// File: src/bonding/CBT.sol



pragma solidity ^0.8.17;

// from https://github.com/lsaether/bonding-curves

import {GF} from "src/GF.sol";
import {SafeTransferLib} from "solady/utils/SafeTransferLib.sol";

import "./BancorFormula.sol";

contract CBT is BancorFormula {
    event CurvedBuy(address indexed sender, uint256 amount, uint256 deposit);
    event CurvedSell(address indexed sender, uint256 amount, uint256 reimbursement);

    GF public gf;
    uint256 public poolBalance;
    uint256 public reserveRatio;

    bool public live;

    constructor(uint256 _reserveRatio) {
        gf = GF(msg.sender);
        reserveRatio = _reserveRatio;
    }

    function artificialSupply() internal view returns (uint256) {
        return gf.totalSupply() - gf.balanceOf(address(this));
    }

    function calculateCurvedMintReturn(uint256 _amount) public view returns (uint256 mintAmount) {
        return calculatePurchaseReturn(artificialSupply(), poolBalance, uint32(reserveRatio), _amount);
    }

    function calculateCurvedBurnReturn(uint256 _amount) public view returns (uint256 burnAmount) {
        return calculateSaleReturn(artificialSupply(), poolBalance, uint32(reserveRatio), _amount);
    }

    modifier onlyLive() {
        require(live, "CurveBondedToken: not live");
        _;
    }

    function buy() public payable onlyLive {
        _curvedBuy(msg.value);
    }

    // @param _amount scaled by 1e18
    function sell(uint256 _amount) public onlyLive {
        uint256 returnAmount = _curvedSell(_amount);
        SafeTransferLib.safeTransferETH(msg.sender, returnAmount);
    }

    function _curvedBuy(uint256 _deposit) internal returns (uint256) {
        uint256 amount = calculateCurvedMintReturn(_deposit);
        poolBalance += _deposit;
        gf.transfer(msg.sender, amount);
        emit CurvedBuy(msg.sender, amount, _deposit);
        return amount;
    }

    function _curvedSell(uint256 _amount) internal returns (uint256) {
        uint256 reimbursement = calculateCurvedBurnReturn(_amount);
        poolBalance -= reimbursement;
        gf.transferFrom(msg.sender, address(this), _amount);
        emit CurvedSell(msg.sender, _amount, reimbursement);
        return reimbursement;
    }

    function start() public payable {
        require(msg.sender == address(gf));
        live = true;
        poolBalance += msg.value;
    }
}

// File: src/GF.sol



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

import {ERC20} from "solady/tokens/ERC20.sol";
import {FixedPointMathLib} from "solady/utils/FixedPointMathLib.sol";
import {DateTimeLib} from "solady/utils/DateTimeLib.sol";
import {SafeTransferLib} from "solady/utils/SafeTransferLib.sol";
import {Ownable} from "solady/auth/Ownable.sol";
import {LibBitmap} from "solady/utils/LibBitmap.sol";
import {MerkleProofLib} from "solady/utils/MerkleProofLib.sol";
import {LinearVRGDA} from "VRGDAs/LinearVRGDA.sol";

import {Staking} from "src/Staking.sol";
import {CBT} from "src/bonding/CBT.sol";

import "forge-std/console.sol";

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contract GF is ERC20, Ownable, LinearVRGDA {
    using FixedPointMathLib for uint256;
    using LibBitmap for LibBitmap.Bitmap;

    event Claimed(address indexed user, uint256 amount);

    error BlessingComplete();

    uint256 public constant maxSupply = 12 * 10 ** 9 * 10 ** 18; // 12 billion
    uint256 public constant targetPricePerToken = 0.00000055 ether;
    uint256 public constant devTax = 400;
    address immutable dev;

    uint256 public toSell = 114 * 10 ** 8 * 10 ** 18; // 11.4 billion
    uint256 public tokensSold; // not scaled by 1e18
    uint256 public startTime;

    Staking public staking;
    CBT public cbt;

    LibBitmap.Bitmap internal claims;
    bytes32 internal merkleRoot; // 1.5% airdropped

    // goes down 5% per unit of time
    // aiming to sell 20% of tokens per unit of time
    // 1 unit of time = 1 hour
    constructor() LinearVRGDA(int256(targetPricePerToken), 0.1e18, 2280000000 * 10 ** 18) {
        _initializeOwner(msg.sender);
        dev = msg.sender;
        startTime = block.timestamp;
        staking = new Staking();
        cbt = new CBT(100000); // 10% CW

        _mint(msg.sender, 420000000 * 10 ** 18); // premint 3.5% for cex
    }

    // ######################################
    // ######################################

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

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

    function secretMessage() public pure returns (string memory) {
        return "buying gf";
    }

    // ######################################
    // ######################################

    function taxRate() public view returns (uint256 bps) {
        // max 10%, min 0%
        bps = 1000 - (staking.totalStaked().divWadUp(totalSupply()) / 10 ** 15);
    }

    function getTimePassed() internal view returns (int256 t) {
        t = int256(DateTimeLib.diffHours(startTime, block.timestamp)) * 1e18;
    }

    function getPrice() external view returns (uint256 price) {
        price = getVRGDAPrice(getTimePassed(), tokensSold);
    }

    function getClaimed(uint256 index) external view returns (bool) {
        return claims.get(index);
    }

    // ######################################
    // ######################################

    /// @param tokensToBuy The amount of tokens to buy, not scaled by 1e18
    function getBlessed(uint256 tokensToBuy) external payable {
        uint256 tokensToBuyScaled = tokensToBuy * 1e18;
        unchecked {
            toSell -= tokensToBuyScaled;
            uint256 price = getVRGDAPrice(getTimePassed(), tokensSold);
            tokensSold += tokensToBuy;
            require(msg.value >= tokensToBuy * price, "UNDERPAID");
            _mint(msg.sender, tokensToBuyScaled);
            SafeTransferLib.safeTransferETH(msg.sender, msg.value - tokensToBuy * price);
            // dev tax
            SafeTransferLib.safeTransferETH(dev, ((tokensToBuy * price) * devTax) / 10000);
        }
    }

    function claim(uint256 index, uint256 amount, bytes32[] calldata proof) external payable {
        require(!claims.get(index), "Already claimed.");
        bytes32 node = keccak256(abi.encodePacked(msg.sender, index, amount));
        require(MerkleProofLib.verify(proof, merkleRoot, node), "Invalid proof.");
        claims.set(index);
        _mint(msg.sender, amount);
        emit Claimed(msg.sender, amount);
    }

