Contract Address Details

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.26;

import {AccessControl} from "@openzeppelin/contracts/access/AccessControl.sol";
import {ReentrancyGuard} from "@openzeppelin/contracts/utils/ReentrancyGuard.sol";
import {IERC20} from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import {SafeERC20} from "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import {Math} from "@openzeppelin/contracts/utils/math/Math.sol";
import {IPulseXRouter, IPulseXFactory, IPulseXPair, ITreasury, ITSI, IEpoch, IBurnable} from "../interfaces/IProtocol.sol";
import {TwapOracle} from "../oracle/TwapOracle.sol";


/// @title BuybackRouter
/// @notice Receives PBURN fee inflows and allocates each chunk across four actions:
///         burn PBURN, buy-and-burn pFLY, add protocol-owned liquidity, and fund the
///         treasury.
/// @dev THE CORE INVARIANT: a single `execute` can never spend more than the chunk it
///      committed to at the start of the call. `chunk` is snapshotted, the four legs
///      are computed from it with the remainder folded into the last leg, and the sum
///      of the legs is asserted to equal the chunk exactly before anything moves.
///      There is no path that reads `balanceOf(this)` again mid-execution, so the
///      router cannot spend fees that arrive during the call.
contract BuybackRouter is AccessControl, ReentrancyGuard {
    using SafeERC20 for IERC20;

    bytes32 public constant PARAMETER_ROLE = keccak256("PARAMETER_ROLE");
    bytes32 public constant KEEPER_ROLE = keccak256("KEEPER_ROLE");

    uint16 public constant BPS_DENOMINATOR = 10_000;
    address public constant DEAD = 0x000000000000000000000000000000000000dEaD;

    struct Allocation {
        uint16 pburnBurnBps;
        uint16 pflyBurnBps;
        /// @dev Never set directly. Carved out of pflyBurnBps at execution time, and
        ///      only when the pCOCK pool can actually absorb the trade.
        uint16 pcockBurnBps;
        uint16 polBps;
        uint16 treasuryBps;
    }

    struct Split {
        uint256 pburnBurn;
        uint256 pflyBurn;
        uint256 pcockBurn;
        uint256 pol;
        uint256 treasury;
    }

    IERC20 public immutable pburn;
    address public immutable pfly;
    address public immutable treasury;
    IPulseXRouter public immutable dexRouter;
    TwapOracle public immutable oracle;

    ITSI public tsi;
    IEpoch public epoch;

    /// @notice Second buyback target. Settable rather than immutable so the leg can ship
    ///         dormant and be pointed at pCOCK once that token and its pool exist.
    address public pcock;

    /// @notice Fallback split used when no Epoch is wired. Whitepaper default 40/40/20.
    Allocation public defaultAllocation =
        Allocation({pburnBurnBps: 4_000, pflyBurnBps: 4_000, pcockBurnBps: 0, polBps: 1_000, treasuryBps: 1_000});

    /// @notice Minimum PBURN balance before `execute` will do anything.
    uint256 public minExecutionAmount = 1_000e18;
    /// @notice Maximum PBURN processed in a single execution, to bound price impact.
    uint256 public maxExecutionAmount = 100_000e18;
    /// @notice Slippage tolerance on router swaps.
    uint16 public maxSlippageBps = 500; // 5%

    /// @notice How far below the TWAP-implied value a fill may land before the trade is
    ///         refused. Covers the 0.29% pool fee plus the trade's own price impact at the
    ///         capped size, with headroom.
    ///
    /// @dev THIS IS THE SAFETY PROPERTY. `maxSlippageBps` is not: it is applied to
    ///      `getAmountsOut`, which reads the reserves of the very pool being traded, so
    ///      after a front-run it is measured against the attacker's own manipulation and
    ///      binds on nothing. The floor below is measured against a time-average the
    ///      attacker cannot move within a block.
    uint16 public twapFloorBps = 200; // 2%

    /// @notice Loosest tolerance governance may set. Ceiling, not a default.
    ///
    /// @dev The acceptance criterion for the whole fix is that loosening the floor breaks a
    ///      test. Without a ceiling that criterion held only against a code change:
    ///      PARAMETER_ROLE could have widened `twapFloorBps` until it bound on nothing and
    ///      the protection would be gone with no diff to review. 1000 is 5x the default,
    ///      which is room to react to a genuinely volatile market and not much more.
    ///
    ///      Raising the floor invalidates the depth table in `docs/PCOCK_ACTIVATION.md`
    ///      proportionally - that table is computed at 200 bps, and the attacker's maximum
    ///      gain scales linearly with this number.
    uint16 public constant MAX_TWAP_FLOOR_BPS = 1_000;

    /// @notice Largest swap cap governance may set, as a fraction of the PBURN reserve.
    uint16 public constant MAX_SWAP_CAP_BPS = 500;

    /// @notice The PulseX fee, in bps. 0.29%, not Uniswap's 0.30%.
    uint16 public constant POOL_FEE_BPS = 29;

    /// @dev Gas each swap is given, exactly - see `_trySwap`. A PulseX V2 swap costs ~120k; pFLY's
    ///      own transfer path can add a fee swap-back of its own. 1M leaves several times that.
    uint256 public constant SWAP_GAS = 1_000_000;

    /// @dev Covers the opcodes between the gas check and the call, chiefly ABI-encoding the path.
    uint256 private constant SWAP_GAS_HEADROOM = 20_000;

    /// @notice Governance's ceiling on the router's flow into the pFLY pool in one run, as a
    ///         fraction of that pool's PBURN side at the TWAP price.
    ///
    /// @dev An impact bound, so `twapFloorBps` can be tight. It is no longer the binding one:
    ///      `maxFlowInto` caps the flow at half a sandwich's break-even - 0.295% of the pool
    ///      at today's fees - and governance cannot raise that. The remainder is not redistributed - the
    ///      chunk itself shrinks, so unspent fees stay in the router and are picked up by the
    ///      next `execute()`. A backlog from a period of refusals therefore still drains.
    uint16 public maxSwapBps = 100; // 1% of the pool's PBURN side

    /// @notice TSI below this biases allocation toward treasury and POL over burning.
    uint256 public tsiStressThreshold = 4_000;
    /// @notice Bps of the pFLY leg redirected to PBURN burn while TSI is healthy and
    ///         pFLY is expensive relative to its TWAP.
    uint16 public pflySpikeRedirectBps = 5_000;

    /// @notice Share of the pFLY buyback leg redirected to pCOCK, when the pCOCK pool can
    ///         take it. Default 25%, so an epoch preset of 40/40/10/10 executes as
    ///         40/30/10/10/10 - the pFLY-primary shape.
    /// @dev Carved from pFLY rather than added as a fifth top-level slot on purpose.
    ///      `IEpoch.allocation()` returns four values and Epoch is already deployed;
    ///      widening that interface would drag Epoch into a redeploy it does not
    ///      otherwise need. Carving also makes the economics explicit: pCOCK competes
    ///      with pFLY for the buyback budget, it does not dilute PBURN burn, POL, or
    ///      treasury.
    uint16 public pcockShareBps = 2_500;

    /// @notice Largest pCOCK trade, as bps of the pool's PBURN-side reserve.
    /// @dev Constant-product loss is monotonic in amountIn/reserveIn, so bounding the
    ///      ratio bounds price impact directly without needing a quote. At the default
    ///      200 bps the leg costs roughly 2.2% against a 0.29% PulseX fee; beyond that
    ///      the pool is too thin to be worth routing through and the leg stands down.
    uint16 public maxPcockTradeBps = 200;

    uint256 public totalPcockBurned;

    uint256 public totalPburnBurned;
    uint256 public totalPflyBurned;
    uint256 public totalPolAdded;
    uint256 public totalTreasuryFunded;

    /// @param tsiSignalAvailable False when no TSI module is wired.
    /// @param spikeSignalAvailable False when the pFLY spike check could not read the
    ///        oracle. Watch this: a long run of false means a protective mechanism is
    ///        off, not that it is finding nothing.
    /// @param pcockLegAvailable False when the pCOCK leg stood down - no token wired, no
    ///        pool, an empty pool, or a pool too thin for this chunk. Same warning
    ///        applies: a long run of false is a leg that is off, not a leg finding
    ///        nothing to do.
    /// @param pflyPoolAvailable False when the PBURN/pFLY pool is missing or empty, which
    ///        stands down BOTH the pFLY buyback leg and the POL leg - POL pairs against
    ///        pFLY, so one drained pool takes out both. Before the pool guard existed this
    ///        state reverted `execute()` outright instead of being reported.
    event Executed(
        uint256 chunk,
        Split split,
        uint256 tsiScore,
        bool tsiSignalAvailable,
        bool spikeSignalAvailable,
        bool pcockLegAvailable,
        bool pflyPoolAvailable,
        address indexed caller
    );
    event PburnBurned(uint256 amount, uint256 newTotalSupply);
    event PflyBurned(uint256 pburnSpent, uint256 pflyReceived);
    event PcockBurned(uint256 pburnSpent, uint256 pcockReceived);
    event PolAdded(uint256 pburnSpent, uint256 pairedSpent, uint256 liquidity);
    event TreasuryFunded(address indexed asset, uint256 amount);
    event AllocationUpdated(Allocation allocation);
    event ExecutionBoundsUpdated(uint256 minAmount, uint256 maxAmount, uint16 maxSlippageBps);
    event ModulesUpdated(address tsi, address epoch);
    event SignalParamsUpdated(uint256 tsiStressThreshold, uint16 pflySpikeRedirectBps);
    event PcockTargetUpdated(address indexed previousToken, address indexed newToken);
    event PcockParamsUpdated(uint16 pcockShareBps, uint16 maxPcockTradeBps);
    event TwapGuardsUpdated(uint16 twapFloorBps, uint16 maxSwapBps);

    /// @notice A trading leg's swap could not fill at or above its floor, so the leg did not
    ///         trade. Its PBURN stays in the router and the next `execute()` picks it up.
    /// @dev `minOut` is the floor the fill had to clear. The usual cause on chain 369 is a
    ///      transfer tax on the OUTPUT token - see `_trySwap`.
    event LegStoodDown(address indexed token, uint256 pburnAmount, uint256 minOut);

    error ZeroAddress();
    error BelowMinimum(uint256 balance, uint256 minimum);
    error AllocationMustTotalDenominator(uint256 provided);
    error InvalidBounds();
    error SplitDoesNotMatchChunk(uint256 sum, uint256 chunk);
    error SwapProducedNothing();

    /// @dev No usable time-average for this pair, so no trade into it can be bounded.
    error TwapUnavailable(address token);

    /// @dev Too little gas left to give a swap its full `SWAP_GAS`. Reverted rather than
    ///      attempted short - see `_trySwap`.
    error InsufficientGasForLeg();

    constructor(address admin, address pburn_, address pfly_, address treasury_, address dexRouter_, address oracle_) {
        if (
            admin == address(0) || pburn_ == address(0) || pfly_ == address(0) || treasury_ == address(0)
                || dexRouter_ == address(0) || oracle_ == address(0)
        ) revert ZeroAddress();

        _grantRole(DEFAULT_ADMIN_ROLE, admin);

        pburn = IERC20(pburn_);
        pfly = pfly_;
        treasury = treasury_;
        dexRouter = IPulseXRouter(dexRouter_);
        oracle = TwapOracle(oracle_);
    }

    // --- Execution ----------------------------------------------------------

    /// @notice Process accrued fees. Permissioned to KEEPER_ROLE so that execution
    ///         timing cannot be used to sandwich the protocol's own swaps.
    function execute() external onlyRole(KEEPER_ROLE) nonReentrant returns (Split memory split) {
        // Snapshot the chunk once. Nothing below re-reads the balance, so fees that
        // land mid-execution are simply left for the next run.
        uint256 balance = pburn.balanceOf(address(this));
        if (balance < minExecutionAmount) revert BelowMinimum(balance, minExecutionAmount);

