//SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.19;

import { ERC20 } from 'solady/tokens/ERC20.sol';
import { SafeTransferLib } from 'solady/utils/SafeTransferLib.sol';
import { FixedPointMathLib } from "solady/utils/FixedPointMathLib.sol";

import { ICatalystChainInterface } from "./interfaces/ICatalystChainInterface.sol";
import { WADWAD } from "./utils/MathConstants.sol";
import { CatalystVaultCommon } from "./CatalystVaultCommon.sol";
import { IntegralsAmplified } from "./IntegralsAmplified.sol";
import { ICatalystReceiver} from "./interfaces/IOnCatalyst.sol";
import "./ICatalystV1Vault.sol";

/**
 * @title Catalyst: Fixed rate cross-chain swap vault.
 * @author Cata Labs Inc.
 * @notice Catalyst multi-chain vault using the asset specific
 * pricing curve: 1/w^\theta (1 - \theta) where \theta is 
 * the vault amplification and w is the vault asset balance.
 *
 * The following contract supports between 1 and 3 assets for
 * atomic swaps. To increase the number of tokens supported,
 * change MAX_ASSETS to the desired maximum token amount.
 * This constant is set in "CatalystVaultCommon.sol"
 *
 * This vault implements the ERC20 specification, such that the
 * contract will be its own vault token.
 * @dev This contract is deployed inactive: It cannot be used as a
 * vault as is. To use it, a proxy contract duplicating the
 * logic of this contract needs to be deployed. In Vyper, this
 * can be done through (vy >= 0.3.4) create_minimal_proxy_to.
 * In Solidity, this can be done through OZ clones: Clones.clone(...)
 * After deployment of the proxy, call setup(...) AND initializeSwapCurves(...).
 * This will initialize the vault and prepare it for cross-chain transactions.
 * However, only the Catalyst factory is allowed to perform these functions.
 * It is important that both setup(...) AND initializeSwapCurves(...) are called
 * in the same transaciton, as otherwise the vault is not fully finalised and
 * may be configured incorrectly by a third-party.
 *
 * If connected to a supported cross-chain interface, call
 * setConnection to connect the vault with vaults on other chains.
 *
 * Finally, call finishSetup to give up the creator's control over the vault. 
 * !If finishSetup is not called, the vault can be drained by the creator!
 */
contract CatalystVaultAmplified is CatalystVaultCommon, IntegralsAmplified {
    //--- Storage ---//
    
    /** 
     * @notice Adjustment used to remove a certain escrow amount from the balance * computation
     */
    mapping(address => uint256) public _underwriteEscrowMatchBalance0;

    //--- ERRORS ---//
    // Errors are defined in interfaces/ICatalystV1VaultErrors.sol

    //--- Config ---//

    /** @notice Minimum time parameter adjustments can be made over. */
    uint256 constant MIN_ADJUSTMENT_TIME = 7 days;

    /**
     * @dev  When the swap is a very small size of the vault, the
     * swaps returns slightly more. To counteract this, an additional 
     * fee slightly larger than the error is added. The below 
     * constants determines when this fee is added and the size.
     */
    uint256 constant SMALL_SWAP_RATIO = 1e12;
    uint256 constant SMALL_SWAP_RETURN = 95e16;

    // For other config options, see CatalystVaultCommon.sol

    //-- Variables --//
    int64 public _oneMinusAmp;
    int64 public _targetAmplification;
 
    /**
     * @dev To keep track of pool ownership, the vault needs to keep track of
     * the local unit balance. That is, do other vaults own or owe assets to this vault?
     */
    int256 public _unitTracker;

    constructor(address factory_, address mathlib_) payable CatalystVaultCommon(factory_, mathlib_) {}

    /**
     * @notice Configures an empty vault.
     * @dev The initial token amounts should have been sent to the vault before setup is called.
     * Since someone can call setup can claim the initial tokens, this needs to be
     * done atomically!
     *
     * If 0 of a token in assets is provided, the setup reverts.
     * @param assets A list of token addresses to be associated with the vault.
     * @param weights Weights brings the price into a true 1:1 swap. That is:
     * i_t \cdot W_i = j_t \cdot W_j \forall i, j when P_i(i_t) = P_j(j_t).
     * in other words, weights are used to compensate for the difference in decimals. (or non 1:1.)
     * @param amp Amplification factor. Should be < 10**18.
     * @param depositor The address to mint tokens to.
     */
    function initializeSwapCurves(
        address[] calldata assets,
        uint256[] calldata weights,
        uint64 amp,
        address depositor
    ) external override {
        // May only be invoked by the FACTORY. The factory only invokes this function for proxy contracts.
        require(msg.sender == FACTORY); // dev: swap curves may only be initialized once by the factory
        require(_tokenIndexing[0] == address(0)); // dev: swap curves may only be initialized once by the factory
        // Check that the amplification is correct.
        require(amp < FixedPointMathLib.WAD);  // dev: amplification not set correctly.
        // Note there is no need to check whether assets.length/weights.length are valid, as invalid arguments
        // will either cause the function to fail (e.g. if assets.length > MAX_ASSETS the assignment
        // to initialBalances[it] will fail) or will cause the vault to get initialized with an undesired state
        // (and the vault shouldn't be used by anyone until its configuration has been finalised). 
        // In any case, the factory does check for valid assets/weights arguments to prevent erroneous configurations.
        // Note Since assets.len != 0 is not checked, the initial depositor may invoke this function many times, resulting
        // in vault tokens being minted for the 'depositor' every time. This is not an issue, since 'INITIAL_MINT_AMOUNT' is
        // an arbitrary number; the value of the vault tokens is determined by the ratio of the vault asset balances and vault
        // tokens supply once setup has finalized. Furthermore, the vault should not be used until setup has finished and the
        // vault configuration has been verified.
        
        unchecked {
            // Amplification is stored as 1 - amp since most equations uses amp this way.
            _oneMinusAmp = int64(uint64(FixedPointMathLib.WAD - amp));
            _targetAmplification = int64(uint64(FixedPointMathLib.WAD - amp));
        }   

        // Compute the security limit.
        uint256[] memory initialBalances = new uint256[](MAX_ASSETS);
        uint256 maxUnitCapacity = 0;
        uint assetLength = assets.length;
        for (uint256 it; it < assetLength;) {

            address tokenAddress = assets[it];
            _tokenIndexing[it] = tokenAddress;

            uint256 weight = weights[it];
            require(weight != 0);  // dev: invalid 0-valued weight provided
            _weight[tokenAddress] = weight;

            // The contract expects the tokens to have been sent to it before setup is
            // called. Make sure the vault has more than 0 tokens.
            // Reverts if tokenAddress is address(0).
            // This contract uses safeTransferLib from Solady. When "safeTransfering", there is no
            // check for smart contract code. This could be an issue if non-tokens are allowed to enter
            // the pool, as then the pool could be expoited by later deploying an address to the addres.
            // The below check ensure that there is a token deployed to the contract.
            uint256 balanceOfSelf = ERC20(tokenAddress).balanceOf(address(this));
            require(balanceOfSelf != 0); // dev: 0 tokens provided in setup.
            initialBalances[it] = balanceOfSelf;

            maxUnitCapacity += weight * balanceOfSelf;

            unchecked {
                ++it;
            }
        }

        // The security limit is implemented as being 50% of the current balance. 
        // Since the security limit is evaluated after balance changes, the limit in
        // storage should be the current balance.
        _maxUnitCapacity = maxUnitCapacity;

        // Mint vault tokens to the vault creator.
        _mint(depositor, INITIAL_MINT_AMOUNT);

        emit VaultDeposit(depositor, INITIAL_MINT_AMOUNT, initialBalances);
    }

    /** 
     * @notice Returns the current cross-chain swap capacity. 
     * @dev Overwrites the common implementation because of the
     * differences as to how it is used. As a result, this always returns
     * half of the common implementation (or of _maxUnitCapacity)
     */
    function getUnitCapacity() public view override returns (uint256) {
        return super.getUnitCapacity() >> 1;  // Equal to divide by 2.
    }

    /**
     * @notice Re-computes the security limit incase funds have been sent to the vault.
     */
    function updateMaxUnitCapacity() external {
        uint256 maxUnitCapacity;
        for (uint256 it; it < MAX_ASSETS;) {
            address asset = _tokenIndexing[it];
            if (asset == address(0)) break;

            maxUnitCapacity += (ERC20(asset).balanceOf(address(this)) - _escrowedTokens[asset]) * _weight[asset];

            unchecked {
                ++it;
            }
        }
        _maxUnitCapacity = maxUnitCapacity;
    }

    //--- Swap integrals ---//

    // Inherited from the Integrals file.

    /**
     * @notice Computes the return of SendAsset excluding fees.
     * @dev Reverts if 'fromAsset' is not a token in the vault or if 
     * 'amount' and the vault asset balance are both 0.
     * Does not contain the swap fee.
     * @param fromAsset Address of the token to sell.
     * @param amount Amount of from token to sell.
     * @return uint256 Units.
     */
    function calcSendAsset(
        address fromAsset,
        uint256 amount
    ) public view override returns (uint256) {
        // A high => fewer units returned. Do not subtract the escrow amount
        uint256 A = ERC20(fromAsset).balanceOf(address(this));
        uint256 W = _weight[fromAsset];

        // If 'fromAsset' is not part of the vault (i.e. W is 0) or if 'amount' and 
        // the vault asset balance (i.e. 'A') are both 0 this will revert, since 0**p is 
        // implemented as exp(ln(0) * p) and ln(0) is undefined.
        uint256 U = _calcPriceCurveArea(amount, A, W, _oneMinusAmp);

        // If the swap is a very small portion of the vault add an additional fee. This covers mathematical errors.
        unchecked { //SMALL_SWAP_RATIO is not zero, and if U * SMALL_SWAP_RETURN overflows, less is returned to the user.
            // Also U * SMALL_SWAP_RETURN cannot overflow, since U depends heavily on amount/A. If this number is small (which it is in this case) then U is also "small".
            if (A/SMALL_SWAP_RATIO >= amount) return U * SMALL_SWAP_RETURN / FixedPointMathLib.WAD;
        }
        
        return U;
    }

    /**
     * @notice Computes the output of ReceiveAsset excluding fees.
     * @dev Reverts if 'toAsset' is not a token in the vault.
     * Does not contain the swap fee.
     * @param toAsset Address of the token to buy.
     * @param U Number of units to convert.
     * @return uint256 Ppurchased tokens.
     */
    function calcReceiveAsset(
        address toAsset,
        uint256 U
    ) public view override returns (uint256) {
        // B low => fewer tokens returned. Subtract the escrow amount to decrease the balance.
        uint256 B = ERC20(toAsset).balanceOf(address(this)) - _escrowedTokens[toAsset];
        uint256 W = _weight[toAsset];

        // If someone were to purchase a token that is not part of the vault on setup
        // they would just add value to the vault. We don't care about it.
        // However, it will revert since the solved integral contains U/W and when
        // W = 0 then U/W returns division by 0 error.
        return _calcPriceCurveLimit(U, B, W, _oneMinusAmp);
    }

    /**
     * @notice Computes the output of localSwap excluding fees.
     * @dev Implemented through _calcCombinedPriceCurves.
     * Reverts if either 'fromAsset' or 'toAsset' is not in the vault, or if the vault 'fromAsset'
     * balance and 'amount' are both 0.
     * Does not contain the swap fee.
     * @param fromAsset Address of the token to sell.
     * @param toAsset Address of the token to buy.
     * @param amount Amount of from token to sell for to token.
     * @return output Output denominated in toAsset.
     */
    function calcLocalSwap(
        address fromAsset,
        address toAsset,
        uint256 amount
    ) public view override returns (uint256 output) {
        uint256 A = ERC20(fromAsset).balanceOf(address(this));
        uint256 B = ERC20(toAsset).balanceOf(address(this)) - _escrowedTokens[toAsset];
        uint256 W_A = _weight[fromAsset];
        uint256 W_B = _weight[toAsset];
        int256 oneMinusAmp = _oneMinusAmp;

        output = _calcPriceCurveLimit(_calcPriceCurveArea(amount, A, W_A, oneMinusAmp), B, W_B, oneMinusAmp);

        // If the swap is a very small portion of the vault add an additional fee. This covers mathematical errors.
        unchecked { //SMALL_SWAP_RATIO is not zero, and if output * SMALL_SWAP_RETURN overflows, less is returned to the user
            if (A/SMALL_SWAP_RATIO >= amount) return output * SMALL_SWAP_RETURN / FixedPointMathLib.WAD;
        }
    }

    /**
     * @notice Deposits a user-configurable amount of tokens.
     * @dev The swap fee is imposed on deposits.
     * Requires approvals for all tokens within the vault.
     * It is advised that the deposit matches the vault's %token distribution.
     * Deposit is done by converting tokenAmounts into units and then using
     * the macro for units to vault tokens. (_calcPriceCurveLimitShare).
     * The elements of tokenAmounts correspond to _tokenIndexing[0...N].
     * @param tokenAmounts Array of the tokens amounts to be deposited.
     * @param minOut Minimum number of vault tokens to be minted.
     * @return vaultTokens Number of minted vault tokens.
     */
    function depositMixed(
        uint256[] memory tokenAmounts,
        uint256 minOut
    ) nonReentrant external override returns(uint256 vaultTokens) {
        // _updateAmplification();
        int256 oneMinusAmp = _oneMinusAmp;

        uint256 it_times_walpha_amped;

        // There is a Stack too deep issue in a later branch. To counteract this,
        // wab is stored short-lived. This requires letting U get negative.
        // As such, we define an additional variable called intU which is signed
        int256 intU;
        
        // Compute walpha_0 to find the reference balances. This lets us evaluate the
        // number of tokens the vault should have If the price in the pool is 1:1.
        // walpha_0 is computed several times in this contract:
        // - DepositMixed
        // - WithdrawMixed
        // - WithdrawAll
        // - sendLiquidity
        // - receiveLiquidity
        // Since the implementation is very similar, it could be computed seperatly.
        // However, some of the implementations differ notably:
        // - DepositMixed: The for loop is reused for computing the value of incoming assets.
        // - WithdrawMixed: The for loop is used to cache tokenIndexed, effAssetBalances, and assetWeight.
        // - WithdrawAll: The for loop is used to cache tokenIndexed, effWeightAssetBalances.
        // - Both sendLiquidity and receiveLiquidity implements the reference computation: computeBalance0().
        // Before each implementation, there will be a short comment to describe how the implementation is different.
        {
            int256 weightedAssetBalanceSum = 0;
            uint256 assetDepositSum = 0;
            for (uint256 it; it < MAX_ASSETS;) {
                address token = _tokenIndexing[it];
                if (token == address(0)) break;
                uint256 weight = _weight[token];
                uint256 tokenAmount = tokenAmounts[it];
                {
                // Whenever balance0 is computed, the true balance should be used.
                uint256 weightAssetBalance = weight * ERC20(token).balanceOf(address(this));

                {
                    // wa^(1-k) is required twice. It is F(A) in the
                    // sendAsset equation and part of the wa_0^(1-k) calculation.
                    // If weightAssetBalance == 0, then this computation would fail. However since 0^(1-k) = 0, we can set it to 0.
                    int256 wab = 0;
                    if (weightAssetBalance != 0) {
                        // calculate balance 0 with the underwritten amount subtracted.
                        wab = FixedPointMathLib.powWad(
                            int256((weightAssetBalance - _underwriteEscrowMatchBalance0[token] * weight) * FixedPointMathLib.WAD),  // If casting overflows to a negative number, powWad fails
                            oneMinusAmp
                        );

                        // if wab == 0, there is no need to add it. So only add if != 0.
                        weightedAssetBalanceSum += wab;

                        wab = FixedPointMathLib.powWad(
                            int256(weightAssetBalance * FixedPointMathLib.WAD),  // If casting overflows to a negative number, powWad fails
                            oneMinusAmp
                        );
                    }
                    
                    // This line is the origin of the stack too deep issue.
                    // Moving intU += before this section would solve the issue but it is not possible since it would evaluate incorrectly.
                    // Save gas if the user provides no tokens, as the rest of the loop has no effect in that case
                    if (tokenAmount == 0) {
                        unchecked {
                            ++it;
                        }
                        continue;
                    }
                    
                    // int_A^{A+x} f(w) dw = F(A+x) - F(A).
                    unchecked {
                        // This is -F(A). Since we are subtracting first, U (i.e. intU) must be able to go negative.
                        // |intU| < weightedAssetBalanceSum since F(A+x) is added to intU in the lines after this.
                        intU -= wab;
                    }
                }
                
                // Add F(A+x).
                // This computation will not revert, since we know tokenAmount != 0.
                intU += FixedPointMathLib.powWad(
                    int256((weightAssetBalance + weight * tokenAmount) * FixedPointMathLib.WAD), // If casting overflows to a negative number, powWad fails
                    oneMinusAmp
                );
                
                }
                assetDepositSum += tokenAmount * weight;
                
                SafeTransferLib.safeTransferFrom(
                    token,
                    msg.sender,
                    address(this),
                    tokenAmount
                );  // dev: Token withdrawal from user failed.

                unchecked {
                    ++it;
                }
            }
            // Increase the security limit by the amount deposited.
            _maxUnitCapacity += assetDepositSum;
            // Short term decrease the security limit by the amount deposited.
            // While one may assume _usedUnitCapacity < _maxUnitCapacity, this is not always the case. As such, this remains checked.
            _usedUnitCapacity += assetDepositSum;
            
            // Compute the reference liquidity.
            // weightedAssetBalanceSum > _unitTracker always, since _unitTracker correlates to exactly
            // the difference between weightedAssetBalanceSum and weightedAssetBalance0Sum and thus
            // _unitTracker < weightedAssetBalance0Sum
            unchecked {
                // weightedAssetBalanceSum - _unitTracker can overflow for negative _unitTracker.
                // The result will be correct once it is casted to uint256.
                it_times_walpha_amped = uint256(weightedAssetBalanceSum - _unitTracker); // By design, weightedAssetBalanceSum > _unitTracker
                // Notice that we are not dividing by it. That is because we would then later have to multiply by it.
            }
        }

        // Subtract fee from U (intU). This prevents people from using deposit and withdrawal as a method of swapping.
        // To reduce costs, the governance fee is not taken. As a result, swapping through deposit+withdrawal circumvents
        // the governance fee. No incentives align for traders to abuse this and is nativly disincentivised by the higher gas cost.
        // intU should not be negative. But in the case it is, the result is very bad. For safety, check it is above 0.
        require(intU >= 0); // dev: U needs to be positive, otherwise, the uint256 casting becomes too larger.
        unchecked {
            // U (intU) is generally small, so the below equation should not overflow.
            // If it does, it has to be (uint256(intU) * (FixedPointMathLib.WAD - _vaultFee)) that overflows.
            // In which case, something close to 0 will be returned. When divided by FixedPointMathLib.WAD
            // it will return 0. The casting to int256 is then 0.
            intU = int256(
                // intU shouldn't be negative but the above check ensures it is ALWAYS positive.
                (uint256(intU) * (FixedPointMathLib.WAD - _vaultFee))/FixedPointMathLib.WAD
            );
        }

        int256 oneMinusAmpInverse = WADWAD / oneMinusAmp;

        // On totalSupply(). Do not add escrow amount, as higher amount results in a larger return.
        vaultTokens = _calcPriceCurveLimitShare(uint256(intU), totalSupply(), it_times_walpha_amped, oneMinusAmpInverse); // uint256: intU is positive by design.

        // Check that the minimum output is honoured.
        if (minOut > vaultTokens) revert ReturnInsufficient(vaultTokens, minOut);

        // Mint the desired number of vault tokens to the user.
        _mint(msg.sender, vaultTokens);

        // Emit the deposit event
        emit VaultDeposit(msg.sender, vaultTokens, tokenAmounts);
    }

    /**
     * @notice Burns vault tokens and releases the symmetrical share of tokens to the burner.
     * This can impact the vault prices.
     * @dev This is the cheapest way to withdraw and only way to withdraw 100% of the liquidity.
     * @param vaultTokens Number of vault tokens to burn.
     * @param minOut Minimum token output. If less is returned, the transaction reverts.
     * @return amounts Array containing the amounts withdrawn.
     */
    function withdrawAll(
        uint256 vaultTokens,
        uint256[] memory minOut
    ) nonReentrant external override returns(uint256[] memory amounts) {
        // _updateAmplification();
        // Burn the desired number of vault tokens to the user.
        // If they don't have it, it saves gas.
        // * Remember to add vaultTokens when accessing totalSupply()
        _burn(msg.sender, vaultTokens);
        // (For everyone else, it is probably cheaper to burn last. However, burning here makes
        // the implementation more similar to the volatile one)

        int256 oneMinusAmp = _oneMinusAmp;

        // Cache weights and balances.
        address[MAX_ASSETS] memory tokenIndexed;
        uint256[MAX_ASSETS] memory effWeightAssetBalances;  // The 'effective' balances (compensated with the escrowed balances)

        uint256 walpha_0_ampped;
        // Compute walpha_0 to find the reference balances. This lets us evaluate the
        // number of tokens the vault should have If the price in the pool is 1:1.

        // This is a balance0 implementation. The for loop is used to cache tokenIndexed and effWeightAssetBalances.
        {
            int256 weightedAssetBalanceSum = 0;
            // The number of iterations, "it", is needed briefly outside the loop.
            uint256 it;
            for (it = 0; it < MAX_ASSETS;) {
                address token = _tokenIndexing[it];
                if (token == address(0)) break;
                tokenIndexed[it] = token;
                uint256 weight = _weight[token];

                // Whenever balance0 is computed, the true balance should be used.
                uint256 weightAssetBalance = weight * ERC20(token).balanceOf(address(this));

                // Since this is used for a withdrawal, the escrow amount needs to be subtracted to return less.
                effWeightAssetBalances[it] = weightAssetBalance - _escrowedTokens[token] * weight; // Store 

                // If weightAssetBalance == 0, then this computation would fail. However since 0^(1-k) = 0, we can set it to 0.
                if (weightAssetBalance != 0) {
                    int256 wab = FixedPointMathLib.powWad(
                        int256((weightAssetBalance - _underwriteEscrowMatchBalance0[token] * weight) * FixedPointMathLib.WAD),  // If casting overflows to a negative number, powWad fails
                        oneMinusAmp
                    );

                    // if wab == 0, there is no need to add it. So only add if != 0.
                    weightedAssetBalanceSum += wab;
                }

                unchecked {
                    ++it;
                }
            }

            // Compute the reference liquidity.
            // weightedAssetBalanceSum > _unitTracker always, since _unitTracker correlates to exactly
            // the difference between weightedAssetBalanceSum and weightedAssetBalance0Sum and thus
            // _unitTracker < weightedAssetBalance0Sum
            unchecked {
                // weightedAssetBalanceSum - _unitTracker can overflow for negative _unitTracker. The result will
                // be correct once it is casted to uint256.
                walpha_0_ampped = uint256(weightedAssetBalanceSum - _unitTracker) / it; // By design, weightedAssetBalanceSum > _unitTracker
            }
        }

        // For later event logging, the amounts transferred from the vault are stored.
        amounts = new uint256[](MAX_ASSETS);
        
        // The vault token to assets equation is:
        // wtk = wa ·(1 - ((wa^(1-k) - wa_0^(1-k) · (1 - (PT-pt)/PT)^(1-k))/wa^(1-k))^(1/(1-k))
        // The inner diff is wa_0^(1-k) · (1 - (PT-pt)/PT)^(1-k).
        // since it doesn't depend on the token, it should only be computed once.
        uint256 innerdiff;
        {
            // Remember to add the number of vault tokens burned to totalSupply()
            // _escrowedVaultTokens is added, since it makes pt_fraction smaller
            uint256 ts = (totalSupply() + _escrowedVaultTokens + vaultTokens);
            uint256 pt_fraction = ((ts - vaultTokens) * FixedPointMathLib.WAD) / ts;

            // If pt_fraction == 0 => 0^oneMinusAmp = powWad(0, oneMinusAmp) => exp(ln(0) * oneMinusAmp) which is undefined.
            // However, we know what 0^oneMinusAmp is: 0!. So we just set it to 0.
            innerdiff = pt_fraction == 0 ? walpha_0_ampped : FixedPointMathLib.mulWad(
                walpha_0_ampped, 
                    FixedPointMathLib.WAD - uint256(FixedPointMathLib.powWad(  // Always casts a positive value
                    int256(pt_fraction),  // Casting always safe, as pt_fraction < 1
                    oneMinusAmp
                ))
            );
        }

        uint256 totalWithdrawn;
        int256 oneMinusAmpInverse = WADWAD / oneMinusAmp;
        for (uint256 it; it < MAX_ASSETS;) {
            address token = tokenIndexed[it];
            if (token == address(0)) break;

            // ampWeightAssetBalance cannot be cached because the balance0 computation does it without the escrow.
            // This computation needs to do it with the escrow.
            uint256 ampWeightAssetBalance = uint256(FixedPointMathLib.powWad(  // Powwad is always positive.
                int256(effWeightAssetBalances[it] * FixedPointMathLib.WAD),  // If casting overflows to a negative number, powWad fails
                oneMinusAmp
            ));
            //! If the vault doesn't have enough assets for a withdrawal, then
            //! withdraw all of the vaults assets. This should be protected against by setting minOut != 0.
            //! This happens because the vault expects assets to come back. (it is owed assets)
            //! We don't want to keep track of debt so we simply return less
            uint256 weightedTokenAmount = effWeightAssetBalances[it];
            //! The above happens if innerdiff >= ampWeightAssetBalance. So if that isn't
            //! the case, we should compute the true value.
            if (innerdiff < ampWeightAssetBalance) {
                // wtk = wa ·(1 - ((wa^(1-k) - wa_0^(1-k) · (1 - (PT-pt)/PT)^(1-k))/wa^(1-k))^(1/(1-k))
                // wtk = wa ·(1 - ((wa^(1-k) - innerdiff)/wa^(1-k))^(1/(1-k))
                // Since ampWeightAssetBalance ** (1/(1-amp)) == effWeightAssetBalances but the
                // mathematical lib returns ampWeightAssetBalance ** (1/(1-amp)) < effWeightAssetBalances.
                // the result is that if innerdiff isn't big enough to make up for the difference
                // the transaction reverts. If that is the case, use withdrawAll.
                // This quirk is "okay", since it means fewer tokens are always returned.

                // Since tokens are withdrawn, the change is negative. As such, multiply the equation by -1.
                weightedTokenAmount = FixedPointMathLib.mulWad(
                    weightedTokenAmount,
                    FixedPointMathLib.WAD - uint256(FixedPointMathLib.powWad(  // The inner is between 0 and 1. Power of < 1 is always between 0 and 1.
                        int256(FixedPointMathLib.divWadUp( // 0 < innerdiff < ampWeightAssetBalance => < 1 thus casting never overflows. 
                            ampWeightAssetBalance - innerdiff,
                            ampWeightAssetBalance
                        )),
                        oneMinusAmpInverse // 1/(1-amp)
                    ))
                );
            }

            // Store the amount withdrawn to subtract from the security limit later.
            totalWithdrawn += weightedTokenAmount;

            unchecked {
                // remove the weight from weightedTokenAmount.
                weightedTokenAmount /= _weight[token];
            }
            
            // Check if the user is satisfied with the output.
            uint256 tokenMinOut = minOut[it];   // GAS SAVING
            if (tokenMinOut > weightedTokenAmount) revert ReturnInsufficient(weightedTokenAmount, tokenMinOut);

            // Store the token amount.
            amounts[it] = weightedTokenAmount;

            // Transfer the released tokens to the user.
            SafeTransferLib.safeTransfer(token, msg.sender, weightedTokenAmount);

            unchecked {
                ++it;
            }
        }

        // Decrease the security limit by the amount withdrawn.
        _maxUnitCapacity -= totalWithdrawn;
        if (_usedUnitCapacity <= totalWithdrawn) {
            _usedUnitCapacity = 0;
        } else {
            unchecked {
                // We know: _usedUnitCapacity > totalWithdrawn.
                _usedUnitCapacity -= totalWithdrawn;
            }
        }

        // Emit the event
        emit VaultWithdraw(msg.sender, vaultTokens, amounts);
    }

    /**
     * @notice Burns vaultTokens and release a token distribution set by the user.
     * @dev It is advised that the withdrawal matches the vault's %token distribution.
     * Notice the special scheme for the ratios used. This is done to optimise gas since it doesn't require a sum or ratios.
     * Cannot be used to withdraw all liquidity. For that, withdrawAll should be used.
     * @param vaultTokens Number of vault tokens to withdraw.
     * @param withdrawRatio Percentage of units used to withdraw. In the following special scheme: U_0 = U · withdrawRatio[0], U_1 = (U - U_0) · withdrawRatio[1], U_2 = (U - U_0 - U_1) · withdrawRatio[2], .... Is WAD.
     * @param minOut Minimum number of tokens withdrawn.
     * @return amounts Array containing the amounts withdrawn.
     */
    function withdrawMixed(
        uint256 vaultTokens,
        uint256[] calldata withdrawRatio,
        uint256[] calldata minOut
    ) nonReentrant external override returns(uint256[] memory amounts) {
        // _updateAmplification();
        // Burn the desired number of vault tokens to the user. If they don't have it, it saves gas.
        // * Remember to add vaultTokens when accessing totalSupply()
        _burn(msg.sender, vaultTokens);
        // (For everyone else, it is probably cheaper to burn last. However, burning here makes
        // the implementation more similar to the volatile one).

        int256 oneMinusAmp = _oneMinusAmp;

        // Cache weights and balances.
        address[MAX_ASSETS] memory tokenIndexed;
        uint256[MAX_ASSETS] memory effAssetBalances; // The 'effective' balances (compensated with the escrowed balances)

        uint256 U = 0;
        // Compute walpha_0 to find the reference balances. This lets us evaluate the
        // number of tokens the vault should have if the price in the pool is 1:1.
        // unlike in withdrawAll, this value is needed to compute U.
        {
            // As such, we don't need to remember the value beyond this section.
            uint256 walpha_0_ampped;

            // This is a balance0 implementation. The for loop is used to cache tokenIndexed, effAssetBalances and assetWeight.
            {
                int256 weightedAssetBalanceSum = 0;
                // A very careful stack optimisation is made here.
                // The number of iterations, "it", is needed briefly outside the loop.
                // To reduce the number of items in the stack, U = it.
                for (U = 0; U < MAX_ASSETS;) {
                    address token = _tokenIndexing[U];
                    if (token == address(0)) break;
                    tokenIndexed[U] = token;
                    uint256 weight = _weight[token];

                    // Whenever balance0 is computed, the true balance should be used.
                    uint256 ab = ERC20(token).balanceOf(address(this));

                    // Later we need to use the asset balances. Since it is for a withdrawal, we should subtract the escrowed tokens
                    // such that less is returned.
                    effAssetBalances[U] = ab - _escrowedTokens[token];

                    // subtract _underwriteEscrowMatchBalance0 since this is used for balance0.
                    uint256 weightAssetBalance = weight * (ab - _underwriteEscrowMatchBalance0[token]);

                    // If weightAssetBalance == 0, then this computation would fail. However since 0^(1-k) = 0, we can set it to 0.
                    int256 wab = 0;
                    if (weightAssetBalance != 0) {
                        wab = FixedPointMathLib.powWad(
                            int256(weightAssetBalance * FixedPointMathLib.WAD),  // If casting overflows to a negative number, powWad fails
                            oneMinusAmp
                        );

                        // if wab == 0, there is no need to add it. So only add if != 0.
                        weightedAssetBalanceSum += wab;
                    }

                    unchecked {
                        ++U;
                    }
                }

                // weightedAssetBalanceSum > _unitTracker always, since _unitTracker correlates to exactly
                // the difference between weightedAssetBalanceSum and weightedAssetBalance0Sum and thus
                // _unitTracker < weightedAssetBalance0Sum
                unchecked {
                    // weightedAssetBalanceSum - _unitTracker can overflow for negative _unitTracker. The result will
                    // be correct once it is casted to uint256.
                    walpha_0_ampped = uint256(weightedAssetBalanceSum - _unitTracker) / U; // By design, weightedAssetBalanceSum > _unitTracker
                }

                // set U = number of tokens in the vault. But that is exactly what it is.
            }
            // Remember to add the number of vault tokens burned to totalSupply()
            uint256 ts = totalSupply() + _escrowedVaultTokens + vaultTokens;
            // Since vault tokens are getting subtracted from the total supply, remember
            // to add a negative sign to vault tokens.
            uint256 pt_fraction = FixedPointMathLib.divWad(ts - vaultTokens, ts);

            // Compute the unit worth of the vault tokens.
            // Recall that U is equal to N already. So we only need to multiply by the right side.
            // Since pt_fraction < 1, the units are negative. This is expected for swap to tokens. As such
            // FixedPointMathLib.WAD is moved in front to make U positive.
            U *= FixedPointMathLib.mulWad(
                walpha_0_ampped, 
                FixedPointMathLib.WAD - uint256(FixedPointMathLib.powWad( // Always casts a positive value
                    int256(pt_fraction), // If casting overflows to a negative number, powWad fails
                    oneMinusAmp
                )) 
            );
        }

        // For later event logging, the amounts transferred to the vault are stored.
        amounts = new uint256[](MAX_ASSETS);
        uint256 totalWithdrawn;
        for (uint256 it; it < MAX_ASSETS;) {
            // Ideally we would collect the token into memory to save gas but there isn't space in the stack.
            if (tokenIndexed[it] == address(0)) break;

            // Units allocated for the specific token.
            uint256 U_i = FixedPointMathLib.mulWad(U, withdrawRatio[it]);
            if (U_i == 0) {
                // After a withdrawRatio of 1, all other withdrawRatios should be 0. Otherwise, there was an input error.
                if (withdrawRatio[it] != 0) revert WithdrawRatioNotZero();
                // Check the minimum output. This is important, since the normal check is skipped.
                if (minOut[it] != 0) revert ReturnInsufficient(0, minOut[it]);

                unchecked {
                    ++it;
                }
                continue;
            }
            U -= U_i;  // Subtract the number of units used. This will underflow for malicious withdrawRatios > 1.
            