    // ######################################
    // ######################################

    function transferFrom(address from, address to, uint256 amount) public override returns (bool) {
        address _staking = address(staking);
        uint256 _taxRate = taxRate();
        // take tax for stakers
        uint256 tax;
        if (to != _staking && to != address(cbt)) {
            tax = (amount * _taxRate) / 10000;
            // burn 80% of tax
            super._burn(from, (tax * 8000) / 10000);
            // 20% left sent to staking contract
            super.transferFrom(from, _staking, (tax * 2000) / 10000);
        }
        return super.transferFrom(from, to, amount - tax);
    }

    function transfer(address to, uint256 amount) public override returns (bool) {
        address _staking = address(staking);
        uint256 _taxRate = taxRate();
        // take tax for stakers
        uint256 tax;
        if (msg.sender != _staking && msg.sender != address(cbt)) {
            tax = (amount * _taxRate) / 10000;
            // burn 80% of tax
            super._burn(msg.sender, (tax * 8000) / 10000);
            // 20% left sent to staking contract
            super.transfer(_staking, (tax * 2000) / 10000);
        }
        return super.transfer(to, amount - tax);
    }

    // ######################################
    // ######################################

    function startCBT() external onlyOwner {
        cbt.start{value: address(this).balance}();
    }

    function setMerkleRoot(bytes32 _merkleRoot) external onlyOwner {
        merkleRoot = _merkleRoot;
    }
}

// File: lib/solady/src/utils/SafeTransferLib.sol



// 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 Caution! This library 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.
    /// Multiply by a small constant (e.g. 2), if needed.
    uint256 internal constant _GAS_STIPEND_NO_GRIEF = 100000;

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

    /// @dev Sends `amount` (in wei) ETH to `to`.
    /// Reverts upon failure.
    function safeTransferETH(address to, uint256 amount) internal {
        /// @solidity memory-safe-assembly
        assembly {
            // Transfer the ETH and check if it succeeded or not.
            if iszero(call(gas(), to, amount, 0, 0, 0, 0)) {
                // Store the function selector of `ETHTransferFailed()`.
                mstore(0x00, 0xb12d13eb)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }
        }
    }

    /// @dev Force sends `amount` (in wei) ETH to `to`, with a `gasStipend`.
    /// The `gasStipend` can be set to a low enough value to prevent
    /// storage writes or gas griefing.
    ///
    /// If sending via the normal procedure fails, force sends the ETH by
    /// creating a temporary contract which uses `SELFDESTRUCT` to force send the ETH.
    ///
    /// Reverts if the current contract has insufficient balance.
    function forceSafeTransferETH(address to, uint256 amount, uint256 gasStipend) internal {
        /// @solidity memory-safe-assembly
        assembly {
            // If insufficient balance, revert.
            if lt(selfbalance(), amount) {
                // Store the function selector of `ETHTransferFailed()`.
                mstore(0x00, 0xb12d13eb)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }
            // Transfer the ETH and check if it succeeded or not.
            if iszero(call(gasStipend, to, amount, 0, 0, 0, 0)) {
                mstore(0x00, to) // Store the address in scratch space.
                mstore8(0x0b, 0x73) // Opcode `PUSH20`.
                mstore8(0x20, 0xff) // Opcode `SELFDESTRUCT`.
                // We can directly use `SELFDESTRUCT` in the contract creation.
                // Compatible with `SENDALL`: https://eips.ethereum.org/EIPS/eip-4758
                if iszero(create(amount, 0x0b, 0x16)) {
                    // For better gas estimation.
                    if iszero(gt(gas(), 1000000)) { revert(0, 0) }
                }
            }
        }
    }

    /// @dev Force sends `amount` (in wei) ETH to `to`, with a gas stipend
    /// equal to `_GAS_STIPEND_NO_GRIEF`. This gas stipend is a reasonable default
    /// for 99% of cases and can be overriden with the three-argument version of this
    /// function if necessary.
    ///
    /// If sending via the normal procedure fails, force sends the ETH by
    /// creating a temporary contract which uses `SELFDESTRUCT` to force send the ETH.
    ///
    /// Reverts if the current contract has insufficient balance.
    function forceSafeTransferETH(address to, uint256 amount) internal {
        // Manually inlined because the compiler doesn't inline functions with branches.
        /// @solidity memory-safe-assembly
        assembly {
            // If insufficient balance, revert.
            if lt(selfbalance(), amount) {
                // Store the function selector of `ETHTransferFailed()`.
                mstore(0x00, 0xb12d13eb)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }
            // Transfer the ETH and check if it succeeded or not.
            if iszero(call(_GAS_STIPEND_NO_GRIEF, to, amount, 0, 0, 0, 0)) {
                mstore(0x00, to) // Store the address in scratch space.
                mstore8(0x0b, 0x73) // Opcode `PUSH20`.
                mstore8(0x20, 0xff) // Opcode `SELFDESTRUCT`.
                // We can directly use `SELFDESTRUCT` in the contract creation.
                // Compatible with `SENDALL`: https://eips.ethereum.org/EIPS/eip-4758
                if iszero(create(amount, 0x0b, 0x16)) {
                    // For better gas estimation.
                    if iszero(gt(gas(), 1000000)) { revert(0, 0) }
                }
            }
        }
    }

    /// @dev Sends `amount` (in wei) ETH to `to`, with a `gasStipend`.
    /// The `gasStipend` can be set to a low enough value to prevent
    /// storage writes or gas griefing.
    ///
    /// Simply use `gasleft()` for `gasStipend` if you don't need a gas stipend.
    ///
    /// Note: Does NOT revert upon failure.
    /// Returns whether the transfer of ETH is successful instead.
    function trySafeTransferETH(address to, uint256 amount, uint256 gasStipend)
        internal
        returns (bool success)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Transfer the ETH and check if it succeeded or not.
            success := call(gasStipend, to, amount, 0, 0, 0, 0)
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                      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.
            // Store the function selector of `transferFrom(address,address,uint256)`.
            mstore(0x0c, 0x23b872dd000000000000000000000000)