        (uint256 chunk, Allocation memory alloc, uint256 tsiScore, bool hasSignal) = _plan(balance);
        split = _splitChunk(chunk, alloc);

        // Hard invariant: the five legs must account for exactly the chunk, no more.
        uint256 sum = split.pburnBurn + split.pflyBurn + split.pcockBurn + split.pol + split.treasury;
        if (sum != chunk) revert SplitDoesNotMatchChunk(sum, chunk);

        // From here `split` is what EXECUTED, not what was planned. A leg that stood down
        // reports zero, so the return value and the event cannot claim a buy that did not
        // happen; `chunk` minus the sum is what stayed in the router for the next run.
        split = _runLegs(split);

        (, bool spikeAvailable) = _pflyAboveTwap();
        emit Executed(
            chunk,
            split,
            tsiScore,
            hasSignal,
            spikeAvailable,
            alloc.pcockBurnBps > 0,
            _pflyPoolUsable(),
            msg.sender
        );
    }

    /// @dev The whole planning step, shared by `execute()` and `previewSplit()`.
    ///
    ///      They were separate once. `execute()` learned to cap before allocating (below) and
    ///      the preview did not, so it went on evaluating the allocation at the UNCAPPED chunk
    ///      and forecasting pFLY legs standing down that would in fact trade. Its only test
    ///      funded 10,000 PBURN against a mock with no reserves, where the cap never binds, so
    ///      the two could not be told apart there. One function cannot drift from itself.
    function _plan(uint256 balance)
        private
        view
        returns (uint256 chunk, Allocation memory alloc, uint256 tsiScore, bool hasSignal)
    {
        chunk = balance > maxExecutionAmount ? maxExecutionAmount : balance;

        (tsiScore, hasSignal) = _readTsi();

        // ORDER MATTERS, and getting it wrong stands every leg down.
        //
        // The cap must be applied BEFORE the allocation is evaluated, because the
        // allocation's guards ask "would this leg fill above the floor?" and the answer
        // depends on the trade's size. Evaluating at the uncapped chunk asks about a trade
        // that will never be placed: a 35,000 PBURN swap has ~3.7% impact against this
        // pool and fails a 2% floor, so the honest path stood itself down while the capped
        // trade it would actually make - around 9,500 - has well under 1%.
        //
        // Whatever the cap holds back is NOT redistributed. It stays in the router's
        // balance and the next execute() picks it up, which is what lets a backlog drain
        // across runs instead of forcing one oversized trade.
        uint256 capped = _capChunkForSwaps(chunk, _baseAllocation());
        bool swapsFitUnderTheCap = capped >= minExecutionAmount;

        if (swapsFitUnderTheCap) {
            chunk = capped;
        }
        // ELSE: the pool is too shallow to take even a minimum-sized run within the cap.
        //
        // Reverting here would be wrong, and an earlier revision did: `BelowMinimum` fired
        // and NOTHING executed, including the PBURN burn and treasury legs, which need no
        // price and no counterparty. A thin pool would have bricked fee processing
        // entirely, and the thinner the pool the more certainly it would stay bricked -
        // the balance grows, the cap does not.
        //
        // So the chunk stays whole and the trading legs stand down instead. The run still
        // happens; it just does not trade.

        alloc = _effectiveAllocation(chunk, tsiScore, hasSignal);
        if (!swapsFitUnderTheCap) {
            alloc = _standDownTradingLegs(alloc);
        }
    }

    /// @dev Returns what executed. The PBURN burn and treasury legs need no counterparty and
    ///      always run; each trading leg either fills at or above its floor or stands down.
    function _runLegs(Split memory planned) private returns (Split memory done) {
        if (planned.pburnBurn > 0) {
            _burnPburn(planned.pburnBurn);
            done.pburnBurn = planned.pburnBurn;
        }
        if (planned.pflyBurn > 0) {
            (bool filled, uint256 received) = _buyAndBurn(pfly, planned.pflyBurn);
            if (filled) {
                done.pflyBurn = planned.pflyBurn;
                totalPflyBurned += received;
                emit PflyBurned(planned.pflyBurn, received);
            }
        }
        if (planned.pcockBurn > 0) {
            (bool filled, uint256 received) = _buyAndBurn(pcock, planned.pcockBurn);
            if (filled) {
                done.pcockBurn = planned.pcockBurn;
                totalPcockBurned += received;
                emit PcockBurned(planned.pcockBurn, received);
            }
        }
        if (planned.pol > 0 && _addPol(planned.pol)) done.pol = planned.pol;
        if (planned.treasury > 0) {
            _fundTreasury(planned.treasury);
            done.treasury = planned.treasury;
        }
    }

    /// @dev Splits `chunk` by bps, folding all integer-division dust into the treasury
    ///      leg so the five parts always re-sum to exactly `chunk`.
    ///
    ///      `SplitDoesNotMatchChunk` remains unreachable by construction, and the third
    ///      leg does not change that. Every branch in `_effectiveAllocation` conserves
    ///      the bps total: the stress branch moves pFLY bps into POL and treasury, the
    ///      spike branch moves pFLY bps into PBURN burn, and the pCOCK carve moves pFLY
    ///      bps into pCOCK. `setDefaultAllocation` rejects any total other than 10000, so
    ///      the first four legs can never exceed the chunk and treasury absorbs exactly
    ///      the integer-division dust. If a future branch ever broke that conservation,
    ///      the subtraction below would panic on underflow before the assertion could
    ///      catch it - so the assertion is a backstop for a wrong-but-non-underflowing
    ///      total, and `testFuzzSplitAlwaysSumsToChunk` pins the property directly.
    function _splitChunk(uint256 chunk, Allocation memory alloc) private pure returns (Split memory split) {
        split.pburnBurn = (chunk * alloc.pburnBurnBps) / BPS_DENOMINATOR;
        split.pflyBurn = (chunk * alloc.pflyBurnBps) / BPS_DENOMINATOR;
        split.pcockBurn = (chunk * alloc.pcockBurnBps) / BPS_DENOMINATOR;
        split.pol = (chunk * alloc.polBps) / BPS_DENOMINATOR;
        split.treasury = chunk - split.pburnBurn - split.pflyBurn - split.pcockBurn - split.pol;
    }

    /// @dev Blends the epoch preset with live TSI and pFLY price signals, then carves the
    ///      pCOCK leg out of whatever pFLY budget survives.
    function _effectiveAllocation(uint256 chunk, uint256 tsiScore, bool hasSignal)
        private
        view
        returns (Allocation memory alloc)
    {
        alloc = _baseAllocation();

        // No TSI module wired: use the base allocation untouched rather than
        // pretending to have a health reading either way.
        if (!hasSignal) return _applyPflyPoolGuard(chunk, _applyPcockCarve(chunk, alloc));

        if (tsiScore < tsiStressThreshold) {
            // Treasury under stress: halve the pFLY burn leg and move it into
            // treasury and POL, which rebuild strength instead of spending it.
            uint16 moved = alloc.pflyBurnBps / 2;
            alloc.pflyBurnBps -= moved;
            uint16 toPol = moved / 2;
            alloc.polBps += toPol;
            alloc.treasuryBps += (moved - toPol);
        } else if (_spikeRedirectApplies()) {
            // pFLY spiking above its own TWAP: buying it now is expensive, so
            // redirect part of that leg into burning PBURN instead.
            uint16 moved = uint16((uint256(alloc.pflyBurnBps) * pflySpikeRedirectBps) / BPS_DENOMINATOR);
            alloc.pflyBurnBps -= moved;
            alloc.pburnBurnBps += moved;
        }

        alloc = _applyPcockCarve(chunk, alloc);
        return _applyPflyPoolGuard(chunk, alloc);
    }

    /// @dev Stands down the two legs that depend on the PBURN/pFLY pool when that pool is
    ///      missing or empty, rather than letting `getAmountsOut` revert the whole
    ///      execution.
    ///
    ///      This was the live bug, and it was not pCOCK-specific: the pFLY leg has always
    ///      called `_minOut` unguarded, and so has the POL leg, which pairs PBURN against
    ///      pFLY. A drained reference pool therefore bricked `execute()` entirely - PBURN
    ///      burn and treasury funding included, neither of which needs the pool at all.
    ///      Adding the pCOCK guard alone would have left that untouched.
    ///
    ///      Where the freed budget goes is chosen to keep doing the nearest useful thing:
    ///      the pFLY buyback becomes a PBURN burn (still deflationary, needs no pool), and
    ///      POL becomes treasury funding (still balance-sheet, needs no pool).
    function _applyPflyPoolGuard(uint256 chunk, Allocation memory alloc)
        private
        view
        returns (Allocation memory)
    {
        uint256 pflyLeg = (chunk * alloc.pflyBurnBps) / BPS_DENOMINATOR;
        uint256 polSwap = ((chunk * alloc.polBps) / BPS_DENOMINATOR) / 2;

        bool poolOk = _pflyPoolUsable();

        // CHECK THE COMBINED SIZE, NOT EACH LEG SEPARATELY.
        //
        // Both legs sell PBURN into the same pool and they execute in sequence, so the
        // first one moves the price the second one gets. Checking them independently
        // against the current price passes two trades that each clear the floor alone and
        // then reverts mid-execution when the second faces the first one's impact -
        // `INSUFFICIENT_OUTPUT_AMOUNT` from inside `_buyAndBurn`, after the burn leg has
        // already run.
        //
        // The combined amount is the conservative test: impact is superlinear in size, so
        // if the whole quantity clears the floor in one hypothetical trade, each sequential
        // piece of it clears with room to spare.
        uint256 totalSwap = pflyLeg + polSwap;
        bool boundOk = totalSwap == 0 || twapBounded(pfly, totalSwap);

        if (poolOk && boundOk) return alloc;

        return _standDownTradingLegs(alloc);
    }

    /// @notice Fold every leg that needs a swap into one that does not.
    function _standDownTradingLegs(Allocation memory alloc)
        private
        pure
        returns (Allocation memory)
    {
        // WHERE THE UNTRADED ALLOCATION GOES, and why:
        //   pFLY burn -> PBURN burn.  Burning PBURN needs no swap, so it cannot be
        //                             sandwiched. The deflationary intent is preserved.
        //   POL       -> treasury.    Adding liquidity requires a swap first; holding the
        //                             PBURN in the treasury needs none.
        //   pCOCK     -> PBURN burn.  Same reasoning as pFLY.
        //
        // Neither destination trades, so an unbounded market cannot cost the protocol
        // anything on this execution. The fees are not skipped - they are redirected to
        // the legs that are safe when no price can be trusted.
        alloc.pburnBurnBps += alloc.pflyBurnBps + alloc.pcockBurnBps;
        alloc.pflyBurnBps = 0;
        alloc.pcockBurnBps = 0;

        alloc.treasuryBps += alloc.polBps;
        alloc.polBps = 0;

        return alloc;
    }

    /// @notice Largest chunk whose swaps into the pFLY pool stay within `maxFlowInto(pfly)`.
    ///
    /// @dev Shrinks the chunk rather than redistributing the excess, so whatever is not
    ///      traded stays in the router and the next `execute()` picks it up. That is what
    ///      makes a backlog drain: each run takes a bounded bite, and the bites continue
    ///      until the balance is gone.
    ///
    ///      The pFLY pool takes two swaps in one run - the buyback and half of POL - and a
    ///      sandwich wraps the whole run, so it is their SUM that is capped, counted before the
    ///      pCOCK carve moves part of the buyback elsewhere so the cap holds whatever the carve
    ///      does. Checking each swap alone would pass two that sum past the break-even.
    ///
    ///      With no time-average for the pool, nothing trades into it this run - its legs stand
    ///      down at their floors - so there is nothing to sandwich, and the cap only sizes the
    ///      bite. The spot reserve does for that: it keeps an outage from routing a whole
    ///      100,000 chunk to burn and treasury in one run.
    function _capChunkForSwaps(uint256 chunk, Allocation memory alloc)
        private
        view
        returns (uint256)
    {
        // The two legs that swap into PBURN/pFLY: the buyback, and half of POL.
        uint256 swapBps = uint256(alloc.pflyBurnBps) + uint256(alloc.polBps) / 2;
        if (swapBps == 0) return chunk;

        uint256 depth = poolDepthAtTwap(pfly);
        if (depth == 0) (, depth) = _poolFor(pfly);
        if (depth == 0) return chunk;