            uint256 assetWeight = _weight[tokenIndexed[it]];
            // Units are shared between "liquidity units" and "token units". As such, we just need to convert the units to tokens.
            uint256 tokenAmount = _calcPriceCurveLimit(U_i, effAssetBalances[it], assetWeight, oneMinusAmp);

            // Ensure the output satisfies the user.
            if (minOut[it] > tokenAmount) revert ReturnInsufficient(tokenAmount, minOut[it]);

            // Store amount for withdraw event.
            amounts[it] = tokenAmount;

            // Transfer the released tokens to the user.
            SafeTransferLib.safeTransfer(tokenIndexed[it], msg.sender, tokenAmount);

            // Decrease the security limit by the amount withdrawn.
            totalWithdrawn += tokenAmount * assetWeight;

            unchecked {
                ++it;
            }
        }
        // Ensure all units are used. This should be done by setting at least one withdrawRatio to 1 (WAD).
        if (U != 0) revert UnusedUnitsAfterWithdrawal(U);
        
        // Decrease the security limit by the amount withdrawn.
        _maxUnitCapacity -= totalWithdrawn;
        if (_usedUnitCapacity <= totalWithdrawn) {
            _usedUnitCapacity = 0;
        } else {
            unchecked {
                // We know: _usedUnitCapacity > totalWithdrawn >= 0.
                _usedUnitCapacity -= totalWithdrawn;
            }
        }

        // Emit the event
        emit VaultWithdraw(msg.sender, vaultTokens, amounts);
    }

    /**
     * @notice A swap between 2 assets within the vault. Is atomic.
     * @param fromAsset Asset the user wants to sell.
     * @param toAsset Asset the user wants to buy.
     * @param amount Amount of fromAsset the user wants to sell.
     * @param minOut Minimum output the user wants. Otherwise, the transaction reverts.
     * @return out The number of tokens purchased.
     */
    function localSwap(
        address fromAsset,
        address toAsset,
        uint256 amount,
        uint256 minOut
    ) nonReentrant external override returns (uint256 out) {
        // _updateAmplification();
        uint256 fee = FixedPointMathLib.mulWad(amount, _vaultFee);

        // Calculate the return value.
        out = calcLocalSwap(fromAsset, toAsset, amount - fee);

        // Ensure the return value is more than the minimum output.
        if (minOut > out) revert ReturnInsufficient(out, minOut);

        // Transfer tokens to the user and collect tokens from the user.
        // The order doesn't matter, since the function is reentrant protected.
        // The transaction that is most likly to revert is first.
        SafeTransferLib.safeTransferFrom(fromAsset, msg.sender, address(this), amount);
        SafeTransferLib.safeTransfer(toAsset, msg.sender, out);

        // Collect potential governance fee
        _collectGovernanceFee(fromAsset, fee);

        // For amplified vaults, the security limit is based on the sum of the tokens in the vault.
        uint256 weightedAmount = amount * _weight[fromAsset];
        uint256 weightedOut = out * _weight[toAsset];
        // The if statement ensures the independent calculations never under or overflow.
        if (weightedOut > weightedAmount) {
            _maxUnitCapacity -= weightedOut - weightedAmount;
        } else {
            _maxUnitCapacity += weightedAmount - weightedOut;
        }

        emit LocalSwap(msg.sender, fromAsset, toAsset, amount, out);
    }

    /** @notice Common logic between sendAsset implementations */
    function _sendAsset(
        RouteDescription calldata routeDescription,
        address fromAsset,
        uint8 toAssetIndex,
        uint256 U,
        uint256 amount,
        uint256 fee,
        uint256 minOut,
        address fallbackUser,
        uint16 underwriteIncentiveX16,
        bytes calldata calldata_
    ) internal {
        // Fallback user cannot be address(0) since this is used as a check for the existance of an escrow.
        // It would also be a silly fallback address.
        require(fallbackUser != address(0));
        // onSendAssetSuccess requires casting U to int256 to update the _unitTracker and must never revert. Check for overflow here.
        require(U < uint256(type(int256).max));  // int256 max fits in uint256
        _unitTracker += int256(U);

        // Send the purchased units to the target vault on the target chain.
        ICatalystChainInterface(_chainInterface).sendCrossChainAsset{value: msg.value}(
            routeDescription,
            toAssetIndex,
            U,
            minOut,
            amount - fee,
            fromAsset,
            underwriteIncentiveX16,
            calldata_
        );

        // Store the escrow information. For that, an index is required. Since we need this index twice, we store it.
        // Only information that is relevant for the escrow has to be hashed. (+ some extra for randomisation)
        // No need to hash context (as token/liquidity escrow data is different), fromVault, toVault, targetAssetIndex, minOut, CallData
        bytes32 sendAssetHash = _computeSendAssetHash(
            routeDescription.toAccount,              // Ensures no collisions between different users
            U,                      // Used to randomise the hash
            amount - fee,           // Required! to validate release escrow data
            fromAsset,              // Required! to validate release escrow data
            uint32(block.number)    // May overflow, but this is desired (% 2**32)
        );

        // Escrow the tokens used to purchase units. These will be sent back if transaction doesn't arrive / timeout.
        _setTokenEscrow(
            sendAssetHash,
            fallbackUser,
            fromAsset,
            amount - fee
        );
        // Notice that the fee is subtracted from the escrow. If this is not done, the escrow can be used as a cheap denial of service vector.
        // This is unfortunate.

        // Collect the tokens from the user.
        SafeTransferLib.safeTransferFrom(fromAsset, msg.sender, address(this), amount);

        // Governance Fee
        _collectGovernanceFee(fromAsset, fee);

        // Adjustment of the security limit is delayed until ack to avoid a router abusing timeout to circumvent the security limit.

        emit SendAsset(
            routeDescription.chainIdentifier,
            routeDescription.toVault,
            routeDescription.toAccount,
            fromAsset,
            toAssetIndex,
            amount,
            minOut,
            U,
            fee,
            underwriteIncentiveX16
        );
    }

    /**
     * @notice Initiate a cross-chain swap by purchasing units and transfering the units to the target vault.
     * @param routeDescription Cross-chain route description that contains the chainIdentifier, toAccount, toVault and relaying incentive.
     * @param fromAsset Asset the user wants to sell.
     * @param toAssetIndex Index of the asset the user wants to buy in the target vault.
     * @param amount Number of fromAsset to sell to the vault.
     * @param minOut Minimum number output of tokens on the target chain.
     * @param fallbackUser If the transaction fails, send the escrowed funds to this address.
     * @param underwriteIncentiveX16 Payment for underwriting the swap (out of type(uint16).max).
     * @param calldata_ Data field if a call should be made on the target chain.
     * Encoding depends on the target chain, with EVM: bytes.concat(bytes20(uint160(<address>)), <data>). At maximum 65535 bytes can be passed.
     * @return U Number of units bought.
     */
    function sendAsset(
        RouteDescription calldata routeDescription,
        address fromAsset,
        uint8 toAssetIndex,
        uint256 amount,
        uint256 minOut,
        address fallbackUser,
        uint16 underwriteIncentiveX16,
        bytes calldata calldata_
    ) nonReentrant onlyConnectedPool(routeDescription.chainIdentifier, routeDescription.toVault) external payable override returns (uint256 U) {
        // _updateAmplification();

        uint256 fee = FixedPointMathLib.mulWad(amount, _vaultFee);

        // Calculate the units bought.
        U = calcSendAsset(fromAsset, amount - fee);

        // Execute the common sendAsset logic.
        _sendAsset(
            routeDescription,
            fromAsset,
            toAssetIndex,
            U,
            amount,
            fee,
            minOut,
            fallbackUser,
            underwriteIncentiveX16,
            calldata_
        );
    }

    /**
     * @notice Initiate a cross-chain swap by purchasing units and transfer them to another vault using a fixed number of units.
     * @dev This function is intended to match an existing underwrite. Since normal sendAssets aren't "exact" in regards to U,
     * this functions makes it easier to hit a specific underwrite.
     * @param routeDescription Cross-chain route description that contains the chainIdentifier, toAccount, toVault and relaying incentive.
     * @param fromAsset Asset the user wants to sell.
     * @param toAssetIndex Index of the asset the user wants to buy in the target vault.
     * @param amount Number of fromAsset to sell to the vault.
     * @param minOut Minimum number output of tokens on the target chain.
     * @param minU Minimum and exact number of units sent.
     * @param fallbackUser If the transaction fails, send the escrowed funds to this address.
     * @param underwriteIncentiveX16 Payment for underwriting the swap (out of type(uint16).max).
     * @param calldata_ Data field if a call should be made on the target chain.
     * Encoding depends on the target chain, with EVM: bytes.concat(bytes20(uint160(<address>)), <data>). At maximum 65535 bytes can be passed..
     * @return U Always equal to minOut, as that is the number of units to be used on the destination chain.
     */
     function sendAssetFixedUnit(
        ICatalystV1Structs.RouteDescription calldata routeDescription,
        address fromAsset,
        uint8 toAssetIndex,
        uint256 amount,
        uint256 minOut,
        uint256 minU,
        address fallbackUser,
        uint16 underwriteIncentiveX16,
        bytes calldata calldata_
    ) nonReentrant onlyConnectedPool(routeDescription.chainIdentifier, routeDescription.toVault) external payable override returns (uint256 U) {
        // _updateAmplification();

        uint256 fee = FixedPointMathLib.mulWad(amount, _vaultFee);

        // Calculate the units bought.
        U = calcSendAsset(fromAsset, amount - fee);

        if (U < minU) revert ReturnInsufficient(U, minU);
        // The set number of units bought to minU.
        U = minU;

        // Execute the common sendAsset logic.
        _sendAsset(
            routeDescription,
            fromAsset,
            toAssetIndex,
            U,
            amount,
            fee,
            minOut,
            fallbackUser,
            underwriteIncentiveX16,
            calldata_
        );
    }

    /**
     * @notice Handles common logic associated with the completion of a cross-chain swap.
     * This function convert incoming Units (expected to be from an incoming cross-chain swap) into a specific token.
     * @dev This function is intended to finalise a receiveAsset call.
     * @param toAsset Asset to buy with the units.
     * @param U Incoming units to be turned into vaults tokens.
     * @param minOut Minimum number of tokens to purchase. Will revert if less.
     * @return purchasedTokens Number of toAsset bought.
     */
    function _receiveAsset(
        address toAsset,
        uint256 U,
        uint256 minOut
    ) internal override returns (uint256 purchasedTokens) {
        // _updateAmplification();

        // Calculate the swap return value. Fee is always taken on the sending token.
        purchasedTokens = calcReceiveAsset(toAsset, U);

        // Check if the swap is according to the swap limits.
        uint256 deltaSecurityLimit = purchasedTokens * _weight[toAsset];
        if (_maxUnitCapacity <= deltaSecurityLimit) revert ExceedsSecurityLimit();
        unchecked {
            // We know that _maxUnitCapacity > deltaSecurityLimit so it cannot underflow.
            _maxUnitCapacity -= deltaSecurityLimit;
        }
        _updateUnitCapacity(deltaSecurityLimit);

        // Ensure the user is satisfied with the number of tokens.
        if (minOut > purchasedTokens) revert ReturnInsufficient(purchasedTokens, minOut);

        // Track units for balance0 computation.
        _unitTracker -= int256(U);
    }

    /**
     * @notice Completes a cross-chain swap by converting units to the desired token.
     * @dev Security checks are performed by _receiveAsset.
     * @param channelId Source chain identifier.
     * @param fromVault Source vault.
     * @param toAssetIndex Index of the asset to be purchased.
     * @param toAccount Recipient of assets on destination chain.
     * @param U Incoming units.
     * @param minOut Minimum number of token to buy. Reverts back to the sending side.
     * @param fromAmount Used to match cross-chain swap events. The input amount minus fees on the sending chain.
     * @param fromAsset Used to match cross-chain swap events. The input asset on the source chain.
     * @param blockNumberMod Used to match cross-chain swap events. The block number from the source chain.
     * @param purchasedTokens Number of toAsset bought.
     */
    function receiveAsset(
        bytes32 channelId,
        bytes calldata fromVault,
        uint256 toAssetIndex,
        address toAccount,
        uint256 U,
        uint256 minOut,
        uint256 fromAmount,
        bytes calldata fromAsset,
        uint32 blockNumberMod
    ) nonReentrant onlyChainInterface onlyConnectedPool(channelId, fromVault) external override returns(uint256 purchasedTokens) {
        // Convert the asset index (toAsset) into the asset to be purchased.
        address toAsset = _tokenIndexing[toAssetIndex];
        purchasedTokens = _receiveAsset(
            toAsset,
            U,
            minOut
        );

        // Send the assets to the user.
        SafeTransferLib.safeTransfer(toAsset, toAccount, purchasedTokens);

        emit ReceiveAsset(
            channelId, 
            fromVault, 
            toAccount, 
            toAsset, 
            U, 
            purchasedTokens, 
            fromAmount,
            fromAsset,
            blockNumberMod
        );
    }

    //--- Liquidity swapping ---//
    // Because of the way vault tokens work in a pool, there needs to be a way for users to easily get
    // a distributed stake. Liquidity swaps is a macro implemented at the smart contract level equivalent to:
    // 1. Withdraw tokens.
    // 2. Convert tokens to units & transfer to target vault.
    // 3. Convert units to an even mix of tokens.
    // 4. Deposit the even mix of tokens.
    // In 1 user invocation.

    /** 
     * @notice Computes balance0**(1-amp) without any special caching.
     * @dev Whenever balance0 is computed, the true balance should be used instead of the one
     * modifed by the escrow. This is because balance0 is constant during swaps. Thus, if the
     * balance was modified, it would not be constant during swaps.
     * The function also returns the vault asset count as it is always used in conjunction with walpha_0_ampped.
     * The external function does not.
     * @return walpha_0_ampped Balance0**(1-amp)
     * @return it the vault asset count
     */
    function _computeBalance0(int256 oneMinusAmp) internal view returns(uint256 walpha_0_ampped, uint256 it) {
        // Compute walpha_0 to find the reference balances. This lets us evaluate the
        // number of tokens the vault should have IF the price in the pool is 1:1.

        // This is a balance0 implementation. The balance 0 implementation here is reference.
        int256 weightedAssetBalanceSum = 0;
        for (it; it < MAX_ASSETS;) {
            address token = _tokenIndexing[it];
            if (token == address(0)) break;
            uint256 weight = _weight[token];

            uint256 weightAssetBalance = weight * (ERC20(token).balanceOf(address(this)) - _underwriteEscrowMatchBalance0[token]);

            // If weightAssetBalance == 0, then this computation would fail. However since 0^(1-k) = 0, we can set it to 0.
            int256 wab = 0;
            if (weightAssetBalance != 0){
                wab = FixedPointMathLib.powWad(
                    int256(weightAssetBalance * FixedPointMathLib.WAD),     // If casting overflows to a negative number, powWad fails
                    oneMinusAmp
                );

                // if wab == 0, there is no need to add it. So only add if != 0.
                weightedAssetBalanceSum += wab;
            }

            unchecked {
                ++it;
            }
        }

        // weightedAssetBalanceSum > _unitTracker always, since _unitTracker correlates to exactly
        // the difference between weightedAssetBalanceSum and weightedAssetBalance0Sum and thus
        // _unitTracker < weightedAssetBalance0Sum
        unchecked {
            // weightedAssetBalanceSum - _unitTracker can overflow for negative _unitTracker. The result will
            // be correct once it is casted to uint256.
            walpha_0_ampped = uint256(weightedAssetBalanceSum - _unitTracker) / it;   // By design, weightedAssetBalanceSum > _unitTracker
        }   
    }

    /** 
     * @notice Computes balance0 for the pool.
     * @dev This can be used as a local invariant. Is constant (or slowly increasing) for swaps.
     * Deposits and withdrawals change balance0 and as such, it cannot be used to examine if a vault is secure
     * by it self.
     * This function does not return balance0 as it, is returns a weighted amplified form.
     * For pretty much any real world usage of the function, this is the relevant form.
     * @return walpha_0 Balance0**(1-amp)
     */
    function computeBalance0() external view returns(uint256 walpha_0) {
        int256 oneMinusAmp = _oneMinusAmp;
       (uint256 walpha_0_ampped, ) = _computeBalance0(oneMinusAmp);

        walpha_0 = uint256( // casting: powWad is not negative.
            FixedPointMathLib.powWad(
                int256(walpha_0_ampped),  // Casting: If overflow, then powWad fails as the overflow is into negative.
                WADWAD / oneMinusAmp
            )
        );
    }

    /**
     * @notice Initiate a cross-chain liquidity swap by withdrawing tokens and converting them to units.
     * @dev While the description says tokens are withdrawn and then converted to units, vault tokens are converted
     * directly into units through the following equation: U = N · wa^(1-k) · (((PT + pt)/PT)^(1-k) - 1)
     * @param routeDescription Cross-chain route description that contains the chainIdentifier, toAccount, toVault, and relaying incentive.
     * @param vaultTokens Number of vault tokens to exchange.
     * @param minOut Array of minout describing: [the minimum number of vault tokens, the minimum number of reference assets].
     * @param fallbackUser If the transaction fails, send the escrowed funds to this address.
     * @param calldata_ Data field if a call should be made on the target chain.
     * Encoding depends on the target chain, with EVM: abi.encodePacket(bytes20(<address>), <data>). At maximum 65535 bytes can be passed.
     * @return U Number of units bought.
     */
    function sendLiquidity(
        RouteDescription calldata routeDescription,
        uint256 vaultTokens,
        uint256[2] calldata minOut,
        address fallbackUser,
        bytes calldata calldata_
    ) nonReentrant onlyConnectedPool(routeDescription.chainIdentifier, routeDescription.toVault) external payable override returns (uint256 U) {
        // Fallback user cannot be address(0) since this is used as a check for the existance of an escrow.
        // It would also be a silly fallback address.
        require(fallbackUser != address(0));
        // Correct address format is checked on the cross-chain interface.

        // _updateAmplification();

        // When accesssing totalSupply, remember that we already burnt the incoming vaultTokens.
        _burn(msg.sender, vaultTokens);

        int256 oneMinusAmp = _oneMinusAmp;

        // Compute walpha_0 to find the reference balances. This lets us evaluate the
        // number of tokens the vault should have If the price in the pool is 1:1.
        (uint256 walpha_0_ampped, uint256 it) = _computeBalance0(oneMinusAmp);

        {
            // Plus _escrowedVaultTokens since we want the withdrawal to return less. Adding vaultTokens as these have already been burnt.
            uint256 ts = totalSupply() + _escrowedVaultTokens + vaultTokens;
            uint256 pt_fraction = FixedPointMathLib.divWad(ts + vaultTokens, ts);

            U = it * FixedPointMathLib.mulWad(
                walpha_0_ampped, 
                uint256(FixedPointMathLib.powWad( // Always casts a positive value
                    int256(pt_fraction), // If casting overflows to a negative number, powWad fails
                    oneMinusAmp
                )) - FixedPointMathLib.WAD
            );
            // onSendLiquiditySuccess requires casting U to int256 to update the _unitTracker and must never revert. Check for overflow here.
            require(U < uint256(type(int256).max)); // int256 max fits in uint256
            _unitTracker += int256(U);
        }

        // Transfer the units to the target vault.
        ICatalystChainInterface(_chainInterface).sendCrossChainLiquidity{value: msg.value}(
            routeDescription,
            U,
            minOut,
            vaultTokens,
            calldata_
        );

        // Store the escrow information. For that, an index is required. Since we need this index twice, we store it.
        // Only information that is relevant for the escrow has to be hashed. (+ some extra for randomisation)
        // No need to hash context (as token/liquidity escrow data is different), fromVault, toVault, targetAssetIndex, minOut, CallData
        bytes32 sendLiquidityHash = _computeSendLiquidityHash(
            routeDescription.toAccount,              // Ensures no collisions between different users
            U,                      // Used to randomise the hash
            vaultTokens,            // Required! to validate release escrow data
            uint32(block.number)    // May overflow, but this is desired (% 2**32)
        );

        // Emit event before setting escrow to clear up variables from stack.
        emit SendLiquidity(
            routeDescription.chainIdentifier,
            routeDescription.toVault,
            routeDescription.toAccount,
            vaultTokens,
            minOut,
            U
        );

        // Escrow the vault token used to purchase units. These will be sent back if transaction doesn't arrive / timeout.
        _setLiquidityEscrow(
            sendLiquidityHash,
            fallbackUser,
            vaultTokens
        );

        // Adjustment of the security limit is delayed until ack to avoid
        // a router abusing timeout to circumvent the security limit at a low cost.
    }

    /**
     * @notice Handles common logic assocaited with the completion of a cross-chain liquidity swap.
     * This function convert incoming units directly to vault tokens.
     * @dev This function is meant to finalise a receiveLiquidity call.
     * @param U Incoming units to be turned into vault tokens.
     * @param minVaultTokens Minimum number of vault tokens to mint (revert if less).
     * @param minReferenceAsset Minimum number of reference tokens the vaults tokens are worth (revert if less).
     * @return vaultTokens Minted vault tokens.
     */
    function _receiveLiquidity(
        uint256 U,
        uint256 minVaultTokens,
        uint256 minReferenceAsset
    ) internal returns (uint256 vaultTokens) {
        // _updateAmplification();

        int256 oneMinusAmp = _oneMinusAmp;

        // Compute walpha_0 to find the reference balances. This lets us evaluate the
        // number of tokens the vault should have If the price in the pool is 1:1.
        (uint256 walpha_0_ampped, uint256 it) = _computeBalance0(oneMinusAmp);

        int256 oneMinusAmpInverse = WADWAD / oneMinusAmp;

        uint256 it_times_walpha_amped = it * walpha_0_ampped;

        // On totalSupply(). Do not add escrow amount, as higher amount results in a larger return.
        vaultTokens = _calcPriceCurveLimitShare(U, totalSupply(), it_times_walpha_amped, oneMinusAmpInverse);

        // Check if more vault tokens than the minimum can be minted.
        if (minVaultTokens > vaultTokens) revert ReturnInsufficient(vaultTokens, minVaultTokens);
        // Then check if the minimum number of reference assets is honoured.
        if (minReferenceAsset != 0) {
            uint256 walpha_0 = uint256(FixedPointMathLib.powWad(  // uint256 casting: Is always positive.
                int256(walpha_0_ampped), // int256 casting: If casts to a negative number, powWad fails because it uses ln which can't take negative numbers.
                oneMinusAmpInverse
            )); 
            // Add escrow to ensure that even if all ongoing transaction revert, the user gets their expected amount.
            // Add vault tokens because they are going to be minted (We want the reference value after mint).
            uint256 walpha_0_owned = ((walpha_0 * vaultTokens) / (totalSupply() + _escrowedVaultTokens + vaultTokens)) / FixedPointMathLib.WAD;
            if (minReferenceAsset > walpha_0_owned) revert ReturnInsufficient(walpha_0_owned, minReferenceAsset);
        }

        // Update the unit tracker:
        _unitTracker -= int256(U);

        // Security limit
        {
            // To calculate the vaultTokenEquiv, we set \alpha_t = \alpha_0.
            // This should be a close enough approximation.
            // If U > it_times_walpha_amped, then U can purchase more than 50% of the vault.
            // And the below calculation doesn't work.
            if (it_times_walpha_amped <= U) revert ExceedsSecurityLimit();
            uint256 vaultTokenEquiv = FixedPointMathLib.mulWadUp(
                uint256(FixedPointMathLib.powWad( // Always casts a positive value
                    int256(it_times_walpha_amped), // If casting overflows to a negative number, powWad fails
                    oneMinusAmpInverse
                )),
                FixedPointMathLib.WAD - uint256(FixedPointMathLib.powWad( // powWad is always <= 1, as 'base' is always <= 1
                    int256(FixedPointMathLib.divWad( // Casting never overflows, as division result is always <= 1
                        it_times_walpha_amped - U,
                        it_times_walpha_amped
                    )),
                    oneMinusAmpInverse
                ))
            );
            // Check if the swap is according to the swap limits
            _updateUnitCapacity(FixedPointMathLib.mulWad(2, vaultTokenEquiv));
        }
    }

    /**
     * @notice Completes a cross-chain liquidity swap by converting units to tokens and depositing.
     * @dev Security checks are performed by _receiveLiquidity.
     * While the description says units are converted to tokens and then deposited, units are converted
     * directly to vault tokens through the following equation: pt = PT · (((N · wa_0^(1-k) + U)/(N · wa_0^(1-k))^(1/(1-k)) - 1)
     * @param channelId Source chain identifier.
     * @param fromVault Source vault.
     * @param toAccount Recipient of vault tokens.
     * @param U Incoming units to be turned into vault tokens.
     * @param minVaultTokens Minimum number of vault tokens to mint (revert if less).
     * @param minReferenceAsset Minimum number of reference tokens the vaults tokens are worth (revert if less).
     * @param fromAmount Used to match cross-chain swap events. The input amount on the source chain.
     * @param blockNumberMod Used to match cross-chain swap events. The block number from the source chain.
     * @return purchasedVaultTokens Minted vault tokens.
     */
    function receiveLiquidity(
        bytes32 channelId,
        bytes calldata fromVault,
        address toAccount,
        uint256 U,
        uint256 minVaultTokens,
        uint256 minReferenceAsset,
        uint256 fromAmount,
        uint32 blockNumberMod
    ) nonReentrant onlyChainInterface onlyConnectedPool(channelId, fromVault) external override returns(uint256 purchasedVaultTokens) {
        purchasedVaultTokens = _receiveLiquidity(
            U,
            minVaultTokens,
            minReferenceAsset
        );

        emit ReceiveLiquidity(channelId, fromVault, toAccount, U, purchasedVaultTokens, fromAmount, blockNumberMod);

        // Mint vault tokens for the user.
        _mint(toAccount, purchasedVaultTokens);
    }

    //-- Escrow Functions --//

    /** 
     * @notice Deletes and releases escrowed tokens to the vault and updates the security limit.
     * @dev Should never revert!
     * The base implementation exists in CatalystVaultCommon. The function adds security limit
     * adjustment to the implementation to swap volume supported.
     * @param toAccount Recipient of the transaction on the target chain.
     * @param U Number of units purchased.
     * @param escrowAmount Number of tokens escrowed.
     * @param escrowToken Token escrowed.
     * @param blockNumberMod Block number at which the swap transaction was commited (mod 32)
     */
    function onSendAssetSuccess(
        bytes32 channelId,
        bytes calldata toAccount,
        uint256 U,
        uint256 escrowAmount,
        address escrowToken,
        uint32 blockNumberMod
    ) public override {
        // Execute common escrow logic.
        super.onSendAssetSuccess(channelId, toAccount, U, escrowAmount, escrowToken, blockNumberMod);

        // Received assets should be subtracted from the used unit capacity.
        // It is assumed if the router was fraudulent no-one would execute a trade.
        // As a result, if people swap into the vault, we should expect that there is exactly
        // the inswapped amount of trust in the vault. If this wasn't implemented, there would be
        // a maximum daily cross chain volume, which is bad for liquidity providers.
        unchecked {
            // escrowAmount * _weight[escrowToken] has been calculated before.
            uint256 escrowAmountTimesWeight = escrowAmount * _weight[escrowToken];

            uint256 UC = _usedUnitCapacity;
            // If UC < escrowAmount and we do UC - escrowAmount < 0 underflow => bad.
            if (UC > escrowAmountTimesWeight) {
                _usedUnitCapacity = UC - escrowAmountTimesWeight; // Does not underflow since _usedUnitCapacity > escrowAmount.
            } else if (UC != 0) {
                // If UC == 0, then we shouldn't do anything. Skip that case.
                // when UC <= escrowAmount => UC - escrowAmount <= 0 => max(UC - escrowAmount, 0) = 0
                _usedUnitCapacity = 0;
            }

            // There is a chance that _maxUnitCapacity + escrowAmount * _weight[escrowToken] will overflow.
            // since the number has never been calculated before. This function should never revert so the computation
            // has to be done unchecked.
            uint256 muc = _maxUnitCapacity;
            uint256 new_muc = muc + escrowAmountTimesWeight; // Might overflow. Can be checked by comparing it against MUC.

            // If new_muc < muc, then new_muc has overflown. As a result, we should set muc = uint256::MAX
            if (new_muc < muc) {
                _maxUnitCapacity = type(uint256).max;
            } else {
                _maxUnitCapacity = new_muc;
            }
        }
    }

    /** 
     * @notice Deletes and releases escrowed tokens to the vault and updates the security limit.
     * @dev Should never revert!
     * The base implementation exists in CatalystVaultCommon. The function adds security limit
     * adjustment to the implementation to swap volume supported.
     * @param toAccount Recipient of the transaction on the target chain.
     * @param U Number of units acquired.
     * @param escrowAmount Number of tokens escrowed.
     * @param escrowToken Token escrowed.
     * @param blockNumberMod Block number at which the swap transaction was commited (mod 32)
     */
    function onSendAssetFailure(
        bytes32 channelId,
        bytes calldata toAccount,
        uint256 U,
        uint256 escrowAmount,
        address escrowToken,
        uint32 blockNumberMod
    ) public override {
        // Execute common escrow logic.
        super.onSendAssetFailure(channelId, toAccount, U, escrowAmount, escrowToken, blockNumberMod);

        // Removed timed-out units from the unit tracker. This will keep the
        // balance0 in balance, since tokens also leave the vault
        _unitTracker -= int256(U);  // It has already been checked on sendAsset that casting to int256 will not overflow.
                                    // Cannot be manipulated by the router as, otherwise, the swapHash check will fail
    }

    // onSendLiquiditySuccess is not overwritten since we are unable to increase
    // the security limit. This is because it is very expensive to compute the update
    // to the security limit. If someone liquidity swapped a significant amount of assets
    // it is assumed the vault has low liquidity. In these cases, liquidity swaps shouldn't be used.

    /** 
     * @notice Deletes and releases liquidity escrowed tokens to the vault and updates the security limit.
     * @dev Should never revert!  
     * The base implementation exists in CatalystVaultCommon.
     * @param toAccount Recipient of the transaction on the target chain. Encoded in bytes32.
     * @param U Number of units initially acquired.
     * @param escrowAmount Number of vault tokens escrowed.
     * @param blockNumberMod Block number at which the swap transaction was commited (mod 32)
     */
    function onSendLiquidityFailure(
        bytes32 channelId,
        bytes calldata toAccount,
        uint256 U,
        uint256 escrowAmount,
        uint32 blockNumberMod
    ) public override {
        super.onSendLiquidityFailure(channelId, toAccount, U, escrowAmount, blockNumberMod);

        // Removed timed-out units from the unit tracker. This will keep the
        // balance0 in balance, since tokens also leave the vault
        _unitTracker -= int256(U);  // It has already been checked on sendAsset that casting to int256 will not overflow.
                                    // Cannot be manipulated by the router as, otherwise, the swapHash check will fail
    }

    function underwriteAsset(
        bytes32 identifier,
        address toAsset,
        uint256 U,
        uint256 minOut
    ) override public returns (uint256 purchasedTokens) {
        // We need to ensure that the conversion in deleteUnderwrite (and receiveAsset) doesn't overflow.
        require(U < uint256(type(int256).max));  // int256 max fits in uint256
        
        purchasedTokens = super.underwriteAsset(identifier, toAsset, U, minOut);

        // unit tracking is handled by _receiveAsset.