            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    // Set success to whether the call reverted, if not we check it either
                    // returned exactly 1 (can't just be non-zero data), or had no return data.
                    or(eq(mload(0x00), 1), iszero(returndatasize())),
                    call(gas(), token, 0, 0x1c, 0x64, 0x00, 0x20)
                )
            ) {
                // Store the function selector of `TransferFromFailed()`.
                mstore(0x00, 0x7939f424)
                // Revert with (offset, size).
                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 at least `amount` 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.
            // Store the function selector of `balanceOf(address)`.
            mstore(0x0c, 0x70a08231000000000000000000000000)
            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)
                )
            ) {
                // Store the function selector of `TransferFromFailed()`.
                mstore(0x00, 0x7939f424)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }

            // Store the function selector of `transferFrom(address,address,uint256)`.
            mstore(0x00, 0x23b872dd)
            // The `amount` argument is already written to the memory word at 0x6c.
            amount := mload(0x60)

            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    // Set success to whether the call reverted, if not we check it either
                    // returned exactly 1 (can't just be non-zero data), or had no return data.
                    or(eq(mload(0x00), 1), iszero(returndatasize())),
                    call(gas(), token, 0, 0x1c, 0x64, 0x00, 0x20)
                )
            ) {
                // Store the function selector of `TransferFromFailed()`.
                mstore(0x00, 0x7939f424)
                // Revert with (offset, size).
                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.
            // Store the function selector of `transfer(address,uint256)`.
            mstore(0x00, 0xa9059cbb000000000000000000000000)

            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    // Set success to whether the call reverted, if not we check it either
                    // returned exactly 1 (can't just be non-zero data), or had no return data.
                    or(eq(mload(0x00), 1), iszero(returndatasize())),
                    call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
                )
            ) {
                // Store the function selector of `TransferFailed()`.
                mstore(0x00, 0x90b8ec18)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }
            // Restore the part of the free memory pointer that was overwritten.
            mstore(0x34, 0)
        }
    }

    /// @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.
            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)
                )
            ) {
                // Store the function selector of `TransferFailed()`.
                mstore(0x00, 0x90b8ec18)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }

            mstore(0x14, to) // Store the `to` argument.
            // The `amount` argument is already written to the memory word at 0x34.
            amount := mload(0x34)
            // Store the function selector of `transfer(address,uint256)`.
            mstore(0x00, 0xa9059cbb000000000000000000000000)

            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    // Set success to whether the call reverted, if not we check it either
                    // returned exactly 1 (can't just be non-zero data), or had no return data.
                    or(eq(mload(0x00), 1), iszero(returndatasize())),
                    call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
                )
            ) {
                // Store the function selector of `TransferFailed()`.
                mstore(0x00, 0x90b8ec18)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }
            // Restore the part of the free memory pointer that was overwritten.
            mstore(0x34, 0)
        }
    }

    /// @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.
            // Store the function selector of `approve(address,uint256)`.
            mstore(0x00, 0x095ea7b3000000000000000000000000)

            if iszero(
                and( // The arguments of `and` are evaluated from right to left.
                    // Set success to whether the call reverted, if not we check it either
                    // returned exactly 1 (can't just be non-zero data), or had no return data.
                    or(eq(mload(0x00), 1), iszero(returndatasize())),
                    call(gas(), token, 0, 0x10, 0x44, 0x00, 0x20)
                )
            ) {
                // Store the function selector of `ApproveFailed()`.
                mstore(0x00, 0x3e3f8f73)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }
            // Restore the part of the free memory pointer that was overwritten.
            mstore(0x34, 0)
        }
    }

    /// @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.
            // Store the function selector of `balanceOf(address)`.
            mstore(0x00, 0x70a08231000000000000000000000000)
            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)
                    )
                )
        }
    }
}

// File: src/bonding/BancorFormula.sol



/* Apache License
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To apply the Apache License to your work, attach the following
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Copyright 2017 Bprotocol Foundation

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
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pragma solidity ^0.8.17;

import "./Power.sol";

/**
 * @title Bancor formula by Bancor
 * @dev Modified from the original by Slava Balasanov
 * https://github.com/bancorprotocol/contracts
 * Split Power.sol out from BancorFormula.sol and replace SafeMath formulas with zeppelin's SafeMath
 * Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements;
 * and to You under the Apache License, Version 2.0. "
 */
contract BancorFormula is Power {
    uint32 private constant MAX_WEIGHT = 1000000;

    /**
     * @dev given a token supply, connector balance, weight and a deposit amount (in the connector token),
     * calculates the return for a given conversion (in the main token)
     *
     * Formula:
     * Return = _supply * ((1 + _depositAmount / _connectorBalance) ^ (_connectorWeight / 1000000) - 1)
     *
     * @param _supply              token total supply
     * @param _connectorBalance    total connector balance
     * @param _connectorWeight     connector weight, represented in ppm, 1-1000000
     * @param _depositAmount       deposit amount, in connector token
     *
     *  @return purchase return amount
     */
    function calculatePurchaseReturn(
        uint256 _supply,
        uint256 _connectorBalance,
        uint32 _connectorWeight,
        uint256 _depositAmount
    ) public view returns (uint256) {
        // validate input
        require(_supply > 0 && _connectorBalance > 0 && _connectorWeight > 0 && _connectorWeight <= MAX_WEIGHT);
        // special case for 0 deposit amount
        if (_depositAmount == 0) {
            return 0;
        }
        // special case if the weight = 100%
        if (_connectorWeight == MAX_WEIGHT) {
            return (_supply * _depositAmount) / _connectorBalance;
        }
        uint256 result;
        uint8 precision;
        uint256 baseN = _depositAmount + _connectorBalance;
        (result, precision) = power(baseN, _connectorBalance, _connectorWeight, MAX_WEIGHT);
        uint256 newTokenSupply = _supply * result >> precision;
        return newTokenSupply - _supply;
    }
    /**
     * @dev given a token supply, connector balance, weight and a sell amount (in the main token),
     * calculates the return for a given conversion (in the connector token)
     *
     * Formula:
     * Return = _connectorBalance * (1 - (1 - _sellAmount / _supply) ^ (1 / (_connectorWeight / 1000000)))
     *
     * @param _supply              token total supply
     * @param _connectorBalance    total connector
     * @param _connectorWeight     constant connector Weight, represented in ppm, 1-1000000
     * @param _sellAmount          sell amount, in the token itself
     *
     * @return sale return amount
     */