        // wouldSwap = chunk * swapBps / BPS must not exceed depth * halfBps / (2 * BPS), so the
        // chunk is at most depth * halfBps / (2 * swapBps) - one division, rounding down.
        uint256 capped = Math.mulDiv(depth, _flowHalfBps(pfly), 2 * swapBps);
        return capped < chunk ? capped : chunk;
    }

    /// @dev Moves `pcockShareBps` of the remaining pFLY leg into the pCOCK leg, but only
    ///      if the pCOCK pool can actually absorb that trade.
    ///
    ///      The fallback is the point of the whole design: when the leg is unavailable
    ///      NOTHING is carved, so the allocation is byte-for-byte what this router would
    ///      have produced without a pCOCK leg at all. That makes the feature safe to ship
    ///      dormant - before the token exists, before the pool is funded - because the
    ///      inert behaviour is provably the previous behaviour rather than a new untested
    ///      path. `testUnavailablePcockMatchesTwoTokenRouterExactly` pins that.
    ///
    ///      Carving last, after the stress and spike branches, means pCOCK takes its
    ///      share of whatever pFLY budget survives those adjustments rather than
    ///      competing with them.
    function _applyPcockCarve(uint256 chunk, Allocation memory alloc)
        private
        view
        returns (Allocation memory)
    {
        uint16 moved = uint16((uint256(alloc.pflyBurnBps) * pcockShareBps) / BPS_DENOMINATOR);
        if (moved == 0 || chunk == 0) return alloc;

        // Never more into the pCOCK pool than half ITS sandwich break-even. The chunk was sized
        // by the pFLY pool, which says nothing about this one - that is how the leg used to
        // outgrow a pool it traded in. A thin pool gets a smaller carve, not a smaller chunk:
        // what it cannot take stays in the pFLY leg, which the chunk cap already sized for it.
        uint256 fits = (maxFlowInto(pcock) * BPS_DENOMINATOR) / chunk;
        if (fits < moved) moved = uint16(fits);
        if (moved == 0) return alloc;

        uint256 pcockLeg = (chunk * moved) / BPS_DENOMINATOR;
        if (!_pcockLegAvailable(pcockLeg)) return alloc;

        // AND it must be priceable. `_pcockLegAvailable` checks only that the pool exists
        // and is deep enough for the size; it says nothing about whether a time-average
        // exists to bound the fill against.
        //
        // Without this the carve went ahead and `_buyAndBurn` hit `_minOut`, which reverts
        // `TwapUnavailable` - taking the entire execution down, including the burn and
        // treasury legs that need no price. A third trading path reaching the floor with
        // no pre-check, where pFLY and POL both had one.
        if (!twapBounded(pcock, pcockLeg)) return alloc;

        alloc.pflyBurnBps -= moved;
        alloc.pcockBurnBps = moved;
        return alloc;
    }

    /// @dev Resolves the PBURN pool for `token`, returning address(0) unless it exists
    ///      AND holds liquidity on both sides.
    /// @return pair The pool, or address(0) if unusable.
    /// @return pburnReserve The PBURN-side reserve, 0 when unusable.
    function _poolFor(address token) private view returns (address pair, uint256 pburnReserve) {
        if (token == address(0)) return (address(0), 0);

        pair = IPulseXFactory(dexRouter.factory()).getPair(address(pburn), token);
        if (pair == address(0)) return (address(0), 0);

        (uint112 reserve0, uint112 reserve1,) = IPulseXPair(pair).getReserves();
        if (reserve0 == 0 || reserve1 == 0) return (address(0), 0);

        pburnReserve = IPulseXPair(pair).token0() == address(pburn) ? reserve0 : reserve1;
    }

    /// @dev Can `amountIn` PBURN be routed through `token`'s pool right now?
    ///
    ///      Every failure mode returns false rather than reverting, and that matters more
    ///      than it looks. `_minOut` calls `getAmountsOut`, which resolves the pair by
    ///      CREATE2 and calls `getReserves()` on it. Against a codeless address that
    ///      reverts on the extcodesize check BEFORE the call, which `try/catch` cannot
    ///      intercept - so an unguarded leg reverts every `execute()` while its pool does
    ///      not exist, taking every OTHER leg down with it. Screening here is what keeps a
    ///      missing pool a dormant leg instead of a bricked router.
    ///
    /// @param maxTradeBps Ceiling on amountIn as a share of the pool's PBURN reserve.
    ///        Pass 0 to check existence and liquidity only, with no size bound.
    function _legTradable(address token, uint256 amountIn, uint16 maxTradeBps)
        private
        view
        returns (bool)
    {
        if (amountIn == 0) return false;

        (address pair, uint256 pburnReserve) = _poolFor(token);
        if (pair == address(0)) return false;
        if (maxTradeBps == 0) return true;

        // Constant-product loss is monotonic in amountIn/reserveIn, so bounding that
        // ratio bounds price impact without needing a quote.
        return amountIn * BPS_DENOMINATOR <= pburnReserve * maxTradeBps;
    }

    function _pcockLegAvailable(uint256 amountIn) private view returns (bool) {
        return _legTradable(pcock, amountIn, maxPcockTradeBps);
    }

    /// @dev The pFLY pool backs BOTH the pFLY buyback leg and the POL leg, since POL
    ///      pairs PBURN against pFLY. One drained pool takes out both.
    ///
    ///      No size ceiling here, deliberately. The bug being fixed is bricking, not
    ///      slippage, and pFLY is the reference pair - imposing a depth cap on the
    ///      primary leg would change live economics to fix a liveness bug. If a pFLY
    ///      depth ceiling is ever wanted it should be its own decision, not a side
    ///      effect of this one.
    function _pflyPoolUsable() private view returns (bool) {
        (address pair,) = _poolFor(pfly);
        return pair != address(0);
    }

    /// @notice Whether the pCOCK pool exists and holds liquidity, independent of size.
    /// @dev Separates "no pool" from "pool too thin for this chunk" for monitoring.
    function pcockPoolReady() external view returns (bool) {
        (address pair,) = _poolFor(pcock);
        return pair != address(0);
    }

    /// @notice Whether the pCOCK leg would fire for a trade of `amountIn` PBURN.
    function pcockLegAvailable(uint256 amountIn) external view returns (bool) {
        return _pcockLegAvailable(amountIn);
    }

    // --- The sandwich bound ---------------------------------------------------------------------
    //
    // A sandwich wraps a whole execute(): the bot sells PBURN into a pool, the router's swaps
    // land at the worse price, the bot sells back. To first order it gains d x flow and pays
    // d x cost x depth, where d is how far it moved the price, `flow` is the PBURN this run
    // sends into that pool, `depth` is the pool's PBURN side and `cost` is what one of its
    // swaps costs it - PulseX's fee plus PBURN's own. The sign does not depend on d, the floor
    // or the TWAP: a sandwich pays exactly when flow > cost x depth. So every pool's flow is
    // capped at HALF of that, and no sandwich pays - whatever the pools hold relative to each
    // other, and whether or not pFLY taxes its pairs. Measured on real pools in
    // test/fork/MainnetLaunchRehearsal.t.sol, section 5. Governance cannot raise this bound:
    // `maxSwapBps` can only tighten it.

    /// @notice What one PBURN-side swap through `token`'s pool costs a sandwich bot, in bps:
    ///         PulseX's fee, plus PBURN's own transfer fee unless the token exempts that pair.
    ///         Read live, so a governance fee cut or a pair exemption tightens the cap with it.
    function sandwichCostBps(address token) public view returns (uint256) {
        (address pair,) = _poolFor(token);
        return uint256(POOL_FEE_BPS) + _pburnFeeOnPair(pair);
    }

    /// @notice `token`'s pool's PBURN side at the TWAP price, `sqrt(k / P_twap)`; 0 when there
    ///         is no pool or no usable time-average.
    /// @dev What a front-run cannot inflate. Selling PBURN in raises the PBURN reserve one for
    ///      one, for free; it raises `k` only by the fee it pays into the pool - real depth,
    ///      bought at 0.29% - and it cannot move the TWAP inside its own block.
    function poolDepthAtTwap(address token) public view returns (uint256) {
        (address pair,) = _poolFor(token);
        if (pair == address(0)) return 0;
        try oracle.consult(pair, address(pburn), 1e18) returns (uint256 otherPerPburn) {
            if (otherPerPburn == 0) return 0;
            (uint112 reserve0, uint112 reserve1,) = IPulseXPair(pair).getReserves();
            return Math.sqrt(Math.mulDiv(uint256(reserve0) * uint256(reserve1), 1e18, otherPerPburn));
        } catch {
            return 0;
        }
    }

    /// @notice Most PBURN one run may send into `token`'s pool: half a sandwich's break-even
    ///         (`sandwichCostBps / 2` of `poolDepthAtTwap`), or `maxSwapBps` if governance set
    ///         that lower. 0 when the depth cannot be measured - and then nothing trades there.
    function maxFlowInto(address token) public view returns (uint256) {
        return Math.mulDiv(poolDepthAtTwap(token), _flowHalfBps(token), 2 * uint256(BPS_DENOMINATOR));
    }

    /// @dev The flow cap in HALF-bps, to keep the half of an odd cost exact: the smaller of the
    ///      sandwich cost (half of it, doubled) and twice `maxSwapBps`. `maxSwapBps` = 0 leaves
    ///      only the sandwich bound, which governance cannot switch off.
    function _flowHalfBps(address token) private view returns (uint256) {
        uint256 cost = sandwichCostBps(token);
        uint256 impact = 2 * uint256(maxSwapBps);
        return maxSwapBps == 0 || cost < impact ? cost : impact;
    }

    /// @dev PBURN's fee on a transfer to or from `pair`: 0 if the token exempts the pair, since
    ///      a bot trading through it then pays only PulseX. The testnet token names the getter
    ///      `isFeeExempt` and the launch token `isExempt`, so both are asked. Read by raw
    ///      staticcall, because a typed call to a getter a token lacks reverts in the caller.
    function _pburnFeeOnPair(address pair) private view returns (uint256) {
        address token = address(pburn);
        if (
            pair != address(0)
                && (
                    _readWord(token, abi.encodeWithSignature("isExempt(address)", pair)) != 0
                        || _readWord(token, abi.encodeWithSignature("isFeeExempt(address)", pair)) != 0
                )
        ) return 0;
        return _readWord(token, abi.encodeWithSignature("feeBps()"));
    }

    /// @dev One 32-byte word from a view call, or 0 when the call fails or returns anything else.
    function _readWord(address target, bytes memory data) private view returns (uint256) {
        (bool ok, bytes memory ret) = target.staticcall(data);
        return ok && ret.length == 32 ? abi.decode(ret, (uint256)) : 0;
    }

    /// @notice Whether the PBURN/pFLY pool can currently back the pFLY and POL legs.
    /// @dev False means those legs stand down and their budget folds into PBURN burn and
    ///      treasury respectively. Before this guard existed, false meant `execute()`
    ///      reverted outright and the whole fee engine stopped.
    function pflyPoolAvailable() external view returns (bool) {
        return _pflyPoolUsable();
    }