        // since _unitTrakcer -= int256(U) has been set but no tokens have
        // let the pool, we need to remove the corresponding amount from
        // the balance 0 computation to ensure it is still correct.
        unchecked {
            // Must be less than the vault balance.
            _underwriteEscrowMatchBalance0[toAsset] += purchasedTokens;
        }
    }

    function releaseUnderwriteAsset(
        address refundTo,
        bytes32 identifier,
        uint256 escrowAmount,
        address escrowToken,
        bytes32 sourceIdentifier,
        bytes calldata fromVault
    )  override public {
         super.releaseUnderwriteAsset(refundTo, identifier, escrowAmount, escrowToken, sourceIdentifier, fromVault);

        unchecked {
            _underwriteEscrowMatchBalance0[escrowToken] -= escrowAmount;
        }
    }

    function deleteUnderwriteAsset(
        bytes32 identifier,
        uint256 U,
        uint256 escrowAmount,
        address escrowToken
    ) override public {
        super.deleteUnderwriteAsset(identifier, U, escrowAmount, escrowToken);
        
        // update the unit tracker. When underwriteAsset was called, the _unitTracker was updated with
        // _unitTrakcer -= int256(U) so we need to cancel that.
        _unitTracker += int256(U);  // It has already been checked on sendAsset that casting to int256 will not overflow.
                                    // Cannot be manipulated by the router as, otherwise, the swapHash check will fail

        unchecked {
            _underwriteEscrowMatchBalance0[escrowToken] -= escrowAmount;
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Simple ERC20 + EIP-2612 implementation.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/tokens/ERC20.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC20.sol)
/// @author Modified from OpenZeppelin (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/token/ERC20/ERC20.sol)
///
/// @dev Note:
/// - The ERC20 standard allows minting and transferring to and from the zero address,
///   minting and transferring zero tokens, as well as self-approvals.
///   For performance, this implementation WILL NOT revert for such actions.
///   Please add any checks with overrides if desired.
/// - The `permit` function uses the ecrecover precompile (0x1).
///
/// If you are overriding:
/// - NEVER violate the ERC20 invariant:
///   the total sum of all balances must be equal to `totalSupply()`.
/// - Check that the overridden function is actually used in the function you want to
///   change the behavior of. Much of the code has been manually inlined for performance.
abstract contract ERC20 {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The total supply has overflowed.
    error TotalSupplyOverflow();

    /// @dev The allowance has overflowed.
    error AllowanceOverflow();

    /// @dev The allowance has underflowed.
    error AllowanceUnderflow();

    /// @dev Insufficient balance.
    error InsufficientBalance();

    /// @dev Insufficient allowance.
    error InsufficientAllowance();

    /// @dev The permit is invalid.
    error InvalidPermit();

    /// @dev The permit has expired.
    error PermitExpired();

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

    /// @dev Emitted when `amount` tokens is transferred from `from` to `to`.
    event Transfer(address indexed from, address indexed to, uint256 amount);

    /// @dev Emitted when `amount` tokens is approved by `owner` to be used by `spender`.
    event Approval(address indexed owner, address indexed spender, uint256 amount);

    /// @dev `keccak256(bytes("Transfer(address,address,uint256)"))`.
    uint256 private constant _TRANSFER_EVENT_SIGNATURE =
        0xddf252ad1be2c89b69c2b068fc378daa952ba7f163c4a11628f55a4df523b3ef;

    /// @dev `keccak256(bytes("Approval(address,address,uint256)"))`.
    uint256 private constant _APPROVAL_EVENT_SIGNATURE =
        0x8c5be1e5ebec7d5bd14f71427d1e84f3dd0314c0f7b2291e5b200ac8c7c3b925;

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

    /// @dev The storage slot for the total supply.
    uint256 private constant _TOTAL_SUPPLY_SLOT = 0x05345cdf77eb68f44c;

    /// @dev The balance slot of `owner` is given by:
    /// ```
    ///     mstore(0x0c, _BALANCE_SLOT_SEED)
    ///     mstore(0x00, owner)
    ///     let balanceSlot := keccak256(0x0c, 0x20)
    /// ```
    uint256 private constant _BALANCE_SLOT_SEED = 0x87a211a2;

    /// @dev The allowance slot of (`owner`, `spender`) is given by:
    /// ```
    ///     mstore(0x20, spender)
    ///     mstore(0x0c, _ALLOWANCE_SLOT_SEED)
    ///     mstore(0x00, owner)
    ///     let allowanceSlot := keccak256(0x0c, 0x34)
    /// ```
    uint256 private constant _ALLOWANCE_SLOT_SEED = 0x7f5e9f20;

    /// @dev The nonce slot of `owner` is given by:
    /// ```
    ///     mstore(0x0c, _NONCES_SLOT_SEED)
    ///     mstore(0x00, owner)
    ///     let nonceSlot := keccak256(0x0c, 0x20)
    /// ```
    uint256 private constant _NONCES_SLOT_SEED = 0x38377508;

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

    /// @dev `(_NONCES_SLOT_SEED << 16) | 0x1901`.
    uint256 private constant _NONCES_SLOT_SEED_WITH_SIGNATURE_PREFIX = 0x383775081901;

    /// @dev `keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)")`.
    bytes32 private constant _DOMAIN_TYPEHASH =
        0x8b73c3c69bb8fe3d512ecc4cf759cc79239f7b179b0ffacaa9a75d522b39400f;

    /// @dev `keccak256("1")`.
    bytes32 private constant _VERSION_HASH =
        0xc89efdaa54c0f20c7adf612882df0950f5a951637e0307cdcb4c672f298b8bc6;

    /// @dev `keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)")`.
    bytes32 private constant _PERMIT_TYPEHASH =
        0x6e71edae12b1b97f4d1f60370fef10105fa2faae0126114a169c64845d6126c9;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       ERC20 METADATA                       */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the name of the token.
    function name() public view virtual returns (string memory);

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

    /// @dev Returns the decimals places of the token.
    function decimals() public view virtual returns (uint8) {
        return 18;
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                           ERC20                            */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the amount of tokens in existence.
    function totalSupply() public view virtual returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := sload(_TOTAL_SUPPLY_SLOT)
        }
    }

    /// @dev Returns the amount of tokens owned by `owner`.
    function balanceOf(address owner) public view virtual returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x0c, _BALANCE_SLOT_SEED)
            mstore(0x00, owner)
            result := sload(keccak256(0x0c, 0x20))
        }
    }

    /// @dev Returns the amount of tokens that `spender` can spend on behalf of `owner`.
    function allowance(address owner, address spender)
        public
        view
        virtual
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x20, spender)
            mstore(0x0c, _ALLOWANCE_SLOT_SEED)
            mstore(0x00, owner)
            result := sload(keccak256(0x0c, 0x34))
        }
    }

    /// @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
    ///
    /// Emits a {Approval} event.
    function approve(address spender, uint256 amount) public virtual returns (bool) {
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the allowance slot and store the amount.
            mstore(0x20, spender)
            mstore(0x0c, _ALLOWANCE_SLOT_SEED)
            mstore(0x00, caller())
            sstore(keccak256(0x0c, 0x34), amount)
            // Emit the {Approval} event.
            mstore(0x00, amount)
            log3(0x00, 0x20, _APPROVAL_EVENT_SIGNATURE, caller(), shr(96, mload(0x2c)))
        }
        return true;
    }

    /// @dev Transfer `amount` tokens from the caller to `to`.
    ///
    /// Requirements:
    /// - `from` must at least have `amount`.
    ///
    /// Emits a {Transfer} event.
    function transfer(address to, uint256 amount) public virtual returns (bool) {
        _beforeTokenTransfer(msg.sender, to, amount);
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the balance slot and load its value.
            mstore(0x0c, _BALANCE_SLOT_SEED)
            mstore(0x00, caller())
            let fromBalanceSlot := keccak256(0x0c, 0x20)
            let fromBalance := sload(fromBalanceSlot)
            // Revert if insufficient balance.
            if gt(amount, fromBalance) {
                mstore(0x00, 0xf4d678b8) // `InsufficientBalance()`.
                revert(0x1c, 0x04)
            }
            // Subtract and store the updated balance.
            sstore(fromBalanceSlot, sub(fromBalance, amount))
            // Compute the balance slot of `to`.
            mstore(0x00, to)
            let toBalanceSlot := keccak256(0x0c, 0x20)
            // Add and store the updated balance of `to`.
            // Will not overflow because the sum of all user balances
            // cannot exceed the maximum uint256 value.
            sstore(toBalanceSlot, add(sload(toBalanceSlot), amount))
            // Emit the {Transfer} event.
            mstore(0x20, amount)
            log3(0x20, 0x20, _TRANSFER_EVENT_SIGNATURE, caller(), shr(96, mload(0x0c)))
        }
        _afterTokenTransfer(msg.sender, to, amount);
        return true;
    }

    /// @dev Transfers `amount` tokens from `from` to `to`.
    ///
    /// Note: Does not update the allowance if it is the maximum uint256 value.
    ///
    /// Requirements:
    /// - `from` must at least have `amount`.
    /// - The caller must have at least `amount` of allowance to transfer the tokens of `from`.
    ///
    /// Emits a {Transfer} event.
    function transferFrom(address from, address to, uint256 amount) public virtual returns (bool) {
        _beforeTokenTransfer(from, to, amount);
        /// @solidity memory-safe-assembly
        assembly {
            let from_ := shl(96, from)
            // Compute the allowance slot and load its value.
            mstore(0x20, caller())
            mstore(0x0c, or(from_, _ALLOWANCE_SLOT_SEED))
            let allowanceSlot := keccak256(0x0c, 0x34)
            let allowance_ := sload(allowanceSlot)
            // If the allowance is not the maximum uint256 value.
            if add(allowance_, 1) {
                // Revert if the amount to be transferred exceeds the allowance.
                if gt(amount, allowance_) {
                    mstore(0x00, 0x13be252b) // `InsufficientAllowance()`.
                    revert(0x1c, 0x04)
                }
                // Subtract and store the updated allowance.
                sstore(allowanceSlot, sub(allowance_, amount))
            }
            // Compute the balance slot and load its value.
            mstore(0x0c, or(from_, _BALANCE_SLOT_SEED))
            let fromBalanceSlot := keccak256(0x0c, 0x20)
            let fromBalance := sload(fromBalanceSlot)
            // Revert if insufficient balance.
            if gt(amount, fromBalance) {
                mstore(0x00, 0xf4d678b8) // `InsufficientBalance()`.
                revert(0x1c, 0x04)
            }
            // Subtract and store the updated balance.
            sstore(fromBalanceSlot, sub(fromBalance, amount))
            // Compute the balance slot of `to`.
            mstore(0x00, to)
            let toBalanceSlot := keccak256(0x0c, 0x20)
            // Add and store the updated balance of `to`.
            // Will not overflow because the sum of all user balances
            // cannot exceed the maximum uint256 value.
            sstore(toBalanceSlot, add(sload(toBalanceSlot), amount))
            // Emit the {Transfer} event.
            mstore(0x20, amount)
            log3(0x20, 0x20, _TRANSFER_EVENT_SIGNATURE, shr(96, from_), shr(96, mload(0x0c)))
        }
        _afterTokenTransfer(from, to, amount);
        return true;
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                          EIP-2612                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev For more performance, override to return the constant value
    /// of `keccak256(bytes(name()))` if `name()` will never change.
    function _constantNameHash() internal view virtual returns (bytes32 result) {}

    /// @dev Returns the current nonce for `owner`.
    /// This value is used to compute the signature for EIP-2612 permit.
    function nonces(address owner) public view virtual returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the nonce slot and load its value.
            mstore(0x0c, _NONCES_SLOT_SEED)
            mstore(0x00, owner)
            result := sload(keccak256(0x0c, 0x20))
        }
    }

    /// @dev Sets `value` as the allowance of `spender` over the tokens of `owner`,
    /// authorized by a signed approval by `owner`.
    ///
    /// Emits a {Approval} event.
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual {
        bytes32 nameHash = _constantNameHash();
        //  We simply calculate it on-the-fly to allow for cases where the `name` may change.
        if (nameHash == bytes32(0)) nameHash = keccak256(bytes(name()));
        /// @solidity memory-safe-assembly
        assembly {
            // Revert if the block timestamp is greater than `deadline`.
            if gt(timestamp(), deadline) {
                mstore(0x00, 0x1a15a3cc) // `PermitExpired()`.
                revert(0x1c, 0x04)
            }
            let m := mload(0x40) // Grab the free memory pointer.
            // Clean the upper 96 bits.
            owner := shr(96, shl(96, owner))
            spender := shr(96, shl(96, spender))
            // Compute the nonce slot and load its value.
            mstore(0x0e, _NONCES_SLOT_SEED_WITH_SIGNATURE_PREFIX)
            mstore(0x00, owner)
            let nonceSlot := keccak256(0x0c, 0x20)
            let nonceValue := sload(nonceSlot)
            // Prepare the domain separator.
            mstore(m, _DOMAIN_TYPEHASH)
            mstore(add(m, 0x20), nameHash)
            mstore(add(m, 0x40), _VERSION_HASH)
            mstore(add(m, 0x60), chainid())
            mstore(add(m, 0x80), address())
            mstore(0x2e, keccak256(m, 0xa0))
            // Prepare the struct hash.
            mstore(m, _PERMIT_TYPEHASH)
            mstore(add(m, 0x20), owner)
            mstore(add(m, 0x40), spender)
            mstore(add(m, 0x60), value)
            mstore(add(m, 0x80), nonceValue)
            mstore(add(m, 0xa0), deadline)
            mstore(0x4e, keccak256(m, 0xc0))
            // Prepare the ecrecover calldata.
            mstore(0x00, keccak256(0x2c, 0x42))
            mstore(0x20, and(0xff, v))
            mstore(0x40, r)
            mstore(0x60, s)
            let t := staticcall(gas(), 1, 0, 0x80, 0x20, 0x20)
            // If the ecrecover fails, the returndatasize will be 0x00,
            // `owner` will be checked if it equals the hash at 0x00,
            // which evaluates to false (i.e. 0), and we will revert.
            // If the ecrecover succeeds, the returndatasize will be 0x20,
            // `owner` will be compared against the returned address at 0x20.
            if iszero(eq(mload(returndatasize()), owner)) {
                mstore(0x00, 0xddafbaef) // `InvalidPermit()`.
                revert(0x1c, 0x04)
            }
            // Increment and store the updated nonce.
            sstore(nonceSlot, add(nonceValue, t)) // `t` is 1 if ecrecover succeeds.
            // Compute the allowance slot and store the value.
            // The `owner` is already at slot 0x20.
            mstore(0x40, or(shl(160, _ALLOWANCE_SLOT_SEED), spender))
            sstore(keccak256(0x2c, 0x34), value)
            // Emit the {Approval} event.
            log3(add(m, 0x60), 0x20, _APPROVAL_EVENT_SIGNATURE, owner, spender)
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero pointer.
        }
    }

    /// @dev Returns the EIP-712 domain separator for the EIP-2612 permit.
    function DOMAIN_SEPARATOR() public view virtual returns (bytes32 result) {
        bytes32 nameHash = _constantNameHash();
        //  We simply calculate it on-the-fly to allow for cases where the `name` may change.
        if (nameHash == bytes32(0)) nameHash = keccak256(bytes(name()));
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Grab the free memory pointer.
            mstore(m, _DOMAIN_TYPEHASH)
            mstore(add(m, 0x20), nameHash)
            mstore(add(m, 0x40), _VERSION_HASH)
            mstore(add(m, 0x60), chainid())
            mstore(add(m, 0x80), address())
            result := keccak256(m, 0xa0)
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  INTERNAL MINT FUNCTIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Mints `amount` tokens to `to`, increasing the total supply.
    ///
    /// Emits a {Transfer} event.
    function _mint(address to, uint256 amount) internal virtual {
        _beforeTokenTransfer(address(0), to, amount);
        /// @solidity memory-safe-assembly
        assembly {
            let totalSupplyBefore := sload(_TOTAL_SUPPLY_SLOT)
            let totalSupplyAfter := add(totalSupplyBefore, amount)
            // Revert if the total supply overflows.
            if lt(totalSupplyAfter, totalSupplyBefore) {
                mstore(0x00, 0xe5cfe957) // `TotalSupplyOverflow()`.
                revert(0x1c, 0x04)
            }
            // Store the updated total supply.
            sstore(_TOTAL_SUPPLY_SLOT, totalSupplyAfter)
            // Compute the balance slot and load its value.
            mstore(0x0c, _BALANCE_SLOT_SEED)
            mstore(0x00, to)
            let toBalanceSlot := keccak256(0x0c, 0x20)
            // Add and store the updated balance.
            sstore(toBalanceSlot, add(sload(toBalanceSlot), amount))
            // Emit the {Transfer} event.
            mstore(0x20, amount)
            log3(0x20, 0x20, _TRANSFER_EVENT_SIGNATURE, 0, shr(96, mload(0x0c)))
        }
        _afterTokenTransfer(address(0), to, amount);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  INTERNAL BURN FUNCTIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Burns `amount` tokens from `from`, reducing the total supply.
    ///
    /// Emits a {Transfer} event.
    function _burn(address from, uint256 amount) internal virtual {
        _beforeTokenTransfer(from, address(0), amount);
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the balance slot and load its value.
            mstore(0x0c, _BALANCE_SLOT_SEED)
            mstore(0x00, from)
            let fromBalanceSlot := keccak256(0x0c, 0x20)
            let fromBalance := sload(fromBalanceSlot)
            // Revert if insufficient balance.
            if gt(amount, fromBalance) {
                mstore(0x00, 0xf4d678b8) // `InsufficientBalance()`.
                revert(0x1c, 0x04)
            }
            // Subtract and store the updated balance.
            sstore(fromBalanceSlot, sub(fromBalance, amount))
            // Subtract and store the updated total supply.
            sstore(_TOTAL_SUPPLY_SLOT, sub(sload(_TOTAL_SUPPLY_SLOT), amount))
            // Emit the {Transfer} event.
            mstore(0x00, amount)
            log3(0x00, 0x20, _TRANSFER_EVENT_SIGNATURE, shr(96, shl(96, from)), 0)
        }
        _afterTokenTransfer(from, address(0), amount);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                INTERNAL TRANSFER FUNCTIONS                 */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Moves `amount` of tokens from `from` to `to`.
    function _transfer(address from, address to, uint256 amount) internal virtual {
        _beforeTokenTransfer(from, to, amount);
        /// @solidity memory-safe-assembly
        assembly {
            let from_ := shl(96, from)
            // Compute the balance slot and load its value.
            mstore(0x0c, or(from_, _BALANCE_SLOT_SEED))
            let fromBalanceSlot := keccak256(0x0c, 0x20)
            let fromBalance := sload(fromBalanceSlot)
            // Revert if insufficient balance.
            if gt(amount, fromBalance) {
                mstore(0x00, 0xf4d678b8) // `InsufficientBalance()`.
                revert(0x1c, 0x04)
            }
            // Subtract and store the updated balance.
            sstore(fromBalanceSlot, sub(fromBalance, amount))
            // Compute the balance slot of `to`.
            mstore(0x00, to)
            let toBalanceSlot := keccak256(0x0c, 0x20)
            // Add and store the updated balance of `to`.
            // Will not overflow because the sum of all user balances
            // cannot exceed the maximum uint256 value.
            sstore(toBalanceSlot, add(sload(toBalanceSlot), amount))
            // Emit the {Transfer} event.
            mstore(0x20, amount)
            log3(0x20, 0x20, _TRANSFER_EVENT_SIGNATURE, shr(96, from_), shr(96, mload(0x0c)))
        }
        _afterTokenTransfer(from, to, amount);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                INTERNAL ALLOWANCE FUNCTIONS                */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Updates the allowance of `owner` for `spender` based on spent `amount`.
    function _spendAllowance(address owner, address spender, uint256 amount) internal virtual {
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the allowance slot and load its value.
            mstore(0x20, spender)
            mstore(0x0c, _ALLOWANCE_SLOT_SEED)
            mstore(0x00, owner)
            let allowanceSlot := keccak256(0x0c, 0x34)
            let allowance_ := sload(allowanceSlot)
            // If the allowance is not the maximum uint256 value.
            if add(allowance_, 1) {
                // Revert if the amount to be transferred exceeds the allowance.
                if gt(amount, allowance_) {
                    mstore(0x00, 0x13be252b) // `InsufficientAllowance()`.
                    revert(0x1c, 0x04)
                }
                // Subtract and store the updated allowance.
                sstore(allowanceSlot, sub(allowance_, amount))
            }
        }
    }

    /// @dev Sets `amount` as the allowance of `spender` over the tokens of `owner`.
    ///
    /// Emits a {Approval} event.
    function _approve(address owner, address spender, uint256 amount) internal virtual {
        /// @solidity memory-safe-assembly
        assembly {
            let owner_ := shl(96, owner)
            // Compute the allowance slot and store the amount.
            mstore(0x20, spender)
            mstore(0x0c, or(owner_, _ALLOWANCE_SLOT_SEED))
            sstore(keccak256(0x0c, 0x34), amount)
            // Emit the {Approval} event.
            mstore(0x00, amount)
            log3(0x00, 0x20, _APPROVAL_EVENT_SIGNATURE, shr(96, owner_), shr(96, mload(0x2c)))
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     HOOKS TO OVERRIDE                      */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Hook that is called before any transfer of tokens.
    /// This includes minting and burning.
    function _beforeTokenTransfer(address from, address to, uint256 amount) internal virtual {}

    /// @dev Hook that is called after any transfer of tokens.
    /// This includes minting and burning.
    function _afterTokenTransfer(address from, address to, uint256 amount) internal virtual {}
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Safe ETH and ERC20 transfer library that gracefully handles missing return values.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/SafeTransferLib.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/SafeTransferLib.sol)
///
/// @dev Note:
/// - For ETH transfers, please use `forceSafeTransferETH` for DoS protection.
/// - For ERC20s, this implementation won't check that a token has code,
///   responsibility is delegated to the caller.
library SafeTransferLib {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The ETH transfer has failed.
    error ETHTransferFailed();

    /// @dev The ERC20 `transferFrom` has failed.
    error TransferFromFailed();

    /// @dev The ERC20 `transfer` has failed.
    error TransferFailed();

    /// @dev The ERC20 `approve` has failed.
    error ApproveFailed();

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

    /// @dev Suggested gas stipend for contract receiving ETH that disallows any storage writes.
    uint256 internal constant GAS_STIPEND_NO_STORAGE_WRITES = 2300;

    /// @dev Suggested gas stipend for contract receiving ETH to perform a few
    /// storage reads and writes, but low enough to prevent griefing.
    uint256 internal constant GAS_STIPEND_NO_GRIEF = 100000;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       ETH OPERATIONS                       */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    // If the ETH transfer MUST succeed with a reasonable gas budget, use the force variants.
    //
    // The regular variants:
    // - Forwards all remaining gas to the target.
    // - Reverts if the target reverts.
    // - Reverts if the current contract has insufficient balance.
    //
    // The force variants:
    // - Forwards with an optional gas stipend
    //   (defaults to `GAS_STIPEND_NO_GRIEF`, which is sufficient for most cases).
    // - If the target reverts, or if the gas stipend is exhausted,
    //   creates a temporary contract to force send the ETH via `SELFDESTRUCT`.
    //   Future compatible with `SENDALL`: https://eips.ethereum.org/EIPS/eip-4758.
    // - Reverts if the current contract has insufficient balance.
    //
    // The try variants:
    // - Forwards with a mandatory gas stipend.
    // - Instead of reverting, returns whether the transfer succeeded.

    /// @dev Sends `amount` (in wei) ETH to `to`.
    function safeTransferETH(address to, uint256 amount) internal {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(call(gas(), to, amount, codesize(), 0x00, codesize(), 0x00)) {
                mstore(0x00, 0xb12d13eb) // `ETHTransferFailed()`.
                revert(0x1c, 0x04)
            }
        }
    }

    /// @dev Sends all the ETH in the current contract to `to`.
    function safeTransferAllETH(address to) internal {
        /// @solidity memory-safe-assembly
        assembly {
            // Transfer all the ETH and check if it succeeded or not.
            if iszero(call(gas(), to, selfbalance(), codesize(), 0x00, codesize(), 0x00)) {
                mstore(0x00, 0xb12d13eb) // `ETHTransferFailed()`.
                revert(0x1c, 0x04)
            }
        }
    }

    /// @dev Force sends `amount` (in wei) ETH to `to`, with a `gasStipend`.
    function forceSafeTransferETH(address to, uint256 amount, uint256 gasStipend) internal {
        /// @solidity memory-safe-assembly
        assembly {
            if lt(selfbalance(), amount) {
                mstore(0x00, 0xb12d13eb) // `ETHTransferFailed()`.
                revert(0x1c, 0x04)
            }
            if iszero(call(gasStipend, to, amount, codesize(), 0x00, codesize(), 0x00)) {
                mstore(0x00, to) // Store the address in scratch space.
                mstore8(0x0b, 0x73) // Opcode `PUSH20`.
                mstore8(0x20, 0xff) // Opcode `SELFDESTRUCT`.
                if iszero(create(amount, 0x0b, 0x16)) { revert(codesize(), codesize()) } // For gas estimation.
            }
        }
    }

    /// @dev Force sends all the ETH in the current contract to `to`, with a `gasStipend`.
    function forceSafeTransferAllETH(address to, uint256 gasStipend) internal {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(call(gasStipend, to, selfbalance(), codesize(), 0x00, codesize(), 0x00)) {
                mstore(0x00, to) // Store the address in scratch space.
                mstore8(0x0b, 0x73) // Opcode `PUSH20`.
                mstore8(0x20, 0xff) // Opcode `SELFDESTRUCT`.
                if iszero(create(selfbalance(), 0x0b, 0x16)) { revert(codesize(), codesize()) } // For gas estimation.
            }
        }
    }

    /// @dev Force sends `amount` (in wei) ETH to `to`, with `GAS_STIPEND_NO_GRIEF`.
    function forceSafeTransferETH(address to, uint256 amount) internal {
        /// @solidity memory-safe-assembly
        assembly {
            if lt(selfbalance(), amount) {
                mstore(0x00, 0xb12d13eb) // `ETHTransferFailed()`.
                revert(0x1c, 0x04)
            }
            if iszero(call(GAS_STIPEND_NO_GRIEF, to, amount, codesize(), 0x00, codesize(), 0x00)) {
                mstore(0x00, to) // Store the address in scratch space.
                mstore8(0x0b, 0x73) // Opcode `PUSH20`.
                mstore8(0x20, 0xff) // Opcode `SELFDESTRUCT`.
                if iszero(create(amount, 0x0b, 0x16)) { revert(codesize(), codesize()) } // For gas estimation.
            }
        }
    }

    /// @dev Force sends all the ETH in the current contract to `to`, with `GAS_STIPEND_NO_GRIEF`.
    function forceSafeTransferAllETH(address to) internal {
        /// @solidity memory-safe-assembly
        assembly {
            // forgefmt: disable-next-item
            if iszero(call(GAS_STIPEND_NO_GRIEF, to, selfbalance(), codesize(), 0x00, codesize(), 0x00)) {
                mstore(0x00, to) // Store the address in scratch space.
                mstore8(0x0b, 0x73) // Opcode `PUSH20`.
                mstore8(0x20, 0xff) // Opcode `SELFDESTRUCT`.
                if iszero(create(selfbalance(), 0x0b, 0x16)) { revert(codesize(), codesize()) } // For gas estimation.
            }
        }
    }

    /// @dev Sends `amount` (in wei) ETH to `to`, with a `gasStipend`.
    function trySafeTransferETH(address to, uint256 amount, uint256 gasStipend)
        internal
        returns (bool success)
    {
        /// @solidity memory-safe-assembly
        assembly {
            success := call(gasStipend, to, amount, codesize(), 0x00, codesize(), 0x00)
        }
    }

    /// @dev Sends all the ETH in the current contract to `to`, with a `gasStipend`.
    function trySafeTransferAllETH(address to, uint256 gasStipend)
        internal
        returns (bool success)
    {
        /// @solidity memory-safe-assembly
        assembly {
            success := call(gasStipend, to, selfbalance(), codesize(), 0x00, codesize(), 0x00)
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                      ERC20 OPERATIONS                      */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Sends `amount` of ERC20 `token` from `from` to `to`.
    /// Reverts upon failure.
    ///
    /// The `from` account must have at least `amount` approved for
    /// the current contract to manage.
    function safeTransferFrom(address token, address from, address to, uint256 amount) internal {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, amount) // Store the `amount` argument.
            mstore(0x40, to) // Store the `to` argument.
            mstore(0x2c, shl(96, from)) // Store the `from` argument.
            mstore(0x0c, 0x23b872dd000000000000000000000000) // `transferFrom(address,address,uint256)`.
            // Perform the transfer, reverting upon failure.
            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
                    call(gas(), token, 0, 0x1c, 0x64, 0x00, 0x20)
                )
            ) {
                mstore(0x00, 0x7939f424) // `TransferFromFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x60, 0) // Restore the zero slot to zero.
            mstore(0x40, m) // Restore the free memory pointer.
        }
    }

    /// @dev Sends all of ERC20 `token` from `from` to `to`.
    /// Reverts upon failure.
    ///
    /// The `from` account must have their entire balance approved for
    /// the current contract to manage.
    function safeTransferAllFrom(address token, address from, address to)
        internal
        returns (uint256 amount)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x40, to) // Store the `to` argument.
            mstore(0x2c, shl(96, from)) // Store the `from` argument.
            mstore(0x0c, 0x70a08231000000000000000000000000) // `balanceOf(address)`.
            // Read the balance, reverting upon failure.
            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    gt(returndatasize(), 0x1f), // At least 32 bytes returned.
                    staticcall(gas(), token, 0x1c, 0x24, 0x60, 0x20)
                )
            ) {
                mstore(0x00, 0x7939f424) // `TransferFromFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x00, 0x23b872dd) // `transferFrom(address,address,uint256)`.
            amount := mload(0x60) // The `amount` is already at 0x60. We'll need to return it.
            // Perform the transfer, reverting upon failure.
            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
                    call(gas(), token, 0, 0x1c, 0x64, 0x00, 0x20)
                )
            ) {
                mstore(0x00, 0x7939f424) // `TransferFromFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x60, 0) // Restore the zero slot to zero.
            mstore(0x40, m) // Restore the free memory pointer.
        }
    }

    /// @dev Sends `amount` of ERC20 `token` from the current contract to `to`.
    /// Reverts upon failure.
    function safeTransfer(address token, address to, uint256 amount) internal {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x14, to) // Store the `to` argument.
            mstore(0x34, amount) // Store the `amount` argument.
            mstore(0x00, 0xa9059cbb000000000000000000000000) // `transfer(address,uint256)`.
            // Perform the transfer, reverting upon failure.
            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
                    call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
                )
            ) {
                mstore(0x00, 0x90b8ec18) // `TransferFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x34, 0) // Restore the part of the free memory pointer that was overwritten.
        }
    }

    /// @dev Sends all of ERC20 `token` from the current contract to `to`.
    /// Reverts upon failure.
    function safeTransferAll(address token, address to) internal returns (uint256 amount) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, 0x70a08231) // Store the function selector of `balanceOf(address)`.
            mstore(0x20, address()) // Store the address of the current contract.
            // Read the balance, reverting upon failure.
            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    gt(returndatasize(), 0x1f), // At least 32 bytes returned.
                    staticcall(gas(), token, 0x1c, 0x24, 0x34, 0x20)
                )
            ) {
                mstore(0x00, 0x90b8ec18) // `TransferFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x14, to) // Store the `to` argument.
            amount := mload(0x34) // The `amount` is already at 0x34. We'll need to return it.
            mstore(0x00, 0xa9059cbb000000000000000000000000) // `transfer(address,uint256)`.
            // Perform the transfer, reverting upon failure.
            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
                    call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
                )
            ) {
                mstore(0x00, 0x90b8ec18) // `TransferFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x34, 0) // Restore the part of the free memory pointer that was overwritten.
        }
    }

    /// @dev Sets `amount` of ERC20 `token` for `to` to manage on behalf of the current contract.
    /// Reverts upon failure.
    function safeApprove(address token, address to, uint256 amount) internal {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x14, to) // Store the `to` argument.
            mstore(0x34, amount) // Store the `amount` argument.
            mstore(0x00, 0x095ea7b3000000000000000000000000) // `approve(address,uint256)`.
            // Perform the approval, reverting upon failure.
            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
                    call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
                )
            ) {
                mstore(0x00, 0x3e3f8f73) // `ApproveFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x34, 0) // Restore the part of the free memory pointer that was overwritten.
        }
    }

    /// @dev Sets `amount` of ERC20 `token` for `to` to manage on behalf of the current contract.
    /// If the initial attempt to approve fails, attempts to reset the approved amount to zero,
    /// then retries the approval again (some tokens, e.g. USDT, requires this).
    /// Reverts upon failure.
    function safeApproveWithRetry(address token, address to, uint256 amount) internal {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x14, to) // Store the `to` argument.
            mstore(0x34, amount) // Store the `amount` argument.
            mstore(0x00, 0x095ea7b3000000000000000000000000) // `approve(address,uint256)`.
            // Perform the approval, retrying upon failure.
            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
                    call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
                )
            ) {
                mstore(0x34, 0) // Store 0 for the `amount`.
                mstore(0x00, 0x095ea7b3000000000000000000000000) // `approve(address,uint256)`.
                pop(call(gas(), token, 0, 0x10, 0x44, codesize(), 0x00)) // Reset the approval.
                mstore(0x34, amount) // Store back the original `amount`.
                // Retry the approval, reverting upon failure.
                if iszero(
                    and(
                        or(eq(mload(0x00), 1), iszero(returndatasize())), // Returned 1 or nothing.
                        call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
                    )
                ) {
                    mstore(0x00, 0x3e3f8f73) // `ApproveFailed()`.
                    revert(0x1c, 0x04)
                }
            }
            mstore(0x34, 0) // Restore the part of the free memory pointer that was overwritten.
        }
    }

    /// @dev Returns the amount of ERC20 `token` owned by `account`.
    /// Returns zero if the `token` does not exist.
    function balanceOf(address token, address account) internal view returns (uint256 amount) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x14, account) // Store the `account` argument.
            mstore(0x00, 0x70a08231000000000000000000000000) // `balanceOf(address)`.
            amount :=
                mul(
                    mload(0x20),
                    and( // The arguments of `and` are evaluated from right to left.
                        gt(returndatasize(), 0x1f), // At least 32 bytes returned.
                        staticcall(gas(), token, 0x10, 0x24, 0x20, 0x20)
                    )
                )
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    /// @dev Calculates `floor(x * y / d)` with full precision.
    /// Throws if result overflows a uint256 or when `d` is zero.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/21/muldiv
    function fullMulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            for {} 1 {} {
                // 512-bit multiply `[p1 p0] = x * y`.
                // Compute the product mod `2**256` and mod `2**256 - 1`
                // then use the Chinese Remainder Theorem to reconstruct
                // the 512 bit result. The result is stored in two 256
                // variables such that `product = p1 * 2**256 + p0`.

