked {
                for (; i < 30; ++i) {
                    if (!s[i].isSymbolChar()) {
                        break;
                    }
                }

                for (; i < 30; ++i) {
                    if (s[i] != 0) {
                        revert UnexpectedCharacter(s[i]);
                    }
                }
            }
        }
    }

    /// @dev Revert if any term is invalid.
    function mustBeValidTerms(Term[] memory terms) internal pure {
        unchecked {
            for (uint256 i = 0; i < terms.length; ++i) {
                terms[i].mustBeValidTerm();
            }
        }
    }

    /// @dev Packs a base and exponent into a term
    function withExponent(Term base_, Rational8 exp) internal pure returns (Term term) {
        term = Term.wrap((base_.raw() & ~uint256(EXPONENT_MASK)) | uint256(uint16(int16(exp.raw()))));
    }

    /// @dev Packs a base and exponent into a term
    function withExponent(address base_, Rational8 exp) internal pure returns (Term term) {
        term = Term.wrap((uint256(uint160(base_)) << ANCHOR_SHIFT) | (ANCHOR_TERM_TYPE << 0xf8)).withExponent(exp);
    }

    /// @dev Return the reciprocal of a term (negates exponent)
    function reciprocal(Term term) internal pure returns (Term reciprocal_) {
        reciprocal_ = term.withExponent(term.exponent().neg());
    }

    /// @dev Return the reciprocal terms. Modifies the input.
    function reciprocal(Term[] memory terms) internal pure returns (Term[] memory reciprocal_) {
        reciprocal_ = terms;
        unchecked {
            for (uint256 i = 0; i < terms.length; ++i) {
                reciprocal_[i] = terms[i].reciprocal();
            }
        }
    }

    /// @dev Return the sqrt of a term (halves exponent)
    function sqrt(Term term) internal pure returns (Term root) {
        root = term.withExponent(term.exponent().div(2));
    }

    /// @dev Return the sqrt terms. Modifies the input.
    function sqrt(Term[] memory terms) internal pure returns (Term[] memory root) {
        root = terms;
        for (uint256 i = 0; i < terms.length; ++i) {
            root[i] = terms[i].sqrt();
        }
    }

    /// @dev Concatenates three strings
    function add(string memory s1, string memory s2, string memory s3) internal pure returns (string memory) {
        return string.concat(s1, s2, s3);
    }

    function toString(bytes30 b) internal pure returns (string memory s) {
        uint256 end;
        unchecked {
            // Find trailing zeros
            for (; end < 30; ++end) {
                if (b[end] == 0) {
                    break;
                }
            }
        }

        bytes memory sb = new bytes(end);

        unchecked {
            for (uint256 i = 0; i < end; ++i) {
                sb[i] = b[i];
            }
        }
        s = string(sb);
    }

    /// @dev Returns the symbol string for a single term
    function symbol(Term term) internal pure returns (string memory symbol_) {
        (,, uint8 t, address a, bytes30 s, int8 n, uint8 d) = term.parts();
        if (n == 0) {
            return ONE_SYMBOL;
        }
        if (t == ANCHOR_TERM_TYPE) {
            symbol_ = Strings.toChecksumHexString(a);
        } else {
            symbol_ = toString(s);
        }
        if (n != 1 || d != 1) {
            symbol_ = symbol_.add("^", Strings.toStringSigned(n));
            if (d != 1) {
                symbol_ = symbol_.add(":", Strings.toString(d));
            }
        }
    }

    /// @dev Returns the full compound unit symbol from an array of terms
    function symbol(Term[] memory terms) internal pure returns (string memory symbol_) {
        if (terms.length == 0) {
            return ONE_SYMBOL;
        }

        string memory mul = ""; // Do not put * before the first term
        unchecked {
            for (uint256 i = 0; i < terms.length; ++i) {
                int256 n = terms[i].exponent().numerator();
                if (n > 0) {
                    symbol_ = symbol_.add(mul, terms[i].symbol());
                    mul = "*";
                }
            }
        }

        if (bytes(symbol_).length == 0) {
            symbol_ = ONE_SYMBOL;
        }

        unchecked {
            for (uint256 i = 0; i < terms.length; ++i) {
                int256 n = terms[i].exponent().numerator();
                if (n < 0) {
                    symbol_ = symbol_.add("/", terms[i].reciprocal().symbol());
                }
            }
        }
    }

    /// @dev Parses a base symbol starting at buffer[start], returns base-packed uint
    function parseAddress(bytes memory buffer, uint256 start)
        internal
        pure
        returns (bool isAddress, Term term, uint256 cursor)
    {
        uint256 end = buffer.length;
        cursor = start + 42;
        if (cursor > end) {
            return (false, term, start);
        }
        if (buffer[start] != "0") {
            return (false, term, start);
        }
        if (buffer[start + 1] != "x") {
            return (false, term, start);
        }
        start += 2;
        uint160 result = 0;
        unchecked {
            for (uint256 i = start; i < cursor; ++i) {
                uint8 c = uint8(buffer[i]);
                if (c >= 48 && c <= 57) {
                    // '0'-'9'
                    result = result * 16 + (c - 48);
                } else if (c >= 65 && c <= 70) {
                    // 'A'-'F'
                    result = result * 16 + (c - 55);
                } else if (c >= 97 && c <= 102) {
                    // 'a'-'f'
                    result = result * 16 + (c - 87);
                } else {
                    return (false, term, start);
                }
            }
        }
        isAddress = true;
        term = address(result).withExponent(ONE_RATIONAL_8);
    }

    /// @dev Parses a base symbol starting at buffer[start], returns base-packed uint
    function parseBase(bytes memory buffer, uint256 start) internal pure returns (Term term, uint256 cursor) {
        uint256 end = buffer.length;
        cursor = start;

        // Advance the cursor past symbol characters.
        while (cursor < end && buffer[cursor].isSymbolChar()) {
            cursor++;
        }

        uint256 baseLength = cursor - start;

        if (baseLength > MAX_SYMBOL_SIZE) {
            revert BaseSymbolTooBig();
        }

        // SAFETY: Reading from memory buffer at validated offset (start < cursor < end)
        // and masking to exact baseLength bytes. No out-of-bounds access possible.
        assembly {
            let word := mload(add(add(buffer, 32), start))
            let shift := sub(256, mul(baseLength, 8))
            let mask := shl(shift, sub(exp(2, mul(baseLength, 8)), 1))
            term := and(word, mask)
        }
    }

    /// @dev Parse an integer starting at buffer[start].
    function parseNumber(bytes memory buffer, uint256 start) internal pure returns (uint256 n, uint256 cursor) {
        uint256 end = buffer.length;
        cursor = start;
        unchecked {
            while (cursor < end && n <= 128 && buffer[cursor] >= "0" && buffer[cursor] <= "9") {
                n = n * 10 + uint8(buffer[cursor]) - 48;
                ++cursor;
            }
        }
    }

    /// @dev Reverts if cursor is not less than end
    function mustBeLessThan(uint256 cursor, uint256 end) internal pure {
        if (cursor >= end) {
            revert UnexpectedEndOfInput();
        }
    }

    /// @dev Parses a full compound symbol into an array of terms
    function parseTerms(string memory symbol_) internal pure returns (Term[] memory terms) {
        bytes memory buffer = bytes(symbol_);
        uint256 end = buffer.length;
        uint256 cursor = 0;

        cursor.mustBeLessThan(end);

        // Count number of terms
        uint256 termCount = 1;
        unchecked {
            for (uint256 j = 1; j < end; ++j) {
                if (buffer[j] == DIVIDE_SYMBOL || buffer[j] == MULTIPLY_SYMBOL) termCount++;
            }
        }

        terms = new Term[](termCount);
        uint256 termIndex = 0;

        while (cursor < end) {
            int256 exp = 1;

            // Skip * or /
            if (cursor > 0) {
                if (buffer[cursor] == MULTIPLY_SYMBOL) {
                    cursor++;
                } else if (buffer[cursor] == DIVIDE_SYMBOL) {
                    exp = -exp;
                    cursor++;
                }
            }

            cursor.mustBeLessThan(end);

            Term term;
            bool isAddress;
            (isAddress, term, cursor) = parseAddress(buffer, cursor);
            if (!isAddress) {
                (term, cursor) = parseBase(buffer, cursor);
            }

            if (term.raw() == 0) {
                revert UnexpectedCharacter(cursor == end ? bytes1(0) : buffer[cursor]);
            }

            uint256 expDenom = 1;

            // Extract exponent if present
            if (cursor < end && buffer[cursor] == POWER_SYMBOL) {
                cursor++;
                cursor.mustBeLessThan(end);

                uint256 pow = 0;
                (pow, cursor) = parseNumber(buffer, cursor);
                exp *= pow.toInt128();

                if (cursor < end && buffer[cursor] == POWER_DIV) {
                    cursor++;
                    cursor.mustBeLessThan(end);
                    (expDenom, cursor) = parseNumber(buffer, cursor);
                }
            }

            Rational8 exp8 = exp.divRational8(expDenom);
            term = term.withExponent(exp8);
            terms[termIndex++] = term;
        }
    }

    function toInt128(uint256 x) internal pure returns (int128 y) {
        if (x <= uint128(type(int128).max)) {
            // forge-lint: disable-next-line(unsafe-typecast)
            y = int128(uint128(x));
        } else {
            revert ExponentTooBig();
        }
    }