    function calculateSaleReturn(
        uint256 _supply,
        uint256 _connectorBalance,
        uint32 _connectorWeight,
        uint256 _sellAmount
    ) public view returns (uint256) {
        // validate input
        require(
            _supply > 0 && _connectorBalance > 0 && _connectorWeight > 0 && _connectorWeight <= MAX_WEIGHT
                && _sellAmount <= _supply
            , "invalid input"
        );
        // special case for 0 sell amount
        if (_sellAmount == 0) {
            return 0;
        }
        // special case for selling the entire supply
        if (_sellAmount == _supply) {
            return _connectorBalance;
        }
        // special case if the weight = 100%
        if (_connectorWeight == MAX_WEIGHT) {
            return (_connectorBalance * _sellAmount) / _supply;
        }
        uint256 result;
        uint8 precision;
        uint256 baseD = _supply - _sellAmount;
        (result, precision) = power(_supply, baseD, MAX_WEIGHT, _connectorWeight);
        uint256 oldBalance = _connectorBalance * result;
        uint256 newBalance = _connectorBalance << precision;
        return (oldBalance - newBalance) / result;
    }
}

// File: lib/solady/src/tokens/ERC20.sol



// 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)
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;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       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 Atomically increases the allowance granted to `spender` by the caller.
    ///
    /// Emits a {Approval} event.
    function increaseAllowance(address spender, uint256 difference) public virtual returns (bool) {
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the allowance slot and load its value.
            mstore(0x20, spender)
            mstore(0x0c, _ALLOWANCE_SLOT_SEED)
            mstore(0x00, caller())
            let allowanceSlot := keccak256(0x0c, 0x34)
            let allowanceBefore := sload(allowanceSlot)
            // Add to the allowance.
            let allowanceAfter := add(allowanceBefore, difference)
            // Revert upon overflow.
            if lt(allowanceAfter, allowanceBefore) {
                mstore(0x00, 0xf9067066) // `AllowanceOverflow()`.
                revert(0x1c, 0x04)
            }
            // Store the updated allowance.
            sstore(allowanceSlot, allowanceAfter)
            // Emit the {Approval} event.
            mstore(0x00, allowanceAfter)
            log3(0x00, 0x20, _APPROVAL_EVENT_SIGNATURE, caller(), shr(96, mload(0x2c)))
        }
        return true;
    }

    /// @dev Atomically decreases the allowance granted to `spender` by the caller.
    ///
    /// Emits a {Approval} event.
    function decreaseAllowance(address spender, uint256 difference) public virtual returns (bool) {
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the allowance slot and load its value.
            mstore(0x20, spender)
            mstore(0x0c, _ALLOWANCE_SLOT_SEED)
            mstore(0x00, caller())
            let allowanceSlot := keccak256(0x0c, 0x34)
            let allowanceBefore := sload(allowanceSlot)
            // Revert if will underflow.
            if lt(allowanceBefore, difference) {
                mstore(0x00, 0x8301ab38) // `AllowanceUnderflow()`.
                revert(0x1c, 0x04)
            }
            // Subtract and store the updated allowance.
            let allowanceAfter := sub(allowanceBefore, difference)
            sstore(allowanceSlot, allowanceAfter)
            // Emit the {Approval} event.
            mstore(0x00, allowanceAfter)
            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 iszero(eq(allowance_, not(0))) {
                // 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 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 domainSeparator = DOMAIN_SEPARATOR();
        /// @solidity memory-safe-assembly
        assembly {
            // Grab the free memory pointer.
            let m := mload(0x40)
            // Revert if the block timestamp greater than `deadline`.
            if gt(timestamp(), deadline) {
                mstore(0x00, 0x1a15a3cc) // `PermitExpired()`.
                revert(0x1c, 0x04)
            }
            // 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(0x0c, _NONCES_SLOT_SEED)
            mstore(0x00, owner)
            let nonceSlot := keccak256(0x0c, 0x20)
            let nonceValue := sload(nonceSlot)
            // Increment and store the updated nonce.
            sstore(nonceSlot, add(nonceValue, 1))
            // Prepare the inner hash.
            // `keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)")`.
            // forgefmt: disable-next-item
            mstore(m, 0x6e71edae12b1b97f4d1f60370fef10105fa2faae0126114a169c64845d6126c9)
            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)
            // Prepare the outer hash.
            mstore(0, 0x1901)
            mstore(0x20, domainSeparator)
            mstore(0x40, keccak256(m, 0xc0))
            // Prepare the ecrecover calldata.
            mstore(0, keccak256(0x1e, 0x42))
            mstore(0x20, and(0xff, v))
            mstore(0x40, r)
            mstore(0x60, s)
            pop(staticcall(gas(), 1, 0, 0x80, 0x20, 0x20))
            // If the ecrecover fails, the returndatasize will be 0x00,
            // `owner` will be 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)
            }
            // 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-2612 domains separator.
    function DOMAIN_SEPARATOR() public view virtual returns (bytes32 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := mload(0x40) // Grab the free memory pointer.
        }
        //  We simply calculate it on-the-fly to allow for cases where the `name` may change.
        bytes32 nameHash = keccak256(bytes(name()));
        /// @solidity memory-safe-assembly
        assembly {
            let m := result
            // `keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)")`.
            // forgefmt: disable-next-item
            mstore(m, 0x8b73c3c69bb8fe3d512ecc4cf759cc79239f7b179b0ffacaa9a75d522b39400f)
            mstore(add(m, 0x20), nameHash)
            // `keccak256("1")`.
            // forgefmt: disable-next-item
            mstore(add(m, 0x40), 0xc89efdaa54c0f20c7adf612882df0950f5a951637e0307cdcb4c672f298b8bc6)
            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 iszero(eq(allowance_, not(0))) {
                // 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 {}
}

// File: lib/solady/src/utils/FixedPointMathLib.sol



// 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 multiplication overflow.
    error MulWadFailed();

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

    /// @dev The multiply-divide 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 output is undefined, as the input is zero.
    error Log2Undefined();