                // Least significant 256 bits of the product.
                result := mul(x, y) // Temporarily use `result` as `p0` to save gas.
                let mm := mulmod(x, y, not(0))
                // Most significant 256 bits of the product.
                let p1 := sub(mm, add(result, lt(mm, result)))

                // Handle non-overflow cases, 256 by 256 division.
                if iszero(p1) {
                    if iszero(d) {
                        mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
                        revert(0x1c, 0x04)
                    }
                    result := div(result, d)
                    break
                }

                // Make sure the result is less than `2**256`. Also prevents `d == 0`.
                if iszero(gt(d, p1)) {
                    mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
                    revert(0x1c, 0x04)
                }

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

                // Make division exact by subtracting the remainder from `[p1 p0]`.
                // Compute remainder using mulmod.
                let r := mulmod(x, y, d)
                // `t` is the least significant bit of `d`.
                // Always greater or equal to 1.
                let t := and(d, sub(0, d))
                // Divide `d` by `t`, which is a power of two.
                d := div(d, t)
                // Invert `d mod 2**256`
                // Now that `d` is an odd number, it has an inverse
                // modulo `2**256` such that `d * inv = 1 mod 2**256`.
                // Compute the inverse by starting with a seed that is correct
                // correct for four bits. That is, `d * inv = 1 mod 2**4`.
                let inv := xor(2, mul(3, d))
                // Now use Newton-Raphson iteration to improve the precision.
                // Thanks to Hensel's lifting lemma, this also works in modular
                // arithmetic, doubling the correct bits in each step.
                inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**8
                inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**16
                inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**32
                inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**64
                inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**128
                result :=
                    mul(
                        // Divide [p1 p0] by the factors of two.
                        // Shift in bits from `p1` into `p0`. For this we need
                        // to flip `t` such that it is `2**256 / t`.
                        or(
                            mul(sub(p1, gt(r, result)), add(div(sub(0, t), t), 1)),
                            div(sub(result, r), t)
                        ),
                        // inverse mod 2**256
                        mul(inv, sub(2, mul(d, inv)))
                    )
                break
            }
        }
    }

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

    /// @dev Returns `floor(x * y / d)`.
    /// Reverts if `x * y` overflows, or `d` is zero.
    function mulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to require(d != 0 && (y == 0 || x <= type(uint256).max / y))
            if iszero(mul(d, iszero(mul(y, gt(x, div(not(0), y)))))) {
                mstore(0x00, 0xad251c27) // `MulDivFailed()`.
                revert(0x1c, 0x04)
            }
            z := div(mul(x, y), d)
        }
    }

    /// @dev Returns `ceil(x * y / d)`.
    /// Reverts if `x * y` overflows, or `d` is zero.
    function mulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to require(d != 0 && (y == 0 || x <= type(uint256).max / y))
            if iszero(mul(d, iszero(mul(y, gt(x, div(not(0), y)))))) {
                mstore(0x00, 0xad251c27) // `MulDivFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(mul(x, y), d))), div(mul(x, y), d))
        }
    }

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

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

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

    /// @dev Returns the square root of `x`.
    function sqrt(uint256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // `floor(sqrt(2**15)) = 181`. `sqrt(2**15) - 181 = 2.84`.
            z := 181 // The "correct" value is 1, but this saves a multiplication later.

            // This segment is to get a reasonable initial estimate for the Babylonian method. With a bad
            // start, the correct # of bits increases ~linearly each iteration instead of ~quadratically.

            // Let `y = x / 2**r`. We check `y >= 2**(k + 8)`
            // but shift right by `k` bits to ensure that if `x >= 256`, then `y >= 256`.
            let r := shl(7, lt(0xffffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffffff, shr(r, x))))
            z := shl(shr(1, r), z)

            // Goal was to get `z*z*y` within a small factor of `x`. More iterations could
            // get y in a tighter range. Currently, we will have y in `[256, 256*(2**16))`.
            // We ensured `y >= 256` so that the relative difference between `y` and `y+1` is small.
            // That's not possible if `x < 256` but we can just verify those cases exhaustively.

            // Now, `z*z*y <= x < z*z*(y+1)`, and `y <= 2**(16+8)`, and either `y >= 256`, or `x < 256`.
            // Correctness can be checked exhaustively for `x < 256`, so we assume `y >= 256`.
            // Then `z*sqrt(y)` is within `sqrt(257)/sqrt(256)` of `sqrt(x)`, or about 20bps.

            // For `s` in the range `[1/256, 256]`, the estimate `f(s) = (181/1024) * (s+1)`
            // is in the range `(1/2.84 * sqrt(s), 2.84 * sqrt(s))`,
            // with largest error when `s = 1` and when `s = 256` or `1/256`.

            // Since `y` is in `[256, 256*(2**16))`, let `a = y/65536`, so that `a` is in `[1/256, 256)`.
            // Then we can estimate `sqrt(y)` using
            // `sqrt(65536) * 181/1024 * (a + 1) = 181/4 * (y + 65536)/65536 = 181 * (y + 65536)/2**18`.

            // There is no overflow risk here since `y < 2**136` after the first branch above.
            z := shr(18, mul(z, add(shr(r, x), 65536))) // A `mul()` is saved from starting `z` at 181.

            // Given the worst case multiplicative error of 2.84 above, 7 iterations should be enough.
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))

            // If `x+1` is a perfect square, the Babylonian method cycles between
            // `floor(sqrt(x))` and `ceil(sqrt(x))`. This statement ensures we return floor.
            // See: https://en.wikipedia.org/wiki/Integer_square_root#Using_only_integer_division
            z := sub(z, lt(div(x, z), z))
        }
    }

    /// @dev Returns the cube root of `x`.
    /// Credit to bout3fiddy and pcaversaccio under AGPLv3 license:
    /// https://github.com/pcaversaccio/snekmate/blob/main/src/utils/Math.vy
    function cbrt(uint256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            let r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))

            z := div(shl(div(r, 3), shl(lt(0xf, shr(r, x)), 0xf)), xor(7, mod(r, 3)))

            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)

            z := sub(z, lt(div(x, mul(z, z)), z))
        }
    }

    /// @dev Returns the square root of `x`, denominated in `WAD`.
    function sqrtWad(uint256 x) internal pure returns (uint256 z) {
        unchecked {
            z = 10 ** 9;
            if (x <= type(uint256).max / 10 ** 36 - 1) {
                x *= 10 ** 18;
                z = 1;
            }
            z *= sqrt(x);
        }
    }

    /// @dev Returns the cube root of `x`, denominated in `WAD`.
    function cbrtWad(uint256 x) internal pure returns (uint256 z) {
        unchecked {
            z = 10 ** 12;
            if (x <= (type(uint256).max / 10 ** 36) * 10 ** 18 - 1) {
                if (x >= type(uint256).max / 10 ** 36) {
                    x *= 10 ** 18;
                    z = 10 ** 6;
                } else {
                    x *= 10 ** 36;
                    z = 1;
                }
            }
            z *= cbrt(x);
        }
    }

    /// @dev Returns the factorial of `x`.
    function factorial(uint256 x) internal pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(lt(x, 58)) {
                mstore(0x00, 0xaba0f2a2) // `FactorialOverflow()`.
                revert(0x1c, 0x04)
            }
            for { result := 1 } x { x := sub(x, 1) } { result := mul(result, x) }
        }
    }

    /// @dev Returns the log2 of `x`.
    /// Equivalent to computing the index of the most significant bit (MSB) of `x`.
    /// Returns 0 if `x` is zero.
    function log2(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            // forgefmt: disable-next-item
            r := or(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
                0x0706060506020504060203020504030106050205030304010505030400000000))
        }
    }

    /// @dev Returns the log2 of `x`, rounded up.
    /// Returns 0 if `x` is zero.
    function log2Up(uint256 x) internal pure returns (uint256 r) {
        r = log2(x);
        /// @solidity memory-safe-assembly
        assembly {
            r := add(r, lt(shl(r, 1), x))
        }
    }

    /// @dev Returns the log10 of `x`.
    /// Returns 0 if `x` is zero.
    function log10(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(lt(x, 100000000000000000000000000000000000000)) {
                x := div(x, 100000000000000000000000000000000000000)
                r := 38
            }
            if iszero(lt(x, 100000000000000000000)) {
                x := div(x, 100000000000000000000)
                r := add(r, 20)
            }
            if iszero(lt(x, 10000000000)) {
                x := div(x, 10000000000)
                r := add(r, 10)
            }
            if iszero(lt(x, 100000)) {
                x := div(x, 100000)
                r := add(r, 5)
            }
            r := add(r, add(gt(x, 9), add(gt(x, 99), add(gt(x, 999), gt(x, 9999)))))
        }
    }

    /// @dev Returns the log10 of `x`, rounded up.
    /// Returns 0 if `x` is zero.
    function log10Up(uint256 x) internal pure returns (uint256 r) {
        r = log10(x);
        /// @solidity memory-safe-assembly
        assembly {
            r := add(r, lt(exp(10, r), x))
        }
    }

    /// @dev Returns the log256 of `x`.
    /// Returns 0 if `x` is zero.
    function log256(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(shr(3, r), lt(0xff, shr(r, x)))
        }
    }

    /// @dev Returns the log256 of `x`, rounded up.
    /// Returns 0 if `x` is zero.
    function log256Up(uint256 x) internal pure returns (uint256 r) {
        r = log256(x);
        /// @solidity memory-safe-assembly
        assembly {
            r := add(r, lt(shl(shl(3, r), 1), x))
        }
    }

    /// @dev Returns the scientific notation format `mantissa * 10 ** exponent` of `x`.
    /// Useful for compressing prices (e.g. using 25 bit mantissa and 7 bit exponent).
    function sci(uint256 x) internal pure returns (uint256 mantissa, uint256 exponent) {
        /// @solidity memory-safe-assembly
        assembly {
            mantissa := x
            if mantissa {
                if iszero(mod(mantissa, 1000000000000000000000000000000000)) {
                    mantissa := div(mantissa, 1000000000000000000000000000000000)
                    exponent := 33
                }
                if iszero(mod(mantissa, 10000000000000000000)) {
                    mantissa := div(mantissa, 10000000000000000000)
                    exponent := add(exponent, 19)
                }
                if iszero(mod(mantissa, 1000000000000)) {
                    mantissa := div(mantissa, 1000000000000)
                    exponent := add(exponent, 12)
                }
                if iszero(mod(mantissa, 1000000)) {
                    mantissa := div(mantissa, 1000000)
                    exponent := add(exponent, 6)
                }
                if iszero(mod(mantissa, 10000)) {
                    mantissa := div(mantissa, 10000)
                    exponent := add(exponent, 4)
                }
                if iszero(mod(mantissa, 100)) {
                    mantissa := div(mantissa, 100)
                    exponent := add(exponent, 2)
                }
                if iszero(mod(mantissa, 10)) {
                    mantissa := div(mantissa, 10)
                    exponent := add(exponent, 1)
                }
            }
        }
    }

    /// @dev Convenience function for packing `x` into a smaller number using `sci`.
    /// The `mantissa` will be in bits [7..255] (the upper 249 bits).
    /// The `exponent` will be in bits [0..6] (the lower 7 bits).
    /// Use `SafeCastLib` to safely ensure that the `packed` number is small
    /// enough to fit in the desired unsigned integer type:
    /// ```
    ///     uint32 packed = SafeCastLib.toUint32(FixedPointMathLib.packSci(777 ether));
    /// ```
    function packSci(uint256 x) internal pure returns (uint256 packed) {
        (x, packed) = sci(x); // Reuse for `mantissa` and `exponent`.
        /// @solidity memory-safe-assembly
        assembly {
            if shr(249, x) {
                mstore(0x00, 0xce30380c) // `MantissaOverflow()`.
                revert(0x1c, 0x04)
            }
            packed := or(shl(7, x), packed)
        }
    }

    /// @dev Convenience function for unpacking a packed number from `packSci`.
    function unpackSci(uint256 packed) internal pure returns (uint256 unpacked) {
        unchecked {
            unpacked = (packed >> 7) * 10 ** (packed & 0x7f);
        }
    }

    /// @dev Returns the average of `x` and `y`.
    function avg(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = (x & y) + ((x ^ y) >> 1);
        }
    }

    /// @dev Returns the average of `x` and `y`.
    function avg(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = (x >> 1) + (y >> 1) + (((x & 1) + (y & 1)) >> 1);
        }
    }

    /// @dev Returns the absolute value of `x`.
    function abs(int256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(sub(0, shr(255, x)), add(sub(0, shr(255, x)), x))
        }
    }

    /// @dev Returns the absolute distance between `x` and `y`.
    function dist(int256 x, int256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(mul(xor(sub(y, x), sub(x, y)), sgt(x, y)), sub(y, x))
        }
    }

    /// @dev Returns the minimum of `x` and `y`.
    function min(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), lt(y, x)))
        }
    }

    /// @dev Returns the minimum of `x` and `y`.
    function min(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), slt(y, x)))
        }
    }

    /// @dev Returns the maximum of `x` and `y`.
    function max(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), gt(y, x)))
        }
    }

    /// @dev Returns the maximum of `x` and `y`.
    function max(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), sgt(y, x)))
        }
    }

    /// @dev Returns `x`, bounded to `minValue` and `maxValue`.
    function clamp(uint256 x, uint256 minValue, uint256 maxValue)
        internal
        pure
        returns (uint256 z)
    {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, minValue), gt(minValue, x)))
            z := xor(z, mul(xor(z, maxValue), lt(maxValue, z)))
        }
    }

    /// @dev Returns `x`, bounded to `minValue` and `maxValue`.
    function clamp(int256 x, int256 minValue, int256 maxValue) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, minValue), sgt(minValue, x)))
            z := xor(z, mul(xor(z, maxValue), slt(maxValue, z)))
        }
    }

    /// @dev Returns greatest common divisor of `x` and `y`.
    function gcd(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            for { z := x } y {} {
                let t := y
                y := mod(z, y)
                z := t
            }
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   RAW NUMBER OPERATIONS                    */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns `x + y`, without checking for overflow.
    function rawAdd(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = x + y;
        }
    }

    /// @dev Returns `x + y`, without checking for overflow.
    function rawAdd(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = x + y;
        }
    }

    /// @dev Returns `x - y`, without checking for underflow.
    function rawSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = x - y;
        }
    }

    /// @dev Returns `x - y`, without checking for underflow.
    function rawSub(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = x - y;
        }
    }

    /// @dev Returns `x * y`, without checking for overflow.
    function rawMul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = x * y;
        }
    }

    /// @dev Returns `x * y`, without checking for overflow.
    function rawMul(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = x * y;
        }
    }

    /// @dev Returns `x / y`, returning 0 if `y` is zero.
    function rawDiv(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := div(x, y)
        }
    }

    /// @dev Returns `x / y`, returning 0 if `y` is zero.
    function rawSDiv(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := sdiv(x, y)
        }
    }

    /// @dev Returns `x % y`, returning 0 if `y` is zero.
    function rawMod(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mod(x, y)
        }
    }

    /// @dev Returns `x % y`, returning 0 if `y` is zero.
    function rawSMod(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := smod(x, y)
        }
    }

    /// @dev Returns `(x + y) % d`, return 0 if `d` if zero.
    function rawAddMod(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := addmod(x, y, d)
        }
    }

    /// @dev Returns `(x * y) % d`, return 0 if `d` if zero.
    function rawMulMod(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mulmod(x, y, d)
        }
    }
}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

import { ICatalystV1Structs } from "./ICatalystV1VaultState.sol";
import { ICrossChainReceiver } from "GeneralisedIncentives/src/interfaces/ICrossChainReceiver.sol";

// Autogenerated
interface ICatalystChainInterface is ICatalystV1Structs, ICrossChainReceiver {

    function EXPIRE_CALLER_REWARD() external view returns (uint256);
    function EXPIRE_CALLER_REWARD_DENOMINATOR() external view returns (uint256);
    function UNDERWRITING_COLLATERAL() external view returns (uint256);
    function UNDERWRITING_COLLATERAL_DENOMINATOR() external view returns (uint256);
    function chainIdentifierToDestinationAddress(bytes32) external view returns (bytes memory);
    function connectNewChain(bytes32 chainIdentifier, bytes memory remoteCCI, bytes memory remoteGARP) external;
    function estimateAdditionalCost() external view returns (address asset, uint256 amount);
    function expireUnderwrite(
        address targetVault,
        address toAsset,
        uint256 U,
        uint256 minOut,
        address toAccount,
        uint16 underwriteIncentiveX16,
        bytes memory cdata
    ) external;
    function getUnderwriteIdentifier(
        address targetVault,
        address toAsset,
        uint256 U,
        uint256 minOut,
        address toAccount,
        uint16 underwriteIncentiveX16,
        bytes memory cdata
    ) external pure returns (bytes32 identifier);
    function maxUnderwritingDuration() external view returns (uint256);
    function minGasFor(bytes32) external view returns (uint48);
    function sendCrossChainAsset(
        RouteDescription memory routeDescription,
        uint8 toAssetIndex,
        uint256 U,
        uint256 minOut,
        uint256 fromAmount,
        address fromAsset,
        uint16 underwriteIncentiveX16,
        bytes memory calldata_
    ) external payable;
    function sendCrossChainLiquidity(
        RouteDescription memory routeDescription,
        uint256 U,
        uint256[2] memory minOut,
        uint256 fromAmount,
        bytes memory calldata_
    ) external payable;
    function setMaxUnderwritingDuration(uint256 newMaxUnderwriteDuration) external;
    function setMinGasFor(bytes32 chainIdentifier, uint48 minGas) external;
    function underwrite(
        address targetVault,
        address toAsset,
        uint256 U,
        uint256 minOut,
        address toAccount,
        uint16 underwriteIncentiveX16,
        bytes memory cdata
    ) external returns (bytes32 identifier);
    function underwriteAndCheckConnection(
        bytes32 sourceIdentifier,
        bytes memory fromVault,
        address targetVault,
        address toAsset,
        uint256 U,
        uint256 minOut,
        address toAccount,
        uint16 underwriteIncentiveX16,
        bytes memory cdata
    ) external;
    function underwritingStorage(bytes32) external view returns (uint256 tokens, address refundTo, uint96 expiry);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;


int256 constant WADWAD = 1e36;
uint256 constant LN2 = 693147180559945344; // from numpy import np; int(np.log(2)*10**18).

// library MathConstants {
//     int256 internal constant WADWAD = 1e36;
//     uint256 internal constant LN2 = 693147180559945344; // from numpy import np; int(np.log(2)*10**18).
// }

//SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.19;

import { Ownable } from "solady/auth/Ownable.sol";
import {ERC20} from 'solady/tokens/ERC20.sol';
import {SafeTransferLib} from 'solady/utils/SafeTransferLib.sol';
import { ReentrancyGuard} from "solady/utils/ReentrancyGuard.sol";
import { Initializable } from "solady/utils/Initializable.sol";
import { Multicallable } from "solady/utils/Multicallable.sol";
import { FixedPointMathLib} from "solady/utils/FixedPointMathLib.sol";

import { IMessageEscrowStructs } from "GeneralisedIncentives/src/interfaces/IMessageEscrowStructs.sol";

import { ICatalystReceiver} from "./interfaces/IOnCatalyst.sol";
import { ICatalystV1Factory } from "./interfaces/ICatalystV1Factory.sol";
import "./interfaces/ICatalystV1VaultErrors.sol";
import { MAX_GOVERNANCE_FEE_SHARE } from"./CatalystFactory.sol";
import { ICatalystV1Vault } from "./ICatalystV1Vault.sol";

/**
 * @title Catalyst: Common Vault Logic
 * @author Cata Labs Inc.
 * @notice This abstract contract defines general logic of a Catalyst vault like:
 * - Vault Token through Solmate's ERC20 implementation.
 * - Connection management
 * - Security limit
 * - Swap Escrow
 *
 * By inheriting this abstract contract, a Vault automatically implements common vault logic.
 * @dev This contract uses the following special notation:
 * CAPITAL_LETTER_VARIABLES are constants or immutable.
 * _ prefixed varaibles are storage.
 * _ prefixed functions are internal.
 * Unless otherwise required, variables are exposed directly. Such that storage functions are
 * prefixed with _.
 *
 * Upon deleting the escrow, this contract special logic in case of refunds. We want to ensure that
 * any acks does not revert to clear up the escrows. However, some tokens can revert on demand (blacklist tokens)
 * For these tokens, we make an optimistic call to the token to send the assets to the user. We don't
 * care if it actually goes through. Cases where this call would fail the user does not get anything.
 * A caveat of the implementation is that tokens that revert by PANIC'ing or spending all gas, are not supported
 * since there is a catch of OOO gas that reverts. It is then dependent on replaying the ack to release the escrow.
 */
abstract contract CatalystVaultCommon is
    Initializable,
    Multicallable,
    ReentrancyGuard,
    ERC20,
    ICatalystV1Vault
{
    /** @notice The fallback user used as a FALLBACK placeholder when underwrite escrows are set. */
    address constant UNDERWRITE_FALLBACK_USER = address(uint160(1));

    //--- Config ---//
    // The following section contains the configurable variables.

    /**
     * @notice Determines how fast the security limit decreases.
     * @dev Needs to be long enough for vault token providers to be notified of a breach but short enough for volatility to not soft-freeze the vault.
     */
    uint256 constant DECAY_RATE = 1 days;

    /** @notice Number of decimals used by the vault's vault tokens */
    uint8 constant DECIMALS = 18;

    /**
     * @notice The vault tokens initially minted to the user who set up the vault.
     * @dev The initial deposit along with this value determines the base value of a vault token.
     */
    uint256 constant INITIAL_MINT_AMOUNT = 1e18; // 10**decimals

    /**
     * @notice Maximum number of assets supported
     * @dev Impacts the cost of some for loops. Can be changed without breaking compatibility.
     */
    uint8 constant MAX_ASSETS = 3;

    //-- ERC20 --//

    string _name;
    string _symbol;

    function name() public override view returns(string memory) {
        return _name;
    }

    function symbol() public override view returns(string memory) {
        return _symbol;
    }

    //-- Variables --//

    // immutable variables can be read by proxies, thus it is safe to set this on the constructor.
    address public immutable FACTORY;
    address public _chainInterface;

    /**
     * @notice The approved connections for this vault, stored as _vaultConnection[connectionId][toVault]
     * @dev to vault is encoded as 64 + 1 bytes.
     */
    mapping(bytes32 => mapping(bytes => bool)) public _vaultConnection;

    /**
     * @notice To indicate which token is desired on the target vault,
     * the desired tokens are provided as an integer which maps to the
     * asset address. This variable is the map.
     */
    mapping(uint256 => address) public _tokenIndexing;

    /** @notice The token weights. Used for maintaining a non-symmetric vault asset balance. */
    mapping(address => uint256) public _weight;

    //-- Parameter Flow & Change variables --//

    // Use getUnitCapacity to indirectly access these variables
    uint256 _usedUnitCapacity;
    uint48 public _adjustmentTarget;

    uint48 public _lastModificationTime;
    uint48 _usedUnitCapacityTimestamp;

    //-- Vault fee variables --//

    /**
     * @notice The total vault fee. Multiplied by 10**18. 
     * @dev To compute the respective fee, use mulWad: FixedPointMathLib.mulWad(amount, _vaultFee);
     */
    uint64 public _vaultFee;

    /**
     * @notice The governance's cut of _vaultFee. 
     * @dev Usage: FixedPointMathLib.mulWad(FixedPointMathLib.mulWad(amount, _vaultFee), _governanceFeeShare);
     */
    uint64 public _governanceFeeShare;

    /** @notice The vault fee can be changed. _feeAdministrator is the address allowed to change it */
    address public _feeAdministrator; 

    /**
     * @notice The setupMaster is the short-term owner of the vault.
     * They can connect the vault to vaults on other chains.
     * @dev !Can extract all of the vault value! Should be set to address(0) once setup is complete via 'finishSetup()'.
     */
    address public _setupMaster;

    //--- Messaging router limit ---//
    // The router is not completely trusted. Some limits are
    // imposed on the DECAY_RATE-ly unidirectional liquidity flow. That is:
    // if the vault observes more than _maxUnitCapacity of incoming
    // units, then it will not accept further incoming units. This means the router
    // can only drain a prefigured percentage of the vault every DECAY_RATE.
    // For amplified vaults, the security limit is denominated in assets rather than Units.

    // Outgoing flow is subtracted from incoming flow until 0.

    /** @notice The max incoming liquidity flow from the router. */
    uint256 public _maxUnitCapacity;

    // Escrow reference
    /** @notice Total current escrowed tokens. */
    mapping(address => uint256) public _escrowedTokens;
    /** @notice Total current escrowed vault tokens. */
    uint256 public _escrowedVaultTokens;

    /** @notice Find escrow information. Used for both normal swaps and liquidity swaps. */
    mapping(bytes32 => address) public _escrowLookup;

    /**
     * @notice A mathematical lib that describes various properties of this contract.
     * These helper functions are not contained in the swap template, since they notisably inflate
     * the contract side which reduceses the number of optimizer runs => increase the gas cost.
     */
    address immutable public MATHLIB;

    constructor(address factory_, address mathlib) payable {
        FACTORY = factory_;
        MATHLIB = mathlib;

        _name = "Catalyst Vault Template";
        _symbol = "";

        // Disable the contract from being initialized. This ensures the factory is
        // used to deploy vaults.
        _disableInitializers();
    }

    /** @notice Get the factory owner. That is the owner that can configure this vault post finishSetup(). */
    function factoryOwner() public view override returns (address) {
        return Ownable(FACTORY).owner();
    }

    /** @notice Governance fee destination. This is the address the governance fee is sent to. */
    function governanceFeeDestination() public view override returns (address) {
        return ICatalystV1Factory(FACTORY)._governanceFeeDestination();
    }

    /**
     * @notice Only allow Governance to change vault parameters
     * @dev Because of dangerous permissions (setConnection, weight changes):
     * !CatalystFactory(_factory).owner() must be set to a timelock! 
     */ 
    modifier onlyFactoryOwner() {
        require(msg.sender == factoryOwner()); // dev: Only factory owner
        _;
    }

    /**
     * @notice Require the sender of the transaction to be the chain interface. 
     */
     modifier onlyChainInterface() {
        require(msg.sender == _chainInterface); // dev: Only chain interface
        _;
    }

    /**
     * @notice Verify a connected pool.
     */ 
    modifier onlyConnectedPool(bytes32 channelId, bytes memory vault) {
        // Only allow connected vaults
        if (!_vaultConnection[channelId][vault]) revert VaultNotConnected();
        _;
    }

    // -- Receive Abstract Functions -- //

    function _receiveAsset(
        address toAsset,
        uint256 U,
        uint256 minOut
    ) virtual internal returns (uint256);

    // -- Setup Functions -- //

    /**
     * @notice Setup a vault.
     * @dev Is initializer.
     * @param name_ Name of the vault token.
     * @param symbol_ Symbol of the vault token.
     * @param chainInterface The chain interface to use. Set address(0) to disable cross-chain swaps.
     * @param vaultFee Initial vault fee, that is the fee charged on swaps.
     * @param governanceFee Initial governance fee, that is the percentage of the vault fee that is sent to designated address.
     * @param feeAdministrator Special address that can modify the pool fees.
     * @param setupMaster User that is configuring the vault.
     */
    function setup(
        string calldata name_,
        string calldata symbol_,
        address chainInterface,
        uint64 vaultFee,
        uint64 governanceFee,
        address feeAdministrator,
        address setupMaster
    ) initializer external override {
        // The vault is designed to be used by a proxy and not as a standalone vault.
        // initializer ensures this function is only called once.

        _chainInterface = chainInterface;
        _setupMaster = setupMaster;

        _setVaultFee(vaultFee);
        _setGovernanceFee(governanceFee);
        _setFeeAdministrator(feeAdministrator);

        // Name the ERC20 vault token
        _name = name_;
        _symbol = symbol_;
    }


    /**
     * @notice Creates a connection to toVault on the channelId.
     * @dev Encoding addresses in 64 + 1 bytes for EVM.
     * For Solidity, this can be done as bytes.concat(bytes1(0x14), bytes32(0), abi.encode(toAddress))
     * @param channelId Target chain identifier. Varies from AMB to AMB.
     * @param toVault 64 + 1 bytes representation of the target vault.
     * @param state Boolean indicating if the connection should be open or closed.
     */
    function setConnection(
        bytes32 channelId,
        bytes calldata toVault,
        bool state
    ) external override {
        require(msg.sender == _setupMaster); // dev: No auth
        require(toVault.length == 65); // dev: Vault addresses are uint8 + 64 bytes.

        _vaultConnection[channelId][toVault] = state;

        emit SetConnection(channelId, toVault, state);
    }

    /**
     * @notice Gives up short-term ownership of the vault. This makes the vault unstoppable.
     * @dev This function should ALWAYS be called before other liquidity providers deposit liquidity.
     * While it is not recommended, swapping should be relativly safe since because of the escrow (assuming a minimum output is set).
     */
    function finishSetup() external override {
        require(msg.sender == _setupMaster); // dev: No auth

        _setupMaster = address(0);

        emit FinishSetup();
    }

    /**
     * @notice View function to signal if a vault is safe to use.
     * @dev Checks if setupMaster has been set to ZERO_ADDRESS.  In other words, has finishSetup been called?
     * This function is not "safe()". To properly verify if a pool is "ready", verify:
     *  - The vault template is trusted.
     *  - The cross-chain interfce is trusted.
     *  - All connections are correctly set. (Valid chains, valid vaults)
     *
     * If you are providing liquidity to a vault, furthermore check:
     *  - All assets in the pool are trusted.
     *
     * The above checks have to be done on every vault in the pool.
     */
    function ready() external view override returns (bool) {
        // _setupMaster == address(0) ensures a safe pool cannot be made unsafe. The setup master can drain the pool!
        // _tokenIndexing[0] != address(0) check if the pool has been initialized correctly.
        // The additional check is there to ensure that the initial deployment returns false. 
        return _setupMaster == address(0) && _tokenIndexing[0] != address(0);
    }


    /**
     * @notice Returns the current cross-chain swap capacity.
     * @dev can be overridden to implement other limit curves.
     */
    function getUnitCapacity() public view virtual override returns (uint256) {
        uint256 MUC = _maxUnitCapacity;

        // The delta change to the limit is: timePassed · slope = timePassed · Max/decayrate
        uint256 unitCapacityReleased;
        unchecked {
            // block.timestamp >= _usedUnitCapacityTimestamp, always.
            // MUC is generally low.
            unitCapacityReleased = block.timestamp - _usedUnitCapacityTimestamp;

            // This line can overflow. While unlikely to, if it does it would semi-freeze the pool until
            // some assets are withdrawn. As a fix, let if overflow. If it overflows, then 
            // unitCapacityReleased becomes smaller so there are no security implications.
            unitCapacityReleased *= MUC;

            // DECAY_RATE != 0.
            unitCapacityReleased /= DECAY_RATE;
        }

        uint256 UC = _usedUnitCapacity;
        // If the change is greater than the units than the spent security limit return maximum.
        //If we computed it as (MUC - UC + unitCapacityReleased > MUC) it would obviously be wrong.
        if (UC <= unitCapacityReleased) return MUC;

        // Amplified vaults can have MUC <= UC since MUC is modified when swapping.
        unchecked {
            // We know UC > unitCapacityReleased.
            if (MUC <= UC - unitCapacityReleased) return 0; 

            // We know UC > unitCapacityReleased and with the above statement we know
            // MUC > (UC - unitCapacityReleased). Thus we can compute the difference unchecked.
            return MUC - (UC - unitCapacityReleased);
        }

    }

    // -- Utils -- // 

    /**
     * @notice Check if the vault supports an inflow of units and decrease
     * unit capacity by the inflow.
     * @dev Implement a lot of similar logic to getUnitCapacity. 
     * @param Units The number of units to check and set.
     */
    function _updateUnitCapacity(uint256 Units) internal {
        uint256 MUC = _maxUnitCapacity;

        // The delta change to the limit is: timePassed · slope = timePassed · Max/decayrate
        uint256 unitCapacityReleased;
        unchecked {
            // block.timestamp > _usedUnitCapacityTimestamp, always.
            // MUC is generally low.
            unitCapacityReleased = (block.timestamp - _usedUnitCapacityTimestamp);

            // This line can overflow. While unlikely to, if it does it would semi-freeze the pool until
            // some assets are withdrawn. As a fix, let if overflow. If it overflows, then 
            // unitCapacityReleased becomes smaller so there are no security implications.
            unitCapacityReleased *= MUC;

            // DECAY_RATE != 0.
            unitCapacityReleased /= DECAY_RATE;
        }

        uint256 UC = _usedUnitCapacity; 
        // If the change is greater than the units than the spent security limit it is at max.
        if (UC <= unitCapacityReleased) {
            // The new limit is MUC, check if more units than MUC are getting spent.
            if (Units > MUC) revert ExceedsSecurityLimit();
            // Set last change and the new spent security limit.
            _usedUnitCapacityTimestamp = uint48(block.timestamp);
            _usedUnitCapacity = Units;
            return;
        }
        
        // Compute the new spent security limit. Start by adding used unit capacity
        // and to be spent units
        uint256 newUnitFlow = UC + Units;
        unchecked {
            // Then subtract the units that have been decayed. We know UC + Units >= UC > unitCapacityReleased
            newUnitFlow -= unitCapacityReleased;
        }
        // Then check if the new spent security limit is larger than maximum. 
        if (newUnitFlow > MUC) revert ExceedsSecurityLimit();

        // Set last change and the new spent security limit.
        _usedUnitCapacityTimestamp = uint48(block.timestamp);
        _usedUnitCapacity = newUnitFlow;
    }


    // -- Governance Functions -- //

    /** @notice Sets a new fee administrator that can configure vault fees. */ 
    function _setFeeAdministrator(address administrator) internal {
        _feeAdministrator = administrator;
        emit SetFeeAdministrator(administrator);
    }

    /**
     * @notice Sets a new vault fee, taken from input amount.
     * @param fee Fee in WAD terms. 12e16 is 12%.
     */
    function _setVaultFee(uint64 fee) internal {
        require(fee <= FixedPointMathLib.WAD); // dev: VaultFee is maximum 100%.
        _vaultFee = fee;
        emit SetVaultFee(fee);
    }

    /**
     * @notice Sets a new governance fee. Taken of the vault fee.
     * @param fee Fee in WAD terms. 12e16 is 12%.
     */
    function _setGovernanceFee(uint64 fee) internal {
        require(fee <= MAX_GOVERNANCE_FEE_SHARE);  // dev: Maximum GovernanceFeeSare exceeded.
        _governanceFeeShare = fee;
        emit SetGovernanceFee(fee);
    }

    /** @notice Allows the factory owner to set a new fee administrator. */
    function setFeeAdministrator(address administrator) public override onlyFactoryOwner {
        _setFeeAdministrator(administrator);
    }

    /** 
     * @notice Allows the factory owner to set the governance fee.
     * @dev Can only be called by factory owner.
     * @param fee Fee in WAD terms. 12e16 is 12%.
     */
    function setGovernanceFee(uint64 fee) public override onlyFactoryOwner {
        _setGovernanceFee(fee);
    }