    /// @dev Returns first n terms from array
    function take(Term[] memory long, uint256 n) internal pure returns (Term[] memory short) {
        if (long.length == n) {
            short = long;
        } else {
            short = new Term[](n);
            unchecked {
                for (uint256 i = 0; i < n; ++i) {
                    short[i] = long[i];
                }
            }
        }
    }

    /// @dev Merges two sorted term arrays
    function product(Term[] memory t1, Term[] memory t2) internal pure returns (Term[] memory t3) {
        uint256 n1 = t1.length;
        uint256 n2 = t2.length;

        if (n1 == 0) {
            return t2;
        }
        if (n2 == 0) {
            return t1;
        }

        t3 = new Term[](n1 + n2);
        uint256 i1 = 0;
        uint256 i2 = 0;
        uint256 i3 = 0;

        while (i1 < n1 && i2 < n2) {
            Term base1 = t1[i1].base();
            Term base2 = t2[i2].base();

            if (base1.raw() < base2.raw()) {
                t3[i3++] = t1[i1++];
            } else if (base2.raw() < base1.raw()) {
                t3[i3++] = t2[i2++];
            } else {
                // Same base, combine exponents
                // Sum using int16 then check for too big.
                Rational8 exp = t1[i1].exponent().add(t2[i2].exponent());
                if (exp.raw() != ZERO_RATIONAL_8.raw()) {
                    t3[i3++] = base1.withExponent(exp);
                }
                i1++;
                i2++;
            }
        }

        // Copy remaining terms
        while (i1 < n1) {
            t3[i3++] = t1[i1++];
        }
        while (i2 < n2) {
            t3[i3++] = t2[i2++];
        }

        t3 = t3.take(i3);
    }

    /// @dev Determine if the terms are in order.
    function inOrder(Term[] memory terms) internal pure returns (bool) {
        uint256 n = terms.length;
        if (n == 0) return true;

        unchecked {
            for (uint256 i = 0; i < n - 1; ++i) {
                if (terms[i].raw() > terms[i + 1].raw()) return false;
            }
        }
        return true;
    }

    /// @dev Sorts terms in ascending base order using heap sort
    function sort(Term[] memory terms) internal pure returns (Term[] memory) {
        if (terms.inOrder()) return terms;

        uint256 n = terms.length;

        // Build max heap
        for (uint256 i = n / 2; i > 0; i--) {
            heapify(terms, n, i - 1);
        }

        // Extract elements from heap one by one
        for (uint256 i = n - 1; i > 0; i--) {
            // Move current root to end
            (terms[0], terms[i]) = (terms[i], terms[0]);
            // call max heapify on the reduced heap
            heapify(terms, i, 0);
        }
        return terms;
    }

    function heapify(Term[] memory terms, uint256 n, uint256 i) private pure {
        uint256 largest = i;
        uint256 left = 2 * i + 1;
        uint256 right = 2 * i + 2;

        if (left < n && terms[left].raw() > terms[largest].raw()) {
            largest = left;
        }
        if (right < n && terms[right].raw() > terms[largest].raw()) {
            largest = right;
        }
        if (largest != i) {
            (terms[i], terms[largest]) = (terms[largest], terms[i]);
            heapify(terms, n, largest);
        }
    }

    /// @dev Sorts and merges duplicate bases
    function sortAndMerge(Term[] memory terms) internal pure returns (Term[] memory) {
        if (terms.length == 0) return terms;

        terms = terms.sort();

        // Quick check if merge is needed or if "1" terms need filtering
        bool needsProcessing = false;
        unchecked {
            for (uint256 i = 0; i < terms.length; ++i) {
                if (terms[i].base().raw() == ONE_TERM) {
                    needsProcessing = true;
                    break;
                }
                if (i > 0 && terms[i].base().raw() == terms[i - 1].base().raw()) {
                    needsProcessing = true;
                    break;
                }
            }
        }
        if (!needsProcessing) return terms;

        uint256 termCount = terms.length;
        uint256 j = 0;
        Term term = terms[0].base();
        Rational exp = terms[0].exponent().toRational();
        unchecked {
            for (uint256 i = 1; i < termCount; ++i) {
                if (terms[i].base().raw() == term.raw()) {
                    exp = exp.add(terms[i].exponent().toRational());
                } else {
                    if (exp.raw() != ZERO_RATIONAL_8.raw() && term.raw() != ONE_TERM) {
                        terms[j] = term.withExponent(exp.toRational8());
                        ++j;
                    }
                    term = terms[i].base();
                    exp = terms[i].exponent().toRational();
                }
            }
            if (exp.raw() != ZERO_RATIONAL_8.raw() && term.raw() != ONE_TERM) {
                terms[j] = term.withExponent(exp.toRational8());
                ++j;
            }
        }

        terms = terms.take(j);
        return terms;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.20;

import {IERC20} from "ierc20/IERC20.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC-20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    /**
     * @dev An operation with an ERC-20 token failed.
     */
    error SafeERC20FailedOperation(address token);

    /**
     * @dev Indicates a failed `decreaseAllowance` request.
     */
    error SafeERC20FailedDecreaseAllowance(address spender, uint256 currentAllowance, uint256 requestedDecrease);

    /**
     * @dev Transfer `value` amount of `token` from the calling contract to `to`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     */
    function safeTransfer(IERC20 token, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeCall(token.transfer, (to, value)));
    }

    /**
     * @dev Transfer `value` amount of `token` from `from` to `to`, spending the approval given by `from` to the
     * calling contract. If `token` returns no value, non-reverting calls are assumed to be successful.
     */
    function safeTransferFrom(IERC20 token, address from, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeCall(token.transferFrom, (from, to, value)));
    }

    /**
     * @dev Variant of {safeTransfer} that returns a bool instead of reverting if the operation is not successful.
     */
    function trySafeTransfer(IERC20 token, address to, uint256 value) internal returns (bool) {
        return _callOptionalReturnBool(token, abi.encodeCall(token.transfer, (to, value)));
    }

    /**
     * @dev Variant of {safeTransferFrom} that returns a bool instead of reverting if the operation is not successful.
     */
    function trySafeTransferFrom(IERC20 token, address from, address to, uint256 value) internal returns (bool) {
        return _callOptionalReturnBool(token, abi.encodeCall(token.transferFrom, (from, to, value)));
    }

    /**
     * @dev Increase the calling contract's allowance toward `spender` by `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     *
     * IMPORTANT: If the token implements ERC-7674 (ERC-20 with temporary allowance), and if the "client"
     * smart contract uses ERC-7674 to set temporary allowances, then the "client" smart contract should avoid using
     * this function. Performing a {safeIncreaseAllowance} or {safeDecreaseAllowance} operation on a token contract
     * that has a non-zero temporary allowance (for that particular owner-spender) will result in unexpected behavior.
     */
    function safeIncreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 oldAllowance = token.allowance(address(this), spender);
        forceApprove(token, spender, oldAllowance + value);
    }

    /**
     * @dev Decrease the calling contract's allowance toward `spender` by `requestedDecrease`. If `token` returns no
     * value, non-reverting calls are assumed to be successful.
     *
     * IMPORTANT: If the token implements ERC-7674 (ERC-20 with temporary allowance), and if the "client"
     * smart contract uses ERC-7674 to set temporary allowances, then the "client" smart contract should avoid using
     * this function. Performing a {safeIncreaseAllowance} or {safeDecreaseAllowance} operation on a token contract
     * that has a non-zero temporary allowance (for that particular owner-spender) will result in unexpected behavior.
     */
    function safeDecreaseAllowance(IERC20 token, address spender, uint256 requestedDecrease) internal {
        unchecked {
            uint256 currentAllowance = token.allowance(address(this), spender);
            if (currentAllowance < requestedDecrease) {
                revert SafeERC20FailedDecreaseAllowance(spender, currentAllowance, requestedDecrease);
            }
            forceApprove(token, spender, currentAllowance - requestedDecrease);
        }
    }

    /**
     * @dev Set the calling contract's allowance toward `spender` to `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful. Meant to be used with tokens that require the approval
     * to be set to zero before setting it to a non-zero value, such as USDT.
     *
     * NOTE: If the token implements ERC-7674, this function will not modify any temporary allowance. This function
     * only sets the "standard" allowance. Any temporary allowance will remain active, in addition to the value being
     * set here.
     */
    function forceApprove(IERC20 token, address spender, uint256 value) internal {
        bytes memory approvalCall = abi.encodeCall(token.approve, (spender, value));

        if (!_callOptionalReturnBool(token, approvalCall)) {
            _callOptionalReturn(token, abi.encodeCall(token.approve, (spender, 0)));
            _callOptionalReturn(token, approvalCall);
        }
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     *
     * This is a variant of {_callOptionalReturnBool} that reverts if call fails to meet the requirements.
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        uint256 returnSize;
        uint256 returnValue;
        assembly ("memory-safe") {
            let success := call(gas(), token, 0, add(data, 0x20), mload(data), 0, 0x20)
            // bubble errors
            if iszero(success) {
                let ptr := mload(0x40)
                returndatacopy(ptr, 0, returndatasize())
                revert(ptr, returndatasize())
            }
            returnSize := returndatasize()
            returnValue := mload(0)
        }

        if (returnSize == 0 ? address(token).code.length == 0 : returnValue != 1) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     *
     * This is a variant of {_callOptionalReturn} that silently catches all reverts and returns a bool instead.
     */
    function _callOptionalReturnBool(IERC20 token, bytes memory data) private returns (bool) {
        bool success;
        uint256 returnSize;
        uint256 returnValue;
        assembly ("memory-safe") {
            success := call(gas(), token, 0, add(data, 0x20), mload(data), 0, 0x20)
            returnSize := returndatasize()
            returnValue := mload(0)
        }
        return success && (returnSize == 0 ? address(token).code.length > 0 : returnValue == 1);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/math/Math.sol)

pragma solidity ^0.8.20;

import {Panic} from "panic/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 Return the 512-bit addition of two uint256.
     *
     * The result is stored in two 256 variables such that sum = high * 2²⁵⁶ + low.
     */
    function add512(uint256 a, uint256 b) internal pure returns (uint256 high, uint256 low) {
        assembly ("memory-safe") {
            low := add(a, b)
            high := lt(low, a)
        }
    }