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         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))) {
                // Store the function selector of `MulWadFailed()`.
                mstore(0x00, 0xbac65e5b)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }
            z := div(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))) {
                // Store the function selector of `MulWadFailed()`.
                mstore(0x00, 0xbac65e5b)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }
            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)))))) {
                // Store the function selector of `DivWadFailed()`.
                mstore(0x00, 0x7c5f487d)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }
            z := div(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)))))) {
                // Store the function selector of `DivWadFailed()`.
                mstore(0x00, 0x7c5f487d)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }
            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`.
    function expWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            // When the result is < 0.5 we return zero. This happens when
            // x <= floor(log(0.5e18) * 1e18) ~ -42e18
            if (x <= -42139678854452767551) return r;

            /// @solidity memory-safe-assembly
            assembly {
                // When the result is > (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)) {
                    // Store the function selector of `ExpOverflow()`.
                    mstore(0x00, 0xa37bfec9)
                    // Revert with (offset, size).
                    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`.
    function lnWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            /// @solidity memory-safe-assembly
            assembly {
                if iszero(sgt(x, 0)) {
                    // Store the function selector of `LnWadUndefined()`.
                    mstore(0x00, 0x1615e638)
                    // Revert with (offset, size).
                    revert(0x1c, 0x04)
                }
            }

            // 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.
            int256 k;
            /// @solidity memory-safe-assembly
            assembly {
                let v := x
                k := shl(7, lt(0xffffffffffffffffffffffffffffffff, v))
                k := or(k, shl(6, lt(0xffffffffffffffff, shr(k, v))))
                k := or(k, shl(5, lt(0xffffffff, shr(k, v))))

                // For the remaining 32 bits, use a De Bruijn lookup.
                // See: https://graphics.stanford.edu/~seander/bithacks.html
                v := shr(k, v)
                v := or(v, shr(1, v))
                v := or(v, shr(2, v))
                v := or(v, shr(4, v))
                v := or(v, shr(8, v))
                v := or(v, shr(16, v))

                // forgefmt: disable-next-item
                k := sub(or(k, byte(shr(251, mul(v, shl(224, 0x07c4acdd))),
                    0x0009010a0d15021d0b0e10121619031e080c141c0f111807131b17061a05041f)), 96)
            }

            // Reduce range of x to (1, 2) * 2**96
            // ln(2^k * x) = k * ln(2) + ln(x)
            x <<= uint256(159 - k);
            x = int256(uint256(x) >> 159);

            // Evaluate using a (8, 8)-term rational approximation.
            // p is made monic, we will multiply by a scale factor later.
            int256 p = x + 3273285459638523848632254066296;
            p = ((p * x) >> 96) + 24828157081833163892658089445524;
            p = ((p * x) >> 96) + 43456485725739037958740375743393;
            p = ((p * x) >> 96) - 11111509109440967052023855526967;
            p = ((p * x) >> 96) - 45023709667254063763336534515857;
            p = ((p * x) >> 96) - 14706773417378608786704636184526;
            p = p * x - (795164235651350426258249787498 << 96);

            // 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.
            int256 q = x + 5573035233440673466300451813936;
            q = ((q * x) >> 96) + 71694874799317883764090561454958;
            q = ((q * x) >> 96) + 283447036172924575727196451306956;
            q = ((q * x) >> 96) + 401686690394027663651624208769553;
            q = ((q * x) >> 96) + 204048457590392012362485061816622;
            q = ((q * x) >> 96) + 31853899698501571402653359427138;
            q = ((q * x) >> 96) + 909429971244387300277376558375;
            /// @solidity memory-safe-assembly
            assembly {
                // Div in assembly because solidity adds a zero check despite the unchecked.
                // The q polynomial is known not to have zeros in the domain.
                // No scaling required because p is already 2**96 too large.
                r := sdiv(p, q)
            }

            // r 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

            // mul s * 5e18 * 2**96, base is now 5**18 * 2**192
            r *= 1677202110996718588342820967067443963516166;
            // add ln(2) * k * 5e18 * 2**192
            r += 16597577552685614221487285958193947469193820559219878177908093499208371 * k;
            // add ln(2**96 / 10**18) * 5e18 * 2**192
            r += 600920179829731861736702779321621459595472258049074101567377883020018308;
            // base conversion: mul 2**18 / 2**192
            r >>= 174;
        }
    }

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

    /// @dev Calculates `floor(a * b / 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 {
            // forgefmt: disable-next-item
            for {} 1 {} {
                // 512-bit multiply `[prod1 prod0] = 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 = prod1 * 2**256 + prod0`.

                // Least significant 256 bits of the product.
                let prod0 := mul(x, y)
                let mm := mulmod(x, y, not(0))
                // Most significant 256 bits of the product.
                let prod1 := sub(mm, add(prod0, lt(mm, prod0)))

                // Handle non-overflow cases, 256 by 256 division.
                if iszero(prod1) {
                    if iszero(d) {
                        // Store the function selector of `FullMulDivFailed()`.
                        mstore(0x00, 0xae47f702)
                        // Revert with (offset, size).
                        revert(0x1c, 0x04)
                    }
                    result := div(prod0, d)
                    break       
                }

                // Make sure the result is less than `2**256`.
                // Also prevents `d == 0`.
                if iszero(gt(d, prod1)) {
                    // Store the function selector of `FullMulDivFailed()`.
                    mstore(0x00, 0xae47f702)
                    // Revert with (offset, size).
                    revert(0x1c, 0x04)
                }

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

                // Make division exact by subtracting the remainder from `[prod1 prod0]`.
                // Compute remainder using mulmod.
                let remainder := mulmod(x, y, d)
                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
                // Factor powers of two out of `d`.
                // Compute largest power of two divisor of `d`.
                // Always greater or equal to 1.
                let twos := and(d, sub(0, d))
                // Divide d by power of two.
                d := div(d, twos)
                // Divide [prod1 prod0] by the factors of two.
                prod0 := div(prod0, twos)
                // Shift in bits from `prod1` into `prod0`. For this we need
                // to flip `twos` such that it is `2**256 / twos`.
                // If `twos` is zero, then it becomes one.
                prod0 := or(prod0, mul(prod1, add(div(sub(0, twos), twos), 1)))
                // 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(mul(3, d), 2)
                // 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(prod0, mul(inv, sub(2, mul(d, inv)))) // inverse mod 2**256
                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/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) {
                if iszero(add(result, 1)) {
                    // Store the function selector of `FullMulDivFailed()`.
                    mstore(0x00, 0xae47f702)
                    // Revert with (offset, size).
                    revert(0x1c, 0x04)
                }
                result := add(result, 1)
            }
        }
    }