    /// @dev Only redirect on a reading we actually have.
    ///
    ///      THE COMMENT HERE USED TO SAY an unavailable signal leaves the base allocation
    ///      in place, "which is neutral rather than permissive". That was wrong, and it is
    ///      the sentence that let audit finding A-2 sit unexamined.
    ///
    ///      Leaving the base allocation meant the router bought pFLY anyway, at a price
    ///      nothing had vouched for. For the spike protection specifically that is
    ///      fail-OPEN: the protection exists to avoid buying during a spike, and the
    ///      degraded path bought during spikes it could not see.
    ///
    ///      What IS fail-closed is the SIGNAL - `_pflyAboveTwap` returns
    ///      `(false, false)` rather than claiming "no spike", so monitoring can tell an
    ///      unavailable check from a quiet one. An honest signal and a safe action are
    ///      different properties, and conflating them is how a router with no working
    ///      price bound was described as failing closed for months.
    ///
    ///      The action is now safe too: `_applyPflyPoolGuard` stands the trading legs down
    ///      before this is reached, so an unavailable reading means no trade rather than an
    ///      unprotected one.
    function _spikeRedirectApplies() private view returns (bool) {
        (bool spiking, bool available) = _pflyAboveTwap();
        return available && spiking;
    }

    function _baseAllocation() private view returns (Allocation memory) {
        IEpoch epoch_ = epoch;
        // A codeless address would revert on the extcodesize check BEFORE the call,
        // which try/catch cannot intercept, so it is screened out here.
        if (address(epoch_) == address(0) || address(epoch_).code.length == 0) return defaultAllocation;

        (uint16 pburnBurnBps, uint16 pflyBurnBps, uint16 polBps, uint16 treasuryBps) = epoch_.allocation();
        // pcockBurnBps is deliberately 0 here. `IEpoch.allocation()` returns four values
        // and Epoch is already deployed; the pCOCK leg is carved out of pflyBurnBps later
        // rather than widening that interface, so an epoch preset never has to know the
        // second buyback target exists.
        return Allocation({
            pburnBurnBps: pburnBurnBps,
            pflyBurnBps: pflyBurnBps,
            pcockBurnBps: 0,
            polBps: polBps,
            treasuryBps: treasuryBps
        });
    }

    /// @dev Reads the TSI health signal.
    /// @return score Composite score, meaningful only when `hasSignal` is true.
    /// @return hasSignal False when no TSI module is wired at all, in which case the
    ///         base allocation is used unmodified.
    ///
    /// A broken or unconfigured TSI is deliberately reported as a score of 0 with
    /// hasSignal true, which drives the conservative stress branch. An earlier
    /// revision returned full health here, so an unreadable signal made the protocol
    /// behave as though the treasury were perfectly healthy - fail-open on exactly
    /// the input that exists to detect trouble.
    ///
    /// The code-length screen matters because Solidity performs the extcodesize check
    /// BEFORE the external call, and that revert is NOT catchable by try/catch.
    function _readTsi() private view returns (uint256, bool) {
        ITSI tsi_ = tsi;
        if (address(tsi_) == address(0)) return (0, false);
        if (address(tsi_).code.length == 0) return (0, true);

        try tsi_.score() returns (uint256 value) {
            return (value, true);
        } catch {
            return (0, true);
        }
    }

    /// @dev Is pFLY spiking above its own TWAP?
    /// @return spiking Meaningful only when `available` is true.
    /// @return available False when no pair is wired, or when the oracle cannot
    ///         currently answer (no observation yet, or the averaging window has not
    ///         reached minPeriod).
    ///
    /// An earlier revision returned a bare `false` for all three of those states, so
    /// the router could not distinguish "no spike" from "could not check". That made
    /// the spike check a silent no-op whenever the oracle was unavailable - the same
    /// shape as the fail-open TSI, one layer down. The allocation behaviour for an
    /// unavailable signal is no longer "unchanged (base allocation)" - the trading legs
    /// stand down - and it is reported
    /// rather than indistinguishable from a real reading.
    function _pflyAboveTwap() private view returns (bool spiking, bool available) {
        address pair = IPulseXFactory(dexRouter.factory()).getPair(address(pburn), pfly);
        if (pair == address(0)) return (false, false);

        try oracle.isQuoteSafe(pair, address(pburn), 1e18) returns (bool safe) {
            if (safe) return (false, true); // within band: genuinely no spike
            // Outside the band. Distinguish a spike from a crash.
            uint256 spot = oracle.spotQuote(pair, address(pburn), 1e18);
            uint256 twap = oracle.consult(pair, address(pburn), 1e18);
            // More pFLY per PBURN than TWAP implies pFLY is cheap, not spiking.
            return (spot < twap, true);
        } catch {
            return (false, false);
        }
    }

    /// @notice Whether the pFLY spike check can currently produce a reading.
    /// @dev Exposed so monitoring can tell an active-and-quiet check apart from an
    ///      unavailable one. A protective mechanism that is silently off is the
    ///      failure mode this protocol has hit repeatedly.
    function spikeCheckAvailable() external view returns (bool) {
        (, bool available) = _pflyAboveTwap();
        return available;
    }

    // --- Legs ---------------------------------------------------------------

    function _burnPburn(uint256 amount) private {
        IBurnable(address(pburn)).burn(amount);
        totalPburnBurned += amount;
        emit PburnBurned(amount, IBurnable(address(pburn)).totalSupply());
    }

    /// @dev Buys `token` with `amount` PBURN and burns what comes back. Shared by the
    ///      pFLY and pCOCK legs so the two cannot drift apart in approval hygiene or
    ///      slippage handling. Accounting and events stay with the caller.
    function _buyAndBurn(address token, uint256 amount) private returns (bool filled, uint256 received) {
        address[] memory path = new address[](2);
        path[0] = address(pburn);
        path[1] = token;

        uint256 minOut = _minOut(path, amount);
        uint256 balanceBefore = IERC20(token).balanceOf(address(this));

        pburn.forceApprove(address(dexRouter), amount);
        filled = _trySwap(token, amount, minOut, path);

        // Clear any allowance the swap did not consume: the DEX router must never
        // retain a standing claim on router funds between executions. On BOTH paths - a
        // stood-down leg consumed nothing and would otherwise leave the whole amount approved.
        pburn.forceApprove(address(dexRouter), 0);
        if (!filled) return (false, 0);

        received = IERC20(token).balanceOf(address(this)) - balanceBefore;
        if (received == 0) revert SwapProducedNothing();

        // These are external tokens: burn by sending to the dead address rather than
        // assuming they expose a burn() entry point.
        IERC20(token).safeTransfer(DEAD, received);
    }

    /// @dev Half the POL leg is swapped for pFLY, then both sides are paired and the
    ///      resulting LP is sent to the Treasury as protocol-owned liquidity.
    function _addPol(uint256 amount) private returns (bool filled) {
        uint256 half = amount / 2;
        uint256 pburnSide = amount - half;

        address[] memory path = new address[](2);
        path[0] = address(pburn);
        path[1] = pfly;

        uint256 balanceBefore = IERC20(pfly).balanceOf(address(this));
        pburn.forceApprove(address(dexRouter), half);
        filled = _trySwap(pfly, half, _minOut(path, half), path);
        if (!filled) {
            // Nothing moved: the swap is the leg's first transfer, and a stood-down swap
            // reverted in full. Clear the approval and leave the whole amount for next run.
            pburn.forceApprove(address(dexRouter), 0);
            return false;
        }
        uint256 pairedReceived = IERC20(pfly).balanceOf(address(this)) - balanceBefore;
        if (pairedReceived == 0) revert SwapProducedNothing();

        pburn.forceApprove(address(dexRouter), pburnSide);
        IERC20(pfly).forceApprove(address(dexRouter), pairedReceived);

        (,, uint256 liquidity) = dexRouter.addLiquidity(
            address(pburn),
            pfly,
            pburnSide,
            pairedReceived,
            _applySlippage(pburnSide),
            _applySlippage(pairedReceived),
            treasury,
            block.timestamp
        );

        // addLiquidity consumes at most the desired amounts and often less, so both
        // allowances are cleared rather than left dangling as a standing claim.
        pburn.forceApprove(address(dexRouter), 0);
        IERC20(pfly).forceApprove(address(dexRouter), 0);

        address pair = IPulseXFactory(dexRouter.factory()).getPair(address(pburn), pfly);
        if (pair != address(0) && liquidity > 0) {
            ITreasury(treasury).recordLpDeposit(pair, liquidity);
        }

        totalPolAdded += amount;
        emit PolAdded(pburnSide, pairedReceived, liquidity);
    }

    /// @dev One swap, isolated so that its failure stands its own leg down instead of
    ///      reverting `execute()`.
    ///
    ///      WHY. pFLY on chain 369 taxes buys 3% and sells 5% through any pair its owner has
    ///      registered, the owner is an EOA, and registering a pair is one call we do not
    ///      control. Once PBURN/pFLY is registered, what reaches this router is 3% under what
    ///      the pool sends. The default floor leaves 71 bps between the pool's own output and
    ///      the minimum (200 floor - 100 cap - 29 fee), so the fill misses and PulseX reverts
    ///      `INSUFFICIENT_OUTPUT_AMOUNT`. Uncaught, that took the WHOLE run down with it -
    ///      including the PBURN burn and treasury legs, which need no counterparty at all.
    ///      Reproduced against mainnet state in test/fork/MainnetLaunchRehearsal.t.sol.
    ///
    ///      The floor still holds: a leg that cannot clear it does not trade. What changes is
    ///      only that one third party's configuration can no longer halt the legs it has
    ///      nothing to do with. This is the same rule `execute()` already applies to a pool
    ///      too thin for the cap - stand the trading legs down, run the rest.
    ///
    ///      WHY A FIXED GAS ALLOWANCE. Catching a failure makes the outcome depend on the gas
    ///      the caller sent, unless something stops it. `eth_estimateGas` searches for the least
    ///      gas at which a transaction does not revert; if a swap starved of gas were caught
    ///      and reported as a stand-down, a short-gas run would "succeed", the estimate would
    ///      settle there, and every keeper run sized by it would skip its trading legs.
    ///
    ///      The first version guarded this after the fact - "if at most 1/64 of the gas is
    ///      left, the callee ran out, so revert" (EIP-150). A test showed that is wrong. When
    ///      the out-of-gas happens two frames down (PulseX -> pair -> token), each intermediate
    ///      frame hands back the 1/64 it kept, the caller sees ~3/64, and the check waves it
    ///      through.
    ///
    ///      So the swap gets exactly `SWAP_GAS`, and the run reverts BEFORE the call if it cannot
    ///      supply that much. Whether a swap fits is then a property of the swap, never of the
    ///      keeper's gas limit: any run that gets past the check behaves the same as a run with
    ///      unlimited gas. A swap that genuinely needs more than `SWAP_GAS` stands down, every
    ///      time, visibly.
    ///
    ///      The revert reason is not captured. The output token is a third-party contract,
    ///      and copying arbitrary returndata is a gas-griefing surface; `minOut` in the event
    ///      is enough to re-simulate the miss.
    function _trySwap(address token, uint256 amountIn, uint256 minOut, address[] memory path)
        private
        returns (bool)
    {
        // EIP-150 forwards at most 63/64 of what remains; make sure the full allowance can
        // actually reach the callee, with headroom for the ABI encoding in between.
        if (gasleft() < (SWAP_GAS * 64) / 63 + SWAP_GAS_HEADROOM) revert InsufficientGasForLeg();

        try dexRouter.swapExactTokensForTokensSupportingFeeOnTransferTokens{gas: SWAP_GAS}(
            amountIn, minOut, path, address(this), block.timestamp
        ) {
            return true;
        } catch {
            emit LegStoodDown(token, amountIn, minOut);
            return false;
        }
    }

    function _fundTreasury(uint256 amount) private {
        pburn.safeTransfer(treasury, amount);
        ITreasury(treasury).recordDeposit(address(pburn), amount);

        totalTreasuryFunded += amount;
        emit TreasuryFunded(address(pburn), amount);
    }