    /**
     * @dev Return the 512-bit multiplication of two uint256.
     *
     * The result is stored in two 256 variables such that product = high * 2²⁵⁶ + low.
     */
    function mul512(uint256 a, uint256 b) internal pure returns (uint256 high, uint256 low) {
        // 512-bit multiply [high low] = x * y. Compute the product mod 2²⁵⁶ and mod 2²⁵⁶ - 1, then use
        // the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
        // variables such that product = high * 2²⁵⁶ + low.
        assembly ("memory-safe") {
            let mm := mulmod(a, b, not(0))
            low := mul(a, b)
            high := sub(sub(mm, low), lt(mm, low))
        }
    }

    /**
     * @dev Returns the addition of two unsigned integers, with a success flag (no overflow).
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a + b;
            success = c >= a;
            result = c * SafeCast.toUint(success);
        }
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, with a success flag (no overflow).
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a - b;
            success = c <= a;
            result = c * SafeCast.toUint(success);
        }
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with a success flag (no overflow).
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a * b;
            assembly ("memory-safe") {
                // Only true when the multiplication doesn't overflow
                // (c / a == b) || (a == 0)
                success := or(eq(div(c, a), b), iszero(a))
            }
            // equivalent to: success ? c : 0
            result = c * SafeCast.toUint(success);
        }
    }

    /**
     * @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 {
            success = b > 0;
            assembly ("memory-safe") {
                // The `DIV` opcode returns zero when the denominator is 0.
                result := div(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 {
            success = b > 0;
            assembly ("memory-safe") {
                // The `MOD` opcode returns zero when the denominator is 0.
                result := mod(a, b)
            }
        }
    }

    /**
     * @dev Unsigned saturating addition, bounds to `2²⁵⁶ - 1` instead of overflowing.
     */
    function saturatingAdd(uint256 a, uint256 b) internal pure returns (uint256) {
        (bool success, uint256 result) = tryAdd(a, b);
        return ternary(success, result, type(uint256).max);
    }

    /**
     * @dev Unsigned saturating subtraction, bounds to zero instead of overflowing.
     */
    function saturatingSub(uint256 a, uint256 b) internal pure returns (uint256) {
        (, uint256 result) = trySub(a, b);
        return result;
    }

    /**
     * @dev Unsigned saturating multiplication, bounds to `2²⁵⁶ - 1` instead of overflowing.
     */
    function saturatingMul(uint256 a, uint256 b) internal pure returns (uint256) {
        (bool success, uint256 result) = tryMul(a, b);
        return ternary(success, result, type(uint256).max);
    }

    /**
     * @dev Branchless ternary evaluation for `a ? b : c`. Gas costs are constant.
     *
     * IMPORTANT: This function may reduce bytecode size and consume less gas when used standalone.
     * However, the compiler may optimize Solidity ternary operations (i.e. `a ? b : c`) to only compute
     * one branch when needed, making this function more expensive.
     */
    function ternary(bool condition, uint256 a, uint256 b) internal pure returns (uint256) {
        unchecked {
            // branchless ternary works because:
            // b ^ (a ^ b) == a
            // b ^ 0 == b
            return b ^ ((a ^ b) * SafeCast.toUint(condition));
        }
    }

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

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return ternary(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 SafeCast.toUint(a > 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 {
            (uint256 high, uint256 low) = mul512(x, y);

            // Handle non-overflow cases, 256 by 256 division.
            if (high == 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 low / denominator;
            }

            // Make sure the result is less than 2²⁵⁶. Also prevents denominator == 0.
            if (denominator <= high) {
                Panic.panic(ternary(denominator == 0, Panic.DIVISION_BY_ZERO, Panic.UNDER_OVERFLOW));
            }

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

            // Make division exact by subtracting the remainder from [high low].
            uint256 remainder;
            assembly ("memory-safe") {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                high := sub(high, gt(remainder, low))
                low := sub(low, 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 ("memory-safe") {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [high low] by twos.
                low := div(low, 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 high into low.
            low |= high * 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 high
            // is no longer required.
            result = low * 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 Calculates floor(x * y >> n) with full precision. Throws if result overflows a uint256.
     */
    function mulShr(uint256 x, uint256 y, uint8 n) internal pure returns (uint256 result) {
        unchecked {
            (uint256 high, uint256 low) = mul512(x, y);
            if (high >= 1 << n) {
                Panic.panic(Panic.UNDER_OVERFLOW);
            }
            return (high << (256 - n)) | (low >> n);
        }
    }

    /**
     * @dev Calculates x * y >> n with full precision, following the selected rounding direction.
     */
    function mulShr(uint256 x, uint256 y, uint8 n, Rounding rounding) internal pure returns (uint256) {
        return mulShr(x, y, n) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, 1 << n) > 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, except 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 Fermat's little theorem and get the
     * inverse using `Math.modExp(a, n - 2, n)`. See {invModPrime}.
     */
    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 ternary(x < 0, n - uint256(-x), uint256(x)); // Wrap the result if it's negative.
        }
    }

    /**
     * @dev Variant of {invMod}. More efficient, but only works if `p` is known to be a prime greater than `2`.
     *
     * From https://en.wikipedia.org/wiki/Fermat%27s_little_theorem[Fermat's little theorem], we know that if p is
     * prime, then `a**(p-1) ≡ 1 mod p`. As a consequence, we have `a * a**(p-2) ≡ 1 mod p`, which means that
     * `a**(p-2)` is the modular multiplicative inverse of a in Fp.
     *
     * NOTE: this function does NOT check that `p` is a prime greater than `2`.
     */
    function invModPrime(uint256 a, uint256 p) internal view returns (uint256) {
        unchecked {
            return Math.modExp(a, p - 2, p);
        }
    }

    /**
     * @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 as 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);
        assembly ("memory-safe") {
            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);

        assembly ("memory-safe") {
            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 x) internal pure returns (uint256 r) {
        // If value has upper 128 bits set, log2 result is at least 128
        r = SafeCast.toUint(x > 0xffffffffffffffffffffffffffffffff) << 7;
        // If upper 64 bits of 128-bit half set, add 64 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffffffffffff) << 6;
        // If upper 32 bits of 64-bit half set, add 32 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffff) << 5;
        // If upper 16 bits of 32-bit half set, add 16 to result
        r |= SafeCast.toUint((x >> r) > 0xffff) << 4;
        // If upper 8 bits of 16-bit half set, add 8 to result
        r |= SafeCast.toUint((x >> r) > 0xff) << 3;
        // If upper 4 bits of 8-bit half set, add 4 to result
        r |= SafeCast.toUint((x >> r) > 0xf) << 2;

        // Shifts value right by the current result and use it as an index into this lookup table:
        //
        // | x (4 bits) |  index  | table[index] = MSB position |
        // |------------|---------|-----------------------------|
        // |    0000    |    0    |        table[0] = 0         |
        // |    0001    |    1    |        table[1] = 0         |
        // |    0010    |    2    |        table[2] = 1         |
        // |    0011    |    3    |        table[3] = 1         |
        // |    0100    |    4    |        table[4] = 2         |
        // |    0101    |    5    |        table[5] = 2         |
        // |    0110    |    6    |        table[6] = 2         |
        // |    0111    |    7    |        table[7] = 2         |
        // |    1000    |    8    |        table[8] = 3         |
        // |    1001    |    9    |        table[9] = 3         |
        // |    1010    |   10    |        table[10] = 3        |
        // |    1011    |   11    |        table[11] = 3        |
        // |    1100    |   12    |        table[12] = 3        |
        // |    1101    |   13    |        table[13] = 3        |
        // |    1110    |   14    |        table[14] = 3        |
        // |    1111    |   15    |        table[15] = 3        |
        //
        // The lookup table is represented as a 32-byte value with the MSB positions for 0-15 in the last 16 bytes.
        assembly ("memory-safe") {
            r := or(r, byte(shr(r, x), 0x0000010102020202030303030303030300000000000000000000000000000000))
        }
    }

    /**
     * @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 x) internal pure returns (uint256 r) {
        // If value has upper 128 bits set, log2 result is at least 128
        r = SafeCast.toUint(x > 0xffffffffffffffffffffffffffffffff) << 7;
        // If upper 64 bits of 128-bit half set, add 64 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffffffffffff) << 6;
        // If upper 32 bits of 64-bit half set, add 32 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffff) << 5;
        // If upper 16 bits of 32-bit half set, add 16 to result
        r |= SafeCast.toUint((x >> r) > 0xffff) << 4;
        // Add 1 if upper 8 bits of 16-bit half set, and divide accumulated result by 8
        return (r >> 3) | SafeCast.toUint((x >> r) > 0xff);
    }