    /// @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)))))) {
                // Store the function selector of `MulDivFailed()`.
                mstore(0x00, 0xad251c27)
                // Revert with (offset, size).
                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)))))) {
                // Store the function selector of `MulDivFailed()`.
                mstore(0x00, 0xad251c27)
                // Revert with (offset, size).
                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) {
                // Store the function selector of `DivFailed()`.
                mstore(0x00, 0x65244e4e)
                // Revert with (offset, size).
                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 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
            // each branch 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
            // Since the ceil is rare, we save gas on the assignment and repeat division in the rare case.
            // If you don't care whether the floor or ceil square root is returned, you can remove this statement.
            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 := shl(add(div(r, 3), lt(0xf, shr(r, x))), 0xff)
            z := div(z, byte(mod(r, 3), shl(232, 0x7f624b)))

            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 factorial of `x`.
    function factorial(uint256 x) internal pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            for {} 1 {} {
                if iszero(lt(10, x)) {
                    // forgefmt: disable-next-item
                    result := and(
                        shr(mul(22, x), 0x375f0016260009d80004ec0002d00001e0000180000180000200000400001),
                        0x3fffff
                    )
                    break
                }
                if iszero(lt(57, x)) {
                    let end := 31
                    result := 8222838654177922817725562880000000
                    if iszero(lt(end, x)) {
                        end := 10
                        result := 3628800
                    }
                    for { let w := not(0) } 1 {} {
                        result := mul(result, x)
                        x := add(x, w)
                        if eq(x, end) { break }
                    }
                    break
                }
                // Store the function selector of `FactorialOverflow()`.
                mstore(0x00, 0xaba0f2a2)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }
        }
    }

    /// @dev Returns the log2 of `x`.
    /// Equivalent to computing the index of the most significant bit (MSB) of `x`.
    function log2(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(x) {
                // Store the function selector of `Log2Undefined()`.
                mstore(0x00, 0x5be3aa5c)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }

            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))))

            // For the remaining 32 bits, use a De Bruijn lookup.
            // See: https://graphics.stanford.edu/~seander/bithacks.html
            x := shr(r, x)
            x := or(x, shr(1, x))
            x := or(x, shr(2, x))
            x := or(x, shr(4, x))
            x := or(x, shr(8, x))
            x := or(x, shr(16, x))

            // forgefmt: disable-next-item
            r := or(r, byte(shr(251, mul(x, shl(224, 0x07c4acdd))),
                0x0009010a0d15021d0b0e10121619031e080c141c0f111807131b17061a05041f))
        }
    }

    /// @dev Returns the log2 of `x`, rounded up.
    function log2Up(uint256 x) internal pure returns (uint256 r) {
        unchecked {
            uint256 isNotPo2;
            assembly {
                isNotPo2 := iszero(iszero(and(x, sub(x, 1))))
            }
            return log2(x) + isNotPo2;
        }
    }

    /// @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 {
            let mask := sub(0, shr(255, x))
            z := xor(mask, add(mask, 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 {
            let a := sub(y, x)
            z := xor(a, mul(xor(a, sub(x, y)), sgt(x, y)))
        }
    }

    /// @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)
    {
        z = min(max(x, minValue), maxValue);
    }

    /// @dev Returns `x`, bounded to `minValue` and `maxValue`.
    function clamp(int256 x, int256 minValue, int256 maxValue) internal pure returns (int256 z) {
        z = min(max(x, minValue), maxValue);
    }

    /// @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 {
            // forgefmt: disable-next-item
            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)
        }
    }
}

// File: lib/solady/src/utils/DateTimeLib.sol



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

/// @notice Library for date time operations.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/DateTimeLib.sol)
///
/// Conventions:
/// --------------------------------------------------------------------+
/// Unit      | Range                | Notes                            |
/// --------------------------------------------------------------------|
/// timestamp | 0..0x1e18549868c76ff | Unix timestamp.                  |
/// epochDay  | 0..0x16d3e098039     | Days since 1970-01-01.           |
/// year      | 1970..0xffffffff     | Gregorian calendar year.         |
/// month     | 1..12                | Gregorian calendar month.        |
/// day       | 1..31                | Gregorian calendar day of month. |
/// weekday   | 1..7                 | The day of the week (1-indexed). |
/// --------------------------------------------------------------------+
/// All timestamps of days are rounded down to 00:00:00 UTC.
library DateTimeLib {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    // Weekdays are 1-indexed for a traditional rustic feel.

    // "And on the seventh day God finished his work that he had done,
    // and he rested on the seventh day from all his work that he had done."
    // -- Genesis 2:2

    uint256 internal constant MON = 1;
    uint256 internal constant TUE = 2;
    uint256 internal constant WED = 3;
    uint256 internal constant THU = 4;
    uint256 internal constant FRI = 5;
    uint256 internal constant SAT = 6;
    uint256 internal constant SUN = 7;

    // Months and days of months are 1-indexed for ease of use.

    uint256 internal constant JAN = 1;
    uint256 internal constant FEB = 2;
    uint256 internal constant MAR = 3;
    uint256 internal constant APR = 4;
    uint256 internal constant MAY = 5;
    uint256 internal constant JUN = 6;
    uint256 internal constant JUL = 7;
    uint256 internal constant AUG = 8;
    uint256 internal constant SEP = 9;
    uint256 internal constant OCT = 10;
    uint256 internal constant NOV = 11;
    uint256 internal constant DEC = 12;

    // These limits are large enough for most practical purposes.
    // Inputs that exceed these limits result in undefined behavior.

    uint256 internal constant MAX_SUPPORTED_YEAR = 0xffffffff;
    uint256 internal constant MAX_SUPPORTED_EPOCH_DAY = 0x16d3e098039;
    uint256 internal constant MAX_SUPPORTED_TIMESTAMP = 0x1e18549868c76ff;