    /// @dev Minimum acceptable output: the GREATER of the spot-derived bound and the
    ///      TWAP-derived floor. **In practice the TWAP floor is the only one that can bind.**
    ///
    ///      An earlier comment here claimed spot was "the tighter of the two in calm
    ///      markets". That is wrong, and worth correcting rather than deleting: the spot
    ///      bound is `getAmountsOut(amountIn) * (1 - maxSlippageBps)`, quoted in the same
    ///      transaction, immediately before the swap that fills at exactly that quote. It
    ///      is a fraction of the number it is checking, so it is satisfied by construction.
    ///      `maxSlippageBps` has never constrained this router and a reader should not be
    ///      left thinking two protections are present when there is one.
    ///
    ///      It is retained for the one case where it is not vacuous: a transfer tax on the
    ///      input. PBURN taxes transfers and the router is currently fee-exempt, so less
    ///      would arrive at the pair than was quoted if that exemption were ever removed,
    ///      and the fill would come in under the quote. Cheap backstop, correctly labelled.
    ///
    ///      Under manipulation the spot bound collapses with the price - it is quoted from
    ///      the manipulated pool - while the TWAP floor does not move. The floor binds.
    ///
    ///      Reverts when no TWAP is available. Callers must not reach here for a token
    ///      whose leg has not been cleared by `_twapBounded`; the revert is a backstop
    ///      against a future caller that forgets, not the intended control flow.
    function _minOut(address[] memory path, uint256 amountIn) private view returns (uint256) {
        uint256[] memory amounts = dexRouter.getAmountsOut(amountIn, path);
        uint256 spotBound = _applySlippage(amounts[amounts.length - 1]);

        (uint256 floor, bool available) = _twapFloor(path[path.length - 1], amountIn);
        if (!available) revert TwapUnavailable(path[path.length - 1]);

        return floor > spotBound ? floor : spotBound;
    }

    /// @notice The TWAP-implied minimum for selling `amountIn` PBURN into the PBURN/`token`
    ///         pool, and whether a usable reading exists at all.
    ///
    /// @dev Deliberately the same shape `BondingVault._lpValueInPburn` already uses:
    ///      `isQuoteSafe` to reject a spot that has diverged from the average, then
    ///      `consult` for the value itself. That pattern was correct in the vault and
    ///      absent from the router; this is not a second design, it is the first one
    ///      applied where it was missing.
    function _twapFloor(address token, uint256 amountIn)
        private
        view
        returns (uint256 floor, bool available)
    {
        (address pair,) = _poolFor(token);
        if (pair == address(0)) return (0, false);

        try oracle.isQuoteSafe(pair, address(pburn), amountIn) returns (bool safe) {
            if (!safe) return (0, false);
        } catch {
            return (0, false);
        }

        try oracle.consult(pair, address(pburn), amountIn) returns (uint256 fair) {
            if (fair == 0) return (0, false);
            return ((fair * (BPS_DENOMINATOR - twapFloorBps)) / BPS_DENOMINATOR, true);
        } catch {
            return (0, false);
        }
    }

    /// @notice Smallest pFLY-pool depth at the TWAP price at which the trading legs run at all.
    ///
    /// @dev Below this the flow cap shrinks the chunk under `minExecutionAmount`, so the
    ///      trading legs stand down and every execution routes to burn and treasury
    ///      instead. That is safe but it is a cliff, and it is invisible from the outside,
    ///      so it is exposed rather than left to be discovered.
    ///
    ///      depth = minExecutionAmount * swapBps * 2 / halfBps
    ///
    ///      With the Phase 1 split (1500 pFLY burn + 4000 POL, half of which swaps) that is
    ///      3500 bps of swap against a 29.5 bps cap at today's fees - half of 0.29% + 0.3% -
    ///      and a 1,000 PBURN minimum: **118,644 PBURN**. Before the sandwich bound, the 100 bps
    ///      `maxSwapBps` made it 35,000.
    function minPoolDepthForTrading() external view returns (uint256) {
        Allocation memory alloc = _baseAllocation();
        uint256 swapBps = uint256(alloc.pflyBurnBps) + uint256(alloc.polBps) / 2;
        if (swapBps == 0) return 0;
        return Math.mulDiv(minExecutionAmount, swapBps * 2, _flowHalfBps(pfly));
    }

    /// @notice Whether a leg trading into `token` can be bounded AND would actually clear
    ///         that bound at the current price.
    ///
    /// @dev Two distinct refusals, and both must stand a leg down rather than revert:
    ///
    ///      1. No usable time-average - nothing to bound against.
    ///      2. A usable average, but the pool would fill below the floor right now.
    ///
    ///      Checking (2) here rather than letting `_minOut` revert inside the swap is the
    ///      difference between "this leg does not trade this run" and "execute() reverts
    ///      and no leg trades, including the ones that need no price at all". The fees are
    ///      not lost either way, but only the first lets the burn and treasury legs run.
    ///
    ///      `isQuoteSafe` (inside `_twapFloor`) tolerates up to `maxDeviationBps` - 10% -
    ///      which is far wider than the 2% floor. Without this second check a manipulation
    ///      inside that band passes availability and then fills below the floor, which is
    ///      precisely the window a sandwicher would choose.
    function twapBounded(address token, uint256 amountIn) public view returns (bool) {
        (uint256 floor, bool available) = _twapFloor(token, amountIn);
        if (!available) return false;
        if (amountIn == 0) return true;

        address[] memory path = new address[](2);
        path[0] = address(pburn);
        path[1] = token;

        try dexRouter.getAmountsOut(amountIn, path) returns (uint256[] memory amounts) {
            return amounts[amounts.length - 1] >= floor;
        } catch {
            return false;
        }
    }

    function _applySlippage(uint256 amount) private view returns (uint256) {
        return (amount * (BPS_DENOMINATOR - maxSlippageBps)) / BPS_DENOMINATOR;
    }

    // --- Views --------------------------------------------------------------

    /// @notice Preview the split that `execute` would apply right now.
    /// @notice The split the next `execute()` would PLAN, from the same `_plan` it uses. A
    ///         trading leg can still stand down at execution if its fill misses the floor -
    ///         `execute()` returns what ran, this returns what was intended.
    function previewSplit() external view returns (uint256 chunk, Split memory split, uint256 tsiScore) {
        Allocation memory alloc;
        (chunk, alloc, tsiScore,) = _plan(pburn.balanceOf(address(this)));
        split = _splitChunk(chunk, alloc);
    }

    function pendingFees() external view returns (uint256) {
        return pburn.balanceOf(address(this));
    }

    // --- Governance ---------------------------------------------------------

    function setDefaultAllocation(Allocation calldata alloc) external onlyRole(PARAMETER_ROLE) {
        uint256 total = uint256(alloc.pburnBurnBps) + alloc.pflyBurnBps + alloc.pcockBurnBps
            + alloc.polBps + alloc.treasuryBps;
        if (total != BPS_DENOMINATOR) revert AllocationMustTotalDenominator(total);

        defaultAllocation = alloc;
        emit AllocationUpdated(alloc);
    }

    function setExecutionBounds(uint256 minAmount, uint256 maxAmount, uint16 slippageBps)
        external
        onlyRole(PARAMETER_ROLE)
    {
        if (minAmount == 0 || maxAmount < minAmount || slippageBps >= BPS_DENOMINATOR) revert InvalidBounds();

        minExecutionAmount = minAmount;
        maxExecutionAmount = maxAmount;
        maxSlippageBps = slippageBps;
        emit ExecutionBoundsUpdated(minAmount, maxAmount, slippageBps);
    }

    /// @dev No credit ledger here on purpose: router burns are protocol-owned and have
    ///      no user to credit. Credit accrual lives in BondingVault and PBURN.
    function setModules(address tsi_, address epoch_) external onlyRole(PARAMETER_ROLE) {
        tsi = ITSI(tsi_);
        epoch = IEpoch(epoch_);
        emit ModulesUpdated(tsi_, epoch_);
    }

    /// @notice Point the second buyback leg at a token, or unset it with address(0).
    /// @dev Unsetting is a deliberate kill switch: the leg stands down and the router
    ///      reverts to its two-token allocation without any other change.
    /// @dev Activating a leg is not the same as being able to trade it safely. Before this
    ///      check, a single governance call opened a PBURN/pCOCK trading path with no
    ///      oracle coverage of any kind - the spike check is pFLY-specific, and `_minOut`
    ///      was spot-derived, so the leg would have traded entirely unbounded.
    ///
    ///      Requiring a mature TWAP here means the pair must have been observed for at
    ///      least `minPeriod` before it can receive a single trade. Note this is a
    ///      necessary condition, not a sufficient one: a TWAP over a thin pool is cheap to
    ///      hold off by the tolerance, so see the minimum-depth guidance in
    ///      `docs/PCOCK_ACTIVATION.md` before pointing this at anything.
    function setPcockTarget(address pcock_) external onlyRole(PARAMETER_ROLE) {
        if (pcock_ == address(pburn) || pcock_ == pfly) revert ZeroAddress();
        if (pcock_ != address(0) && !twapBounded(pcock_, 1e18)) revert TwapUnavailable(pcock_);
        address previous = pcock;
        pcock = pcock_;
        emit PcockTargetUpdated(previous, pcock_);
    }

    function setPcockParams(uint16 pcockShareBps_, uint16 maxPcockTradeBps_)
        external
        onlyRole(PARAMETER_ROLE)
    {
        if (pcockShareBps_ > BPS_DENOMINATOR || maxPcockTradeBps_ > BPS_DENOMINATOR) {
            revert InvalidBounds();
        }
        pcockShareBps = pcockShareBps_;
        maxPcockTradeBps = maxPcockTradeBps_;
        emit PcockParamsUpdated(pcockShareBps_, maxPcockTradeBps_);
    }

    function setSignalParams(uint256 tsiStressThreshold_, uint16 pflySpikeRedirectBps_)
        external
        onlyRole(PARAMETER_ROLE)
    {
        if (pflySpikeRedirectBps_ > BPS_DENOMINATOR) revert InvalidBounds();

        tsiStressThreshold = tsiStressThreshold_;
        pflySpikeRedirectBps = pflySpikeRedirectBps_;
        emit SignalParamsUpdated(tsiStressThreshold_, pflySpikeRedirectBps_);
    }

    /// @notice Tune the TWAP floor and the swap-size cap together.
    ///
    /// @dev Together, deliberately. The two numbers are not independent: a swap of
    ///      `maxSwapBps` of the reserve moves price by roughly that fraction on constant
    ///      product and pays `POOL_FEE_BPS` on top, so unless that total fits inside the
    ///      floor's tolerance the leg can never fill. Separate setters would let a
    ///      well-intentioned operator raise the cap on Monday and discover on Friday that
    ///      every trading leg had been standing down since - the failure is silent, because
    ///      standing down is also what a healthy refusal looks like.
    ///
    ///      The bounds below are what governance cannot do:
    ///        - disable the floor (`0`), which reads as maximum strictness and is in fact a
    ///          permanent stand-down, since a real fill is always below the average;
    ///        - widen it past `MAX_TWAP_FLOOR_BPS`, which is what would let the sandwich
    ///          defence be removed without a code change;
    ///        - disable the swap cap (`0` is the uncapped sentinel in `_capChunkForSwaps`);
    ///        - set a cap whose own price impact does not fit inside the floor.
    function setTwapGuards(uint16 twapFloorBps_, uint16 maxSwapBps_)
        external
        onlyRole(PARAMETER_ROLE)
    {
        if (twapFloorBps_ == 0 || twapFloorBps_ > MAX_TWAP_FLOOR_BPS) revert InvalidBounds();
        if (maxSwapBps_ == 0 || maxSwapBps_ > MAX_SWAP_CAP_BPS) revert InvalidBounds();
        if (uint256(maxSwapBps_) + POOL_FEE_BPS >= twapFloorBps_) revert InvalidBounds();

        twapFloorBps = twapFloorBps_;
        maxSwapBps = maxSwapBps_;
        emit TwapGuardsUpdated(twapFloorBps_, maxSwapBps_);
    }
}
        

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

pragma solidity ^0.8.20;

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

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.26;

import {AccessControl} from "@openzeppelin/contracts/access/AccessControl.sol";
import {IPulseXPair} from "../interfaces/IProtocol.sol";