    /**
     * @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 v5.1.0) (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.20;

import {IERC20} from "./IERC20.sol";

/**
 * @dev Interface for the optional metadata functions from the ERC-20 standard.
 */
interface IERC20Metadata is IERC20 {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

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

    /**
     * @dev Returns the decimals places of the token.
     */
    function decimals() external view returns (uint8);
}

// SPDX-License-Identifier: LicenseRef-Uniteum

pragma solidity ^0.8.30;

import {IERC20} from "ierc20/IERC20.sol";

/**
 * @title IMigratable
 * @notice Interface for tokens that support migration from an upstream version.
 * @dev Tokens implementing this interface can accept upstream tokens and issue
 *      an equivalent amount of this token in exchange.
 * @author Paul Reinholdtsen (reinholdtsen.eth)
 */
interface IMigratable {
    /**
     * @notice Upstream token this contract accepts for migration.
     * @dev Circulating supply is conserved across all migrations.
     * @return upstream token this contract accepts for migration.
     */
    function UPSTREAM() external view returns (IERC20 upstream);

    /**
     * @notice Migrate upstream tokens to this token.
     * @dev The caller must approve this contract to transfer the upstream tokens.
     *      The upstream tokens are transferred from the caller to this contract,
     *      and an equivalent amount of this token is minted/transferred to the caller.
     * @param amount The number of tokens to migrate.
     */
    function migrate(uint256 amount) external;

    /**
     * @notice Reverse migrate this token to its upstream token.
     * @dev The caller's tokens are transferred to this contract,
     *      and an equivalent amount of upstream tokens is transferred to the caller.
     * @param amount The number of tokens to reverse migrate.
     */
    function unmigrate(uint256 amount) external;

    /**
     * @notice Emitted when tokens are migrated from upstream to downstream.
     * @param upstream The upstream token address (source).
     * @param downstream The downstream token address (destination).
     * @param amount The number of tokens migrated.
     */
    event Migrated(address indexed upstream, address indexed downstream, uint256 amount);

    /**
     * @notice Emitted when tokens are reverse migrated from downstream to upstream.
     * @param upstream The upstream token address (destination).
     * @param downstream The downstream token address (source).
     * @param amount The number of tokens reverse migrated.
     */
    event Unmigrated(address indexed upstream, address indexed downstream, uint256 amount);
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.30;

import {Clones} from "clones/Clones.sol";

/**
 * @title Prototype
 * @notice Base contract for self-cloning minimal proxy implementations using EIP-1167.
 * @dev
 * The contract deployed as the Prototype acts as:
 *   - the reference implementation with canonical logic, and
 *   - a factory that deterministically deploys minimal proxy clones of itself.
 *
 * Each clone:
 *   - delegates all logic to the Prototype via DELEGATECALL,
 *   - maintains its own isolated storage,
 *   - preserves the original msg.sender through the proxy,
 *   - inherits the same immutable PROTOTYPE address.
 *
 * **Deterministic Deployment:**
 * All clones are deployed with CREATE2 using salts derived from initialization
 * data via keccak256(abi.encode(initData)), ensuring predictable, repeatable
 * addresses. Calling __clone with identical initData will return the same
 * address without redeploying.
 *
 * **Usage Pattern:**
 * 1. Deploy Prototype implementation contract
 * 2. Call __clone(initData) to create instances
 * 3. Each clone is automatically initialized via __initialize(initData)
 * 4. Clones can call __clone to create more clones (forwarded to Prototype)
 *
 * @author Paul Reinholdtsen (reinholdtsen.eth)
 */
abstract contract Prototype {
    // ============ State Variables ============

    /**
     * @notice Address of the original Prototype implementation.
     * @dev Clones inherit this immutable value through bytecode; on the Prototype
     *      itself it equals address(this). This creates a shared reference point
     *      for all clones to delegate calls to and query state from.
     *
     *      Immutables are embedded in bytecode during deployment, so each clone's
     *      bytecode contains the Prototype address even though storage is separate.
     */
    address internal immutable PROTOTYPE = address(this);

    /**
     * @dev Registry mapping clone addresses to their CREATE2 salts.
     *      Only populated on the Prototype contract, not on clones.
     *
     *      Maps: clone address → CREATE2 salt
     *
     *      A non-zero value indicates the address was deployed as a valid clone.
     *      Used by isClone() for verification and to prevent duplicate deployments.
     */
    mapping(address => bytes32) private salts;

    // ============ View Functions ============

    /**
     * @notice Returns true if `check` is a clone of this Prototype.
     * @dev When called on the Prototype: checks the salts registry directly.
     *      When called on a clone: delegates to the Prototype for verification.
     *
     *      This pattern ensures a single source of truth (the Prototype's registry)
     *      while allowing verification from any context.
     *
     * @param check Address to examine.
     * @return yes True if the address was deployed as a clone via __clone().
     */
    function isClone(address check) public view returns (bool yes) {
        yes = address(this) == PROTOTYPE ? salts[check] != 0x0 : Prototype(PROTOTYPE).isClone(check);
    }

    /**
     * @notice Returns the immutable Prototype address.
     * @dev Identical for both the implementation and all clones because it reads
     *      from the immutable PROTOTYPE field embedded in bytecode.
     *
     *      Useful for:
     *      - Accessing the canonical registry (salts mapping)
     *      - Delegating operations back to the implementation
     *      - Verifying clone authenticity
     *
     * @return The address of the Prototype implementation contract.
     */
    function prototype() public view returns (address) {
        return PROTOTYPE;
    }

    /**
     * @notice Predicts the clone address for a given salt.
     * @dev Uses OpenZeppelin's Clones library to compute the deterministic address
     *      based on the Prototype address and salt. This is a view function that
     *      does not deploy anything.
     *
     *      The address is computed as: CREATE2(PROTOTYPE, salt, PROTOTYPE, initcode)
     *      where the deployer is the Prototype itself.
     *
     * @param newSalt The CREATE2 salt that will be used.
     * @return predicted The deterministic clone address that would be deployed.
     */
    function __predict(bytes32 newSalt) public view returns (address predicted) {
        predicted = Clones.predictDeterministicAddress(PROTOTYPE, newSalt, PROTOTYPE);
    }

    /**
     * @notice Predicts the clone address for initialization data.
     * @dev Salt is deterministically derived from initData as:
     *      keccak256(abi.encode(initData))
     *
     *      Note: abi.encode is used (not abi.encodePacked) to ensure proper
     *      ABI encoding with type information, preventing collisions.
     *
     *      This overload is the primary entry point for predicting addresses
     *      when you have initialization parameters but not a precomputed salt.
     *
     * @param initData Initialization calldata for the clone.
     * @return predicted Deterministic clone address.
     * @return newSalt The CREATE2 salt derived from initData.
     */
    function __predict(bytes memory initData) public view returns (address predicted, bytes32 newSalt) {
        newSalt = keccak256(abi.encode(initData));
        predicted = __predict(newSalt);
    }

    // ============ Factory Functions ============

    /**
     * @notice Deploys a deterministic minimal proxy clone.
     * @dev
     * **When called on the Prototype:**
     *   1. Computes salt from keccak256(abi.encode(initData))
     *   2. Predicts clone address using CREATE2 formula
     *   3. If no code at address: deploys clone, records salt, calls __initialize
     *   4. If code exists: returns existing address (idempotent)
     *   5. Calls __initialize(initData) on newly deployed clones only
     *
     * **When called on a clone:**
     *   - Forwards the request back to PROTOTYPE.__clone(initData)
     *   - This enables clones to create other clones transparently
     *
     * **Idempotency:**
     * Calling __clone with the same initData multiple times returns the same
     * address. Only the first call performs deployment and initialization.
     *
     * **Security:**
     * Only the Prototype can call __initialize due to onlyPrototype modifier.
     * Clones cannot initialize themselves or other clones directly.
     *
     * @param initData Initialization data passed to the clone's __initialize.
     * @return instance The deployed (or existing) clone address.
     * @return newSalt The CREATE2 salt used for deterministic deployment.
     */
    function __clone(bytes memory initData) public returns (address instance, bytes32 newSalt) {
        if (address(this) == PROTOTYPE) {
            (instance, newSalt) = __predict(initData);

            if (instance.code.length == 0) {
                instance = Clones.cloneDeterministic(PROTOTYPE, newSalt, 0);
                salts[instance] = newSalt;
                Prototype(instance).__initialize(initData);
            }
        } else {
            (instance, newSalt) = Prototype(PROTOTYPE).__clone(initData);
        }
    }

    /**
     * @notice Initialize a newly deployed clone.
     * @dev **Must be implemented by derived classes.**
     *
     *      **Security considerations:**
     *      - MUST use the onlyPrototype modifier to prevent unauthorized calls
     *      - SHOULD validate initData to prevent malicious initialization
     *      - SHOULD consider using a reentrancy guard if calling external contracts
     *      - MUST NOT assume msg.sender is the end user (it's always PROTOTYPE)
     *
     *      **Initialization pattern:**
     *      Decode initData, set storage variables, emit events. The actual user
     *      who called __clone is typically encoded in initData, not msg.sender.
     *
     *      **Called automatically** by __clone during clone deployment.
     *
     * @param initData ABI-encoded initialization parameters.
     */
    function __initialize(bytes memory initData) public virtual;