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

    /// @dev Returns the number of days since 1970-01-01 from (`year`,`month`,`day`).
    /// See: https://howardhinnant.github.io/date_algorithms.html
    /// Note: Inputs outside the supported ranges result in undefined behavior.
    /// Use {isSupportedDate} to check if the inputs are supported.
    function dateToEpochDay(uint256 year, uint256 month, uint256 day)
        internal
        pure
        returns (uint256 epochDay)
    {
        /// @solidity memory-safe-assembly
        assembly {
            year := sub(year, lt(month, 3))
            let doy := add(shr(11, add(mul(62719, mod(add(month, 9), 12)), 769)), day)
            let yoe := mod(year, 400)
            let doe := sub(add(add(mul(yoe, 365), shr(2, yoe)), doy), div(yoe, 100))
            epochDay := sub(add(mul(div(year, 400), 146097), doe), 719469)
        }
    }

    /// @dev Returns (`year`,`month`,`day`) from the number of days since 1970-01-01.
    /// Note: Inputs outside the supported ranges result in undefined behavior.
    /// Use {isSupportedDays} to check if the inputs is supported.
    function epochDayToDate(uint256 epochDay)
        internal
        pure
        returns (uint256 year, uint256 month, uint256 day)
    {
        /// @solidity memory-safe-assembly
        assembly {
            epochDay := add(epochDay, 719468)
            let doe := mod(epochDay, 146097)
            let yoe :=
                div(sub(sub(add(doe, div(doe, 36524)), div(doe, 1460)), eq(doe, 146096)), 365)
            let doy := sub(doe, sub(add(mul(365, yoe), shr(2, yoe)), div(yoe, 100)))
            let mp := div(add(mul(5, doy), 2), 153)
            day := add(sub(doy, shr(11, add(mul(mp, 62719), 769))), 1)
            month := sub(add(mp, 3), mul(gt(mp, 9), 12))
            year := add(add(yoe, mul(div(epochDay, 146097), 400)), lt(month, 3))
        }
    }

    /// @dev Returns the unix timestamp from (`year`,`month`,`day`).
    /// Note: Inputs outside the supported ranges result in undefined behavior.
    /// Use {isSupportedDate} to check if the inputs are supported.
    function dateToTimestamp(uint256 year, uint256 month, uint256 day)
        internal
        pure
        returns (uint256 result)
    {
        unchecked {
            result = dateToEpochDay(year, month, day) * 86400;
        }
    }

    /// @dev Returns (`year`,`month`,`day`) from the given unix timestamp.
    /// Note: Inputs outside the supported ranges result in undefined behavior.
    /// Use {isSupportedTimestamp} to check if the inputs are supported.
    function timestampToDate(uint256 timestamp)
        internal
        pure
        returns (uint256 year, uint256 month, uint256 day)
    {
        (year, month, day) = epochDayToDate(timestamp / 86400);
    }

    /// @dev Returns the unix timestamp from
    /// (`year`,`month`,`day`,`hour`,`minute`,`second`).
    /// Note: Inputs outside the supported ranges result in undefined behavior.
    /// Use {isSupportedDateTime} to check if the inputs are supported.
    function dateTimeToTimestamp(
        uint256 year,
        uint256 month,
        uint256 day,
        uint256 hour,
        uint256 minute,
        uint256 second
    ) internal pure returns (uint256 result) {
        unchecked {
            result = dateToEpochDay(year, month, day) * 86400 + hour * 3600 + minute * 60 + second;
        }
    }

    /// @dev Returns (`year`,`month`,`day`,`hour`,`minute`,`second`)
    /// from the given unix timestamp.
    /// Note: Inputs outside the supported ranges result in undefined behavior.
    /// Use {isSupportedTimestamp} to check if the inputs are supported.
    function timestampToDateTime(uint256 timestamp)
        internal
        pure
        returns (
            uint256 year,
            uint256 month,
            uint256 day,
            uint256 hour,
            uint256 minute,
            uint256 second
        )
    {
        unchecked {
            (year, month, day) = epochDayToDate(timestamp / 86400);
            uint256 secs = timestamp % 86400;
            hour = secs / 3600;
            secs = secs % 3600;
            minute = secs / 60;
            second = secs % 60;
        }
    }

    /// @dev Returns if the `year` is leap.
    function isLeapYear(uint256 year) internal pure returns (bool leap) {
        /// @solidity memory-safe-assembly
        assembly {
            leap := iszero(and(add(mul(iszero(mod(year, 25)), 12), 3), year))
        }
    }

    /// @dev Returns number of days in given `month` of `year`.
    function daysInMonth(uint256 year, uint256 month) internal pure returns (uint256 result) {
        bool flag = isLeapYear(year);
        /// @solidity memory-safe-assembly
        assembly {
            // `daysInMonths = [31,28,31,30,31,30,31,31,30,31,30,31]`.
            // `result = daysInMonths[month - 1] + isLeapYear(year)`.
            result :=
                add(byte(month, shl(152, 0x1F1C1F1E1F1E1F1F1E1F1E1F)), and(eq(month, 2), flag))
        }
    }

    /// @dev Returns the weekday from the unix timestamp.
    /// Monday: 1, Tuesday: 2, ....., Sunday: 7.
    function weekday(uint256 timestamp) internal pure returns (uint256 result) {
        unchecked {
            result = ((timestamp / 86400 + 3) % 7) + 1;
        }
    }

    /// @dev Returns if (`year`,`month`,`day`) is a supported date.
    /// - `1970 <= year <= MAX_SUPPORTED_YEAR`.
    /// - `1 <= month <= 12`.
    /// - `1 <= day <= daysInMonth(year, month)`.
    function isSupportedDate(uint256 year, uint256 month, uint256 day)
        internal
        pure
        returns (bool result)
    {
        uint256 md = daysInMonth(year, month);
        /// @solidity memory-safe-assembly
        assembly {
            let w := not(0)
            result :=
                and(
                    lt(sub(year, 1970), sub(MAX_SUPPORTED_YEAR, 1969)),
                    and(lt(add(month, w), 12), lt(add(day, w), md))
                )
        }
    }