/// @title TwapOracle
/// @notice Time-weighted average price oracle over PulseX (Uniswap V2) cumulative prices.
/// @dev Bond pricing and router allocation both read TWAP, never spot. Spot is used
///      only as a sanity bound: if spot deviates from TWAP by more than
///      `maxDeviationBps`, consumers can reject the quote. That combination resists
///      both flash-loan manipulation (which moves spot, not a long TWAP) and stale
///      oracles (which `maxStaleness` rejects).
contract TwapOracle is AccessControl {
    bytes32 public constant UPDATER_ROLE = keccak256("UPDATER_ROLE");

    uint16 public constant BPS_DENOMINATOR = 10_000;

    struct Observation {
        uint256 price0Cumulative;
        uint256 price1Cumulative;
        uint32 timestamp;
        bool initialized;
    }

    /// @notice The newest observation for a pair. May be immature immediately after an
    ///         `update()`, in which case reads fall back to `previousObservations`.
    mapping(address => Observation) public observations;

    /// @notice The observation `update()` displaced. Always at least `minPeriod` older than
    ///         `observations[pair]`, because `update()` refuses to run any sooner.
    ///
    /// @dev THIS SLOT IS THE FIX. With one slot, `update()` reset the averaging window to
    ///      zero and the feed went dark for `minPeriod` - and since `update()`'s own rate
    ///      limit is also `minPeriod`, any caller could hold it dark indefinitely for the
    ///      price of one transaction per window.
    ///
    ///      Keeping the displaced observation means a fresh one never blanks the feed: it
    ///      queues behind a mature one. Availability then depends only on elapsed time,
    ///      which is the property `test/OracleAvailabilityInvariant.t.sol` pins.
    mapping(address => Observation) public previousObservations;

    /// @notice Minimum seconds between observations. Shorter windows are easier to manipulate.
    uint32 public minPeriod = 30 minutes;
    /// @notice An observation older than this is considered unusable.
    /// @notice Oldest observation `consult` will answer from.
    ///
    /// @dev WAS 24 HOURS, AND THAT IS UNUSABLE ONCE THE TWAP IS A TRADING FLOOR.
    ///
    ///      `consult` averages over the whole elapsed window, so a stale observation does
    ///      not merely risk being out of date - it produces a LONGER average, which lags
    ///      spot further in any trend. The router's floor budget is 2%, of which the
    ///      trade's own impact (1% cap) and the pool fee (0.29%) consume 1.29%, leaving
    ///      0.71% for the gap between spot and the average:
    ///
    ///        window   0.5%/h trend   1%/h    2%/h
    ///          30m        0.1%       0.2%    0.5%   <- inside budget
    ///           1h        0.2%       0.5%    1.0%
    ///           2h        0.5%       1.0%    2.0%
    ///          24h        6.0%      12.0%   24.0%   <- 3x the entire floor
    ///
    ///      Both directions hurt, differently. A falling market pushes spot below the
    ///      average and the legs stand down - safe, but the protocol stops buying exactly
    ///      when it is cheapest. A rising market leaves the floor BELOW spot by the lag,
    ///      and that gap is room a sandwicher can take while still clearing the floor.
    ///
    ///      Two hours is the backstop, not the operating point: with `update()` called
    ///      every `minPeriod` the window in use stays at 30-60 minutes, and this only
    ///      binds after three consecutive missed refreshes.
    uint32 public maxStaleness = 2 hours;
    /// @notice Maximum tolerated spot-vs-TWAP divergence before a quote is unsafe.
    uint16 public maxDeviationBps = 1_000; // 10%

    event ObservationUpdated(address indexed pair, uint256 price0Cumulative, uint256 price1Cumulative, uint32 timestamp);
    event OracleParamsUpdated(uint32 minPeriod, uint32 maxStaleness, uint16 maxDeviationBps);

    error PairNotInitialized(address pair);
    error PeriodNotElapsed(address pair, uint32 elapsed, uint32 required);
    error ObservationStale(address pair, uint32 age, uint32 maxAge);
    error NoLiquidity(address pair);
    error TokenNotInPair(address pair, address token);
    error InvalidParams();

    constructor(address admin) {
        if (admin == address(0)) revert InvalidParams();
        _grantRole(DEFAULT_ADMIN_ROLE, admin);
    }

    // --- Observation maintenance --------------------------------------------

    /// @notice Seed the first observation for a pair. Callable once per pair.
    function initialize(address pair) external {
        Observation storage obs = observations[pair];
        if (obs.initialized) return;

        (uint256 price0Cumulative, uint256 price1Cumulative, uint32 timestamp) = currentCumulativePrices(pair);
        obs.price0Cumulative = price0Cumulative;
        obs.price1Cumulative = price1Cumulative;
        obs.timestamp = timestamp;
        obs.initialized = true;

        emit ObservationUpdated(pair, price0Cumulative, price1Cumulative, timestamp);
    }

    /// @notice Roll the observation forward. Permissionless: anyone may keep the
    ///         oracle fresh, but `minPeriod` bounds how often it can be moved.
    function update(address pair) external {
        Observation storage obs = observations[pair];
        if (!obs.initialized) revert PairNotInitialized(pair);

        (uint256 price0Cumulative, uint256 price1Cumulative, uint32 timestamp) = currentCumulativePrices(pair);
        uint32 elapsed;
        unchecked {
            elapsed = timestamp - obs.timestamp; // wraps correctly on uint32 overflow
        }
        if (elapsed < minPeriod) revert PeriodNotElapsed(pair, elapsed, minPeriod);

        // Rotate, do not overwrite. The displaced observation is what keeps the feed
        // answering during the `minPeriod` the new one needs to mature.
        previousObservations[pair] = obs;

        obs.price0Cumulative = price0Cumulative;
        obs.price1Cumulative = price1Cumulative;
        obs.timestamp = timestamp;

        emit ObservationUpdated(pair, price0Cumulative, price1Cumulative, timestamp);
    }

    /// @notice The newest observation that has matured, which is what every read uses.
    ///
    /// @dev Prefers `observations[pair]` once it is at least `minPeriod` old, because a
    ///      more recent window is a tighter average. Falls back to the displaced one while
    ///      the newest is still maturing.
    ///
    ///      The fallback is guaranteed usable rather than merely likely: `update()` reverts
    ///      unless `minPeriod` has elapsed, so anything it displaces is by construction at
    ///      least that old. There is no state in which both slots are immature except
    ///      during the first `minPeriod` after `initialize()`, which is honest - nothing
    ///      has been observed for long enough to average yet.
    function _readable(address pair)
        private
        view
        returns (Observation storage obs, uint32 elapsed)
    {
        (,, uint32 timestamp) = currentCumulativePrices(pair);

        obs = observations[pair];
        unchecked {
            elapsed = timestamp - obs.timestamp;
        }
        if (elapsed >= minPeriod) return (obs, elapsed);

        Observation storage prev = previousObservations[pair];
        if (prev.initialized) {
            uint32 prevElapsed;
            unchecked {
                prevElapsed = timestamp - prev.timestamp;
            }
            if (prevElapsed >= minPeriod) return (prev, prevElapsed);
        }

        // Neither has matured. Return the newest so the caller's own floor/staleness
        // checks produce the accurate error rather than a misleading one.
        return (obs, elapsed);
    }

    // --- Quotes -------------------------------------------------------------

    /// @notice TWAP quote: how much of the other token `amountIn` of `tokenIn` is worth.
    /// @dev Reverts if the observation is missing or stale.
    function consult(address pair, address tokenIn, uint256 amountIn) public view returns (uint256 amountOut) {
        if (!observations[pair].initialized) revert PairNotInitialized(pair);

        (uint256 price0Cumulative, uint256 price1Cumulative,) = currentCumulativePrices(pair);

        // The newest MATURE observation, not simply the newest. See `_readable`.
        (Observation storage obs, uint32 elapsed) = _readable(pair);
        // The averaging window must be at least minPeriod, not merely non-zero.
        //
        // A TWAP is only manipulation-resistant in proportion to the time it averages
        // over. An earlier revision rejected only elapsed == 0, so a one-second-old
        // observation produced a one-second average - spot price wearing a TWAP label.
        // Worse, isQuoteSafe compares spot against that same near-spot average, so the
        // deviation guard endorsed the manipulated number instead of rejecting it.
        //
        // This is NOT specific to initialize(). The exposure recurred after every
        // update(), which is permissionless, so any caller could reset the window and
        // read a manipulated price one block later. Enforcing the floor here fixes both
        // at the read side, where the actual decision is made.
        if (elapsed < minPeriod) revert PeriodNotElapsed(pair, elapsed, minPeriod);
        if (elapsed > maxStaleness) revert ObservationStale(pair, elapsed, maxStaleness);

        address token0 = IPulseXPair(pair).token0();
        address token1 = IPulseXPair(pair).token1();

        uint256 priceAverage;
        if (tokenIn == token0) {
            unchecked {
                priceAverage = (price0Cumulative - obs.price0Cumulative) / elapsed;
            }
        } else if (tokenIn == token1) {
            unchecked {
                priceAverage = (price1Cumulative - obs.price1Cumulative) / elapsed;
            }
        } else {
            revert TokenNotInPair(pair, tokenIn);
        }

        // priceAverage is UQ112x112; shift back down after multiplying.
        amountOut = (priceAverage * amountIn) >> 112;
    }

    /// @notice Current spot quote straight from reserves, for the deviation guard only.
    function spotQuote(address pair, address tokenIn, uint256 amountIn) public view returns (uint256) {
        (uint112 reserve0, uint112 reserve1,) = IPulseXPair(pair).getReserves();
        if (reserve0 == 0 || reserve1 == 0) revert NoLiquidity(pair);

        address token0 = IPulseXPair(pair).token0();
        address token1 = IPulseXPair(pair).token1();

        if (tokenIn == token0) {
            return (amountIn * reserve1) / reserve0;
        } else if (tokenIn == token1) {
            return (amountIn * reserve0) / reserve1;
        }
        revert TokenNotInPair(pair, tokenIn);
    }

    /// @notice True when spot sits within `maxDeviationBps` of the TWAP.
    /// @dev Consumers should treat `false` as "do not trade right now".
    function isQuoteSafe(address pair, address tokenIn, uint256 amountIn) external view returns (bool) {
        uint256 twap = consult(pair, tokenIn, amountIn);
        if (twap == 0) return false;

        uint256 spot = spotQuote(pair, tokenIn, amountIn);
        uint256 diff = spot > twap ? spot - twap : twap - spot;
        return (diff * BPS_DENOMINATOR) / twap <= maxDeviationBps;
    }

    /// @notice Seconds until the observation `consult` reads is `minPeriod` old, or 0 once
    ///         it is. Reverts only if the pair was never initialized.
    ///
    ///         0 does not mean `consult` answers - `isQuotable` says that. Past
    ///         `maxStaleness` this reads 0 too: while nobody refreshes, and for up to
    ///         `minPeriod` after a refresh that came too late, when the observation it
    ///         displaced is the readable one. In the second case the wait is what remains
    ///         of `minPeriod` on `observations(pair)`; in the first, only `update()` starts it.
    /// @dev A quote refusal during an immature window is a safety behaviour, but it
    ///      reaches a user as a revert, which is indistinguishable from a broken
    ///      contract. This lets a caller render "try again in N seconds" instead, so
    ///      nobody is tempted to "fix" the safety behaviour later. Read it together with
    ///      `isQuotable`, as `scripts/lib/oracle-state.js` does.
    function secondsUntilQuotable(address pair) external view returns (uint256) {
        if (!observations[pair].initialized) revert PairNotInitialized(pair);

        // Must agree with `consult`, which reads the newest MATURE observation. Reading
        // the raw newest slot here would report a wait that consult does not actually
        // impose - the reporting bug that hides the fix rather than the defect.
        (, uint32 elapsed) = _readable(pair);
        return elapsed >= minPeriod ? 0 : minPeriod - elapsed;
    }