    // ============ Internal Functions ============

    /**
     * @notice Restricts calls to the Prototype implementation contract only.
     * @dev Applied to __initialize to ensure only the Prototype can initialize
     *      new clones during deployment. Prevents external actors or clones
     *      themselves from calling initialization logic.
     *
     *      Uses internal _onlyPrototype() for the actual check.
     */
    modifier onlyPrototype() {
        _onlyPrototype();
        _;
    }

    /**
     * @dev Reverts if msg.sender is not the Prototype implementation.
     *
     *      This check ensures that only the factory (Prototype) can call
     *      protected functions, preventing unauthorized initialization or
     *      configuration of clones.
     *
     *      Reverts with Unauthorized() custom error for gas efficiency.
     */
    function _onlyPrototype() internal view {
        if (msg.sender != PROTOTYPE) {
            revert Unauthorized();
        }
    }

    // ============ Errors ============

    /**
     * @notice Error raised when a caller lacks permission to execute a protected function.
     * @dev Thrown by the onlyPrototype modifier when msg.sender != PROTOTYPE.
     *      Custom errors are more gas-efficient than require strings.
     */
    error Unauthorized();
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.30;

import {Context} from "./Context.sol";
import {IERC20Metadata, IERC20} from "ierc20/IERC20Metadata.sol";
import {IERC20Errors} from "ierc20/IERC20Errors.sol";

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * The default value of {decimals} is 18. To change this, you should override
 * this function so it returns a different value.
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC-20
 * applications.
 */
abstract contract ERC20 is Context, IERC20, IERC20Metadata, IERC20Errors {
    mapping(address account => uint256) private _balances;

    mapping(address account => mapping(address spender => uint256)) private _allowances;

    uint256 private _totalSupply;

    string internal _name;
    string internal _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * Both values are immutable: they can only be set once during construction.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view virtual returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the default value returned by this function, unless
     * it's overridden.
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual returns (uint8) {
        return 18;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() public view virtual returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual returns (uint256) {
        return _balances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `value`.
     */
    function transfer(address to, uint256 value) public virtual returns (bool) {
        address owner = _msgSender();
        _transfer(owner, to, value);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * NOTE: If `value` is the maximum `uint256`, the allowance is not updated on
     * `transferFrom`. This is semantically equivalent to an infinite approval.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 value) public virtual returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, value);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Skips emitting an {Approval} event indicating an allowance update. This is not
     * required by the ERC. See {xref-ERC20-_approve-address-address-uint256-bool-}[_approve].
     *
     * NOTE: Does not update the allowance if the current allowance
     * is the maximum `uint256`.
     *
     * Requirements:
     *
     * - `from` and `to` cannot be the zero address.
     * - `from` must have a balance of at least `value`.
     * - the caller must have allowance for ``from``'s tokens of at least
     * `value`.
     */
    function transferFrom(address from, address to, uint256 value) public virtual returns (bool) {
        address spender = _msgSender();
        _spendAllowance(from, spender, value);
        _transfer(from, to, value);
        return true;
    }

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to`.
     *
     * This internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead.
     */
    function _transfer(address from, address to, uint256 value) internal {
        if (from == address(0)) {
            revert ERC20InvalidSender(address(0));
        }
        if (to == address(0)) {
            revert ERC20InvalidReceiver(address(0));
        }
        _update(from, to, value);
    }

    /**
     * @dev Transfers a `value` amount of tokens from `from` to `to`, or alternatively mints (or burns) if `from`
     * (or `to`) is the zero address. All customizations to transfers, mints, and burns should be done by overriding
     * this function.
     *
     * Emits a {Transfer} event.
     */
    function _update(address from, address to, uint256 value) internal virtual {
        if (from == address(0)) {
            // Overflow check required: The rest of the code assumes that totalSupply never overflows
            _totalSupply += value;
        } else {
            uint256 fromBalance = _balances[from];
            if (fromBalance < value) {
                revert ERC20InsufficientBalance(from, fromBalance, value);
            }
            unchecked {
                // Overflow not possible: value <= fromBalance <= totalSupply.
                _balances[from] = fromBalance - value;
            }
        }

        if (to == address(0)) {
            unchecked {
                // Overflow not possible: value <= totalSupply or value <= fromBalance <= totalSupply.
                _totalSupply -= value;
            }
        } else {
            unchecked {
                // Overflow not possible: balance + value is at most totalSupply, which we know fits into a uint256.
                _balances[to] += value;
            }
        }

        emit Transfer(from, to, value);
    }

    /**
     * @dev Creates a `value` amount of tokens and assigns them to `account`, by transferring it from address(0).
     * Relies on the `_update` mechanism
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead.
     */
    function _mint(address account, uint256 value) internal {
        if (account == address(0)) {
            revert ERC20InvalidReceiver(address(0));
        }
        _update(address(0), account, value);
    }

    /**
     * @dev Destroys a `value` amount of tokens from `account`, lowering the total supply.
     * Relies on the `_update` mechanism.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead
     */
    function _burn(address account, uint256 value) internal {
        if (account == address(0)) {
            revert ERC20InvalidSender(address(0));
        }
        _update(account, address(0), value);
    }

    /**
     * @dev Sets `value` as the allowance of `spender` over the `owner`'s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     *
     * Overrides to this logic should be done to the variant with an additional `bool emitEvent` argument.
     */
    function _approve(address owner, address spender, uint256 value) internal {
        _approve(owner, spender, value, true);
    }

    /**
     * @dev Variant of {_approve} with an optional flag to enable or disable the {Approval} event.
     *
     * By default (when calling {_approve}) the flag is set to true. On the other hand, approval changes made by
     * `_spendAllowance` during the `transferFrom` operation set the flag to false. This saves gas by not emitting any
     * `Approval` event during `transferFrom` operations.
     *
     * Anyone who wishes to continue emitting `Approval` events on the`transferFrom` operation can force the flag to
     * true using the following override:
     *
     * ```solidity
     * function _approve(address owner, address spender, uint256 value, bool) internal virtual override {
     *     super._approve(owner, spender, value, true);
     * }
     * ```
     *
     * Requirements are the same as {_approve}.
     */
    function _approve(address owner, address spender, uint256 value, bool emitEvent) internal virtual {
        if (owner == address(0)) {
            revert ERC20InvalidApprover(address(0));
        }
        if (spender == address(0)) {
            revert ERC20InvalidSpender(address(0));
        }
        _allowances[owner][spender] = value;
        if (emitEvent) {
            emit Approval(owner, spender, value);
        }
    }

    /**
     * @dev Updates `owner`'s allowance for `spender` based on spent `value`.
     *
     * Does not update the allowance value in case of infinite allowance.
     * Revert if not enough allowance is available.
     *
     * Does not emit an {Approval} event.
     */
    function _spendAllowance(address owner, address spender, uint256 value) internal virtual {
        uint256 currentAllowance = allowance(owner, spender);
        if (currentAllowance < type(uint256).max) {
            if (currentAllowance < value) {
                revert ERC20InsufficientAllowance(spender, currentAllowance, value);
            }
            unchecked {
                _approve(owner, spender, currentAllowance - value, false);
            }
        }
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.30;

/**
 * @title Term — Unit Term Type
 * @dev Type for unit term operations.
 * Base unit terms are packed into uint:
 * The last two bytes (30, 31) are a rational exponent.
 * Symbolic terms have the first 30 bytes as the base symbol.
 * Address terms have the first byte = 1, and the next 20 bytes are an address.
 * +0......0|1.........................20|21................29|30...........31+
 * | Symbol                                                   |    Exponent   |
 * |----------------------------------------------------------| ± num / den   |
 * | Type=1 | Address [1..20]            | Reserved           |  int8 | uint8 |
 * +255................................96|95................16|15....8|7.....0+
 * Example 1: meter^2:3
 * |6d 6574657200000000000000000000000000000000 000000000000000000 02 03|
 * |  |                                        |                  |  |  |
 * |01 c02aaa39b223fe8d0a0e5c4f27ead9083c756cc2 000000000000000000 ff 01|
 * Example 2: 1/[address of WETH]
 */
type Term is uint256;

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.30;

import {Rational, Rational8} from "./Rational.sol";
import {Strings} from "strings/Strings.sol";

/**
 * @title Rationals
 * @notice Library for rational number arithmetic with 128-bit and 8-bit representations
 * @dev Rational: int256 with high 128 bits = numerator, low 128 bits = denominator
 *      Rational8: int16 with high 8 bits = numerator, low 8 bits = denominator
 *      All rationals are stored in reduced form (lowest terms)
 */
library Rationals {
    int128 constant NUMERATOR_MAX = type(int128).max;
    uint128 constant DENOMINATOR_MAX = type(uint128).max;
    int8 constant NUMERATOR8_MAX = type(int8).max;
    uint8 constant DENOMINATOR8_MAX = type(uint8).max;

    using Rationals for *;
    using Strings for *;

    /**
     * @dev Reverts when a denominator is zero
     */
    error ZeroDenominator();

    /**
     * @dev Reverts when a value cannot safely downcast to a smaller type
     */
    error ExponentTooBig();
    error DenominatorTooBig(uint256 d);
    error NumeratorTooBig(int256 n);

    /**
     * @dev Reverts when exact Rat16 encoding is impossible
     */
    error Rat16EncodingImpossible();

    /**
     * @notice Unwraps a Rational to its underlying int256 representation
     */
    function raw(Rational n) internal pure returns (int256) {
        return Rational.unwrap(n);
    }

    /**
     * @notice Unwraps a Rational8 to its underlying int16 representation
     */
    function raw(Rational8 n) internal pure returns (int256) {
        return Rational8.unwrap(n);
    }