    /**
     * @notice Allows the feeAdministrator to modify the vault fee.
     * @dev Can only be called by feeAdministrator
     * @param fee Fee in WAD terms. 12e16 is 12%.
     */
    function setVaultFee(uint64 fee) public override {
        require(msg.sender == _feeAdministrator); // dev: Only feeAdministrator can set new fee
        _setVaultFee(fee);
    }

    /**
     * @notice Collect the governance fee share of the specified vault fee.
     * @dev The governance fee share is transfered to governanceFeeDestination.
     */
    function _collectGovernanceFee(address asset, uint256 vaultFeeAmount) internal {
        uint256 governanceFeeShare = _governanceFeeShare;

        // If governanceFeeShare == 0, then skip the rest of the logic.
        if (governanceFeeShare != 0) {
            uint256 governanceFeeAmount = FixedPointMathLib.mulWad(vaultFeeAmount, governanceFeeShare);
            SafeTransferLib.safeTransfer(asset, governanceFeeDestination(), governanceFeeAmount);
        }
    }

    //-- Escrow Functions --//

    /**
     * @notice Create a token escrow for a swap.
     * @dev It is not checked if fallbackUser is set to address(0) but if it is, the escrow is lost.
     * @param sendAssetHash The escrow context hash. Will be used to recover the escrow.
     * From a implementation / usage perspective, if this hash contains fromAsset and amount
     * it will improves by allowing on to verify these values independently.
     * @param fallbackUser The user who the escrow belongs to. Do not set to address(0).
     * @param fromAsset Asset to escrow.
     * @param amount Amount to escrow.
     */
    function _setTokenEscrow(
        bytes32 sendAssetHash,
        address fallbackUser,
        address fromAsset,
        uint256 amount
    ) internal {
        if (_escrowLookup[sendAssetHash] != address(0))  revert EscrowAlreadyExists();
        _escrowLookup[sendAssetHash] = fallbackUser;
        unchecked {
            // Must be less than the vault balance.
            _escrowedTokens[fromAsset] += amount;
        }
    }

    /**
     * @notice Create a liquidity escrow for a swap.
     * @dev It is not checked if fallbackUser is set to address(0) but if it is, the escrow is lost.
     * @param sendLiquidityHash The escrow context hash. Will be used to recover the escrow.
     * From a implementation / usage perspective, if this hash contains vaultTokens
     * it will improves by allowing on to verify these values independently.
     * @param fallbackUser The user who the escrow belongs to. Do not set to address(0).
     * @param vaultTokens Number of vault tokens to escrow.
     */
    function _setLiquidityEscrow(
        bytes32 sendLiquidityHash,
        address fallbackUser,
        uint256 vaultTokens
    ) internal {
        if (_escrowLookup[sendLiquidityHash] != address(0)) revert EscrowAlreadyExists();
        _escrowLookup[sendLiquidityHash] = fallbackUser;

        // Escrow vault tokens are first burned and then escrowed. As a result, this may overflow unlike _escrowedTokens.
        _escrowedVaultTokens += vaultTokens;
    }

    /**
     * @notice Returns the fallbackUser for the escrow and cleans up the escrow information.
     * @dev 'delete _escrowLookup[sendAssetHash]' ensures this function can only be called once.
     */
    function _releaseAssetEscrow(
        bytes32 sendAssetHash,
        uint256 escrowAmount,
        address escrowToken
    ) internal returns(address) {
        address fallbackUser = _escrowLookup[sendAssetHash]; // Passing in an invalid swapHash returns address(0).
        require(fallbackUser != address(0)); // dev: Invalid swapHash. Alt: Escrow doesn't exist.
        delete _escrowLookup[sendAssetHash]; // Stops timeout and further acks from being called.

        unchecked {
            // escrowAmount \subseteq _escrowedTokens => escrowAmount <= _escrowedTokens. 
            // Cannot be called twice since the 3 lines before ensure this can only be reached once.
            _escrowedTokens[escrowToken] -= escrowAmount;
        }
        
        return fallbackUser;
    }

    /**
     * @notice Returns the fallbackUser for the escrow and cleans up the escrow information.
     * @dev 'delete _escrowLookup[sendAssetHash]' ensures this function can only be called once.
     */
    function _releaseLiquidityEscrow(
        bytes32 sendLiquidityHash,
        uint256 escrowAmount
    ) internal returns(address) {
        address fallbackUser = _escrowLookup[sendLiquidityHash]; // Passing in an invalid swapHash returns address(0).
        require(fallbackUser != address(0)); // dev: Invalid swapHash. Alt: Escrow doesn't exist.
        delete _escrowLookup[sendLiquidityHash]; // Stops timeout and further acks from being called.

        unchecked {
            // escrowAmount \subseteq _escrowedVaultTokens => escrowAmount <= _escrowedVaultTokens.
            // Cannot be called twice since the 3 lines before ensure this can only be reached once.
            _escrowedVaultTokens -= escrowAmount;
        }

        return fallbackUser;
    }

    /** 
     * @notice Implements basic ack logic: Deletes and releases tokens to the vault
     * @dev Should never revert! For security limit adjustments, the implementation may have to be overwritten.
     * @param toAccount Recipient of the transaction on the target chain.
     * @param U Number of units initially purchased.
     * @param escrowAmount Number of tokens escrowed.
     * @param escrowToken Address of the escrowed token.
     * @param blockNumberMod Block number when the transaction was commited (mod 32)
     */
    function onSendAssetSuccess(
        bytes32 channelId,
        bytes calldata toAccount,
        uint256 U,
        uint256 escrowAmount,
        address escrowToken,
        uint32 blockNumberMod
    ) onlyChainInterface public override virtual {
        // We need to find the location of the escrow using the information below.
        // We need to do this twice: 1. Get the address. 2. Delete the escrow.
        // To save a bit of gas, this hash is computed, cached, and then used.
        bytes32 sendAssetHash = _computeSendAssetHash( // Computing the hash doesn't revert.
            toAccount,      // Ensures no collisions between different users
            U,              // Used to randomise the hash
            escrowAmount,   // Required! to validate release escrow data
            escrowToken,    // Required! to validate release escrow data
            blockNumberMod  // Used to randomize the hash.
        );

        _releaseAssetEscrow(sendAssetHash, escrowAmount, escrowToken); // Only reverts for missing escrow

        emit SendAssetSuccess(
            channelId,
            toAccount,
            U,
            escrowAmount,
            escrowToken,
            blockNumberMod
        );
    }

    /** 
     * @notice Implements basic timeout logic: Deletes and sends tokens to the user.
     * @dev Should never revert!
     * For blacklist tokens, this function contains custom logic to support failing ERC20 transfer.
     * If an ERC20 transfer fails (say because of a blocklist), we only revert if it was because of OOO.
     * This implies that if an ERC20 transfer fails, then the escrow is lost. This shouldn't be the cast
     * except if a token is paused, blacklisted, or the vault is exploited such that it has less assets
     * than the escrow.
     * @param toAccount Recipient of the transaction on the target chain. Encoded in bytes32.
     * @param U Number of units initially purchased.
     * @param escrowAmount Number of tokens escrowed.
     * @param escrowToken Token escrowed.
     * @param blockNumberMod Block number of the transaction that commited the swap (mod 32)
     */
    function onSendAssetFailure(
        bytes32 channelId,
        bytes calldata toAccount,
        uint256 U,
        uint256 escrowAmount,
        address escrowToken,
        uint32 blockNumberMod
    ) onlyChainInterface public override virtual {
        // We need to find the location of the escrow using the information below.
        // We need to do this twice: 1. Get the address. 2. Delete the escrow.
        // To save a bit of gas, this hash is computed and saved and then used.
        bytes32 sendAssetHash = _computeSendAssetHash( // Computing the hash doesn't revert.
            toAccount,      // Ensures no collisions between different users
            U,              // Used to randomise the hash
            escrowAmount,   // Required! to validate release escrow data
            escrowToken,    // Required! to validate release escrow data
            blockNumberMod  // Used to randomize the hash.
        );

        // This call provides re-entry protection against re-entering this call. Otherwise, this call can always be called.
        address fallbackAddress = _releaseAssetEscrow(sendAssetHash, escrowAmount, escrowToken); // Only reverts for missing escrow,

        // We are going to make a low-level call. It may revert (see comment below) but it should not revert if it runs out of gas (that should be raised).
        // As such, get the current gas in the contract.
        uint256 gasLeftBeforeCall = gasleft();

        bool success;
        // Make a low level call such that the transfer never fails. This is important for tokens using block lists.
        // This also implies that if you get blacklisted between when you initiated the swap and the swap failed, you would lose the tokens.
        bytes memory payload = abi.encodeWithSignature("transfer(address,uint256)", fallbackAddress, escrowAmount);
        assembly ("memory-safe") {
            // The gas limit is set to 0x8000000000000000000000000000000000000000000000000000000000000000.
            // This is essentially all gas since the actual gas forwarded is min(gasForwarded, gasleft * 63/64).
            success := call(0x8000000000000000000000000000000000000000000000000000000000000000, escrowToken, 0,  add(payload, 0x20), mload(payload), 0, 0)
            // SafeTransferLib.safeTransferFrom(escrowToken, fallbackAddress, escrowAmount);
        }

        // If the call failed, check if it failed with OOO (If the call used all of the gas it has available).
        if (!success) if (gasleft() < gasLeftBeforeCall * 1 / 63) revert NotEnoughGas();

        emit SendAssetFailure(
            channelId,
            toAccount,
            U,
            escrowAmount,
            escrowToken,
            blockNumberMod
        );
    }

    /** 
     * @notice Implements basic liquidity ack logic: Deletes and releases vault tokens to the vault.
     * @dev Should never revert! For security limit adjustments, the implementation should be overwritten.
     * @param toAccount Recipient of the transaction on the target chain.
     * @param U Number of units initially acquired.
     * @param escrowAmount Number of vault tokens escrowed.
     * @param blockNumberMod Block number at which the swap transaction was commited (mod 32)
     */
    function onSendLiquiditySuccess(
        bytes32 channelId,
        bytes calldata toAccount,
        uint256 U,
        uint256 escrowAmount,
        uint32 blockNumberMod
    ) onlyChainInterface public override virtual {

        // We need to find the location of the escrow using the information below.
        // We need to do this twice: 1. Get the address. 2. Delete the escrow.
        // To save a bit of gas, this hash is computed and saved and then used.
        bytes32 sendLiquidityHash = _computeSendLiquidityHash(
            toAccount,      // Ensures no collisions between different users
            U,              // Used to randomise the hash
            escrowAmount,   // Required! to validate release escrow data
            blockNumberMod  // Used to randomize the hash.
        );

        _releaseLiquidityEscrow(sendLiquidityHash, escrowAmount); // Reverts for missing escrow

        emit SendLiquiditySuccess(
            channelId,
            toAccount,
            U,
            escrowAmount,
            blockNumberMod
        );
    }

    /** 
     * @notice Implements basic liquidity timeout logic: Deletes and sends vault tokens to the user.
     * @dev Should never revert!
     * @param toAccount Recipient of the transaction on the target chain. Encoded in bytes32.
     * @param U Number of units initially acquired.
     * @param escrowAmount Number of vault tokens escrowed.
     * @param blockNumberMod Block number at which the swap transaction was commited (mod 32)
     */
    function onSendLiquidityFailure(
        bytes32 channelId,
        bytes calldata toAccount,
        uint256 U,
        uint256 escrowAmount,
        uint32 blockNumberMod
    ) onlyChainInterface public override virtual {

        bytes32 sendLiquidityHash = _computeSendLiquidityHash(
            toAccount,      // Ensures no collisions between different users
            U,              // Used to randomise the hash
            escrowAmount,   // Required! to validate release escrow data
            blockNumberMod  // Used to randomize the hash.
        );

        // This function only allows entering this function once. Once called, it can never be called without reverting again.
        address fallbackAddress = _releaseLiquidityEscrow(sendLiquidityHash, escrowAmount); // Reverts for missing escrow

        _mint(fallbackAddress, escrowAmount); // Never reverts.

        emit SendLiquidityFailure(
            channelId,
            toAccount,
            U,
            escrowAmount,
            blockNumberMod
        );
    }

    /** 
     * @notice Computes a unique identifier for a swap. This unique identifier can be used to identify swaps cross-chain.
     * However, it is never exposed. This is done to let the hashing algorithm be flexible between implementations.
     */
    function _computeSendAssetHash(
        bytes calldata toAccount,
        uint256 U,
        uint256 amount,
        address fromAsset,
        uint32 blockNumberMod
    ) internal pure returns(bytes32) {
        return keccak256(
            bytes.concat(
                toAccount,               // Ensures no collisions between different users.
                bytes32(U),              // Used to randomise the hash.
                bytes32(amount),         // Required! to validate release escrow data.
                bytes20(fromAsset),      // Required! to validate release escrow data.
                bytes4(blockNumberMod)   // Used to randomize the hash.
            )
        );
    }

    /**
     * @notice Computes a unique identifier for a swap. This unique identifier can be used to identify swaps cross-chain.
     * However, it is never exposed. This is done to let the hashing algorithm be flexible between implementations.
     */
    function _computeSendLiquidityHash(
        bytes calldata toAccount,
        uint256 U,
        uint256 amount,
        uint32 blockNumberMod
    ) internal pure returns(bytes32) {
        return keccak256(
            bytes.concat(
                toAccount,               // Ensures no collisions between different users.
                bytes32(U),              // Used to randomise the hash.
                bytes32(amount),         // Required! to validate release escrow data.
                bytes4(blockNumberMod)   // Used to randomize the hash.
            )
        );
    }

    // -- Underwrite Asset Swaps -- //

    function underwriteAsset(
        bytes32 identifier,
        address toAsset,
        uint256 U,
        uint256 minOut
    ) onlyChainInterface virtual public returns (uint256 purchasedTokens) {
        // Simulate a receiveAsset call. This gets us the purchased tokens.
        purchasedTokens = _receiveAsset(toAsset, U, minOut);

        // Set the escrow.
        _setTokenEscrow(
            identifier,
            UNDERWRITE_FALLBACK_USER,
            toAsset,
            purchasedTokens
        );

        emit SwapUnderwritten(
            identifier,
            toAsset,
            U,
            purchasedTokens
        );
    }

    /**
     * @notice Release assets associated with an underwrite escrow.
     * @param refundTo Released assets are sent to this address.
     * @param identifier Underwriting identifier. Is used to index the storage for valid escrows.
     * @param escrowAmount Number of tokens escrowed.
     * @param escrowToken Escrowed token address.
     * @param sourceIdentifier The source chain identifier.
     * @param fromVault The originating vault.
     */
    function releaseUnderwriteAsset(
        address refundTo,
        bytes32 identifier,
        uint256 escrowAmount,
        address escrowToken,
        bytes32 sourceIdentifier,
        bytes calldata fromVault
    ) onlyChainInterface onlyConnectedPool(sourceIdentifier, fromVault) virtual public {
        _releaseAssetEscrow(identifier, escrowAmount, escrowToken); // Reverts for missing escrow.

        // Send the assets to the user.
        SafeTransferLib.safeTransfer(escrowToken, refundTo, escrowAmount);
    }

    /**
     * @notice Delete an underwrite escrow without releasing any tokens.
     * @dev The unsued parameter U is used for overwrites. (see CataulystVaultAmplified.sol)
     * @param identifier Underwriting identifier. Is used to index the storage for valid escrows.
     * param U Number of underwritten units. Is used for Amplified vaults to modify the unit tracker.
     * @param escrowAmount Number of tokens escrowed.
     * @param escrowToken Escrowed token address.
     */
    function deleteUnderwriteAsset(
        bytes32 identifier,
        uint256 /* U */,
        uint256 escrowAmount,
        address escrowToken
    ) onlyChainInterface virtual public {
        _releaseAssetEscrow(identifier, escrowAmount, escrowToken); // Reverts for missing escrow.
    }

}

//SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.19;

import { FixedPointMathLib } from "solady/utils/FixedPointMathLib.sol";

import { WADWAD } from "./utils/MathConstants.sol";

/**
 * @title Catalyst: Amplified Integrals
 * @author Catalyst Labs Inc.
 */
contract IntegralsAmplified {
    /**
     * @notice Computes the integral \int_{wA}^{wA+wx} 1/w^k · (1-k) dw
     *     = (wA + wx)^(1-k) - wA^(1-k)
     * The value is returned as units, which is always WAD.
     * @dev All input amounts should be the raw numbers and not WAD.
     * Since units are always denominated in WAD, the function should be treated as mathematically *native*.
     * @param input Input amount.
     * @param A Current vault balance of the x token.
     * @param W Weight of the x token.
     * @param oneMinusAmp Amplification. Provided as (1-k).
     * @return uint256 Units (units are **always** WAD).
     */
    function _calcPriceCurveArea(
        uint256 input,
        uint256 A,
        uint256 W,
        int256 oneMinusAmp
    ) internal pure returns (uint256) {
        // Will revert if W = 0. 
        // Or if A + input == 0.
        int256 calc = FixedPointMathLib.powWad(
            int256(W * (A + input) * FixedPointMathLib.WAD), // If casting overflows to a negative number, powWad fails.
            oneMinusAmp
        );

        // If the vault contains 0 assets, the below computation will fail. This is bad.
        // Instead, check if A is 0. If it is then skip because: (W · A)^(1-k) = (W · 0)^(1-k) = 0
        if (A != 0) {
            unchecked {
                // W * A * FixedPointMathLib.WAD < W * (A + input) * FixedPointMathLib.WAD 
                calc -= FixedPointMathLib.powWad(
                    int256(W * A * FixedPointMathLib.WAD), // If casting overflows to a negative number, powWad fails
                    oneMinusAmp
                );
            }
        }
        
        return uint256(calc); // Casting always safe, as calc always > =0
    }

    /**
     * @notice Solves the equation U = \int_{wA-_wy}^{wA} W/w^k · (1-k) dw for y
     *     = B · (1 - (
     *             (wB^(1-k) - U) / (wB^(1-k))
     *         )^(1/(1-k))
     *     )
     * The value is returned as output token. (not WAD)
     * @dev All input amounts should be the raw numbers and not WAD.
     * Since units are always multiplied by WAD, the function should be treated as mathematically *native*.
     * @param U Incoming vault specific units.
     * @param B Current vault balance of the y token.
     * @param W Weight of the y token.
     * @return uint25 Output denominated in output token. (not WAD)
     */
    function _calcPriceCurveLimit(
        uint256 U,
        uint256 B,
        uint256 W,
        int256 oneMinusAmp
    ) internal pure returns (uint256) {
        // W_B · B^(1-k) is repeated twice and requires 1 power. As a result, we compute it and cache it.
        uint256 W_BxBtoOMA = uint256( // Always casts a positive value.
            FixedPointMathLib.powWad(
                int256(W * B * FixedPointMathLib.WAD), // If casting overflows to a negative number, powWad fails.
                oneMinusAmp
            )
        );

        return FixedPointMathLib.mulWad(
            B,
            FixedPointMathLib.WAD - uint256( // Always casts a positive value
                FixedPointMathLib.powWad(
                    int256(FixedPointMathLib.divWadUp(W_BxBtoOMA - U, W_BxBtoOMA)), // Casting never overflows, as division result is always < 1
                    WADWAD / oneMinusAmp 
                )
            )
        );
    }

    /**
     * @notice Solves the equation
     *     \int_{wA}^{wA + wx} 1/w^k · (1-k) dw = \int_{wB-wy}^{wB} 1/w^k · (1-k) dw for y
     *         => out = B · (1 - (
     *                 (wB^(1-k) - (wA+wx)^(1-k) - wA^(1-k)) / (wB^(1-k))
     *             )^(1/(1-k))
     *         )
     * Alternatively, the integral can be computed through:
     * _calcPriceCurveLimit(_calcPriceCurveArea(input, A, W_A, amp), B, W_B, amp).
     * @dev All input amounts should be the raw numbers and not WAD.
     * @param input Input amount.
     * @param A Current vault balance of the x token.
     * @param B Current vault balance of the y token.
     * @param W_A Weight of the x token.
     * @param W_B Weight of the y token.
     * @param oneMinusAmp Amplification.
     * @return uint256 Output denominated in output token.
     */
    function _calcCombinedPriceCurves(
        uint256 input,
        uint256 A,
        uint256 B,
        uint256 W_A,
        uint256 W_B,
        int256 oneMinusAmp
    ) internal pure returns (uint256) {
        // uint256 W_BxBtoOMA = uint256(FixedPointMathLib.powWad(
        //     int256(W_B * B * FixedPointMathLib.WAD),
        //     oneMinusAmp
        // ));

        // uint256 U = uint256(FixedPointMathLib.powWad(
        //     int256(W_A * (A + input) * FixedPointMathLib.WAD),
        //     oneMinusAmp
        // ) - FixedPointMathLib.powWad(
        //     int256(W_A * A * FixedPointMathLib.WAD),
        //     oneMinusAmp
        // )); // _calcPriceCurveArea(input, A, W_A, amp)

        // return B * (FixedPointMathLib.WAD - uint256(FixedPointMathLib.powWad(
        //             int256(FixedPointMathLib.divWadUp(W_BxBtoOMA - U, W_BxBtoOMA)),
        //             int256(FixedPointMathLib.WAD * FixedPointMathLib.WAD / uint256(oneMinusAmp)))
        //         )) / FixedPointMathLib.WAD; // _calcPriceCurveLimit
        return _calcPriceCurveLimit(_calcPriceCurveArea(input, A, W_A, oneMinusAmp), B, W_B, oneMinusAmp);
    }

    /**
     * @notice Converts units into vault tokens with the below formula
     *      pt = PT · (((N · wa_0^(1-k) + U)/(N · wa_0^(1-k))^(1/(1-k)) - 1)
     * @dev The function leaves a lot of computation to the external implementation. This is done to avoid recomputing values several times.
     * @param U Number of units to convert into vault tokens.
     * @param ts Current vault token supply. The escrowed vault tokens should not be added, since the function then returns more.
     * @param it_times_walpha_amped wa_0^(1-k)
     * @param oneMinusAmpInverse Vault amplification.
     * @return uint256 Output denominated in vault tokens.
     */
    function _calcPriceCurveLimitShare(uint256 U, uint256 ts, uint256 it_times_walpha_amped, int256 oneMinusAmpInverse) internal pure returns (uint256) {
        uint256 vaultTokens = FixedPointMathLib.mulWad(
            ts,
            uint256( // Always casts a positive value, as powWad >= 1, hence powWad - WAD >= 0
                FixedPointMathLib.powWad( // poWad always >= 1, as the 'base' is always >= 1
                    int256(FixedPointMathLib.divWad( // If casting overflows to a negative number, powWad fails
                        it_times_walpha_amped + U,
                        it_times_walpha_amped
                    )),
                    oneMinusAmpInverse
                ) - int256(FixedPointMathLib.WAD)
            )
        );

        return vaultTokens;
    }
}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

interface ICatalystReceiver {
    /** 
     * @notice The callback from a catalyst call. To determine if the swap was an asset or liquidity swap, either the current balance should be checked or it should be encoded into data.
     * @dev If you want full finality (not just economical finality)
     * revert on underwritten == true.
     */
    function onCatalystCall(uint256 purchasedTokens, bytes calldata data, bool underwritten) external;
}

//SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.19;

import "./interfaces/ICatalystV1VaultSuccessFailure.sol";
import "./interfaces/ICatalystV1VaultAdministration.sol";
import "./interfaces/ICatalystV1VaultDerived.sol";
import "./interfaces/ICatalystV1VaultErrors.sol";
import "./interfaces/ICatalystV1VaultEvents.sol";
import "./interfaces/ICatalystV1VaultImmutables.sol";
import "./interfaces/ICatalystV1VaultPermissionless.sol";
import "./interfaces/ICatalystV1VaultState.sol";
import "./interfaces/ICatalystV1Underwriting.sol";

interface ICatalystV1Vault is
    ICatalystV1VaultSuccessFailure,
    ICatalystV1VaultAdministration,
    ICatalystV1VaultDerived,
    ICatalystV1VaultEvents,
    ICatalystV1VaultImmutables,
    ICatalystV1VaultPermissionless,
    ICatalystV1VaultState,
    ICatalystV1Structs,
    ICatalystV1Underwriting
{}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

import { IMessageEscrowStructs } from "GeneralisedIncentives/src/interfaces/IMessageEscrowStructs.sol";

interface ICatalystV1Structs is IMessageEscrowStructs {
    /**
     * @param chainIdentifier target chain identifier.
     * @param toVault Target vault on the target chain. Encoded in 64 + 1 bytes.
     * @param toAccount Recipient of the transaction on the target chain. Encoded in 64 + 1 bytes.
     * @param incentive Cross-chain relaying incentive description.
     */
    struct RouteDescription {
        bytes32 chainIdentifier;
        bytes toVault;
        bytes toAccount;
        IncentiveDescription incentive;
        uint64 deadline;
    }
}

/**
 * @title Vault state
 * @notice Contains all vault storage which depends on the vault state.
 */
interface ICatalystV1VaultState {
    /** @notice Token weights. Used for maintaining a non symmetric vault asset balance. */
    function _weight(address token) external view returns (uint256);

    function _adjustmentTarget() external view returns (uint48);

    function _lastModificationTime() external view returns (uint48);

    /** @notice The vault fee in WAD. Implementation of fee: mulWadDown(_amount, _vaultFee) */
    function _vaultFee() external view returns (uint64);

    function _governanceFeeShare() external view returns (uint64);

    /** @notice The address of the responsible for adjusting the fees. */
    function _feeAdministrator() external view returns (address);

    /** @notice The setupMaster is the short-term owner of the vault. They can connect the vault to vaults on other chains. */
    function _setupMaster() external view returns (address);

    // Security limit
    /** @notice The max incoming liquidity flow from the router. */
    function _maxUnitCapacity() external view returns (uint256);

    // Escrow reference
    /** @notice Total current escrowed tokens */
    function _escrowedTokens(address token) external view returns (uint256);

    /** @notice Find escrow information. Used for both normal swaps and liquidity swaps. */
    function _escrowLookup(bytes32 sendAssetHash) external view returns (address);

    /** @notice Total current escrowed vault tokens */
    function _escrowedVaultTokens() external view returns (uint256);

    /** @notice Checks if there is a connection to the described vault */
    function _vaultConnection(bytes32 sourceIdentifier, bytes calldata fromVault) external view returns (bool);

    function factoryOwner() external view returns (address);

    function governanceFeeDestination() external view returns (address);

    /**
     * @notice External view function purely used to signal if a vault is safe to use.
     * @dev Just checks if the setup master has been set to ZERO_ADDRESS. In other words, has finishSetup been called?
     */
    function ready() external view returns (bool);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

interface ICrossChainReceiver {
    /**
     * @notice Handles the acknowledgement from the destination
     * @dev acknowledgement is exactly the output of receiveMessage except if receiveMessage failed, then it is error code (0xff or 0xfe) + original message.
     * If an acknowledgement isn't needed, this can be implemented as {}.
     * - This function can be called by someone else again! Ensure that if this endpoint is called twice with the same message nothing bad happens.
     * - If the application expects that the maxGasAck will be provided, then it should check that it got enough and revert if it didn't.
     * Otherwise, it is assumed that you didn't need the extra gas.
     * @param destinationIdentifier An identifier for the destination chain.
     * @param messageIdentifier A unique identifier for the message. The identifier matches the identifier returned when escrowed the message.
     * This identifier can be mismanaged by the messaging protocol.
     * @param acknowledgement The acknowledgement sent back by receiveMessage. Is 0xff if receiveMessage reverted.
     */
    function receiveAck(bytes32 destinationIdentifier, bytes32 messageIdentifier, bytes calldata acknowledgement) external;

    /**
     * @notice receiveMessage from a cross-chain call.
     * @dev The application needs to check the fromApplication combined with sourceIdentifierbytes to figure out if the call is authenticated.
     * - If the application expects that the maxGasDelivery will be provided, then it should check that it got enough and revert if it didn't.
     * Otherwise, it is assumed that you didn't need the extra gas.
     * @return acknowledgement Information which is passed to receiveAck. 
     *  If you return 0xff, you cannot know the difference between Executed but "failed" and outright failed.
     */
    function receiveMessage(bytes32 sourceIdentifierbytes, bytes32 messageIdentifier, bytes calldata fromApplication, bytes calldata message) external returns(bytes memory acknowledgement);
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Simple single owner authorization mixin.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/auth/Ownable.sol)
///
/// @dev Note:
/// This implementation does NOT auto-initialize the owner to `msg.sender`.
/// You MUST call the `_initializeOwner` in the constructor / initializer.
///
/// While the ownable portion follows
/// [EIP-173](https://eips.ethereum.org/EIPS/eip-173) for compatibility,
/// the nomenclature for the 2-step ownership handover may be unique to this codebase.
abstract contract Ownable {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The caller is not authorized to call the function.
    error Unauthorized();

    /// @dev The `newOwner` cannot be the zero address.
    error NewOwnerIsZeroAddress();

    /// @dev The `pendingOwner` does not have a valid handover request.
    error NoHandoverRequest();

    /// @dev Cannot double-initialize.
    error AlreadyInitialized();

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

    /// @dev The ownership is transferred from `oldOwner` to `newOwner`.
    /// This event is intentionally kept the same as OpenZeppelin's Ownable to be
    /// compatible with indexers and [EIP-173](https://eips.ethereum.org/EIPS/eip-173),
    /// despite it not being as lightweight as a single argument event.
    event OwnershipTransferred(address indexed oldOwner, address indexed newOwner);

    /// @dev An ownership handover to `pendingOwner` has been requested.
    event OwnershipHandoverRequested(address indexed pendingOwner);

    /// @dev The ownership handover to `pendingOwner` has been canceled.
    event OwnershipHandoverCanceled(address indexed pendingOwner);

    /// @dev `keccak256(bytes("OwnershipTransferred(address,address)"))`.
    uint256 private constant _OWNERSHIP_TRANSFERRED_EVENT_SIGNATURE =
        0x8be0079c531659141344cd1fd0a4f28419497f9722a3daafe3b4186f6b6457e0;

    /// @dev `keccak256(bytes("OwnershipHandoverRequested(address)"))`.
    uint256 private constant _OWNERSHIP_HANDOVER_REQUESTED_EVENT_SIGNATURE =
        0xdbf36a107da19e49527a7176a1babf963b4b0ff8cde35ee35d6cd8f1f9ac7e1d;

    /// @dev `keccak256(bytes("OwnershipHandoverCanceled(address)"))`.
    uint256 private constant _OWNERSHIP_HANDOVER_CANCELED_EVENT_SIGNATURE =
        0xfa7b8eab7da67f412cc9575ed43464468f9bfbae89d1675917346ca6d8fe3c92;

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

    /// @dev The owner slot is given by:
    /// `bytes32(~uint256(uint32(bytes4(keccak256("_OWNER_SLOT_NOT")))))`.
    /// It is intentionally chosen to be a high value
    /// to avoid collision with lower slots.
    /// The choice of manual storage layout is to enable compatibility
    /// with both regular and upgradeable contracts.
    bytes32 internal constant _OWNER_SLOT =
        0xffffffffffffffffffffffffffffffffffffffffffffffffffffffff74873927;

    /// The ownership handover slot of `newOwner` is given by:
    /// ```
    ///     mstore(0x00, or(shl(96, user), _HANDOVER_SLOT_SEED))
    ///     let handoverSlot := keccak256(0x00, 0x20)
    /// ```
    /// It stores the expiry timestamp of the two-step ownership handover.
    uint256 private constant _HANDOVER_SLOT_SEED = 0x389a75e1;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     INTERNAL FUNCTIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Override to return true to make `_initializeOwner` prevent double-initialization.
    function _guardInitializeOwner() internal pure virtual returns (bool guard) {}

    /// @dev Initializes the owner directly without authorization guard.
    /// This function must be called upon initialization,
    /// regardless of whether the contract is upgradeable or not.
    /// This is to enable generalization to both regular and upgradeable contracts,
    /// and to save gas in case the initial owner is not the caller.
    /// For performance reasons, this function will not check if there
    /// is an existing owner.
    function _initializeOwner(address newOwner) internal virtual {
        if (_guardInitializeOwner()) {
            /// @solidity memory-safe-assembly
            assembly {
                let ownerSlot := _OWNER_SLOT
                if sload(ownerSlot) {
                    mstore(0x00, 0x0dc149f0) // `AlreadyInitialized()`.
                    revert(0x1c, 0x04)
                }
                // Clean the upper 96 bits.
                newOwner := shr(96, shl(96, newOwner))
                // Store the new value.
                sstore(ownerSlot, or(newOwner, shl(255, iszero(newOwner))))
                // Emit the {OwnershipTransferred} event.
                log3(0, 0, _OWNERSHIP_TRANSFERRED_EVENT_SIGNATURE, 0, newOwner)
            }
        } else {
            /// @solidity memory-safe-assembly
            assembly {
                // Clean the upper 96 bits.
                newOwner := shr(96, shl(96, newOwner))
                // Store the new value.
                sstore(_OWNER_SLOT, newOwner)
                // Emit the {OwnershipTransferred} event.
                log3(0, 0, _OWNERSHIP_TRANSFERRED_EVENT_SIGNATURE, 0, newOwner)
            }
        }
    }

    /// @dev Sets the owner directly without authorization guard.
    function _setOwner(address newOwner) internal virtual {
        if (_guardInitializeOwner()) {
            /// @solidity memory-safe-assembly
            assembly {
                let ownerSlot := _OWNER_SLOT
                // Clean the upper 96 bits.
                newOwner := shr(96, shl(96, newOwner))
                // Emit the {OwnershipTransferred} event.
                log3(0, 0, _OWNERSHIP_TRANSFERRED_EVENT_SIGNATURE, sload(ownerSlot), newOwner)
                // Store the new value.
                sstore(ownerSlot, or(newOwner, shl(255, iszero(newOwner))))
            }
        } else {
            /// @solidity memory-safe-assembly
            assembly {
                let ownerSlot := _OWNER_SLOT
                // Clean the upper 96 bits.
                newOwner := shr(96, shl(96, newOwner))
                // Emit the {OwnershipTransferred} event.
                log3(0, 0, _OWNERSHIP_TRANSFERRED_EVENT_SIGNATURE, sload(ownerSlot), newOwner)
                // Store the new value.
                sstore(ownerSlot, newOwner)
            }
        }
    }