    /// @notice True when `consult` would answer for this pair right now.
    function isQuotable(address pair) external view returns (bool) {
        if (!observations[pair].initialized) return false;

        // Same source of truth as `consult`. These two disagreeing is how a monitor
        // reports a healthy feed that cannot answer, or a dark feed that can.
        (, uint32 elapsed) = _readable(pair);
        return elapsed >= minPeriod && elapsed <= maxStaleness;
    }

    // --- Cumulative price reader --------------------------------------------

    /// @notice Cumulative prices brought forward to `block.timestamp`.
    /// @dev Mirrors UniswapV2OracleLibrary: the pair only writes cumulatives on sync,
    ///      so the elapsed-since-sync portion must be added in by the reader.
    function currentCumulativePrices(address pair)
        public
        view
        returns (uint256 price0Cumulative, uint256 price1Cumulative, uint32 blockTimestamp)
    {
        blockTimestamp = uint32(block.timestamp % 2 ** 32);
        price0Cumulative = IPulseXPair(pair).price0CumulativeLast();
        price1Cumulative = IPulseXPair(pair).price1CumulativeLast();

        (uint112 reserve0, uint112 reserve1, uint32 blockTimestampLast) = IPulseXPair(pair).getReserves();
        if (reserve0 == 0 || reserve1 == 0) revert NoLiquidity(pair);

        if (blockTimestampLast != blockTimestamp) {
            uint32 timeElapsed;
            unchecked {
                timeElapsed = blockTimestamp - blockTimestampLast;
                price0Cumulative += uint256(_encodeDiv(reserve1, reserve0)) * timeElapsed;
                price1Cumulative += uint256(_encodeDiv(reserve0, reserve1)) * timeElapsed;
            }
        }
    }

    /// @dev UQ112x112 encode-then-divide: (numerator << 112) / denominator.
    function _encodeDiv(uint112 numerator, uint112 denominator) private pure returns (uint224) {
        return uint224((uint224(numerator) << 112) / denominator);
    }

    // --- Governance ---------------------------------------------------------

    function setParams(uint32 minPeriod_, uint32 maxStaleness_, uint16 maxDeviationBps_)
        external
        onlyRole(DEFAULT_ADMIN_ROLE)
    {
        if (minPeriod_ == 0 || maxStaleness_ < minPeriod_ || maxDeviationBps_ > BPS_DENOMINATOR) {
            revert InvalidParams();
        }
        minPeriod = minPeriod_;
        maxStaleness = maxStaleness_;
        maxDeviationBps = maxDeviationBps_;
        emit OracleParamsUpdated(minPeriod_, maxStaleness_, maxDeviationBps_);
    }
}
          

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

pragma solidity ^0.8.20;

import {IAccessControl} from "./IAccessControl.sol";
import {Context} from "../utils/Context.sol";
import {ERC165} from "../utils/introspection/ERC165.sol";

/**
 * @dev Contract module that allows children to implement role-based access
 * control mechanisms. This is a lightweight version that doesn't allow enumerating role
 * members except through off-chain means by accessing the contract event logs. Some
 * applications may benefit from on-chain enumerability, for those cases see
 * {AccessControlEnumerable}.
 *
 * Roles are referred to by their `bytes32` identifier. These should be exposed
 * in the external API and be unique. The best way to achieve this is by
 * using `public constant` hash digests:
 *
 * ```solidity
 * bytes32 public constant MY_ROLE = keccak256("MY_ROLE");
 * ```
 *
 * Roles can be used to represent a set of permissions. To restrict access to a
 * function call, use {hasRole}:
 *
 * ```solidity
 * function foo() public {
 *     require(hasRole(MY_ROLE, msg.sender));
 *     ...
 * }
 * ```
 *
 * Roles can be granted and revoked dynamically via the {grantRole} and
 * {revokeRole} functions. Each role has an associated admin role, and only
 * accounts that have a role's admin role can call {grantRole} and {revokeRole}.
 *
 * By default, the admin role for all roles is `DEFAULT_ADMIN_ROLE`, which means
 * that only accounts with this role will be able to grant or revoke other
 * roles. More complex role relationships can be created by using
 * {_setRoleAdmin}.
 *
 * WARNING: The `DEFAULT_ADMIN_ROLE` is also its own admin: it has permission to
 * grant and revoke this role. Extra precautions should be taken to secure
 * accounts that have been granted it. We recommend using {AccessControlDefaultAdminRules}
 * to enforce additional security measures for this role.
 */
abstract contract AccessControl is Context, IAccessControl, ERC165 {
    struct RoleData {
        mapping(address account => bool) hasRole;
        bytes32 adminRole;
    }

    mapping(bytes32 role => RoleData) private _roles;

    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;

    /**
     * @dev Modifier that checks that an account has a specific role. Reverts
     * with an {AccessControlUnauthorizedAccount} error including the required role.
     */
    modifier onlyRole(bytes32 role) {
        _checkRole(role);
        _;
    }

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

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) public view virtual returns (bool) {
        return _roles[role].hasRole[account];
    }

    /**
     * @dev Reverts with an {AccessControlUnauthorizedAccount} error if `_msgSender()`
     * is missing `role`. Overriding this function changes the behavior of the {onlyRole} modifier.
     */
    function _checkRole(bytes32 role) internal view virtual {
        _checkRole(role, _msgSender());
    }

    /**
     * @dev Reverts with an {AccessControlUnauthorizedAccount} error if `account`
     * is missing `role`.
     */
    function _checkRole(bytes32 role, address account) internal view virtual {
        if (!hasRole(role, account)) {
            revert AccessControlUnauthorizedAccount(account, role);
        }
    }

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) public view virtual returns (bytes32) {
        return _roles[role].adminRole;
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     *
     * May emit a {RoleGranted} event.
     */
    function grantRole(bytes32 role, address account) public virtual onlyRole(getRoleAdmin(role)) {
        _grantRole(role, account);
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     *
     * May emit a {RoleRevoked} event.
     */
    function revokeRole(bytes32 role, address account) public virtual onlyRole(getRoleAdmin(role)) {
        _revokeRole(role, account);
    }

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been revoked `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `callerConfirmation`.
     *
     * May emit a {RoleRevoked} event.
     */
    function renounceRole(bytes32 role, address callerConfirmation) public virtual {
        if (callerConfirmation != _msgSender()) {
            revert AccessControlBadConfirmation();
        }

        _revokeRole(role, callerConfirmation);
    }

    /**
     * @dev Sets `adminRole` as ``role``'s admin role.
     *
     * Emits a {RoleAdminChanged} event.
     */
    function _setRoleAdmin(bytes32 role, bytes32 adminRole) internal virtual {
        bytes32 previousAdminRole = getRoleAdmin(role);
        _roles[role].adminRole = adminRole;
        emit RoleAdminChanged(role, previousAdminRole, adminRole);
    }

    /**
     * @dev Attempts to grant `role` to `account` and returns a boolean indicating if `role` was granted.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleGranted} event.
     */
    function _grantRole(bytes32 role, address account) internal virtual returns (bool) {
        if (!hasRole(role, account)) {
            _roles[role].hasRole[account] = true;
            emit RoleGranted(role, account, _msgSender());
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Attempts to revoke `role` to `account` and returns a boolean indicating if `role` was revoked.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleRevoked} event.
     */
    function _revokeRole(bytes32 role, address account) internal virtual returns (bool) {
        if (hasRole(role, account)) {
            _roles[role].hasRole[account] = false;
            emit RoleRevoked(role, account, _msgSender());
            return true;
        } else {
            return false;
        }
    }
}
          

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

pragma solidity ^0.8.20;

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

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

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

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

pragma solidity ^0.8.20;

/**
 * @dev Collection of common custom errors used in multiple contracts
 *
 * IMPORTANT: Backwards compatibility is not guaranteed in future versions of the library.
 * It is recommended to avoid relying on the error API for critical functionality.
 *
 * _Available since v5.1._
 */
library Errors {
    /**
     * @dev The ETH balance of the account is not enough to perform the operation.
     */
    error InsufficientBalance(uint256 balance, uint256 needed);

    /**
     * @dev A call to an address target failed. The target may have reverted.
     */
    error FailedCall();

    /**
     * @dev The deployment failed.
     */
    error FailedDeployment();

    /**
     * @dev A necessary precompile is missing.
     */
    error MissingPrecompile(address);
}
          

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

pragma solidity ^0.8.20;

/**
 * @dev External interface of AccessControl declared to support ERC-165 detection.
 */
interface IAccessControl {
    /**
     * @dev The `account` is missing a role.
     */
    error AccessControlUnauthorizedAccount(address account, bytes32 neededRole);

    /**
     * @dev The caller of a function is not the expected one.
     *
     * NOTE: Don't confuse with {AccessControlUnauthorizedAccount}.
     */
    error AccessControlBadConfirmation();

    /**
     * @dev Emitted when `newAdminRole` is set as ``role``'s admin role, replacing `previousAdminRole`
     *
     * `DEFAULT_ADMIN_ROLE` is the starting admin for all roles, despite
     * {RoleAdminChanged} not being emitted signaling this.
     */
    event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);

    /**
     * @dev Emitted when `account` is granted `role`.
     *
     * `sender` is the account that originated the contract call. This account bears the admin role (for the granted role).
     * Expected in cases where the role was granted using the internal {AccessControl-_grantRole}.
     */
    event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Emitted when `account` is revoked `role`.
     *
     * `sender` is the account that originated the contract call:
     *   - if using `revokeRole`, it is the admin role bearer
     *   - if using `renounceRole`, it is the role bearer (i.e. `account`)
     */
    event RoleRevoked(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) external view returns (bool);

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {AccessControl-_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) external view returns (bytes32);

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been granted `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `callerConfirmation`.
     */
    function renounceRole(bytes32 role, address callerConfirmation) external;
}
          

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

pragma solidity ^0.8.20;

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

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev There's no code at `target` (it is not a contract).
     */
    error AddressEmptyCode(address target);

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.8.20/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        if (address(this).balance < amount) {
            revert Errors.InsufficientBalance(address(this).balance, amount);
        }

        (bool success, ) = recipient.call{value: amount}("");
        if (!success) {
            revert Errors.FailedCall();
        }
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason or custom error, it is bubbled
     * up by this function (like regular Solidity function calls). However, if
     * the call reverted with no returned reason, this function reverts with a
     * {Errors.FailedCall} error.
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        if (address(this).balance < value) {
            revert Errors.InsufficientBalance(address(this).balance, value);
        }
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and reverts if the target
     * was not a contract or bubbling up the revert reason (falling back to {Errors.FailedCall}) in case
     * of an unsuccessful call.
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata
    ) internal view returns (bytes memory) {
        if (!success) {
            _revert(returndata);
        } else {
            // only check if target is a contract if the call was successful and the return data is empty
            // otherwise we already know that it was a contract
            if (returndata.length == 0 && target.code.length == 0) {
                revert AddressEmptyCode(target);
            }
            return returndata;
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and reverts if it wasn't, either by bubbling the
     * revert reason or with a default {Errors.FailedCall} error.
     */
    function verifyCallResult(bool success, bytes memory returndata) internal pure returns (bytes memory) {
        if (!success) {
            _revert(returndata);
        } else {
            return returndata;
        }
    }

    /**
     * @dev Reverts with returndata if present. Otherwise reverts with {Errors.FailedCall}.
     */
    function _revert(bytes memory returndata) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            assembly ("memory-safe") {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert Errors.FailedCall();
        }
    }
}
          

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

pragma solidity ^0.8.20;

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

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Floor, // Toward negative infinity
        Ceil, // Toward positive infinity
        Trunc, // Toward zero
        Expand // Away from zero
    }

    /**
     * @dev Returns the addition of two unsigned integers, with an success flag (no overflow).
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a + b;
            if (c < a) return (false, 0);
            return (true, c);
        }
    }