    /**
     * @notice Decodes a Ratio128 value into numerator and denominator
     * @param a A Ratio128-encoded int value
     * @return n Signed 128-bit numerator
     * @return d Unsigned 128-bit denominator
     */
    function parts(Rational a) internal pure returns (int256 n, uint256 d) {
        int256 r = a.raw();
        n = r >> 128;
        // forge-lint: disable-next-line(unsafe-typecast)
        d = uint256(r) & DENOMINATOR_MAX;
    }

    /**
     * @notice Encodes a numerator and denominator as a Rational, reduced to lowest terms
     * @param n Signed 128-bit numerator
     * @param d Unsigned 128-bit denominator (must be nonzero)
     * @return a Encoded Rational value in reduced form
     */
    function divRational(int256 n, uint256 d) internal pure returns (Rational a) {
        if (d == 0) {
            revert ZeroDenominator();
        }

        uint256 g = gcd(_abs(n), d);
        // forge-lint: disable-next-line(unsafe-typecast)
        n /= int128(uint128(g));
        // forge-lint: disable-next-line(unsafe-typecast)
        d /= uint128(g);

        if (n < -NUMERATOR_MAX || NUMERATOR_MAX < n) {
            revert NumeratorTooBig(n);
        }

        if (d > DENOMINATOR_MAX) {
            revert DenominatorTooBig(d);
        }

        // forge-lint: disable-next-line(unsafe-typecast)
        a = Rational.wrap((n << 128) | int256(uint256(d)));
    }

    /**
     * @notice Negates a Ratio128-encoded value
     * @param a A Ratio128-encoded int value
     * @return Negated Ratio128-encoded value
     */
    function neg(Rational a) internal pure returns (Rational) {
        (int256 n, uint256 d) = a.parts();
        return (-n).divRational(d);
    }

    /**
     * @notice Adds two Rational values and returns normalized result
     * @dev Computes a/b + c/d by finding common denominator using LCM
     */
    function add(Rational a, Rational b) internal pure returns (Rational) {
        (int256 an, uint256 ad) = a.parts();
        (int256 bn, uint256 bd) = b.parts();
        uint256 gd = gcd(ad, bd);
        // forge-lint: disable-next-line(divide-before-multiply)
        uint256 d = (ad / gd) * bd;
        // forge-lint: disable-next-line(unsafe-typecast)
        int256 n = an * int256(d / ad) + bn * int256(d / bd);

        return n.divRational(d);
    }

    /**
     * @notice Subtracts two Rational values and returns normalized result
     * @dev Computes a - b as a + (-b)
     */
    function sub(Rational a, Rational b) internal pure returns (Rational) {
        return a.add(b.neg());
    }

    /**
     * @notice Multiplies two Rational values and returns normalized result
     * @dev Computes (a/b) * (c/d) = (a*c)/(b*d), then reduces using GCD
     */
    function mul(Rational a, Rational b) internal pure returns (Rational) {
        (int256 an, uint256 ad) = a.parts();
        (int256 bn, uint256 bd) = b.parts();
        int256 n = int256(an) * int256(bn);
        uint256 d = uint256(ad) * uint256(bd);
        uint256 g = gcd(uint256(_abs(n)), d);
        return (n / g.toInt256()).divRational(d / g);
    }

    /**
     * @notice Divides Rational a by Rational b and returns normalized result
     * @dev Computes (a/b) / (c/d) = (a*d)/(b*c), handling sign normalization
     */
    function div(Rational a, Rational b) internal pure returns (Rational r) {
        (int256 an, uint256 ad) = a.parts();
        (int256 bn, uint256 bd) = b.parts();
        if (bn == 0) {
            revert ZeroDenominator();
        }
        int256 n = an * bd.toInt256();
        int256 d = ad.toInt256() * bn;
        if (d < 0) {
            n = -n;
            d = -d;
        }
        // forge-lint: disable-next-line(unsafe-typecast)
        r = n.divRational(uint256(d));
    }

    /**
     * @notice Extracts the numerator from a Rational8 value
     */
    function numerator(Rational8 a8) internal pure returns (int256 n) {
        n = int8(a8.raw() >> 8);
    }

    /**
     * @notice Extracts the denominator from a Rational8 value
     */
    function denominator(Rational8 a8) internal pure returns (uint256 d) {
        d = uint8(uint256(a8.raw()));
    }

    /**
     * @notice Decodes a Rational8 value into numerator and denominator
     * @param a A Rational8-encoded int value
     * @return n Signed 8-bit numerator
     * @return d Unsigned 8-bit denominator
     */
    function parts(Rational8 a) internal pure returns (int8 n, uint8 d) {
        int256 r = a.raw();
        // forge-lint: disable-next-line(unsafe-typecast)
        n = int8(r >> 8);
        // forge-lint: disable-next-line(unsafe-typecast)
        d = uint8(uint256(r) & DENOMINATOR8_MAX);
    }

    /**
     * @notice Encodes a numerator and denominator as a Rational8, reduced to lowest terms
     * @param n Signed 8-bit numerator
     * @param d Unsigned 8-bit denominator (must be nonzero)
     * @return a Rational8 value in reduced form
     */
    function divRational8(int256 n, uint256 d) internal pure returns (Rational8 a) {
        if (d == 0) {
            revert ZeroDenominator();
        }

        uint256 g = gcd(_abs(n), d);
        // forge-lint: disable-next-line(unsafe-typecast)
        n /= int256(g);
        // forge-lint: disable-next-line(unsafe-typecast)
        d /= g;

        if (n < -NUMERATOR8_MAX || n > NUMERATOR8_MAX) {
            revert NumeratorTooBig(n);
        }
        if (d > DENOMINATOR8_MAX) {
            revert DenominatorTooBig(d);
        }
        // forge-lint: disable-next-line(unsafe-typecast)
        int256 encoded = (n << 8) | int256(uint256(d));
        // forge-lint: disable-next-line(unsafe-typecast)
        a = Rational8.wrap(int16(encoded));
    }

    /**
     * @notice Negates a Rational8-encoded value
     * @param a A Rational8-encoded int16 value
     * @return Negated Rational8-encoded value
     */
    function neg(Rational8 a) internal pure returns (Rational8) {
        (int8 n, uint8 d) = a.parts();
        return divRational8(-n, d);
    }

    /**
     * @notice Adds two Rational8 values by converting to Rational, adding, then converting back
     */
    function add(Rational8 a, Rational8 b) internal pure returns (Rational8) {
        return a.toRational().add(b.toRational()).toRational8();
    }

    /**
     * @notice Divides a Rational8 values by an unsigned integer
     */
    function div(Rational8 a, uint256 b) internal pure returns (Rational8 q) {
        (int256 n, uint256 d) = a.parts();
        q = n.divRational8(d * b);
    }

    /**
     * @notice Converts a Rational to an exact Rational8, reverts if not representable
     */
    function toRational8(Rational a) internal pure returns (Rational8 a8) {
        (int256 n, uint256 d) = a.parts();
        a8 = n.divRational8(d);
    }

    /**
     * @notice Converts a Rational8 value to Rational
     */
    function toRational(Rational8 a8) internal pure returns (Rational a) {
        (int256 n, uint256 d) = a8.parts();
        a = n.divRational(d);
    }

    /**
     * @notice Safely converts uint256 to int256, reverting on overflow
     */
    function toInt256(uint256 x) internal pure returns (int256 y) {
        if (x <= uint256(type(int256).max)) {
            // forge-lint: disable-next-line(unsafe-typecast)
            y = int256(uint256(x));
        } else {
            revert ExponentTooBig();
        }
    }

    /**
     * @notice Computes greatest common divisor using Euclidean algorithm
     */
    function gcd(uint256 a, uint256 b) public pure returns (uint256) {
        while (b != 0) {
            uint256 t = b;
            b = a % b;
            a = t;
        }
        return a;
    }

    /**
     * @notice Computes least common multiple of two denominators
     * @dev Uses identity lcm(a, b) = (a / gcd(a, b)) * b
     */
    function lcm(uint256 a, uint256 b) public pure returns (uint256) {
        // forge-lint: disable-next-line(divide-before-multiply)
        return (a / gcd(a, b)) * b;
    }

    /**
     * @notice Returns the absolute value of an int256
     * @dev Handles type(int256).min safely using unchecked negation
     */
    function _abs(int256 x) internal pure returns (uint256) {
        if (x >= 0) {
            // forge-lint: disable-next-line(unsafe-typecast)
            return uint256(x);
        } else {
            unchecked {
                // forge-lint: disable-next-line(unsafe-typecast)
                return uint256(-x);
            }
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (utils/Strings.sol)

pragma solidity ^0.8.20;

import {Math} from "math/Math.sol";
import {SafeCast} from "math/SafeCast.sol";
import {SignedMath} from "math/SignedMath.sol";

/**
 * @dev String operations.
 */
library Strings {
    using SafeCast for *;

    bytes16 private constant HEX_DIGITS = "0123456789abcdef";
    uint8 private constant ADDRESS_LENGTH = 20;
    uint256 private constant SPECIAL_CHARS_LOOKUP =
        (1 << 0x08) | // backspace
            (1 << 0x09) | // tab
            (1 << 0x0a) | // newline
            (1 << 0x0c) | // form feed
            (1 << 0x0d) | // carriage return
            (1 << 0x22) | // double quote
            (1 << 0x5c); // backslash