    /// @dev Throws if the sender is not the owner.
    function _checkOwner() internal view virtual {
        /// @solidity memory-safe-assembly
        assembly {
            // If the caller is not the stored owner, revert.
            if iszero(eq(caller(), sload(_OWNER_SLOT))) {
                mstore(0x00, 0x82b42900) // `Unauthorized()`.
                revert(0x1c, 0x04)
            }
        }
    }

    /// @dev Returns how long a two-step ownership handover is valid for in seconds.
    /// Override to return a different value if needed.
    /// Made internal to conserve bytecode. Wrap it in a public function if needed.
    function _ownershipHandoverValidFor() internal view virtual returns (uint64) {
        return 48 * 3600;
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  PUBLIC UPDATE FUNCTIONS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Allows the owner to transfer the ownership to `newOwner`.
    function transferOwnership(address newOwner) public payable virtual onlyOwner {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(shl(96, newOwner)) {
                mstore(0x00, 0x7448fbae) // `NewOwnerIsZeroAddress()`.
                revert(0x1c, 0x04)
            }
        }
        _setOwner(newOwner);
    }

    /// @dev Allows the owner to renounce their ownership.
    function renounceOwnership() public payable virtual onlyOwner {
        _setOwner(address(0));
    }

    /// @dev Request a two-step ownership handover to the caller.
    /// The request will automatically expire in 48 hours (172800 seconds) by default.
    function requestOwnershipHandover() public payable virtual {
        unchecked {
            uint256 expires = block.timestamp + _ownershipHandoverValidFor();
            /// @solidity memory-safe-assembly
            assembly {
                // Compute and set the handover slot to `expires`.
                mstore(0x0c, _HANDOVER_SLOT_SEED)
                mstore(0x00, caller())
                sstore(keccak256(0x0c, 0x20), expires)
                // Emit the {OwnershipHandoverRequested} event.
                log2(0, 0, _OWNERSHIP_HANDOVER_REQUESTED_EVENT_SIGNATURE, caller())
            }
        }
    }

    /// @dev Cancels the two-step ownership handover to the caller, if any.
    function cancelOwnershipHandover() public payable virtual {
        /// @solidity memory-safe-assembly
        assembly {
            // Compute and set the handover slot to 0.
            mstore(0x0c, _HANDOVER_SLOT_SEED)
            mstore(0x00, caller())
            sstore(keccak256(0x0c, 0x20), 0)
            // Emit the {OwnershipHandoverCanceled} event.
            log2(0, 0, _OWNERSHIP_HANDOVER_CANCELED_EVENT_SIGNATURE, caller())
        }
    }

    /// @dev Allows the owner to complete the two-step ownership handover to `pendingOwner`.
    /// Reverts if there is no existing ownership handover requested by `pendingOwner`.
    function completeOwnershipHandover(address pendingOwner) public payable virtual onlyOwner {
        /// @solidity memory-safe-assembly
        assembly {
            // Compute and set the handover slot to 0.
            mstore(0x0c, _HANDOVER_SLOT_SEED)
            mstore(0x00, pendingOwner)
            let handoverSlot := keccak256(0x0c, 0x20)
            // If the handover does not exist, or has expired.
            if gt(timestamp(), sload(handoverSlot)) {
                mstore(0x00, 0x6f5e8818) // `NoHandoverRequest()`.
                revert(0x1c, 0x04)
            }
            // Set the handover slot to 0.
            sstore(handoverSlot, 0)
        }
        _setOwner(pendingOwner);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   PUBLIC READ FUNCTIONS                    */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the owner of the contract.
    function owner() public view virtual returns (address result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := sload(_OWNER_SLOT)
        }
    }

    /// @dev Returns the expiry timestamp for the two-step ownership handover to `pendingOwner`.
    function ownershipHandoverExpiresAt(address pendingOwner)
        public
        view
        virtual
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the handover slot.
            mstore(0x0c, _HANDOVER_SLOT_SEED)
            mstore(0x00, pendingOwner)
            // Load the handover slot.
            result := sload(keccak256(0x0c, 0x20))
        }
    }

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

    /// @dev Marks a function as only callable by the owner.
    modifier onlyOwner() virtual {
        _checkOwner();
        _;
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Reentrancy guard mixin.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/ReentrancyGuard.sol)
abstract contract ReentrancyGuard {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Unauthorized reentrant call.
    error Reentrancy();

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

    /// @dev Equivalent to: `uint72(bytes9(keccak256("_REENTRANCY_GUARD_SLOT")))`.
    /// 9 bytes is large enough to avoid collisions with lower slots,
    /// but not too large to result in excessive bytecode bloat.
    uint256 private constant _REENTRANCY_GUARD_SLOT = 0x929eee149b4bd21268;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                      REENTRANCY GUARD                      */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Guards a function from reentrancy.
    modifier nonReentrant() virtual {
        /// @solidity memory-safe-assembly
        assembly {
            if eq(sload(_REENTRANCY_GUARD_SLOT), address()) {
                mstore(0x00, 0xab143c06) // `Reentrancy()`.
                revert(0x1c, 0x04)
            }
            sstore(_REENTRANCY_GUARD_SLOT, address())
        }
        _;
        /// @solidity memory-safe-assembly
        assembly {
            sstore(_REENTRANCY_GUARD_SLOT, codesize())
        }
    }

    /// @dev Guards a view function from read-only reentrancy.
    modifier nonReadReentrant() virtual {
        /// @solidity memory-safe-assembly
        assembly {
            if eq(sload(_REENTRANCY_GUARD_SLOT), address()) {
                mstore(0x00, 0xab143c06) // `Reentrancy()`.
                revert(0x1c, 0x04)
            }
        }
        _;
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Initializable mixin for the upgradeable contracts.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/Initializable.sol)
/// @author Modified from OpenZeppelin (https://github.com/OpenZeppelin/openzeppelin-contracts/tree/master/contracts/proxy/utils/Initializable.sol)
abstract contract Initializable {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The contract is already initialized.
    error InvalidInitialization();

    /// @dev The contract is not initializing.
    error NotInitializing();

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

    /// @dev Triggered when the contract has been initialized.
    event Initialized(uint64 version);

    /// @dev `keccak256(bytes("Initialized(uint64)"))`.
    bytes32 private constant _INTIALIZED_EVENT_SIGNATURE =
        0xc7f505b2f371ae2175ee4913f4499e1f2633a7b5936321eed1cdaeb6115181d2;

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

    /// @dev The default initializable slot is given by:
    /// `bytes32(~uint256(uint32(bytes4(keccak256("_INITIALIZABLE_SLOT")))))`.
    ///
    /// Bits Layout:
    /// - [0]     `initializing`
    /// - [1..64] `initializedVersion`
    bytes32 private constant _INITIALIZABLE_SLOT =
        0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffbf601132;

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

    /// @dev Override to return a custom storage slot if required.
    function _initializableSlot() internal pure virtual returns (bytes32) {
        return _INITIALIZABLE_SLOT;
    }

    /// @dev Guards an initializer function so that it can be invoked at most once.
    ///
    /// You can guard a function with `onlyInitializing` such that it can be called
    /// through a function guarded with `initializer`.
    ///
    /// This is similar to `reinitializer(1)`, except that in the context of a constructor,
    /// an `initializer` guarded function can be invoked multiple times.
    /// This can be useful during testing and is not expected to be used in production.
    ///
    /// Emits an {Initialized} event.
    modifier initializer() virtual {
        bytes32 s = _initializableSlot();
        /// @solidity memory-safe-assembly
        assembly {
            let i := sload(s)
            // Set `initializing` to 1, `initializedVersion` to 1.
            sstore(s, 3)
            // If `!(initializing == 0 && initializedVersion == 0)`.
            if i {
                // If `!(address(this).code.length == 0 && initializedVersion == 1)`.
                if iszero(lt(extcodesize(address()), eq(shr(1, i), 1))) {
                    mstore(0x00, 0xf92ee8a9) // `InvalidInitialization()`.
                    revert(0x1c, 0x04)
                }
                s := shl(shl(255, i), s) // Skip initializing if `initializing == 1`.
            }
        }
        _;
        /// @solidity memory-safe-assembly
        assembly {
            if s {
                // Set `initializing` to 0, `initializedVersion` to 1.
                sstore(s, 2)
                // Emit the {Initialized} event.
                mstore(0x20, 1)
                log1(0x20, 0x20, _INTIALIZED_EVENT_SIGNATURE)
            }
        }
    }

    /// @dev Guards an reinitialzer function so that it can be invoked at most once.
    ///
    /// You can guard a function with `onlyInitializing` such that it can be called
    /// through a function guarded with `reinitializer`.
    ///
    /// Emits an {Initialized} event.
    modifier reinitializer(uint64 version) virtual {
        bytes32 s = _initializableSlot();
        /// @solidity memory-safe-assembly
        assembly {
            version := and(version, 0xffffffffffffffff) // Clean upper bits.
            let i := sload(s)
            // If `initializing == 1 || initializedVersion >= version`.
            if iszero(lt(and(i, 1), lt(shr(1, i), version))) {
                mstore(0x00, 0xf92ee8a9) // `InvalidInitialization()`.
                revert(0x1c, 0x04)
            }
            // Set `initializing` to 1, `initializedVersion` to `version`.
            sstore(s, or(1, shl(1, version)))
        }
        _;
        /// @solidity memory-safe-assembly
        assembly {
            // Set `initializing` to 0, `initializedVersion` to `version`.
            sstore(s, shl(1, version))
            // Emit the {Initialized} event.
            mstore(0x20, version)
            log1(0x20, 0x20, _INTIALIZED_EVENT_SIGNATURE)
        }
    }

    /// @dev Guards a function such that it can only be called in the scope
    /// of a function guarded with `initializer` or `reinitializer`.
    modifier onlyInitializing() virtual {
        _checkInitializing();
        _;
    }

    /// @dev Reverts if the contract is not initializing.
    function _checkInitializing() internal view virtual {
        bytes32 s = _initializableSlot();
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(and(1, sload(s))) {
                mstore(0x00, 0xd7e6bcf8) // `NotInitializing()`.
                revert(0x1c, 0x04)
            }
        }
    }

    /// @dev Locks any future initializations by setting the initialized version to `2**64 - 1`.
    ///
    /// Calling this in the constructor will prevent the contract from being initialized
    /// or reinitialized. It is recommended to use this to lock implementation contracts
    /// that are designed to be called through proxies.
    ///
    /// Emits an {Initialized} event the first time it is successfully called.
    function _disableInitializers() internal virtual {
        bytes32 s = _initializableSlot();
        /// @solidity memory-safe-assembly
        assembly {
            let i := sload(s)
            if and(i, 1) {
                mstore(0x00, 0xf92ee8a9) // `InvalidInitialization()`.
                revert(0x1c, 0x04)
            }
            let uint64max := shr(192, s) // Computed to save bytecode.
            if iszero(eq(shr(1, i), uint64max)) {
                // Set `initializing` to 0, `initializedVersion` to `2**64 - 1`.
                sstore(s, shl(1, uint64max))
                // Emit the {Initialized} event.
                mstore(0x20, uint64max)
                log1(0x20, 0x20, _INTIALIZED_EVENT_SIGNATURE)
            }
        }
    }

    /// @dev Returns the highest version that has been initialized.
    function _getInitializedVersion() internal view virtual returns (uint64 version) {
        bytes32 s = _initializableSlot();
        /// @solidity memory-safe-assembly
        assembly {
            version := shr(1, sload(s))
        }
    }

    /// @dev Returns whether the contract is currently initializing.
    function _isInitializing() internal view virtual returns (bool result) {
        bytes32 s = _initializableSlot();
        /// @solidity memory-safe-assembly
        assembly {
            result := and(1, sload(s))
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Contract that enables a single call to call multiple methods on itself.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/Multicallable.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/Multicallable.sol)
///
/// WARNING:
/// This implementation is NOT to be used with ERC2771 out-of-the-box.
/// https://blog.openzeppelin.com/arbitrary-address-spoofing-vulnerability-erc2771context-multicall-public-disclosure
/// This also applies to potentially other ERCs / patterns appending to the back of calldata.
///
/// We do NOT have a check for ERC2771, as we do not inherit from OpenZeppelin's context.
/// Moreover, it is infeasible and inefficient for us to add checks and mitigations
/// for all possible ERC / patterns appending to the back of calldata.
///
/// We would highly recommend using an alternative pattern such as
/// https://github.com/Vectorized/multicaller
/// which is more flexible, futureproof, and safer by default.
abstract contract Multicallable {
    /// @dev Apply `DELEGATECALL` with the current contract to each calldata in `data`,
    /// and store the `abi.encode` formatted results of each `DELEGATECALL` into `results`.
    /// If any of the `DELEGATECALL`s reverts, the entire context is reverted,
    /// and the error is bubbled up.
    ///
    /// This function is deliberately made non-payable to guard against double-spending.
    /// (See: https://www.paradigm.xyz/2021/08/two-rights-might-make-a-wrong)
    ///
    /// For efficiency, this function will directly return the results, terminating the context.
    /// If called internally, it must be called at the end of a function
    /// that returns `(bytes[] memory)`.
    function multicall(bytes[] calldata data) public virtual returns (bytes[] memory) {
        assembly {
            mstore(0x00, 0x20)
            mstore(0x20, data.length) // Store `data.length` into `results`.
            // Early return if no data.
            if iszero(data.length) { return(0x00, 0x40) }

            let results := 0x40
            // `shl` 5 is equivalent to multiplying by 0x20.
            let end := shl(5, data.length)
            // Copy the offsets from calldata into memory.
            calldatacopy(0x40, data.offset, end)
            // Offset into `results`.
            let resultsOffset := end
            // Pointer to the end of `results`.
            end := add(results, end)

            for {} 1 {} {
                // The offset of the current bytes in the calldata.
                let o := add(data.offset, mload(results))
                let m := add(resultsOffset, 0x40)
                // Copy the current bytes from calldata to the memory.
                calldatacopy(
                    m,
                    add(o, 0x20), // The offset of the current bytes' bytes.
                    calldataload(o) // The length of the current bytes.
                )
                if iszero(delegatecall(gas(), address(), m, calldataload(o), codesize(), 0x00)) {
                    // Bubble up the revert if the delegatecall reverts.
                    returndatacopy(0x00, 0x00, returndatasize())
                    revert(0x00, returndatasize())
                }
                // Append the current `resultsOffset` into `results`.
                mstore(results, resultsOffset)
                results := add(results, 0x20)
                // Append the `returndatasize()`, and the return data.
                mstore(m, returndatasize())
                returndatacopy(add(m, 0x20), 0x00, returndatasize())
                // Advance the `resultsOffset` by `returndatasize() + 0x20`,
                // rounded up to the next multiple of 32.
                resultsOffset :=
                    and(add(add(resultsOffset, returndatasize()), 0x3f), 0xffffffffffffffe0)
                if iszero(lt(results, end)) { break }
            }
            return(0x00, add(resultsOffset, 0x40))
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

interface IMessageEscrowStructs {
    struct IncentiveDescription {
        uint48 maxGasDelivery;      // 0: 6/32 bytes
        uint48 maxGasAck;           // 0: 12/32 bytes
        address refundGasTo;        // 0: 32/32 bytes
        uint96 priceOfDeliveryGas;  // 1: 12/32 bytes
        uint96 priceOfAckGas;       // 1: 24/32 bytes
        uint64 targetDelta;         // 1: 32/32 bytes
    }
}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

import { ICatalystV1FactoryEvents } from "./ICatalystV1FactoryEvents.sol";

interface ICatalystV1Factory is ICatalystV1FactoryEvents {
    function _defaultGovernanceFee() external view returns (uint64);
    function _governanceFeeDestination() external view returns (address);
    function deployVault(
        address vaultTemplate,
        address[] memory assets,
        uint256[] memory init_balances,
        uint256[] memory weights,
        uint64 amp,
        uint64 vaultFee,
        string memory name,
        string memory symbol,
        address chainInterface
    ) external returns (address);
    function isCreatedByFactory(address, address) external view returns (bool);
    function setDefaultGovernanceFee(uint64 fee) external;
    function setGovernanceFeeDestination(address feeDestination) external;
}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

error EscrowAlreadyExists(); // 0xed778779
error ExceedsSecurityLimit(); // 0x7c1e66d0
error NotEnoughGas(); // 0xdd629f86
error ReturnInsufficient(uint256,uint256); // 0x24557f05
error UnusedUnitsAfterWithdrawal(uint256); // 0x0289311f
error VaultNotConnected(); // 0x2c64c1b2
error WithdrawRatioNotZero(); // 0xb8003bfa

// SPDX-License-Identifier: BUSL-1.1
pragma solidity ^0.8.19;

import { Ownable } from "solady/auth/Ownable.sol";
import { SafeTransferLib } from 'solady/utils/SafeTransferLib.sol';
import { LibClone } from "solady/utils/LibClone.sol";

import { ICatalystV1Factory } from "./interfaces/ICatalystV1Factory.sol";
import { ICatalystV1Vault } from "./ICatalystV1Vault.sol";

uint256 constant MAX_GOVERNANCE_FEE_SHARE = 75e16;   // 75%

/**
 * @title Catalyst Swap Factory
 * @author Cata Labs Inc.
 * @notice Allows permissionless deployment Catalyst vaults and defines governance address for vaults to read.
 * Importantly, this vault allows anyone to deploy a vault using any vault template and vault cross-chain interface.
 * As a result, just because a vault was deployed using this contract does not imply that it is safe. Vaults should
 * be cross-checked for their template, cross-chain interface, and if they are setup correctly. It may even be
 * that some vault templates only work with some cross-chain interfaces.
 *
 * Using the reference Catalyst Vault Templates, the owner of the factory is also the _owner_ of the Vaults.
 * They have certain privilege that may be able to be abused depending on the vault. One of these is configurating
 * fees. As a result:
 * !The owner of the factory must be a timelock!
 */
contract CatalystFactory is Ownable, ICatalystV1Factory {

    error InvalidAssetCount();
    error InvalidWeightCount();
    error FeeDestinationAddress0();
    error MaximumGovernanceFeeShare();

    /**
     * @notice A mapping which describes if a vault has been created by this factory.
     * Indexed by chainInterface then vault address.
     */
    mapping(address => mapping(address => bool)) public isCreatedByFactory;

    /** 
     * @notice Default governance fee. When a vault is created, this is the governance fee applied to that vault.
     */
    uint64 public _defaultGovernanceFee;

    /**
     * @notice The address to send governance fees to.
     * @dev Not enforced by the factory but vaults are expected to follow it.
     */
    address public _governanceFeeDestination;

    // The 2 above storage slots are packed together.

    constructor(address defaultOwner) payable {
        _initializeOwner(defaultOwner);
        _governanceFeeDestination = defaultOwner;
    }

    /**
     * @notice Set default governance fee share. 
     * @dev The set governance fee only applies to newly created vaults. Vaults have to be individual modified post creation. 
     * Is in WAD, (1e18 terms). So 1e16 is 1%. Cannot be set larger than 75% (75e16).
     */
    function setDefaultGovernanceFee(uint64 fee) override public onlyOwner {
        if (fee > MAX_GOVERNANCE_FEE_SHARE) revert MaximumGovernanceFeeShare();

        emit SetDefaultGovernanceFee(fee);

        _defaultGovernanceFee = fee;
    }

    /**
     * @notice Set the recipient of the governance.
     * @dev It is expected that vaults read this value and send their governance fees here.
     * This contract has no way to enforce if vaults honour this value.
     * Cannot be set to address(0). If wish to burn, set to 0xdead.
     */
    function setGovernanceFeeDestination(address feeDestination) override public onlyOwner {
        if (feeDestination == address(0)) revert FeeDestinationAddress0();
        emit SetGovernanceFeeDestination(feeDestination);

        _governanceFeeDestination = feeDestination;
    }

    /**
     * @notice Deploys a Catalyst vault, funds the vault with tokens, and calls setup.
     * When deploying vaults, there are 2 stages that needs to happen:
     * 1. We need to setup the vaults with the correct configuration.
     * 2. We need to set the vault swap curve. This consists of setting assets, vaults, amplification, etc.
     * The reason it is done in 2 steps is because of the stack limit. By spreading it across 2 calls, it is
     * cheaper gas wise.
     * This is done in a safe way by expecting both of these init. calls to be done in a single transaction.
     * As a result, the vaults are never left in a vulnerable state. It is expected that the latter call
     * (initializeSwapCurves) completes initialization and blocks the setup functions from being called again.
     * @dev The deployer needs to set relevant approvals to this contract before calling deployVault.
     * @param vaultTemplate The template the transparent proxy should target.
     * @param assets The list of assets the vault should support.
     * @param init_balances The initial balances of the vault. (Should be approved)
     * @param weights The weights of the tokens.
     * @param amp Token parameter 1. (Amplification)
     * @param vaultFee The vault fee.
     * @param name Name of the Vault token.
     * @param symbol Symbol for the Vault token.
     * @param chainInterface The cross chain interface used for cross-chain swaps. (Can be address(0) to disable cross-chain swaps.)
     * @return vault The address of the created Catalyst Vault. (minimal transparent proxy)
     */
    function deployVault(
        address vaultTemplate,
        address[] calldata assets,
        uint256[] calldata init_balances,
        uint256[] calldata weights,
        uint64 amp,
        uint64 vaultFee,
        string memory name,
        string memory symbol,
        address chainInterface
    ) override external returns (address vault) {
        // Check if an invalid asset count has been provided
        if (assets.length == 0) revert InvalidAssetCount();
        // Check if an invalid weight count has been provided
        if (weights.length != assets.length) revert InvalidWeightCount();
        // init_balances length not checked: if shorter than assets, the funds transfer loop
        // will fail. If longer, values will just be ignored.

        // Create a minimal transparent proxy:
        vault = LibClone.clone(vaultTemplate);

        // The vault expects the balances to exist in the vault when setup is called.
        uint256 assetLength = assets.length;
        for (uint256 it; it < assetLength;) {
            SafeTransferLib.safeTransferFrom(
                assets[it],
                msg.sender,
                vault,
                init_balances[it]
            );

            unchecked {
                ++it;
            }
        }

        // Call setup
        ICatalystV1Vault(vault).setup(
            name,
            symbol,
            chainInterface,
            vaultFee,
            _defaultGovernanceFee,
            owner(),        // Fee administrator
            msg.sender      // setup master
        );

        // Initialize swap curves
        ICatalystV1Vault(vault).initializeSwapCurves(
            assets,
            weights,
            amp,
            msg.sender
        );

        // Emit event for vault discovery.
        emit VaultDeployed(
            vaultTemplate,
            chainInterface,
            msg.sender,
            vault,
            assets,
            amp
        );
        isCreatedByFactory[chainInterface][vault] = true;

        return vault;
    }
}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

/**
 * @title Escrow related functions defined by Catalyst v1 Vaults
 * @notice Contains the functions used to manage escrows by the cross-chain interface.
 */
interface ICatalystV1VaultSuccessFailure {
    /** @notice Release the escrowed tokens into the vault.  */
    function onSendAssetSuccess(
        bytes32 channelId,
        bytes calldata toAccount,
        uint256 U,
        uint256 escrowAmount,
        address escrowToken,
        uint32 blockNumberMod
    ) external;

    /** @notice Returned the escrowed tokens to the user */
    function onSendAssetFailure(
        bytes32 channelId,
        bytes calldata toAccount,
        uint256 U,
        uint256 escrowAmount,
        address escrowToken,
        uint32 blockNumberMod
    ) external;

    /** @notice Release the escrowed tokens into the vault.  */
    function onSendLiquiditySuccess(
        bytes32 channelId,
        bytes calldata toAccount,
        uint256 U,
        uint256 escrowAmount,
        uint32 blockNumberMod
    ) external;

    /** @notice Returned the escrowed tokens to the user */
    function onSendLiquidityFailure(
        bytes32 channelId,
        bytes calldata toAccount,
        uint256 U,
        uint256 escrowAmount,
        uint32 blockNumberMod
    ) external;
}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;
/**
 * @title Administrative actions defined by Catalyst v1 Vaults
 * @notice Contains all functions which can only be called by privileged users.
 */
interface ICatalystV1VaultAdministration {
    function setFeeAdministrator(address administrator) external;

    function setVaultFee(uint64 fee) external;

    function setGovernanceFee(uint64 fee) external;

    /**
     * @notice Initializes the vault pricing parameters.
     * @param assets The list of assets the vault will support.
     * @param weights The weights of the tokens.
     * @param amp Vault amplification.
     * @param depositor The account to which the initial vault tokens are minted to.
     */
    function initializeSwapCurves(
        address[] calldata assets,
        uint256[] calldata weights,
        uint64 amp,
        address depositor
    ) external;

    /**
     * @notice Creates a connection to the vault toVault on the channel _channelId.
     * @dev if _vaultReceiving is an EVM vault, it can be computes as:
     *     Vyper: convert(_vaultAddress, bytes32)
     *     Solidity: abi.encode(_vaultAddress)
     *     Brownie: brownie.convert.to_bytes(_vaultAddress, type_str="bytes32")
     * setupMaster == ZERO_ADDRESS
     * @param channelId The _channelId of the target vault.
     * @param toVault The bytes32 representation of the target vault
     * @param state Boolean indicating if the connection should be open or closed.
     */
    function setConnection(
        bytes32 channelId,
        bytes calldata toVault,
        bool state
    ) external;

    /**
     * @notice Gives up short term ownership of the vault. This makes the vault unstoppable.
     */
    function finishSetup() external;
}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

/**
 * @title Derived Vault state
 * @notice Contains all vault state which is derived from vault storage
 */
interface ICatalystV1VaultDerived {
    /** @notice  Returns the current cross-chain unit capacity. */
    function getUnitCapacity() external view returns (uint256);

    function calcSendAsset(address from, uint256 amount) external view returns (uint256);

    /**
     * @notice Computes the output of ReceiveAsset, without executing one.
     * @param to The address of the token to buy.
     * @param U The number of units used to buy to.
     * @return uint256 Number of purchased tokens.
     */
    function calcReceiveAsset(address to, uint256 U) external view returns (uint256);

    /**
     * @notice Computes the output of localSwap, without executing one.
     * @param from The address of the token to sell.
     * @param to The address of the token to buy.
     * @param amount The amount of from token to sell for to token.
     * @return Output denominated in to token.
     */
    function calcLocalSwap(address from, address to, uint256 amount) external view returns (uint256);
}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

/**
 * @title Events emitted by Catalyst v1 Vaults
 * @notice Contains all events emitted by the vault
 * @dev When using events to match transations, the combination of: channelId, fromVault, toAccount, toAsset, units, and block number is semi-guranteed to be unique.
 *      If more than 2**32 blocks exist, then all instances are guaranteed to be non-overlapping
 */
interface ICatalystV1VaultEvents {
    /**
     * @notice  Describes an atomic swap between the 2 tokens: _fromAsset and _toAsset.
     * @param account The user / exchange who facilitated the trade (msg.sender)
     * @param fromAsset The asset which was sold in exchange for _toAsset
     * @param toAsset The asset which was purchased with _fromAsset
     * @param fromAmount The number of _fromAsset sold
     * @param toAmount The number of tokens provided to toAccount
     */
    event LocalSwap(
        address indexed account,
        address fromAsset,
        address toAsset,
        uint256 fromAmount,
        uint256 toAmount
    );

    /**
     * @notice Describes the creation of an external swap: Cross-chain swap.
     * @param channelId The target chain identifier
     * @param toVault The target vault.
     * @param toAccount The recipient of the trade. The person who bought the trade is not present.
     * @param fromAsset The asset which was sold in exchange for _toAsset.
     * @param toAssetIndex The token index of the asset to purchase on _toChain.
     * @param fromAmount The number of _fromAsset sold.
     * @param minOut The minimum output to be accepted of fromAsset.
     * @param units The calculated number of units bought. Will be sold to buy _toAsset
     * @param underwriteIncentiveX16 The incentive out of 2**16 - 1 provided to the underwriter.
     * @param fee The number of tokens paid to the vault in fees.
     */
    event SendAsset(
        bytes32 channelId,
        bytes toVault,
        bytes toAccount,
        address fromAsset,
        uint8 toAssetIndex,
        uint256 fromAmount,
        uint256 minOut,
        uint256 units,
        uint256 fee,
        uint16 underwriteIncentiveX16
    );

    /**
     * @notice Describes the arrival of an external swap: Cross-chain swap.
     * If toAccount is used to match trades, remember to convert it into 64 + 1 bytes.
     * @param channelId The target chain identifier
     * @param fromVault The source vault.
     * @param toAccount The recipient of the trade.
     * @param toAsset The asset which was purchased with _fromAsset
     * @param units The number of units sent from the other chain.
     * @param toAmount The number of tokens provided to toAccount
     * @param fromAmount The amount spent to get units on the source side.
     * @param fromAsset The provided asset on the source side.
     * @param sourceBlockNumberMod The block number of the sending transaction mod 2**32 - 1
     */
    event ReceiveAsset(
        bytes32 channelId,
        bytes fromVault,
        address toAccount,
        address toAsset,
        uint256 units,
        uint256 toAmount,
        uint256 fromAmount,
        bytes fromAsset,
        uint32 sourceBlockNumberMod

    );

    /**
     * @notice Describes the creation of a liquidity swap
     * @param channelId The target chain identifier
     * @param toVault The target vault.
     * @param toAccount The recipient of the liquidity. The person who bought the trade is not present.
     * @param fromAmount The number of _fromAsset sold
     * @param minOut An array containing a list of minimum outputs [minVaultTokens, minReferenceAssets]
     * @param units The calculated number of liquidity units bought.
     */
    event SendLiquidity(
        bytes32 channelId,
        bytes toVault,
        bytes toAccount,
        uint256 fromAmount,
        uint256[2] minOut,
        uint256 units
    );

    /**
     * @notice Describes the arrival of a liquidity swap
     * @param channelId The target chain identifier
     * @param fromVault The source vault.
     * @param toAccount The recipient of the liquidity.
     * @param units The number of liquidity units sent from the other chain.
     * @param toAmount The number of vault tokens provided to toAccount
     * @param fromAmount The amount spent to get units on the source side.
     * @param sourceBlockNumberMod The block number of the sending transaction mod 2**32 - 1
     */
    event ReceiveLiquidity(
        bytes32 channelId,
        bytes fromVault,
        address toAccount,
        uint256 units,
        uint256 toAmount,
        uint256 fromAmount,
        uint256 sourceBlockNumberMod
    );

    /**
     * @notice Emitted on liquidity deposits.
     * @param toAccount The depositor. Is credited with _mints vault tokens.
     * @param mint The number of minted vault tokens credited to toAccount
     * @param assets An array of the number of deposited assets.
     */
    event VaultDeposit(address indexed toAccount, uint256 mint, uint256[] assets);

    /**
     * @notice Emitted on liquidity withdrawal.
     * @param toAccount The withdrawer. Is debited _burns vault tokens.
     * @param burn The number of burned vault tokens.
     * @param assets An array of the token amounts returned
     */
    event VaultWithdraw(address indexed toAccount, uint256 burn, uint256[] assets);

    /** @notice Called upon successful asset swap. */
    event SendAssetSuccess(
        bytes32 channelId,
        bytes toAccount,
        uint256 units,
        uint256 escrowAmount,
        address escrowToken,
        uint32 blockNumberMod
    );

    /** @notice Called upon failed asset swap. */
    event SendAssetFailure(
        bytes32 channelId,
        bytes toAccount,
        uint256 units,
        uint256 escrowAmount,
        address escrowToken,
        uint32 blockNumberMod
    );

    /** @notice Called upon successful liquidity swap. */
    event SendLiquiditySuccess(
        bytes32 channelId,
        bytes toAccount,
        uint256 units,
        uint256 escrowAmount,
        uint32 blockNumberMod
    );

    /** @notice Called upon failed liquidity swap. */
    event SendLiquidityFailure(
        bytes32 channelId,
        bytes toAccount,
        uint256 units,
        uint256 escrowAmount,
        uint32 blockNumberMod
    );

    /** @notice Vault setup has been finalised. */
    event FinishSetup();

    /**
     * @notice Emitted on fee administrator adjustment
     * @param administrator The new vault fee administrator
     */
    event SetFeeAdministrator(
        address administrator
    );

    /**
     * @notice Emitted on vault fee adjustment
     * @param fee The new vault fee
     */
    event SetVaultFee(
        uint64 fee
    );

    /**
     * @notice Emitted on governance fee adjustment
     * @param fee The new governance fee
     */
    event SetGovernanceFee(
        uint64 fee
    );

    /**
     * @notice Emitted on weights modification
     * @param targetTime Time at which the weights adjustment must complete.
     * @param targetWeights The desired new weights.
     */
    event SetWeights(
        uint248 targetTime,
        uint256[] targetWeights
    );

    /**
     * @notice Amplification has been modification
     * @param targetTime Time at which the amplification adjustment must complete.
     * @param targetAmplification The desired new amplification.
     */
    event SetAmplification(
        uint48 targetTime,
        uint256 targetAmplification
    );

    /**
     * @notice A connection has been modified
     * @param channelId Target chain identifier.
     * @param toVault Bytes32 representation of the target vault.
     * @param newState Boolean indicating if the connection should be open or closed.
     */
    event SetConnection(
        bytes32 channelId,
        bytes toVault,
        bool newState
    );

    //-- Underwriting Events --//

    /**
     * @notice A swap has been underwritten.
     */
    event SwapUnderwritten(
        bytes32 indexed identifier,
        address toAsset,
        uint256 U,
        uint256 purchasedTokens
    );

}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

/**
 * @title Immutable vault state
 * @notice Contains all vault state which doesn't change once set.
 */
interface ICatalystV1VaultImmutables {
    function _chainInterface() external view returns (address);

    function FACTORY() external view returns (address);

    function MATHLIB() external view returns (address);