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

    /**
     * @dev Returns the multiplication of two unsigned integers, with an success flag (no overflow).
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
            // benefit is lost if 'b' is also tested.
            // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
            if (a == 0) return (true, 0);
            uint256 c = a * b;
            if (c / a != b) return (false, 0);
            return (true, c);
        }
    }

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

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

    /**
     * @dev 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 {
            // 512-bit multiply [prod1 prod0] = 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 = prod1 * 2²⁵⁶ + prod0.
            uint256 prod0 = x * y; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return prod0 / denominator;
            }

            // Make sure the result is less than 2²⁵⁶. Also prevents denominator == 0.
            if (denominator <= prod1) {
                Panic.panic(ternary(denominator == 0, Panic.DIVISION_BY_ZERO, Panic.UNDER_OVERFLOW));
            }

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

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

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

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

            uint256 twos = denominator & (0 - denominator);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

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

                // Flip twos such that it is 2²⁵⁶ / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2²⁵⁶. Now that denominator is an odd number, it has an inverse modulo 2²⁵⁶ such
            // that denominator * inv ≡ 1 mod 2²⁵⁶. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv ≡ 1 mod 2⁴.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also
            // works in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2⁸
            inverse *= 2 - denominator * inverse; // inverse mod 2¹⁶
            inverse *= 2 - denominator * inverse; // inverse mod 2³²
            inverse *= 2 - denominator * inverse; // inverse mod 2⁶⁴
            inverse *= 2 - denominator * inverse; // inverse mod 2¹²⁸
            inverse *= 2 - denominator * inverse; // inverse mod 2²⁵⁶

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2²⁵⁶. Since the preconditions guarantee that the outcome is
            // less than 2²⁵⁶, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @dev Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        return mulDiv(x, y, denominator) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, denominator) > 0);
    }

    /**
     * @dev Calculate the modular multiplicative inverse of a number in Z/nZ.
     *
     * If n is a prime, then Z/nZ is a field. In that case all elements are inversible, 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 value) internal pure returns (uint256) {
        uint256 result = 0;
        uint256 exp;
        unchecked {
            exp = 128 * SafeCast.toUint(value > (1 << 128) - 1);
            value >>= exp;
            result += exp;

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

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

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

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

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

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

            result += SafeCast.toUint(value > 1);
        }
        return result;
    }

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

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

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

    /**
     * @dev Return the log in base 256 of a positive value rounded towards zero.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        uint256 isGt;
        unchecked {
            isGt = SafeCast.toUint(value > (1 << 128) - 1);
            value >>= isGt * 128;
            result += isGt * 16;

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

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

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

            result += SafeCast.toUint(value > (1 << 8) - 1);
        }
        return result;
    }

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + SafeCast.toUint(unsignedRoundsUp(rounding) && 1 << (result << 3) < value);
        }
    }

    /**
     * @dev Returns whether a provided rounding mode is considered rounding up for unsigned integers.
     */
    function unsignedRoundsUp(Rounding rounding) internal pure returns (bool) {
        return uint8(rounding) % 2 == 1;
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (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 v5.1.0) (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) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.20;

import {IERC20} from "../IERC20.sol";
import {IERC1363} from "../../../interfaces/IERC1363.sol";
import {Address} from "../../../utils/Address.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 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 Performs an {ERC1363} transferAndCall, with a fallback to the simple {ERC20} transfer if the target has no
     * code. This can be used to implement an {ERC721}-like safe transfer that rely on {ERC1363} checks when
     * targeting contracts.
     *
     * Reverts if the returned value is other than `true`.
     */
    function transferAndCallRelaxed(IERC1363 token, address to, uint256 value, bytes memory data) internal {
        if (to.code.length == 0) {
            safeTransfer(token, to, value);
        } else if (!token.transferAndCall(to, value, data)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Performs an {ERC1363} transferFromAndCall, with a fallback to the simple {ERC20} transferFrom if the target
     * has no code. This can be used to implement an {ERC721}-like safe transfer that rely on {ERC1363} checks when
     * targeting contracts.
     *
     * Reverts if the returned value is other than `true`.
     */
    function transferFromAndCallRelaxed(
        IERC1363 token,
        address from,
        address to,
        uint256 value,
        bytes memory data
    ) internal {
        if (to.code.length == 0) {
            safeTransferFrom(token, from, to, value);
        } else if (!token.transferFromAndCall(from, to, value, data)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Performs an {ERC1363} approveAndCall, with a fallback to the simple {ERC20} approve if the target has no
     * code. This can be used to implement an {ERC721}-like safe transfer that rely on {ERC1363} checks when
     * targeting contracts.
     *
     * NOTE: When the recipient address (`to`) has no code (i.e. is an EOA), this function behaves as {forceApprove}.
     * Opposedly, when the recipient address (`to`) has code, this function only attempts to call {ERC1363-approveAndCall}
     * once without retrying, and relies on the returned value to be true.
     *
     * Reverts if the returned value is other than `true`.
     */
    function approveAndCallRelaxed(IERC1363 token, address to, uint256 value, bytes memory data) internal {
        if (to.code.length == 0) {
            forceApprove(token, to, value);
        } else if (!token.approveAndCall(to, value, data)) {
            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 {_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 v5.1.0) (utils/introspection/ERC165.sol)

pragma solidity ^0.8.20;

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

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

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

pragma solidity ^0.8.20;

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

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.26;

/// @notice Minimal PulseX (Uniswap V2) surface used across the protocol.
interface IPulseXFactory {
    function getPair(address tokenA, address tokenB) external view returns (address pair);
    function createPair(address tokenA, address tokenB) external returns (address pair);
}

interface IPulseXPair {
    function token0() external view returns (address);
    function token1() external view returns (address);
    function getReserves() external view returns (uint112 reserve0, uint112 reserve1, uint32 blockTimestampLast);
    function price0CumulativeLast() external view returns (uint256);
    function price1CumulativeLast() external view returns (uint256);
    function totalSupply() external view returns (uint256);
    /// @dev A V2 pair is itself the LP ERC-20, so holdings are read from the pair.
    function balanceOf(address account) external view returns (uint256);
}

interface IPulseXRouter {
    function factory() external view returns (address);
    function swapExactTokensForTokensSupportingFeeOnTransferTokens(
        uint256 amountIn,
        uint256 amountOutMin,
        address[] calldata path,
        address to,
        uint256 deadline
    ) external;
    function addLiquidity(
        address tokenA,
        address tokenB,
        uint256 amountADesired,
        uint256 amountBDesired,
        uint256 amountAMin,
        uint256 amountBMin,
        address to,
        uint256 deadline
    ) external returns (uint256 amountA, uint256 amountB, uint256 liquidity);
    function getAmountsOut(uint256 amountIn, address[] calldata path) external view returns (uint256[] memory amounts);
}

/// @notice Burnable subset of PBURN used by the router and the credit ledger.
interface IBurnable {
    function burn(uint256 amount) external;
    function totalSupply() external view returns (uint256);
}

/// @notice Credit accrual hook. Only protocol contracts may call the granting functions.
interface IBurnCreditLedger {
    function creditsOf(address account) external view returns (uint256);
    function feeDiscountBps(address account) external view returns (uint16);
    function grantForBurn(address account, uint256 burnedAmount) external;
    function grantForBond(address account, uint256 lpValue) external;
    function grantForGovernance(address account, uint256 weight) external;
}

/// @notice Read-only composite treasury health score consumed by the router.
interface ITSI {
    /// @return score Composite score in basis points (0..10000).
    function score() external view returns (uint256);
    function components()
        external
        view
        returns (uint256 treasuryValue, uint256 polValue, uint256 burnRate, uint256 liquidityDepth, uint256 supplyTrend);
}

/// @notice Treasury deposit surface used by the router and bonding vault.
interface ITreasury {
    function recordDeposit(address asset, uint256 amount) external;
    function recordLpDeposit(address pair, uint256 amount) external;
}

/// @notice Epoch parameter presets consumed by the router.
interface IEpoch {
    enum Phase {
        Bootstrapping,
        AcceleratedBurn,
        GovernanceAndGrowth,
        Sustainability
    }

    function currentPhase() external view returns (Phase);
    function allocation() external view returns (uint16 pburnBurnBps, uint16 pflyBurnBps, uint16 polBps, uint16 treasuryBps);
}
          

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

pragma solidity ^0.8.20;

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If EIP-1153 (transient storage) is available on the chain you're deploying at,
 * consider using {ReentrancyGuardTransient} instead.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuard {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant NOT_ENTERED = 1;
    uint256 private constant ENTERED = 2;

    uint256 private _status;

    /**
     * @dev Unauthorized reentrant call.
     */
    error ReentrancyGuardReentrantCall();

    constructor() {
        _status = NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and making it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        _nonReentrantBefore();
        _;
        _nonReentrantAfter();
    }

    function _nonReentrantBefore() private {
        // On the first call to nonReentrant, _status will be NOT_ENTERED
        if (_status == ENTERED) {
            revert ReentrancyGuardReentrantCall();
        }

        // Any calls to nonReentrant after this point will fail
        _status = ENTERED;
    }

    function _nonReentrantAfter() private {
        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = NOT_ENTERED;
    }

    /**
     * @dev Returns true if the reentrancy guard is currently set to "entered", which indicates there is a
     * `nonReentrant` function in the call stack.
     */
    function _reentrancyGuardEntered() internal view returns (bool) {
        return _status == ENTERED;
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (interfaces/IERC1363.sol)

pragma solidity ^0.8.20;

import {IERC20} from "./IERC20.sol";
import {IERC165} from "./IERC165.sol";

/**
 * @title IERC1363
 * @dev Interface of the ERC-1363 standard as defined in the https://eips.ethereum.org/EIPS/eip-1363[ERC-1363].
 *
 * Defines an extension interface for ERC-20 tokens that supports executing code on a recipient contract
 * after `transfer` or `transferFrom`, or code on a spender contract after `approve`, in a single transaction.
 */
interface IERC1363 is IERC20, IERC165 {
    /*
     * Note: the ERC-165 identifier for this interface is 0xb0202a11.
     * 0xb0202a11 ===
     *   bytes4(keccak256('transferAndCall(address,uint256)')) ^
     *   bytes4(keccak256('transferAndCall(address,uint256,bytes)')) ^
     *   bytes4(keccak256('transferFromAndCall(address,address,uint256)')) ^
     *   bytes4(keccak256('transferFromAndCall(address,address,uint256,bytes)')) ^
     *   bytes4(keccak256('approveAndCall(address,uint256)')) ^
     *   bytes4(keccak256('approveAndCall(address,uint256,bytes)'))
     */

    /**
     * @dev Moves a `value` amount of tokens from the caller's account to `to`
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferAndCall(address to, uint256 value) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from the caller's account to `to`
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @param data Additional data with no specified format, sent in call to `to`.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferAndCall(address to, uint256 value, bytes calldata data) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to` using the allowance mechanism
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param from The address which you want to send tokens from.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferFromAndCall(address from, address to, uint256 value) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to` using the allowance mechanism
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param from The address which you want to send tokens from.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @param data Additional data with no specified format, sent in call to `to`.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferFromAndCall(address from, address to, uint256 value, bytes calldata data) external returns (bool);

    /**
     * @dev Sets a `value` amount of tokens as the allowance of `spender` over the
     * caller's tokens and then calls {IERC1363Spender-onApprovalReceived} on `spender`.
     * @param spender The address which will spend the funds.
     * @param value The amount of tokens to be spent.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function approveAndCall(address spender, uint256 value) external returns (bool);

    /**
     * @dev Sets a `value` amount of tokens as the allowance of `spender` over the
     * caller's tokens and then calls {IERC1363Spender-onApprovalReceived} on `spender`.
     * @param spender The address which will spend the funds.
     * @param value The amount of tokens to be spent.
     * @param data Additional data with no specified format, sent in call to `spender`.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function approveAndCall(address spender, uint256 value, bytes calldata data) 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/introspection/IERC165.sol)

pragma solidity ^0.8.20;

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