    /**
     * @dev The `value` string doesn't fit in the specified `length`.
     */
    error StringsInsufficientHexLength(uint256 value, uint256 length);

    /**
     * @dev The string being parsed contains characters that are not in scope of the given base.
     */
    error StringsInvalidChar();

    /**
     * @dev The string being parsed is not a properly formatted address.
     */
    error StringsInvalidAddressFormat();

    /**
     * @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;
            assembly ("memory-safe") {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                assembly ("memory-safe") {
                    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 Converts an `address` with fixed length of 20 bytes to its checksummed ASCII `string` hexadecimal
     * representation, according to EIP-55.
     */
    function toChecksumHexString(address addr) internal pure returns (string memory) {
        bytes memory buffer = bytes(toHexString(addr));

        // hash the hex part of buffer (skip length + 2 bytes, length 40)
        uint256 hashValue;
        assembly ("memory-safe") {
            hashValue := shr(96, keccak256(add(buffer, 0x22), 40))
        }

        for (uint256 i = 41; i > 1; --i) {
            // possible values for buffer[i] are 48 (0) to 57 (9) and 97 (a) to 102 (f)
            if (hashValue & 0xf > 7 && uint8(buffer[i]) > 96) {
                // case shift by xoring with 0x20
                buffer[i] ^= 0x20;
            }
            hashValue >>= 4;
        }
        return string(buffer);
    }

    /**
     * @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));
    }

    /**
     * @dev Parse a decimal string and returns the value as a `uint256`.
     *
     * Requirements:
     * - The string must be formatted as `[0-9]*`
     * - The result must fit into an `uint256` type
     */
    function parseUint(string memory input) internal pure returns (uint256) {
        return parseUint(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseUint-string} that parses a substring of `input` located between position `begin` (included) and
     * `end` (excluded).
     *
     * Requirements:
     * - The substring must be formatted as `[0-9]*`
     * - The result must fit into an `uint256` type
     */
    function parseUint(string memory input, uint256 begin, uint256 end) internal pure returns (uint256) {
        (bool success, uint256 value) = tryParseUint(input, begin, end);
        if (!success) revert StringsInvalidChar();
        return value;
    }

    /**
     * @dev Variant of {parseUint-string} that returns false if the parsing fails because of an invalid character.
     *
     * NOTE: This function will revert if the result does not fit in a `uint256`.
     */
    function tryParseUint(string memory input) internal pure returns (bool success, uint256 value) {
        return _tryParseUintUncheckedBounds(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseUint-string-uint256-uint256} that returns false if the parsing fails because of an invalid
     * character.
     *
     * NOTE: This function will revert if the result does not fit in a `uint256`.
     */
    function tryParseUint(
        string memory input,
        uint256 begin,
        uint256 end
    ) internal pure returns (bool success, uint256 value) {
        if (end > bytes(input).length || begin > end) return (false, 0);
        return _tryParseUintUncheckedBounds(input, begin, end);
    }

    /**
     * @dev Implementation of {tryParseUint-string-uint256-uint256} that does not check bounds. Caller should make sure that
     * `begin <= end <= input.length`. Other inputs would result in undefined behavior.
     */
    function _tryParseUintUncheckedBounds(
        string memory input,
        uint256 begin,
        uint256 end
    ) private pure returns (bool success, uint256 value) {
        bytes memory buffer = bytes(input);

        uint256 result = 0;
        for (uint256 i = begin; i < end; ++i) {
            uint8 chr = _tryParseChr(bytes1(_unsafeReadBytesOffset(buffer, i)));
            if (chr > 9) return (false, 0);
            result *= 10;
            result += chr;
        }
        return (true, result);
    }

    /**
     * @dev Parse a decimal string and returns the value as a `int256`.
     *
     * Requirements:
     * - The string must be formatted as `[-+]?[0-9]*`
     * - The result must fit in an `int256` type.
     */
    function parseInt(string memory input) internal pure returns (int256) {
        return parseInt(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseInt-string} that parses a substring of `input` located between position `begin` (included) and
     * `end` (excluded).
     *
     * Requirements:
     * - The substring must be formatted as `[-+]?[0-9]*`
     * - The result must fit in an `int256` type.
     */
    function parseInt(string memory input, uint256 begin, uint256 end) internal pure returns (int256) {
        (bool success, int256 value) = tryParseInt(input, begin, end);
        if (!success) revert StringsInvalidChar();
        return value;
    }

    /**
     * @dev Variant of {parseInt-string} that returns false if the parsing fails because of an invalid character or if
     * the result does not fit in a `int256`.
     *
     * NOTE: This function will revert if the absolute value of the result does not fit in a `uint256`.
     */
    function tryParseInt(string memory input) internal pure returns (bool success, int256 value) {
        return _tryParseIntUncheckedBounds(input, 0, bytes(input).length);
    }

    uint256 private constant ABS_MIN_INT256 = 2 ** 255;

    /**
     * @dev Variant of {parseInt-string-uint256-uint256} that returns false if the parsing fails because of an invalid
     * character or if the result does not fit in a `int256`.
     *
     * NOTE: This function will revert if the absolute value of the result does not fit in a `uint256`.
     */
    function tryParseInt(
        string memory input,
        uint256 begin,
        uint256 end
    ) internal pure returns (bool success, int256 value) {
        if (end > bytes(input).length || begin > end) return (false, 0);
        return _tryParseIntUncheckedBounds(input, begin, end);
    }

    /**
     * @dev Implementation of {tryParseInt-string-uint256-uint256} that does not check bounds. Caller should make sure that
     * `begin <= end <= input.length`. Other inputs would result in undefined behavior.
     */
    function _tryParseIntUncheckedBounds(
        string memory input,
        uint256 begin,
        uint256 end
    ) private pure returns (bool success, int256 value) {
        bytes memory buffer = bytes(input);

        // Check presence of a negative sign.
        bytes1 sign = begin == end ? bytes1(0) : bytes1(_unsafeReadBytesOffset(buffer, begin)); // don't do out-of-bound (possibly unsafe) read if sub-string is empty
        bool positiveSign = sign == bytes1("+");
        bool negativeSign = sign == bytes1("-");
        uint256 offset = (positiveSign || negativeSign).toUint();

        (bool absSuccess, uint256 absValue) = tryParseUint(input, begin + offset, end);

        if (absSuccess && absValue < ABS_MIN_INT256) {
            return (true, negativeSign ? -int256(absValue) : int256(absValue));
        } else if (absSuccess && negativeSign && absValue == ABS_MIN_INT256) {
            return (true, type(int256).min);
        } else return (false, 0);
    }

    /**
     * @dev Parse a hexadecimal string (with or without "0x" prefix), and returns the value as a `uint256`.
     *
     * Requirements:
     * - The string must be formatted as `(0x)?[0-9a-fA-F]*`
     * - The result must fit in an `uint256` type.
     */
    function parseHexUint(string memory input) internal pure returns (uint256) {
        return parseHexUint(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseHexUint-string} that parses a substring of `input` located between position `begin` (included) and
     * `end` (excluded).
     *
     * Requirements:
     * - The substring must be formatted as `(0x)?[0-9a-fA-F]*`
     * - The result must fit in an `uint256` type.
     */
    function parseHexUint(string memory input, uint256 begin, uint256 end) internal pure returns (uint256) {
        (bool success, uint256 value) = tryParseHexUint(input, begin, end);
        if (!success) revert StringsInvalidChar();
        return value;
    }

    /**
     * @dev Variant of {parseHexUint-string} that returns false if the parsing fails because of an invalid character.
     *
     * NOTE: This function will revert if the result does not fit in a `uint256`.
     */
    function tryParseHexUint(string memory input) internal pure returns (bool success, uint256 value) {
        return _tryParseHexUintUncheckedBounds(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseHexUint-string-uint256-uint256} that returns false if the parsing fails because of an
     * invalid character.
     *
     * NOTE: This function will revert if the result does not fit in a `uint256`.
     */
    function tryParseHexUint(
        string memory input,
        uint256 begin,
        uint256 end
    ) internal pure returns (bool success, uint256 value) {
        if (end > bytes(input).length || begin > end) return (false, 0);
        return _tryParseHexUintUncheckedBounds(input, begin, end);
    }

    /**
     * @dev Implementation of {tryParseHexUint-string-uint256-uint256} that does not check bounds. Caller should make sure that
     * `begin <= end <= input.length`. Other inputs would result in undefined behavior.
     */
    function _tryParseHexUintUncheckedBounds(
        string memory input,
        uint256 begin,
        uint256 end
    ) private pure returns (bool success, uint256 value) {
        bytes memory buffer = bytes(input);

        // skip 0x prefix if present
        bool hasPrefix = (end > begin + 1) && bytes2(_unsafeReadBytesOffset(buffer, begin)) == bytes2("0x"); // don't do out-of-bound (possibly unsafe) read if sub-string is empty
        uint256 offset = hasPrefix.toUint() * 2;

        uint256 result = 0;
        for (uint256 i = begin + offset; i < end; ++i) {
            uint8 chr = _tryParseChr(bytes1(_unsafeReadBytesOffset(buffer, i)));
            if (chr > 15) return (false, 0);
            result *= 16;
            unchecked {
                // Multiplying by 16 is equivalent to a shift of 4 bits (with additional overflow check).
                // This guarantees that adding a value < 16 will not cause an overflow, hence the unchecked.
                result += chr;
            }
        }
        return (true, result);
    }