    /** 
     * @notice To indicate which token is desired on the target vault,the _toAsset is an integer
     * from 0 to MAX_ASSETS indicating which asset the vault should purchase with units.
     */
    function _tokenIndexing(uint256 tokenIndex) external view returns (address);
}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

import { ICatalystV1Structs } from "./ICatalystV1VaultState.sol";

interface ICatalystV1VaultPermissionless {
    /** 
     * @notice Setup a vault.
     * @param name_ Name of the Vault token.
     * @param symbol_ Symbol for the Vault token.
     * @param chainInterface Cross chain interface used for cross-chain swaps. (Can be address(0) to disable cross-chain swaps.)
     * @param vaultFee Vault fee.
     * @param governanceFee Governance fee share.
     * @param feeAdministrator Account that can modify the fees.
     * @param setupMaster Short-term owner of the vault (until finishSetup is called).
     */
    function setup(
        string calldata name_,
        string calldata symbol_,
        address chainInterface,
        uint64 vaultFee,
        uint64 governanceFee,
        address feeAdministrator,
        address setupMaster
    ) external;

    //--- Balance Changes ---//

    /**
     * @notice Deposits a user configurable amount of tokens.
     * @dev Requires approvals for all deposited tokens within the vault.
     * Volatile: It is advised that the deposit matches the vault's %token distribution.
     * Amplified: It is advised that the deposit is as close to 1,1,... as possible.
     *            Otherwise between 1,1,... and the vault's %token distribution.
     * @param tokenAmounts Array of the tokens amounts to be deposited.
     * @param minOut Minimum number of vault tokens to be minted.
     */
    function depositMixed(uint256[] calldata tokenAmounts, uint256 minOut)
        external returns(uint256);

    /**
     * @notice Burns baseAmount and releases the symmetrical share
     * of tokens to the burner. This doesn't change the vault price.
     * @param baseAmount Number of vault tokens to burn.
     */
    function withdrawAll(uint256 baseAmount, uint256[] calldata minOut)
        external returns(uint256[] memory);

    /**
     * @notice Burns vaultTokens and release a token distribution which can be set by the user.
     * @dev Requires approvals for all tokens within the vault.
     * Volatile: It is advised that the deposit matches the vault's %token distribution.
     * Amplified: It is advised that the deposit matches the vault's %token distribution.
     *            Otherwise it should be weighted towards the tokens the vault has more of.
     * @param vaultTokens Number of vault tokens to withdraw.
     * @param withdrawRatio Percentage of units used to withdraw. In the following special scheme: U_0 = U · withdrawRatio[0], U_1 = (U - U_0) · withdrawRatio[1], U_2 = (U - U_0 - U_1) · withdrawRatio[2], .... Is WAD.
     * @param minOut Minimum number of tokens minted.
     */
    function withdrawMixed(
        uint256 vaultTokens,
        uint256[] calldata withdrawRatio,
        uint256[] calldata minOut
    ) external returns(uint256[] memory);

    //--- Swaps ---//

    /**
     * @notice A swap between 2 assets which both are inside the vault. Is atomic.
     * @param fromAsset Asset the user wants to sell.
     * @param toAsset Asset the user wants to buy.
     * @param amount Amount of fromAsset the user wants to sell.
     * @param minOut Minimum output of _toAsset the user wants.
     */
    function localSwap(
        address fromAsset,
        address toAsset,
        uint256 amount,
        uint256 minOut
    ) external returns (uint256);

    /**
     * @notice Initiate a cross-chain swap by purchasing units and transfer them to another vault.
     * @dev Addresses are encoded in 64 + 1 bytes. To encode for EVM, encode as:
     * Solidity: abi.encodePacket(uint8(20), bytes32(0), abi.encode(<vaultAddress>))
     * @param routeDescription A cross-chain route description which contains the chainIdentifier, toAccount, toVault and relaying incentive.
     * @param fromAsset Asset the user wants to sell.
     * @param toAssetIndex Index of the asset the user wants to buy in the target vault.
     * @param amount Number of fromAsset to sell to the vault.
     * @param minOut Minimum number of returned tokens to the toAccount on the target chain.
     * @param fallbackUser If the transaction fails, send the escrowed funds to this address.
     * @param underwriteIncentiveX16 Payment for underwriting the swap (out of type(uint16.max))
     * @param calldata_ Data field if a call should be made on the target chain.
     * Encoding depends on the target chain, with EVM: abi.encodePacket(bytes20(<address>), <data>). At maximum 65535 bytes can be passed.
     * @return uint256 The number of units minted.
     */
    function sendAsset(
        ICatalystV1Structs.RouteDescription calldata routeDescription,
        address fromAsset,
        uint8 toAssetIndex,
        uint256 amount,
        uint256 minOut,
        address fallbackUser,
        uint16 underwriteIncentiveX16,
        bytes calldata calldata_
    ) external payable returns (uint256);

    /**
     * @notice Initiate a cross-chain swap by purchasing units and transfer them to another vault using a fixed number of units.
     * @dev Addresses are encoded in 64 + 1 bytes. To encode for EVM, encode as:
     * Solidity: abi.encodePacket(uint8(20), bytes32(0), abi.encode(<vaultAddress>))
     * @param routeDescription A cross-chain route description which contains the chainIdentifier, toAccount, toVault and relaying incentive.
     * @param fromAsset Asset the user wants to sell.
     * @param toAssetIndex Index of the asset the user wants to buy in the target vault.
     * @param amount Number of fromAsset to sell to the vault.
     * @param minOut Minimum number of returned tokens to the toAccount on the target chain.
     * @param minU Minimum and exact number of units sent.
     * @param fallbackUser If the transaction fails, send the escrowed funds to this address.
     * @param calldata_ Data field if a call should be made on the target chain.
     * Encoding depends on the target chain, with evm being: abi.encodePacket(bytes20(<address>), <data>)
     * @param underwriteIncentiveX16 Payment for underwriting the swap (out of type(uint16.max))
     * @return uint256 Number of units minted.
     */
    function sendAssetFixedUnit(
        ICatalystV1Structs.RouteDescription calldata routeDescription,
        address fromAsset,
        uint8 toAssetIndex,
        uint256 amount,
        uint256 minOut,
        uint256 minU,
        address fallbackUser,
        uint16 underwriteIncentiveX16,
        bytes calldata calldata_
    ) external payable returns (uint256);

    /**
     * @notice Completes a cross-chain swap by converting units to the desired token (toAsset)
     * @dev Can only be called by the chainInterface.
     * @param channelId The incoming connection identifier.
     * @param fromVault The source vault.
     * @param toAssetIndex Index of the asset to be purchased with Units.
     * @param toAccount The recipient.
     * @param U Number of units to convert into toAsset.
     * @param minOut Minimum number of tokens bought. Reverts if less.
     * @param fromAmount Used to match cross-chain swap events. The input amount on the sending chain.
     * @param fromAsset Used to match cross-chain swap events. The input asset on the sending chain.
     * @param blockNumberMod Used to match cross-chain swap events. The block number from the host side.
     */
    function receiveAsset(
        bytes32 channelId,
        bytes calldata fromVault,
        uint256 toAssetIndex,
        address toAccount,
        uint256 U,
        uint256 minOut,
        uint256 fromAmount,
        bytes calldata fromAsset,
        uint32 blockNumberMod
    ) external returns(uint256 purchasedTokens);

    /**
     * @notice Initiate a cross-chain liquidity swap by withdrawing tokens and converting them to units.
     * @dev While the description says tokens are withdrawn and then converted to units, vault tokens are converted
     * directly into units through the following equation:
     *      U = ln(PT/(PT-pt)) * \sum W_i
     * @param routeDescription A cross-chain route description which contains the chainIdentifier, toAccount, toVault and relaying incentive.
     * @param vaultTokens Number of vault tokens to exchange.
     * @param minOut Array of minout describing: [the minimum number of vault tokens, the minimum number of reference assets].
     * @param fallbackUser If the transaction fails, send the escrowed funds to this address.
     * @param calldata_ Data field if a call should be made on the target chain.
     * Encoding depends on the target chain, with EVM: abi.encodePacket(bytes20(<address>), <data>). At maximum 65535 bytes can be passed.
     * @return uint256 Number of units minted.
     */
    function sendLiquidity(
        ICatalystV1Structs.RouteDescription calldata routeDescription,
        uint256 vaultTokens,
        uint256[2] calldata minOut,
        address fallbackUser,
        bytes calldata calldata_
    ) external payable returns (uint256);

    /**
     * @notice Completes a cross-chain liquidity swap by converting units to tokens and depositing.
     * @dev Called exclusively by the chainInterface.
     * @param fromVault Source vault
     * @param toAccount Recipient of the vault tokens
     * @param U Number of units to convert into vault tokens.
     * @param minVaultTokens Minimum number of vault tokens to mint on target vault. Otherwise: Reject
     * @param minReferenceAsset Minimum number of reference asset the vaults tokens are worth. Otherwise: Reject
     * @param fromAmount Used to match cross-chain swap events. The input amount on the sending chain.
     * @param blockNumberMod Used to match cross-chain swap events. The block number from the host side.
     */
    function receiveLiquidity(
        bytes32 channelId,
        bytes calldata fromVault,
        address toAccount,
        uint256 U,
        uint256 minVaultTokens,
        uint256 minReferenceAsset,
        uint256 fromAmount,
        uint32 blockNumberMod
    ) external returns(uint256 purchasedVaultTokens);
}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

/** @title Extensions to vaults which supports underwriting. */
interface ICatalystV1Underwriting {
    function underwriteAsset(
        bytes32 identifier,
        address toAsset,
        uint256 U,
        uint256 minOut
    ) external returns (uint256);

    function releaseUnderwriteAsset(
        address refundTo,
        bytes32 identifier,
        uint256 escrowAmount,
        address escrowToken,
        bytes32 sourceIdentifier,
        bytes calldata fromVault
    ) external;

    function deleteUnderwriteAsset(
        bytes32 identifier,
        uint256 U,
        uint256 escrowAmount,
        address escrowToken
    ) external;
}

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;

/**
 * @title Events emitted by Catalyst v1 Factory
 * @notice Contains all events emitted by the Factory
*/
interface ICatalystV1FactoryEvents {
    /**
     * @notice  Describes the deployment of a new vault as a proxy of the given vault template.
     * @dev Should be used for vault discovery and pathing.
     * @param vaultTemplate The address of the template used by the transparent proxy.
     * @param chainInterface The address of the CCI used by the transparent proxy.
     * @param vaultAddress The minimal transparent proxy address for the vault.
     * @param assets List of the assets the vault supports.
     * @param k Set to 10**18 if the vault is volatile, otherwise the vault is an amplified vault.
     */
    event VaultDeployed(
        address indexed vaultTemplate,
        address indexed chainInterface, 
        address indexed deployer,
        address vaultAddress,
        address[] assets,
        uint256 k
    );

    /**
     * @notice Describes governance fee changes.
     * @dev Only applies to new vaults, has no impact on existing vaults.
     * @param fee The new governance fee.
     */
    event SetDefaultGovernanceFee(
        uint256 fee
    );

    /**
     * @notice Sets a new destination for governance fees.
     */
    event SetGovernanceFeeDestination(
        address newFeeDestination
    );
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Minimal proxy library.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/LibClone.sol)
/// @author Minimal proxy by 0age (https://github.com/0age)
/// @author Clones with immutable args by wighawag, zefram.eth, Saw-mon & Natalie
/// (https://github.com/Saw-mon-and-Natalie/clones-with-immutable-args)
/// @author Minimal ERC1967 proxy by jtriley-eth (https://github.com/jtriley-eth/minimum-viable-proxy)
///
/// @dev Minimal proxy:
/// Although the sw0nt pattern saves 5 gas over the erc-1167 pattern during runtime,
/// it is not supported out-of-the-box on Etherscan. Hence, we choose to use the 0age pattern,
/// which saves 4 gas over the erc-1167 pattern during runtime, and has the smallest bytecode.
///
/// @dev Minimal proxy (PUSH0 variant):
/// This is a new minimal proxy that uses the PUSH0 opcode introduced during Shanghai.
/// It is optimized first for minimal runtime gas, then for minimal bytecode.
/// The PUSH0 clone functions are intentionally postfixed with a jarring "_PUSH0" as
/// many EVM chains may not support the PUSH0 opcode in the early months after Shanghai.
/// Please use with caution.
///
/// @dev Clones with immutable args (CWIA):
/// The implementation of CWIA here implements a `receive()` method that emits the
/// `ReceiveETH(uint256)` event. This skips the `DELEGATECALL` when there is no calldata,
/// enabling us to accept hard gas-capped `sends` & `transfers` for maximum backwards
/// composability. The minimal proxy implementation does not offer this feature.
///
/// @dev Minimal ERC1967 proxy:
/// An minimal ERC1967 proxy, intended to be upgraded with UUPS.
/// This is NOT the same as ERC1967Factory's transparent proxy, which includes admin logic.
///
/// @dev ERC1967I proxy:
/// An variant of the minimal ERC1967 proxy, with a special code path that activates
/// if `calldatasize() == 1`. This code path skips the delegatecall and directly returns the
/// `implementation` address. The returned implementation is guaranteed to be valid if the
/// keccak256 of the proxy's code is equal to `ERC1967I_CODE_HASH`.
library LibClone {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The keccak256 of the deployed code for the ERC1967 proxy.
    bytes32 internal constant ERC1967_CODE_HASH =
        0xaaa52c8cc8a0e3fd27ce756cc6b4e70c51423e9b597b11f32d3e49f8b1fc890d;

    /// @dev The keccak256 of the deployed code for the ERC1967I proxy.
    bytes32 internal constant ERC1967I_CODE_HASH =
        0xce700223c0d4cea4583409accfc45adac4a093b3519998a9cbbe1504dadba6f7;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Unable to deploy the clone.
    error DeploymentFailed();

    /// @dev The salt must start with either the zero address or `by`.
    error SaltDoesNotStartWith();

    /// @dev The ETH transfer has failed.
    error ETHTransferFailed();

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  MINIMAL PROXY OPERATIONS                  */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Deploys a clone of `implementation`.
    function clone(address implementation) internal returns (address instance) {
        instance = clone(0, implementation);
    }

    /// @dev Deploys a clone of `implementation`.
    /// Deposits `value` ETH during deployment.
    function clone(uint256 value, address implementation) internal returns (address instance) {
        /// @solidity memory-safe-assembly
        assembly {
            /**
             * --------------------------------------------------------------------------+
             * CREATION (9 bytes)                                                        |
             * --------------------------------------------------------------------------|
             * Opcode     | Mnemonic          | Stack     | Memory                       |
             * --------------------------------------------------------------------------|
             * 60 runSize | PUSH1 runSize     | r         |                              |
             * 3d         | RETURNDATASIZE    | 0 r       |                              |
             * 81         | DUP2              | r 0 r     |                              |
             * 60 offset  | PUSH1 offset      | o r 0 r   |                              |
             * 3d         | RETURNDATASIZE    | 0 o r 0 r |                              |
             * 39         | CODECOPY          | 0 r       | [0..runSize): runtime code   |
             * f3         | RETURN            |           | [0..runSize): runtime code   |
             * --------------------------------------------------------------------------|
             * RUNTIME (44 bytes)                                                        |
             * --------------------------------------------------------------------------|
             * Opcode  | Mnemonic       | Stack                  | Memory                |
             * --------------------------------------------------------------------------|
             *                                                                           |
             * ::: keep some values in stack ::::::::::::::::::::::::::::::::::::::::::: |
             * 3d      | RETURNDATASIZE | 0                      |                       |
             * 3d      | RETURNDATASIZE | 0 0                    |                       |
             * 3d      | RETURNDATASIZE | 0 0 0                  |                       |
             * 3d      | RETURNDATASIZE | 0 0 0 0                |                       |
             *                                                                           |
             * ::: copy calldata to memory ::::::::::::::::::::::::::::::::::::::::::::: |
             * 36      | CALLDATASIZE   | cds 0 0 0 0            |                       |
             * 3d      | RETURNDATASIZE | 0 cds 0 0 0 0          |                       |
             * 3d      | RETURNDATASIZE | 0 0 cds 0 0 0 0        |                       |
             * 37      | CALLDATACOPY   | 0 0 0 0                | [0..cds): calldata    |
             *                                                                           |
             * ::: delegate call to the implementation contract :::::::::::::::::::::::: |
             * 36      | CALLDATASIZE   | cds 0 0 0 0            | [0..cds): calldata    |
             * 3d      | RETURNDATASIZE | 0 cds 0 0 0 0          | [0..cds): calldata    |
             * 73 addr | PUSH20 addr    | addr 0 cds 0 0 0 0     | [0..cds): calldata    |
             * 5a      | GAS            | gas addr 0 cds 0 0 0 0 | [0..cds): calldata    |
             * f4      | DELEGATECALL   | success 0 0            | [0..cds): calldata    |
             *                                                                           |
             * ::: copy return data to memory :::::::::::::::::::::::::::::::::::::::::: |
             * 3d      | RETURNDATASIZE | rds success 0 0        | [0..cds): calldata    |
             * 3d      | RETURNDATASIZE | rds rds success 0 0    | [0..cds): calldata    |
             * 93      | SWAP4          | 0 rds success 0 rds    | [0..cds): calldata    |
             * 80      | DUP1           | 0 0 rds success 0 rds  | [0..cds): calldata    |
             * 3e      | RETURNDATACOPY | success 0 rds          | [0..rds): returndata  |
             *                                                                           |
             * 60 0x2a | PUSH1 0x2a     | 0x2a success 0 rds     | [0..rds): returndata  |
             * 57      | JUMPI          | 0 rds                  | [0..rds): returndata  |
             *                                                                           |
             * ::: revert :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * fd      | REVERT         |                        | [0..rds): returndata  |
             *                                                                           |
             * ::: return :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 5b      | JUMPDEST       | 0 rds                  | [0..rds): returndata  |
             * f3      | RETURN         |                        | [0..rds): returndata  |
             * --------------------------------------------------------------------------+
             */
            mstore(0x21, 0x5af43d3d93803e602a57fd5bf3)
            mstore(0x14, implementation)
            mstore(0x00, 0x602c3d8160093d39f33d3d3d3d363d3d37363d73)
            instance := create(value, 0x0c, 0x35)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x21, 0) // Restore the overwritten part of the free memory pointer.
        }
    }

    /// @dev Deploys a deterministic clone of `implementation` with `salt`.
    function cloneDeterministic(address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        instance = cloneDeterministic(0, implementation, salt);
    }

    /// @dev Deploys a deterministic clone of `implementation` with `salt`.
    /// Deposits `value` ETH during deployment.
    function cloneDeterministic(uint256 value, address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x21, 0x5af43d3d93803e602a57fd5bf3)
            mstore(0x14, implementation)
            mstore(0x00, 0x602c3d8160093d39f33d3d3d3d363d3d37363d73)
            instance := create2(value, 0x0c, 0x35, salt)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x21, 0) // Restore the overwritten part of the free memory pointer.
        }
    }

    /// @dev Returns the initialization code of the clone of `implementation`.
    function initCode(address implementation) internal pure returns (bytes memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40)
            mstore(add(result, 0x40), 0x5af43d3d93803e602a57fd5bf30000000000000000000000)
            mstore(add(result, 0x28), implementation)
            mstore(add(result, 0x14), 0x602c3d8160093d39f33d3d3d3d363d3d37363d73)
            mstore(result, 0x35) // Store the length.
            mstore(0x40, add(result, 0x60)) // Allocate memory.
        }
    }

    /// @dev Returns the initialization code hash of the clone of `implementation`.
    /// Used for mining vanity addresses with create2crunch.
    function initCodeHash(address implementation) internal pure returns (bytes32 hash) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x21, 0x5af43d3d93803e602a57fd5bf3)
            mstore(0x14, implementation)
            mstore(0x00, 0x602c3d8160093d39f33d3d3d3d363d3d37363d73)
            hash := keccak256(0x0c, 0x35)
            mstore(0x21, 0) // Restore the overwritten part of the free memory pointer.
        }
    }

    /// @dev Returns the address of the deterministic clone of `implementation`,
    /// with `salt` by `deployer`.
    /// Note: The returned result has dirty upper 96 bits. Please clean if used in assembly.
    function predictDeterministicAddress(address implementation, bytes32 salt, address deployer)
        internal
        pure
        returns (address predicted)
    {
        bytes32 hash = initCodeHash(implementation);
        predicted = predictDeterministicAddress(hash, salt, deployer);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*          MINIMAL PROXY OPERATIONS (PUSH0 VARIANT)          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Deploys a PUSH0 clone of `implementation`.
    function clone_PUSH0(address implementation) internal returns (address instance) {
        instance = clone_PUSH0(0, implementation);
    }

    /// @dev Deploys a PUSH0 clone of `implementation`.
    /// Deposits `value` ETH during deployment.
    function clone_PUSH0(uint256 value, address implementation)
        internal
        returns (address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            /**
             * --------------------------------------------------------------------------+
             * CREATION (9 bytes)                                                        |
             * --------------------------------------------------------------------------|
             * Opcode     | Mnemonic          | Stack     | Memory                       |
             * --------------------------------------------------------------------------|
             * 60 runSize | PUSH1 runSize     | r         |                              |
             * 5f         | PUSH0             | 0 r       |                              |
             * 81         | DUP2              | r 0 r     |                              |
             * 60 offset  | PUSH1 offset      | o r 0 r   |                              |
             * 5f         | PUSH0             | 0 o r 0 r |                              |
             * 39         | CODECOPY          | 0 r       | [0..runSize): runtime code   |
             * f3         | RETURN            |           | [0..runSize): runtime code   |
             * --------------------------------------------------------------------------|
             * RUNTIME (45 bytes)                                                        |
             * --------------------------------------------------------------------------|
             * Opcode  | Mnemonic       | Stack                  | Memory                |
             * --------------------------------------------------------------------------|
             *                                                                           |
             * ::: keep some values in stack ::::::::::::::::::::::::::::::::::::::::::: |
             * 5f      | PUSH0          | 0                      |                       |
             * 5f      | PUSH0          | 0 0                    |                       |
             *                                                                           |
             * ::: copy calldata to memory ::::::::::::::::::::::::::::::::::::::::::::: |
             * 36      | CALLDATASIZE   | cds 0 0                |                       |
             * 5f      | PUSH0          | 0 cds 0 0              |                       |
             * 5f      | PUSH0          | 0 0 cds 0 0            |                       |
             * 37      | CALLDATACOPY   | 0 0                    | [0..cds): calldata    |
             *                                                                           |
             * ::: delegate call to the implementation contract :::::::::::::::::::::::: |
             * 36      | CALLDATASIZE   | cds 0 0                | [0..cds): calldata    |
             * 5f      | PUSH0          | 0 cds 0 0              | [0..cds): calldata    |
             * 73 addr | PUSH20 addr    | addr 0 cds 0 0         | [0..cds): calldata    |
             * 5a      | GAS            | gas addr 0 cds 0 0     | [0..cds): calldata    |
             * f4      | DELEGATECALL   | success                | [0..cds): calldata    |
             *                                                                           |
             * ::: copy return data to memory :::::::::::::::::::::::::::::::::::::::::: |
             * 3d      | RETURNDATASIZE | rds success            | [0..cds): calldata    |
             * 5f      | PUSH0          | 0 rds success          | [0..cds): calldata    |
             * 5f      | PUSH0          | 0 0 rds success        | [0..cds): calldata    |
             * 3e      | RETURNDATACOPY | success                | [0..rds): returndata  |
             *                                                                           |
             * 60 0x29 | PUSH1 0x29     | 0x29 success           | [0..rds): returndata  |
             * 57      | JUMPI          |                        | [0..rds): returndata  |
             *                                                                           |
             * ::: revert :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d      | RETURNDATASIZE | rds                    | [0..rds): returndata  |
             * 5f      | PUSH0          | 0 rds                  | [0..rds): returndata  |
             * fd      | REVERT         |                        | [0..rds): returndata  |
             *                                                                           |
             * ::: return :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 5b      | JUMPDEST       |                        | [0..rds): returndata  |
             * 3d      | RETURNDATASIZE | rds                    | [0..rds): returndata  |
             * 5f      | PUSH0          | 0 rds                  | [0..rds): returndata  |
             * f3      | RETURN         |                        | [0..rds): returndata  |
             * --------------------------------------------------------------------------+
             */
            mstore(0x24, 0x5af43d5f5f3e6029573d5ffd5b3d5ff3) // 16
            mstore(0x14, implementation) // 20
            mstore(0x00, 0x602d5f8160095f39f35f5f365f5f37365f73) // 9 + 9
            instance := create(value, 0x0e, 0x36)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x24, 0) // Restore the overwritten part of the free memory pointer.
        }
    }

    /// @dev Deploys a deterministic PUSH0 clone of `implementation` with `salt`.
    function cloneDeterministic_PUSH0(address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        instance = cloneDeterministic_PUSH0(0, implementation, salt);
    }

    /// @dev Deploys a deterministic PUSH0 clone of `implementation` with `salt`.
    /// Deposits `value` ETH during deployment.
    function cloneDeterministic_PUSH0(uint256 value, address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x24, 0x5af43d5f5f3e6029573d5ffd5b3d5ff3) // 16
            mstore(0x14, implementation) // 20
            mstore(0x00, 0x602d5f8160095f39f35f5f365f5f37365f73) // 9 + 9
            instance := create2(value, 0x0e, 0x36, salt)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x24, 0) // Restore the overwritten part of the free memory pointer.
        }
    }

    /// @dev Returns the initialization code of the PUSH0 clone of `implementation`.
    function initCode_PUSH0(address implementation) internal pure returns (bytes memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40)
            mstore(add(result, 0x40), 0x5af43d5f5f3e6029573d5ffd5b3d5ff300000000000000000000) // 16
            mstore(add(result, 0x26), implementation) // 20
            mstore(add(result, 0x12), 0x602d5f8160095f39f35f5f365f5f37365f73) // 9 + 9
            mstore(result, 0x36) // Store the length.
            mstore(0x40, add(result, 0x60)) // Allocate memory.
        }
    }

    /// @dev Returns the initialization code hash of the PUSH0 clone of `implementation`.
    /// Used for mining vanity addresses with create2crunch.
    function initCodeHash_PUSH0(address implementation) internal pure returns (bytes32 hash) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x24, 0x5af43d5f5f3e6029573d5ffd5b3d5ff3) // 16
            mstore(0x14, implementation) // 20
            mstore(0x00, 0x602d5f8160095f39f35f5f365f5f37365f73) // 9 + 9
            hash := keccak256(0x0e, 0x36)
            mstore(0x24, 0) // Restore the overwritten part of the free memory pointer.
        }
    }

    /// @dev Returns the address of the deterministic PUSH0 clone of `implementation`,
    /// with `salt` by `deployer`.
    /// Note: The returned result has dirty upper 96 bits. Please clean if used in assembly.
    function predictDeterministicAddress_PUSH0(
        address implementation,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        bytes32 hash = initCodeHash_PUSH0(implementation);
        predicted = predictDeterministicAddress(hash, salt, deployer);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*           CLONES WITH IMMUTABLE ARGS OPERATIONS            */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    // Note: This implementation of CWIA differs from the original implementation.
    // If the calldata is empty, it will emit a `ReceiveETH(uint256)` event and skip the `DELEGATECALL`.

    /// @dev Deploys a clone of `implementation` with immutable arguments encoded in `data`.
    function clone(address implementation, bytes memory data) internal returns (address instance) {
        instance = clone(0, implementation, data);
    }

    /// @dev Deploys a clone of `implementation` with immutable arguments encoded in `data`.
    /// Deposits `value` ETH during deployment.
    function clone(uint256 value, address implementation, bytes memory data)
        internal
        returns (address instance)
    {
        assembly {
            // Compute the boundaries of the data and cache the memory slots around it.
            let mBefore3 := mload(sub(data, 0x60))
            let mBefore2 := mload(sub(data, 0x40))
            let mBefore1 := mload(sub(data, 0x20))
            let dataLength := mload(data)
            let dataEnd := add(add(data, 0x20), dataLength)
            let mAfter1 := mload(dataEnd)

            // +2 bytes for telling how much data there is appended to the call.
            let extraLength := add(dataLength, 2)
            // The `creationSize` is `extraLength + 108`
            // The `runSize` is `creationSize - 10`.

            /**
             * ---------------------------------------------------------------------------------------------------+
             * CREATION (10 bytes)                                                                                |
             * ---------------------------------------------------------------------------------------------------|
             * Opcode     | Mnemonic          | Stack     | Memory                                                |
             * ---------------------------------------------------------------------------------------------------|
             * 61 runSize | PUSH2 runSize     | r         |                                                       |
             * 3d         | RETURNDATASIZE    | 0 r       |                                                       |
             * 81         | DUP2              | r 0 r     |                                                       |
             * 60 offset  | PUSH1 offset      | o r 0 r   |                                                       |
             * 3d         | RETURNDATASIZE    | 0 o r 0 r |                                                       |
             * 39         | CODECOPY          | 0 r       | [0..runSize): runtime code                            |
             * f3         | RETURN            |           | [0..runSize): runtime code                            |
             * ---------------------------------------------------------------------------------------------------|
             * RUNTIME (98 bytes + extraLength)                                                                   |
             * ---------------------------------------------------------------------------------------------------|
             * Opcode   | Mnemonic       | Stack                    | Memory                                      |
             * ---------------------------------------------------------------------------------------------------|
             *                                                                                                    |
             * ::: if no calldata, emit event & return w/o `DELEGATECALL` ::::::::::::::::::::::::::::::::::::::: |
             * 36       | CALLDATASIZE   | cds                      |                                             |
             * 60 0x2c  | PUSH1 0x2c     | 0x2c cds                 |                                             |
             * 57       | JUMPI          |                          |                                             |
             * 34       | CALLVALUE      | cv                       |                                             |
             * 3d       | RETURNDATASIZE | 0 cv                     |                                             |
             * 52       | MSTORE         |                          | [0..0x20): callvalue                        |
             * 7f sig   | PUSH32 0x9e..  | sig                      | [0..0x20): callvalue                        |
             * 59       | MSIZE          | 0x20 sig                 | [0..0x20): callvalue                        |
             * 3d       | RETURNDATASIZE | 0 0x20 sig               | [0..0x20): callvalue                        |
             * a1       | LOG1           |                          | [0..0x20): callvalue                        |
             * 00       | STOP           |                          | [0..0x20): callvalue                        |
             * 5b       | JUMPDEST       |                          |                                             |
             *                                                                                                    |
             * ::: copy calldata to memory :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 36       | CALLDATASIZE   | cds                      |                                             |
             * 3d       | RETURNDATASIZE | 0 cds                    |                                             |
             * 3d       | RETURNDATASIZE | 0 0 cds                  |                                             |
             * 37       | CALLDATACOPY   |                          | [0..cds): calldata                          |
             *                                                                                                    |
             * ::: keep some values in stack :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d       | RETURNDATASIZE | 0                        | [0..cds): calldata                          |
             * 3d       | RETURNDATASIZE | 0 0                      | [0..cds): calldata                          |
             * 3d       | RETURNDATASIZE | 0 0 0                    | [0..cds): calldata                          |
             * 3d       | RETURNDATASIZE | 0 0 0 0                  | [0..cds): calldata                          |
             * 61 extra | PUSH2 extra    | e 0 0 0 0                | [0..cds): calldata                          |
             *                                                                                                    |
             * ::: copy extra data to memory :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 80       | DUP1           | e e 0 0 0 0              | [0..cds): calldata                          |
             * 60 0x62  | PUSH1 0x62     | 0x62 e e 0 0 0 0         | [0..cds): calldata                          |
             * 36       | CALLDATASIZE   | cds 0x62 e e 0 0 0 0     | [0..cds): calldata                          |
             * 39       | CODECOPY       | e 0 0 0 0                | [0..cds): calldata, [cds..cds+e): extraData |
             *                                                                                                    |
             * ::: delegate call to the implementation contract ::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 36       | CALLDATASIZE   | cds e 0 0 0 0            | [0..cds): calldata, [cds..cds+e): extraData |
             * 01       | ADD            | cds+e 0 0 0 0            | [0..cds): calldata, [cds..cds+e): extraData |
             * 3d       | RETURNDATASIZE | 0 cds+e 0 0 0 0          | [0..cds): calldata, [cds..cds+e): extraData |
             * 73 addr  | PUSH20 addr    | addr 0 cds+e 0 0 0 0     | [0..cds): calldata, [cds..cds+e): extraData |
             * 5a       | GAS            | gas addr 0 cds+e 0 0 0 0 | [0..cds): calldata, [cds..cds+e): extraData |
             * f4       | DELEGATECALL   | success 0 0              | [0..cds): calldata, [cds..cds+e): extraData |
             *                                                                                                    |
             * ::: copy return data to memory ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d       | RETURNDATASIZE | rds success 0 0          | [0..cds): calldata, [cds..cds+e): extraData |
             * 3d       | RETURNDATASIZE | rds rds success 0 0      | [0..cds): calldata, [cds..cds+e): extraData |
             * 93       | SWAP4          | 0 rds success 0 rds      | [0..cds): calldata, [cds..cds+e): extraData |
             * 80       | DUP1           | 0 0 rds success 0 rds    | [0..cds): calldata, [cds..cds+e): extraData |
             * 3e       | RETURNDATACOPY | success 0 rds            | [0..rds): returndata                        |
             *                                                                                                    |
             * 60 0x60  | PUSH1 0x60     | 0x60 success 0 rds       | [0..rds): returndata                        |
             * 57       | JUMPI          | 0 rds                    | [0..rds): returndata                        |
             *                                                                                                    |
             * ::: revert ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * fd       | REVERT         |                          | [0..rds): returndata                        |
             *                                                                                                    |
             * ::: return ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 5b       | JUMPDEST       | 0 rds                    | [0..rds): returndata                        |
             * f3       | RETURN         |                          | [0..rds): returndata                        |
             * ---------------------------------------------------------------------------------------------------+
             */
            mstore(data, 0x5af43d3d93803e606057fd5bf3) // Write the bytecode before the data.
            mstore(sub(data, 0x0d), implementation) // Write the address of the implementation.
            // Write the rest of the bytecode.
            mstore(
                sub(data, 0x21),
                or(shl(0x48, extraLength), 0x593da1005b363d3d373d3d3d3d610000806062363936013d73)
            )
            // `keccak256("ReceiveETH(uint256)")`
            mstore(
                sub(data, 0x3a), 0x9e4ac34f21c619cefc926c8bd93b54bf5a39c7ab2127a895af1cc0691d7e3dff
            )
            mstore(
                // Do a out-of-gas revert if `extraLength` is too big. 0xffff - 0x62 + 0x01 = 0xff9e.
                // The actual EVM limit may be smaller and may change over time.
                sub(data, add(0x59, lt(extraLength, 0xff9e))),
                or(shl(0x78, add(extraLength, 0x62)), 0xfd6100003d81600a3d39f336602c57343d527f)
            )
            mstore(dataEnd, shl(0xf0, extraLength))

            instance := create(value, sub(data, 0x4c), add(extraLength, 0x6c))
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }

            // Restore the overwritten memory surrounding `data`.
            mstore(dataEnd, mAfter1)
            mstore(data, dataLength)
            mstore(sub(data, 0x20), mBefore1)
            mstore(sub(data, 0x40), mBefore2)
            mstore(sub(data, 0x60), mBefore3)
        }
    }

    /// @dev Deploys a deterministic clone of `implementation`
    /// with immutable arguments encoded in `data` and `salt`.
    function cloneDeterministic(address implementation, bytes memory data, bytes32 salt)
        internal
        returns (address instance)
    {
        instance = cloneDeterministic(0, implementation, data, salt);
    }

    /// @dev Deploys a deterministic clone of `implementation`
    /// with immutable arguments encoded in `data` and `salt`.
    function cloneDeterministic(
        uint256 value,
        address implementation,
        bytes memory data,
        bytes32 salt
    ) internal returns (address instance) {
        assembly {
            // Compute the boundaries of the data and cache the memory slots around it.
            let mBefore3 := mload(sub(data, 0x60))
            let mBefore2 := mload(sub(data, 0x40))
            let mBefore1 := mload(sub(data, 0x20))
            let dataLength := mload(data)
            let dataEnd := add(add(data, 0x20), dataLength)
            let mAfter1 := mload(dataEnd)

            // +2 bytes for telling how much data there is appended to the call.
            let extraLength := add(dataLength, 2)

            mstore(data, 0x5af43d3d93803e606057fd5bf3) // Write the bytecode before the data.
            mstore(sub(data, 0x0d), implementation) // Write the address of the implementation.
            // Write the rest of the bytecode.
            mstore(
                sub(data, 0x21),
                or(shl(0x48, extraLength), 0x593da1005b363d3d373d3d3d3d610000806062363936013d73)
            )
            // `keccak256("ReceiveETH(uint256)")`
            mstore(
                sub(data, 0x3a), 0x9e4ac34f21c619cefc926c8bd93b54bf5a39c7ab2127a895af1cc0691d7e3dff
            )
            mstore(
                // Do a out-of-gas revert if `extraLength` is too big. 0xffff - 0x62 + 0x01 = 0xff9e.
                // The actual EVM limit may be smaller and may change over time.
                sub(data, add(0x59, lt(extraLength, 0xff9e))),
                or(shl(0x78, add(extraLength, 0x62)), 0xfd6100003d81600a3d39f336602c57343d527f)
            )
            mstore(dataEnd, shl(0xf0, extraLength))

            instance := create2(value, sub(data, 0x4c), add(extraLength, 0x6c), salt)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }

            // Restore the overwritten memory surrounding `data`.
            mstore(dataEnd, mAfter1)
            mstore(data, dataLength)
            mstore(sub(data, 0x20), mBefore1)
            mstore(sub(data, 0x40), mBefore2)
            mstore(sub(data, 0x60), mBefore3)
        }
    }

    /// @dev Returns the initialization code hash of the clone of `implementation`
    /// using immutable arguments encoded in `data`.
    function initCode(address implementation, bytes memory data)
        internal
        pure
        returns (bytes memory result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40)
            let dataLength := mload(data)

            // Do a out-of-gas revert if `dataLength` is too big. 0xffff - 0x02 - 0x62 = 0xff9b.
            // The actual EVM limit may be smaller and may change over time.
            returndatacopy(returndatasize(), returndatasize(), gt(dataLength, 0xff9b))

            let o := add(result, 0x8c)
            let end := add(o, dataLength)

            // Copy the `data` into `result`.
            for { let d := sub(add(data, 0x20), o) } 1 {} {
                mstore(o, mload(add(o, d)))
                o := add(o, 0x20)
                if iszero(lt(o, end)) { break }
            }

            // +2 bytes for telling how much data there is appended to the call.
            let extraLength := add(dataLength, 2)

            mstore(add(result, 0x6c), 0x5af43d3d93803e606057fd5bf3) // Write the bytecode before the data.
            mstore(add(result, 0x5f), implementation) // Write the address of the implementation.
            // Write the rest of the bytecode.
            mstore(
                add(result, 0x4b),
                or(shl(0x48, extraLength), 0x593da1005b363d3d373d3d3d3d610000806062363936013d73)
            )
            // `keccak256("ReceiveETH(uint256)")`
            mstore(
                add(result, 0x32),
                0x9e4ac34f21c619cefc926c8bd93b54bf5a39c7ab2127a895af1cc0691d7e3dff
            )
            mstore(
                add(result, 0x12),
                or(shl(0x78, add(extraLength, 0x62)), 0x6100003d81600a3d39f336602c57343d527f)
            )
            mstore(end, shl(0xf0, extraLength))
            mstore(add(end, 0x02), 0) // Zeroize the slot after the result.
            mstore(result, add(extraLength, 0x6c)) // Store the length.
            mstore(0x40, add(0x22, end)) // Allocate memory.
        }
    }

    /// @dev Returns the initialization code hash of the clone of `implementation`
    /// using immutable arguments encoded in `data`.
    /// Used for mining vanity addresses with create2crunch.
    function initCodeHash(address implementation, bytes memory data)
        internal
        pure
        returns (bytes32 hash)
    {
        assembly {
            // Compute the boundaries of the data and cache the memory slots around it.
            let mBefore3 := mload(sub(data, 0x60))
            let mBefore2 := mload(sub(data, 0x40))
            let mBefore1 := mload(sub(data, 0x20))
            let dataLength := mload(data)
            let dataEnd := add(add(data, 0x20), dataLength)
            let mAfter1 := mload(dataEnd)

            // Do a out-of-gas revert if `dataLength` is too big. 0xffff - 0x02 - 0x62 = 0xff9b.
            // The actual EVM limit may be smaller and may change over time.
            returndatacopy(returndatasize(), returndatasize(), gt(dataLength, 0xff9b))

            // +2 bytes for telling how much data there is appended to the call.
            let extraLength := add(dataLength, 2)

            mstore(data, 0x5af43d3d93803e606057fd5bf3) // Write the bytecode before the data.
            mstore(sub(data, 0x0d), implementation) // Write the address of the implementation.
            // Write the rest of the bytecode.
            mstore(
                sub(data, 0x21),
                or(shl(0x48, extraLength), 0x593da1005b363d3d373d3d3d3d610000806062363936013d73)
            )
            // `keccak256("ReceiveETH(uint256)")`
            mstore(
                sub(data, 0x3a), 0x9e4ac34f21c619cefc926c8bd93b54bf5a39c7ab2127a895af1cc0691d7e3dff
            )
            mstore(
                sub(data, 0x5a),
                or(shl(0x78, add(extraLength, 0x62)), 0x6100003d81600a3d39f336602c57343d527f)
            )
            mstore(dataEnd, shl(0xf0, extraLength))

            hash := keccak256(sub(data, 0x4c), add(extraLength, 0x6c))

            // Restore the overwritten memory surrounding `data`.
            mstore(dataEnd, mAfter1)
            mstore(data, dataLength)
            mstore(sub(data, 0x20), mBefore1)
            mstore(sub(data, 0x40), mBefore2)
            mstore(sub(data, 0x60), mBefore3)
        }
    }

    /// @dev Returns the address of the deterministic clone of
    /// `implementation` using immutable arguments encoded in `data`, with `salt`, by `deployer`.
    /// Note: The returned result has dirty upper 96 bits. Please clean if used in assembly.
    function predictDeterministicAddress(
        address implementation,
        bytes memory data,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        bytes32 hash = initCodeHash(implementation, data);
        predicted = predictDeterministicAddress(hash, salt, deployer);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*              MINIMAL ERC1967 PROXY OPERATIONS              */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    // Note: The ERC1967 proxy here is intended to be upgraded with UUPS.
    // This is NOT the same as ERC1967Factory's transparent proxy, which includes admin logic.

    /// @dev Deploys a minimal ERC1967 proxy with `implementation`.
    function deployERC1967(address implementation) internal returns (address instance) {
        instance = deployERC1967(0, implementation);
    }

    /// @dev Deploys a minimal ERC1967 proxy with `implementation`.
    /// Deposits `value` ETH during deployment.
    function deployERC1967(uint256 value, address implementation)
        internal
        returns (address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            /**
             * ---------------------------------------------------------------------------------+
             * CREATION (34 bytes)                                                              |
             * ---------------------------------------------------------------------------------|
             * Opcode     | Mnemonic       | Stack            | Memory                          |
             * ---------------------------------------------------------------------------------|
             * 60 runSize | PUSH1 runSize  | r                |                                 |
             * 3d         | RETURNDATASIZE | 0 r              |                                 |
             * 81         | DUP2           | r 0 r            |                                 |
             * 60 offset  | PUSH1 offset   | o r 0 r          |                                 |
             * 3d         | RETURNDATASIZE | 0 o r 0 r        |                                 |
             * 39         | CODECOPY       | 0 r              | [0..runSize): runtime code      |
             * 73 impl    | PUSH20 impl    | impl 0 r         | [0..runSize): runtime code      |
             * 60 slotPos | PUSH1 slotPos  | slotPos impl 0 r | [0..runSize): runtime code      |
             * 51         | MLOAD          | slot impl 0 r    | [0..runSize): runtime code      |
             * 55         | SSTORE         | 0 r              | [0..runSize): runtime code      |
             * f3         | RETURN         |                  | [0..runSize): runtime code      |
             * ---------------------------------------------------------------------------------|
             * RUNTIME (61 bytes)                                                               |
             * ---------------------------------------------------------------------------------|
             * Opcode     | Mnemonic       | Stack            | Memory                          |
             * ---------------------------------------------------------------------------------|
             *                                                                                  |
             * ::: copy calldata to memory :::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 36         | CALLDATASIZE   | cds              |                                 |
             * 3d         | RETURNDATASIZE | 0 cds            |                                 |
             * 3d         | RETURNDATASIZE | 0 0 cds          |                                 |
             * 37         | CALLDATACOPY   |                  | [0..calldatasize): calldata     |
             *                                                                                  |
             * ::: delegatecall to implementation ::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d         | RETURNDATASIZE | 0                |                                 |
             * 3d         | RETURNDATASIZE | 0 0              |                                 |
             * 36         | CALLDATASIZE   | cds 0 0          | [0..calldatasize): calldata     |
             * 3d         | RETURNDATASIZE | 0 cds 0 0        | [0..calldatasize): calldata     |
             * 7f slot    | PUSH32 slot    | s 0 cds 0 0      | [0..calldatasize): calldata     |
             * 54         | SLOAD          | i 0 cds 0 0      | [0..calldatasize): calldata     |
             * 5a         | GAS            | g i 0 cds 0 0    | [0..calldatasize): calldata     |
             * f4         | DELEGATECALL   | succ             | [0..calldatasize): calldata     |
             *                                                                                  |
             * ::: copy returndata to memory :::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d         | RETURNDATASIZE | rds succ         | [0..calldatasize): calldata     |
             * 60 0x00    | PUSH1 0x00     | 0 rds succ       | [0..calldatasize): calldata     |
             * 80         | DUP1           | 0 0 rds succ     | [0..calldatasize): calldata     |
             * 3e         | RETURNDATACOPY | succ             | [0..returndatasize): returndata |
             *                                                                                  |
             * ::: branch on delegatecall status :::::::::::::::::::::::::::::::::::::::::::::: |
             * 60 0x38    | PUSH1 0x38     | dest succ        | [0..returndatasize): returndata |
             * 57         | JUMPI          |                  | [0..returndatasize): returndata |
             *                                                                                  |
             * ::: delegatecall failed, revert :::::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d         | RETURNDATASIZE | rds              | [0..returndatasize): returndata |
             * 60 0x00    | PUSH1 0x00     | 0 rds            | [0..returndatasize): returndata |
             * fd         | REVERT         |                  | [0..returndatasize): returndata |
             *                                                                                  |
             * ::: delegatecall succeeded, return ::::::::::::::::::::::::::::::::::::::::::::: |
             * 5b         | JUMPDEST       |                  | [0..returndatasize): returndata |
             * 3d         | RETURNDATASIZE | rds              | [0..returndatasize): returndata |
             * 60 0x00    | PUSH1 0x00     | 0 rds            | [0..returndatasize): returndata |
             * f3         | RETURN         |                  | [0..returndatasize): returndata |
             * ---------------------------------------------------------------------------------+
             */
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, 0xcc3735a920a3ca505d382bbc545af43d6000803e6038573d6000fd5b3d6000f3)
            mstore(0x40, 0x5155f3363d3d373d3d363d7f360894a13ba1a3210667c828492db98dca3e2076)
            mstore(0x20, 0x6009)
            mstore(0x1e, implementation)
            mstore(0x0a, 0x603d3d8160223d3973)
            instance := create(value, 0x21, 0x5f)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero slot.
        }
    }

    /// @dev Deploys a deterministic minimal ERC1967 proxy with `implementation` and `salt`.
    function deployDeterministicERC1967(address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        instance = deployDeterministicERC1967(0, implementation, salt);
    }

    /// @dev Deploys a deterministic minimal ERC1967 proxy with `implementation` and `salt`.
    /// Deposits `value` ETH during deployment.
    function deployDeterministicERC1967(uint256 value, address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, 0xcc3735a920a3ca505d382bbc545af43d6000803e6038573d6000fd5b3d6000f3)
            mstore(0x40, 0x5155f3363d3d373d3d363d7f360894a13ba1a3210667c828492db98dca3e2076)
            mstore(0x20, 0x6009)
            mstore(0x1e, implementation)
            mstore(0x0a, 0x603d3d8160223d3973)
            instance := create2(value, 0x21, 0x5f, salt)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero slot.
        }
    }

    /// @dev Creates a deterministic minimal ERC1967 proxy with `implementation` and `salt`.
    /// Note: This method is intended for use in ERC4337 factories,
    /// which are expected to NOT revert if the proxy is already deployed.
    function createDeterministicERC1967(address implementation, bytes32 salt)
        internal
        returns (bool alreadyDeployed, address instance)
    {
        return createDeterministicERC1967(0, implementation, salt);
    }

    /// @dev Creates a deterministic minimal ERC1967 proxy with `implementation` and `salt`.
    /// Deposits `value` ETH during deployment.
    /// Note: This method is intended for use in ERC4337 factories,
    /// which are expected to NOT revert if the proxy is already deployed.
    function createDeterministicERC1967(uint256 value, address implementation, bytes32 salt)
        internal
        returns (bool alreadyDeployed, address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, 0xcc3735a920a3ca505d382bbc545af43d6000803e6038573d6000fd5b3d6000f3)
            mstore(0x40, 0x5155f3363d3d373d3d363d7f360894a13ba1a3210667c828492db98dca3e2076)
            mstore(0x20, 0x6009)
            mstore(0x1e, implementation)
            mstore(0x0a, 0x603d3d8160223d3973)
            // Compute and store the bytecode hash.
            mstore(add(m, 0x35), keccak256(0x21, 0x5f))
            mstore(m, shl(88, address()))
            mstore8(m, 0xff) // Write the prefix.
            mstore(add(m, 0x15), salt)
            instance := keccak256(m, 0x55)
            for {} 1 {} {
                if iszero(extcodesize(instance)) {
                    instance := create2(value, 0x21, 0x5f, salt)
                    if iszero(instance) {
                        mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                        revert(0x1c, 0x04)
                    }
                    break
                }
                alreadyDeployed := 1
                if iszero(value) { break }
                if iszero(call(gas(), instance, value, codesize(), 0x00, codesize(), 0x00)) {
                    mstore(0x00, 0xb12d13eb) // `ETHTransferFailed()`.
                    revert(0x1c, 0x04)
                }
                break
            }
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero slot.
        }
    }

    /// @dev Returns the initialization code of the minimal ERC1967 proxy of `implementation`.
    function initCodeERC1967(address implementation) internal pure returns (bytes memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40)
            mstore(
                add(result, 0x60),
                0x3735a920a3ca505d382bbc545af43d6000803e6038573d6000fd5b3d6000f300
            )
            mstore(
                add(result, 0x40),
                0x55f3363d3d373d3d363d7f360894a13ba1a3210667c828492db98dca3e2076cc
            )
            mstore(add(result, 0x20), or(shl(24, implementation), 0x600951))
            mstore(add(result, 0x09), 0x603d3d8160223d3973)
            mstore(result, 0x5f) // Store the length.
            mstore(0x40, add(result, 0x80)) // Allocate memory.
        }
    }

    /// @dev Returns the initialization code hash of the minimal ERC1967 proxy of `implementation`.
    /// Used for mining vanity addresses with create2crunch.
    function initCodeHashERC1967(address implementation) internal pure returns (bytes32 hash) {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, 0xcc3735a920a3ca505d382bbc545af43d6000803e6038573d6000fd5b3d6000f3)
            mstore(0x40, 0x5155f3363d3d373d3d363d7f360894a13ba1a3210667c828492db98dca3e2076)
            mstore(0x20, 0x6009)
            mstore(0x1e, implementation)
            mstore(0x0a, 0x603d3d8160223d3973)
            hash := keccak256(0x21, 0x5f)
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero slot.
        }
    }

    /// @dev Returns the address of the deterministic ERC1967 proxy of `implementation`,
    /// with `salt` by `deployer`.
    /// Note: The returned result has dirty upper 96 bits. Please clean if used in assembly.
    function predictDeterministicAddressERC1967(
        address implementation,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        bytes32 hash = initCodeHashERC1967(implementation);
        predicted = predictDeterministicAddress(hash, salt, deployer);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                 ERC1967I PROXY OPERATIONS                  */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    // Note: This proxy has a special code path that activates if `calldatasize() == 1`.
    // This code path skips the delegatecall and directly returns the `implementation` address.
    // The returned implementation is guaranteed to be valid if the keccak256 of the
    // proxy's code is equal to `ERC1967I_CODE_HASH`.

    /// @dev Deploys a minimal ERC1967I proxy with `implementation`.
    function deployERC1967I(address implementation) internal returns (address instance) {
        instance = deployERC1967I(0, implementation);
    }

    /// @dev Deploys a ERC1967I proxy with `implementation`.
    /// Deposits `value` ETH during deployment.
    function deployERC1967I(uint256 value, address implementation)
        internal
        returns (address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            /**
             * ---------------------------------------------------------------------------------+
             * CREATION (34 bytes)                                                              |
             * ---------------------------------------------------------------------------------|
             * Opcode     | Mnemonic       | Stack            | Memory                          |
             * ---------------------------------------------------------------------------------|
             * 60 runSize | PUSH1 runSize  | r                |                                 |
             * 3d         | RETURNDATASIZE | 0 r              |                                 |
             * 81         | DUP2           | r 0 r            |                                 |
             * 60 offset  | PUSH1 offset   | o r 0 r          |                                 |
             * 3d         | RETURNDATASIZE | 0 o r 0 r        |                                 |
             * 39         | CODECOPY       | 0 r              | [0..runSize): runtime code      |
             * 73 impl    | PUSH20 impl    | impl 0 r         | [0..runSize): runtime code      |
             * 60 slotPos | PUSH1 slotPos  | slotPos impl 0 r | [0..runSize): runtime code      |
             * 51         | MLOAD          | slot impl 0 r    | [0..runSize): runtime code      |
             * 55         | SSTORE         | 0 r              | [0..runSize): runtime code      |
             * f3         | RETURN         |                  | [0..runSize): runtime code      |
             * ---------------------------------------------------------------------------------|
             * RUNTIME (82 bytes)                                                               |
             * ---------------------------------------------------------------------------------|
             * Opcode     | Mnemonic       | Stack            | Memory                          |
             * ---------------------------------------------------------------------------------|
             *                                                                                  |
             * ::: check calldatasize ::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 36         | CALLDATASIZE   | cds              |                                 |
             * 58         | PC             | 1 cds            |                                 |
             * 14         | EQ             | eqs              |                                 |
             * 60 0x43    | PUSH1 0x43     | dest eqs         |                                 |
             * 57         | JUMPI          |                  |                                 |
             *                                                                                  |
             * ::: copy calldata to memory :::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 36         | CALLDATASIZE   | cds              |                                 |
             * 3d         | RETURNDATASIZE | 0 cds            |                                 |
             * 3d         | RETURNDATASIZE | 0 0 cds          |                                 |
             * 37         | CALLDATACOPY   |                  | [0..calldatasize): calldata     |
             *                                                                                  |
             * ::: delegatecall to implementation ::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d         | RETURNDATASIZE | 0                |                                 |
             * 3d         | RETURNDATASIZE | 0 0              |                                 |
             * 36         | CALLDATASIZE   | cds 0 0          | [0..calldatasize): calldata     |
             * 3d         | RETURNDATASIZE | 0 cds 0 0        | [0..calldatasize): calldata     |
             * 7f slot    | PUSH32 slot    | s 0 cds 0 0      | [0..calldatasize): calldata     |
             * 54         | SLOAD          | i 0 cds 0 0      | [0..calldatasize): calldata     |
             * 5a         | GAS            | g i 0 cds 0 0    | [0..calldatasize): calldata     |
             * f4         | DELEGATECALL   | succ             | [0..calldatasize): calldata     |
             *                                                                                  |
             * ::: copy returndata to memory :::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d         | RETURNDATASIZE | rds succ         | [0..calldatasize): calldata     |
             * 60 0x00    | PUSH1 0x00     | 0 rds succ       | [0..calldatasize): calldata     |
             * 80         | DUP1           | 0 0 rds succ     | [0..calldatasize): calldata     |
             * 3e         | RETURNDATACOPY | succ             | [0..returndatasize): returndata |
             *                                                                                  |
             * ::: branch on delegatecall status :::::::::::::::::::::::::::::::::::::::::::::: |
             * 60 0x3E    | PUSH1 0x3E     | dest succ        | [0..returndatasize): returndata |
             * 57         | JUMPI          |                  | [0..returndatasize): returndata |
             *                                                                                  |
             * ::: delegatecall failed, revert :::::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d         | RETURNDATASIZE | rds              | [0..returndatasize): returndata |
             * 60 0x00    | PUSH1 0x00     | 0 rds            | [0..returndatasize): returndata |
             * fd         | REVERT         |                  | [0..returndatasize): returndata |
             *                                                                                  |
             * ::: delegatecall succeeded, return ::::::::::::::::::::::::::::::::::::::::::::: |
             * 5b         | JUMPDEST       |                  | [0..returndatasize): returndata |
             * 3d         | RETURNDATASIZE | rds              | [0..returndatasize): returndata |
             * 60 0x00    | PUSH1 0x00     | 0 rds            | [0..returndatasize): returndata |
             * f3         | RETURN         |                  | [0..returndatasize): returndata |
             *                                                                                  |
             * ::: implementation , return :::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 5b         | JUMPDEST       |                  |                                 |
             * 60 0x20    | PUSH1 0x20     | 32               |                                 |
             * 60 0x0F    | PUSH1 0x0F     | o 32             |                                 |
             * 3d         | RETURNDATASIZE | 0 o 32           |                                 |
             * 39         | CODECOPY       |                  | [0..32): implementation slot    |
             * 3d         | RETURNDATASIZE | 0                | [0..32): implementation slot    |
             * 51         | MLOAD          | slot             | [0..32): implementation slot    |
             * 54         | SLOAD          | impl             | [0..32): implementation slot    |
             * 3d         | RETURNDATASIZE | 0 impl           | [0..32): implementation slot    |
             * 52         | MSTORE         |                  | [0..32): implementation address |
             * 59         | MSIZE          | 32               | [0..32): implementation address |
             * 3d         | RETURNDATASIZE | 0 32             | [0..32): implementation address |
             * f3         | RETURN         |                  | [0..32): implementation address |
             *                                                                                  |
             * ---------------------------------------------------------------------------------+
             */
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, 0x3d6000803e603e573d6000fd5b3d6000f35b6020600f3d393d51543d52593df3)
            mstore(0x40, 0xa13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc545af4)
            mstore(0x20, 0x600f5155f3365814604357363d3d373d3d363d7f360894)
            mstore(0x09, or(shl(160, 0x60523d8160223d3973), shr(96, shl(96, implementation))))
            instance := create(value, 0x0c, 0x74)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero slot.
        }
    }

    /// @dev Deploys a deterministic ERC1967I proxy with `implementation` and `salt`.
    function deployDeterministicERC1967I(address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        instance = deployDeterministicERC1967I(0, implementation, salt);
    }

    /// @dev Deploys a deterministic ERC1967I proxy with `implementation` and `salt`.
    /// Deposits `value` ETH during deployment.
    function deployDeterministicERC1967I(uint256 value, address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, 0x3d6000803e603e573d6000fd5b3d6000f35b6020600f3d393d51543d52593df3)
            mstore(0x40, 0xa13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc545af4)
            mstore(0x20, 0x600f5155f3365814604357363d3d373d3d363d7f360894)
            mstore(0x09, or(shl(160, 0x60523d8160223d3973), shr(96, shl(96, implementation))))
            instance := create2(value, 0x0c, 0x74, salt)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero slot.
        }
    }

    /// @dev Creates a deterministic ERC1967I proxy with `implementation` and `salt`.
    /// Note: This method is intended for use in ERC4337 factories,
    /// which are expected to NOT revert if the proxy is already deployed.
    function createDeterministicERC1967I(address implementation, bytes32 salt)
        internal
        returns (bool alreadyDeployed, address instance)
    {
        return createDeterministicERC1967I(0, implementation, salt);
    }

    /// @dev Creates a deterministic ERC1967I proxy with `implementation` and `salt`.
    /// Deposits `value` ETH during deployment.
    /// Note: This method is intended for use in ERC4337 factories,
    /// which are expected to NOT revert if the proxy is already deployed.
    function createDeterministicERC1967I(uint256 value, address implementation, bytes32 salt)
        internal
        returns (bool alreadyDeployed, address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, 0x3d6000803e603e573d6000fd5b3d6000f35b6020600f3d393d51543d52593df3)
            mstore(0x40, 0xa13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc545af4)
            mstore(0x20, 0x600f5155f3365814604357363d3d373d3d363d7f360894)
            mstore(0x09, or(shl(160, 0x60523d8160223d3973), shr(96, shl(96, implementation))))
            // Compute and store the bytecode hash.
            mstore(add(m, 0x35), keccak256(0x0c, 0x74))
            mstore(m, shl(88, address()))
            mstore8(m, 0xff) // Write the prefix.
            mstore(add(m, 0x15), salt)
            instance := keccak256(m, 0x55)
            for {} 1 {} {
                if iszero(extcodesize(instance)) {
                    instance := create2(value, 0x0c, 0x74, salt)
                    if iszero(instance) {
                        mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                        revert(0x1c, 0x04)
                    }
                    break
                }
                alreadyDeployed := 1
                if iszero(value) { break }
                if iszero(call(gas(), instance, value, codesize(), 0x00, codesize(), 0x00)) {
                    mstore(0x00, 0xb12d13eb) // `ETHTransferFailed()`.
                    revert(0x1c, 0x04)
                }
                break
            }
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero slot.
        }
    }

    /// @dev Returns the initialization code of the minimal ERC1967 proxy of `implementation`.
    function initCodeERC1967I(address implementation) internal pure returns (bytes memory result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40)
            mstore(
                add(result, 0x74),
                0x3d6000803e603e573d6000fd5b3d6000f35b6020600f3d393d51543d52593df3
            )
            mstore(
                add(result, 0x54),
                0xa13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc545af4
            )
            mstore(add(result, 0x34), 0x600f5155f3365814604357363d3d373d3d363d7f360894)
            mstore(add(result, 0x1d), implementation)
            mstore(add(result, 0x09), 0x60523d8160223d3973)
            mstore(add(result, 0x94), 0)
            mstore(result, 0x74) // Store the length.
            mstore(0x40, add(result, 0xa0)) // Allocate memory.
        }
    }

    /// @dev Returns the initialization code hash of the minimal ERC1967 proxy of `implementation`.
    /// Used for mining vanity addresses with create2crunch.
    function initCodeHashERC1967I(address implementation) internal pure returns (bytes32 hash) {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, 0x3d6000803e603e573d6000fd5b3d6000f35b6020600f3d393d51543d52593df3)
            mstore(0x40, 0xa13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc545af4)
            mstore(0x20, 0x600f5155f3365814604357363d3d373d3d363d7f360894)
            mstore(0x09, or(shl(160, 0x60523d8160223d3973), shr(96, shl(96, implementation))))
            hash := keccak256(0x0c, 0x74)
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero slot.
        }
    }

    /// @dev Returns the address of the deterministic ERC1967I proxy of `implementation`,
    /// with `salt` by `deployer`.
    /// Note: The returned result has dirty upper 96 bits. Please clean if used in assembly.
    function predictDeterministicAddressERC1967I(
        address implementation,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        bytes32 hash = initCodeHashERC1967I(implementation);
        predicted = predictDeterministicAddress(hash, salt, deployer);
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                      OTHER OPERATIONS                      */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the address when a contract with initialization code hash,
    /// `hash`, is deployed with `salt`, by `deployer`.
    /// Note: The returned result has dirty upper 96 bits. Please clean if used in assembly.
    function predictDeterministicAddress(bytes32 hash, bytes32 salt, address deployer)
        internal
        pure
        returns (address predicted)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Compute and store the bytecode hash.
            mstore8(0x00, 0xff) // Write the prefix.
            mstore(0x35, hash)
            mstore(0x01, shl(96, deployer))
            mstore(0x15, salt)
            predicted := keccak256(0x00, 0x55)
            mstore(0x35, 0) // Restore the overwritten part of the free memory pointer.
        }
    }

    /// @dev Requires that `salt` starts with either the zero address or `by`.
    function checkStartsWith(bytes32 salt, address by) internal pure {
        /// @solidity memory-safe-assembly
        assembly {
            // If the salt does not start with the zero address or `by`.
            if iszero(or(iszero(shr(96, salt)), eq(shr(96, shl(96, by)), shr(96, salt)))) {
                mstore(0x00, 0x0c4549ef) // `SaltDoesNotStartWith()`.
                revert(0x1c, 0x04)
            }
        }
    }
}

{
  "remappings": [
    "forge-std/=lib/forge-std/src/",
    "ds-test/=lib/forge-std/lib/ds-test/src/",
    "openzeppelin-contracts/=lib/openzeppelin-contracts/",
    "solmate/=lib/solmate/src/",
    "GeneralisedIncentives/=lib/GeneralisedIncentives/",
    "@lazyledger/protobuf3-solidity-lib/=lib/GeneralisedIncentives/lib/vibc-core-smart-contracts/lib/protobuf3-solidity-lib/",
    "@openzeppelin-upgradeable/=lib/GeneralisedIncentives/lib/vibc-core-smart-contracts/lib/openzeppelin-contracts-upgradeable/",
    "@openzeppelin/=lib/GeneralisedIncentives/lib/vibc-core-smart-contracts/lib/openzeppelin-contracts/",
    "@openzeppelin/contracts/=lib/openzeppelin-contracts/contracts/",
    "base64/=lib/GeneralisedIncentives/lib/vibc-core-smart-contracts/lib/base64/",
    "clones-with-immutable-args/=lib/GeneralisedIncentives/lib/vibc-core-smart-contracts/lib/optimism/packages/contracts-bedrock/lib/clones-with-immutable-args/src/",
    "erc4626-tests/=lib/openzeppelin-contracts/lib/erc4626-tests/",
    "openzeppelin-contracts-upgradeable/=lib/GeneralisedIncentives/lib/vibc-core-smart-contracts/lib/openzeppelin-contracts-upgradeable/",
    "openzeppelin-contracts/=lib/openzeppelin-contracts/",
    "openzeppelin/=lib/GeneralisedIncentives/lib/openzeppelin-contracts/contracts/",
    "optimism/=lib/GeneralisedIncentives/lib/vibc-core-smart-contracts/lib/",
    "proto/=lib/GeneralisedIncentives/lib/vibc-core-smart-contracts/lib/proto/",
    "protobuf3-solidity-lib/=lib/GeneralisedIncentives/lib/vibc-core-smart-contracts/lib/protobuf3-solidity-lib/contracts/",
    "safe-contracts/=lib/GeneralisedIncentives/lib/vibc-core-smart-contracts/lib/optimism/packages/contracts-bedrock/lib/safe-contracts/contracts/",
    "solady/=lib/solady/src/",
    "solmate/=lib/GeneralisedIncentives/lib/vibc-core-smart-contracts/lib/optimism/packages/contracts-bedrock/lib/solmate/src/",
    "vibc-core-smart-contracts/=lib/GeneralisedIncentives/lib/vibc-core-smart-contracts/"
  ],
  "optimizer": {
    "enabled": true,
    "runs": 10000
  },
  "metadata": {
    "useLiteralContent": false,
    "bytecodeHash": "ipfs",
    "appendCBOR": true
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "abi"
      ]
    }
  },
  "evmVersion": "paris",
  "viaIR": true,
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