    /**
     * @dev Parse a hexadecimal string (with or without "0x" prefix), and returns the value as an `address`.
     *
     * Requirements:
     * - The string must be formatted as `(0x)?[0-9a-fA-F]{40}`
     */
    function parseAddress(string memory input) internal pure returns (address) {
        return parseAddress(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseAddress-string} that parses a substring of `input` located between position `begin` (included) and
     * `end` (excluded).
     *
     * Requirements:
     * - The substring must be formatted as `(0x)?[0-9a-fA-F]{40}`
     */
    function parseAddress(string memory input, uint256 begin, uint256 end) internal pure returns (address) {
        (bool success, address value) = tryParseAddress(input, begin, end);
        if (!success) revert StringsInvalidAddressFormat();
        return value;
    }

    /**
     * @dev Variant of {parseAddress-string} that returns false if the parsing fails because the input is not a properly
     * formatted address. See {parseAddress-string} requirements.
     */
    function tryParseAddress(string memory input) internal pure returns (bool success, address value) {
        return tryParseAddress(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseAddress-string-uint256-uint256} that returns false if the parsing fails because input is not a properly
     * formatted address. See {parseAddress-string-uint256-uint256} requirements.
     */
    function tryParseAddress(
        string memory input,
        uint256 begin,
        uint256 end
    ) internal pure returns (bool success, address value) {
        if (end > bytes(input).length || begin > end) return (false, address(0));

        bool hasPrefix = (end > begin + 1) && bytes2(_unsafeReadBytesOffset(bytes(input), begin)) == bytes2("0x"); // don't do out-of-bound (possibly unsafe) read if sub-string is empty
        uint256 expectedLength = 40 + hasPrefix.toUint() * 2;

        // check that input is the correct length
        if (end - begin == expectedLength) {
            // length guarantees that this does not overflow, and value is at most type(uint160).max
            (bool s, uint256 v) = _tryParseHexUintUncheckedBounds(input, begin, end);
            return (s, address(uint160(v)));
        } else {
            return (false, address(0));
        }
    }

    function _tryParseChr(bytes1 chr) private pure returns (uint8) {
        uint8 value = uint8(chr);

        // Try to parse `chr`:
        // - Case 1: [0-9]
        // - Case 2: [a-f]
        // - Case 3: [A-F]
        // - otherwise not supported
        unchecked {
            if (value > 47 && value < 58) value -= 48;
            else if (value > 96 && value < 103) value -= 87;
            else if (value > 64 && value < 71) value -= 55;
            else return type(uint8).max;
        }

        return value;
    }

    /**
     * @dev Escape special characters in JSON strings. This can be useful to prevent JSON injection in NFT metadata.
     *
     * WARNING: This function should only be used in double quoted JSON strings. Single quotes are not escaped.
     *
     * NOTE: This function escapes all unicode characters, and not just the ones in ranges defined in section 2.5 of
     * RFC-4627 (U+0000 to U+001F, U+0022 and U+005C). ECMAScript's `JSON.parse` does recover escaped unicode
     * characters that are not in this range, but other tooling may provide different results.
     */
    function escapeJSON(string memory input) internal pure returns (string memory) {
        bytes memory buffer = bytes(input);
        bytes memory output = new bytes(2 * buffer.length); // worst case scenario
        uint256 outputLength = 0;

        for (uint256 i; i < buffer.length; ++i) {
            bytes1 char = bytes1(_unsafeReadBytesOffset(buffer, i));
            if (((SPECIAL_CHARS_LOOKUP & (1 << uint8(char))) != 0)) {
                output[outputLength++] = "\\";
                if (char == 0x08) output[outputLength++] = "b";
                else if (char == 0x09) output[outputLength++] = "t";
                else if (char == 0x0a) output[outputLength++] = "n";
                else if (char == 0x0c) output[outputLength++] = "f";
                else if (char == 0x0d) output[outputLength++] = "r";
                else if (char == 0x5c) output[outputLength++] = "\\";
                else if (char == 0x22) {
                    // solhint-disable-next-line quotes
                    output[outputLength++] = '"';
                }
            } else {
                output[outputLength++] = char;
            }
        }
        // write the actual length and deallocate unused memory
        assembly ("memory-safe") {
            mstore(output, outputLength)
            mstore(0x40, add(output, shl(5, shr(5, add(outputLength, 63)))))
        }

        return string(output);
    }

    /**
     * @dev Reads a bytes32 from a bytes array without bounds checking.
     *
     * NOTE: making this function internal would mean it could be used with memory unsafe offset, and marking the
     * assembly block as such would prevent some optimizations.
     */
    function _unsafeReadBytesOffset(bytes memory buffer, uint256 offset) private pure returns (bytes32 value) {
        // This is not memory safe in the general case, but all calls to this private function are within bounds.
        assembly ("memory-safe") {
            value := mload(add(buffer, add(0x20, offset)))
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (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 v5.1.0) (utils/Panic.sol)

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].
 *
 * _Available since v5.1._
 */
// 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 {
        assembly ("memory-safe") {
            mstore(0x00, 0x4e487b71)
            mstore(0x20, code)
            revert(0x1c, 0x24)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (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) {
        assembly ("memory-safe") {
            u := iszero(iszero(b))
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (proxy/Clones.sol)

pragma solidity ^0.8.30;

/**
 * @dev https://eips.ethereum.org/EIPS/eip-1167[ERC-1167] is a standard for
 * deploying minimal proxy contracts, also known as "clones".
 *
 * > To simply and cheaply clone contract functionality in an immutable way, this standard specifies
 * > a minimal bytecode implementation that delegates all calls to a known, fixed address.
 *
 * This is a stripped-down version of OpenZeppelin's Clones library (v5.3.0), containing only
 * deterministic CREATE2 deployment functions with explicit value parameter support.
 * The following functions have been removed: clone(), and the overloads of cloneDeterministic()
 * and predictDeterministicAddress() that omit the value or deployer parameters.
 *
 * Original source: https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v5.3.0/contracts/proxy/Clones.sol
 */
library Clones {
    /**
     * @dev Deploys and returns the address of a clone that mimics the behavior of `implementation`.
     *
     * This function uses the create2 opcode and a `salt` to deterministically deploy
     * the clone. Using the same `implementation` and `salt` multiple times will revert, since
     * the clones cannot be deployed twice at the same address.
     *
     * NOTE: Using a non-zero value at creation will require the contract using this function (e.g. a factory)
     * to always have enough balance for new deployments. Consider exposing this function under a payable method.
     */
    function cloneDeterministic(
        address implementation,
        bytes32 salt,
        uint256 value
    ) internal returns (address instance) {
        assembly ("memory-safe") {
            // Cleans the upper 96 bits of the `implementation` word, then packs the first 3 bytes
            // of the `implementation` address with the bytecode before the address.
            mstore(
                0x00,
                or(
                    shr(0xe8, shl(0x60, implementation)),
                    0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000
                )
            )
            // Packs the remaining 17 bytes of `implementation` with the bytecode after the address.
            mstore(
                0x20,
                or(shl(0x78, implementation), 0x5af43d82803e903d91602b57fd5bf3)
            )
            instance := create2(value, 0x09, 0x37, salt)
        }
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministic}.
     */
    function predictDeterministicAddress(
        address implementation,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        assembly ("memory-safe") {
            let ptr := mload(0x40)
            mstore(add(ptr, 0x38), deployer)
            mstore(add(ptr, 0x24), 0x5af43d82803e903d91602b57fd5bf3ff)
            mstore(add(ptr, 0x14), implementation)
            mstore(ptr, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73)
            mstore(add(ptr, 0x58), salt)
            mstore(add(ptr, 0x78), keccak256(add(ptr, 0x0c), 0x37))
            predicted := and(
                keccak256(add(ptr, 0x43), 0x55),
                0xffffffffffffffffffffffffffffffffffffffff
            )
        }
    }
}

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

pragma solidity ^0.8.30;

/**
 * @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 v5.1.0) (interfaces/draft-IERC6093.sol)
pragma solidity ^0.8.30;

/**
 * @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);
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.30;

type Rational is int256;
type Rational8 is int16;

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.20;

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

/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Branchless ternary evaluation for `a ? b : c`. Gas costs are constant.
     *
     * IMPORTANT: This function may reduce bytecode size and consume less gas when used standalone.
     * However, the compiler may optimize Solidity ternary operations (i.e. `a ? b : c`) to only compute
     * one branch when needed, making this function more expensive.
     */
    function ternary(bool condition, int256 a, int256 b) internal pure returns (int256) {
        unchecked {
            // branchless ternary works because:
            // b ^ (a ^ b) == a
            // b ^ 0 == b
            return b ^ ((a ^ b) * int256(SafeCast.toUint(condition)));
        }
    }

    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return ternary(a > b, a, b);
    }

    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return ternary(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 `bytes32(0)` (if n is positive) or `~bytes32(0)` (if n is negative).
            int256 mask = n >> 255;

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

{
  "remappings": [
    "forge-std/=lib/forge-std/src/",
    "clones/=lib/clones/",
    "ierc20/=lib/ierc20/",
    "erc20/=lib/erc20/",
    "math/=lib/math/",
    "strings/=lib/strings/",
    "panic/=lib/panic/"
  ],
  "optimizer": {
    "enabled": true,
    "runs": 200
  },
  "metadata": {
    "useLiteralContent": false,
    "bytecodeHash": "ipfs",
    "appendCBOR": true
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "evmVersion": "cancun",
  "viaIR": true,
  "debug": {
    "revertStrings": "default"
  }
}

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