    /// @dev Returns if (`year`,`month`,`day`,`hour`,`minute`,`second`) is a supported date time.
    /// - `1970 <= year <= MAX_SUPPORTED_YEAR`.
    /// - `1 <= month <= 12`.
    /// - `1 <= day <= daysInMonth(year, month)`.
    /// - `hour < 24`.
    /// - `minute < 60`.
    /// - `second < 60`.
    function isSupportedDateTime(
        uint256 year,
        uint256 month,
        uint256 day,
        uint256 hour,
        uint256 minute,
        uint256 second
    ) internal pure returns (bool result) {
        if (isSupportedDate(year, month, day)) {
            /// @solidity memory-safe-assembly
            assembly {
                result := and(lt(hour, 24), and(lt(minute, 60), lt(second, 60)))
            }
        }
    }

    /// @dev Returns if `epochDay` is a supported unix epoch day.
    function isSupportedEpochDay(uint256 epochDay) internal pure returns (bool result) {
        unchecked {
            result = epochDay < MAX_SUPPORTED_EPOCH_DAY + 1;
        }
    }

    /// @dev Returns if `timestamp` is a supported unix timestamp.
    function isSupportedTimestamp(uint256 timestamp) internal pure returns (bool result) {
        unchecked {
            result = timestamp < MAX_SUPPORTED_TIMESTAMP + 1;
        }
    }

    /// @dev Returns the unix timestamp of the given `n`th weekday `wd`, in `month` of `year`.
    /// Example: 3rd Friday of Feb 2022 is `nthWeekdayInMonthOfYearTimestamp(2022, 2, 3, 5)`
    /// Note: `n` is 1-indexed for traditional consistency.
    /// Invalid weekdays (i.e. `wd == 0 || wd > 7`) result in undefined behavior.
    function nthWeekdayInMonthOfYearTimestamp(uint256 year, uint256 month, uint256 n, uint256 wd)
        internal
        pure
        returns (uint256 result)
    {
        uint256 d = dateToEpochDay(year, month, 1);
        uint256 md = daysInMonth(year, month);
        /// @solidity memory-safe-assembly
        assembly {
            let diff := sub(wd, add(mod(add(d, 3), 7), 1))
            let date := add(mul(sub(n, 1), 7), add(mul(gt(diff, 6), 7), diff))
            result := mul(mul(86400, add(date, d)), and(lt(date, md), iszero(iszero(n))))
        }
    }

    /// @dev Returns the unix timestamp of the most recent Monday.
    function mondayTimestamp(uint256 timestamp) internal pure returns (uint256 result) {
        uint256 t = timestamp;
        /// @solidity memory-safe-assembly
        assembly {
            let day := div(t, 86400)
            result := mul(mul(sub(day, mod(add(day, 3), 7)), 86400), gt(t, 345599))
        }
    }

    /// @dev Returns whether the unix timestamp falls on a Saturday or Sunday.
    /// To check whether it is a week day, just take the negation of the result.
    function isWeekEnd(uint256 timestamp) internal pure returns (bool result) {
        result = weekday(timestamp) > FRI;
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*              DATE TIME ARITHMETIC OPERATIONS               */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Adds `numYears` to the unix timestamp, and returns the result.
    /// Note: The result will share the same Gregorian calendar month,
    /// but different Gregorian calendar years for non-zero `numYears`.
    /// If the Gregorian calendar month of the result has less days
    /// than the Gregorian calendar month day of the `timestamp`,
    /// the result's month day will be the maximum possible value for the month.
    /// (e.g. from 29th Feb to 28th Feb)
    function addYears(uint256 timestamp, uint256 numYears) internal pure returns (uint256 result) {
        (uint256 year, uint256 month, uint256 day) = epochDayToDate(timestamp / 86400);
        result = _offsetted(year + numYears, month, day, timestamp);
    }

    /// @dev Adds `numMonths` to the unix timestamp, and returns the result.
    /// Note: If the Gregorian calendar month of the result has less days
    /// than the Gregorian calendar month day of the `timestamp`,
    /// the result's month day will be the maximum possible value for the month.
    /// (e.g. from 29th Feb to 28th Feb)
    function addMonths(uint256 timestamp, uint256 numMonths)
        internal
        pure
        returns (uint256 result)
    {
        (uint256 year, uint256 month, uint256 day) = epochDayToDate(timestamp / 86400);
        month = _sub(month + numMonths, 1);
        result = _offsetted(year + month / 12, _add(month % 12, 1), day, timestamp);
    }

    /// @dev Adds `numDays` to the unix timestamp, and returns the result.
    function addDays(uint256 timestamp, uint256 numDays) internal pure returns (uint256 result) {
        result = timestamp + numDays * 86400;
    }

    /// @dev Adds `numHours` to the unix timestamp, and returns the result.
    function addHours(uint256 timestamp, uint256 numHours) internal pure returns (uint256 result) {
        result = timestamp + numHours * 3600;
    }

    /// @dev Adds `numMinutes` to the unix timestamp, and returns the result.
    function addMinutes(uint256 timestamp, uint256 numMinutes)
        internal
        pure
        returns (uint256 result)
    {
        result = timestamp + numMinutes * 60;
    }

    /// @dev Adds `numSeconds` to the unix timestamp, and returns the result.
    function addSeconds(uint256 timestamp, uint256 numSeconds)
        internal
        pure
        returns (uint256 result)
    {
        result = timestamp + numSeconds;
    }

    /// @dev Subtracts `numYears` from the unix timestamp, and returns the result.
    /// Note: The result will share the same Gregorian calendar month,
    /// but different Gregorian calendar years for non-zero `numYears`.
    /// If the Gregorian calendar month of the result has less days
    /// than the Gregorian calendar month day of the `timestamp`,
    /// the result's month day will be the maximum possible value for the month.
    /// (e.g. from 29th Feb to 28th Feb)
    function subYears(uint256 timestamp, uint256 numYears) internal pure returns (uint256 result) {
        (uint256 year, uint256 month, uint256 day) = epochDayToDate(timestamp / 86400);
        result = _offsetted(year - numYears, month, day, timestamp);
    }

    /// @dev Subtracts `numYears` from the unix timestamp, and returns the result.
    /// Note: If the Gregorian calendar month of the result has less days
    /// than the Gregorian calendar month day of the `timestamp`,
    /// the result's month day will be the maximum possible value for the month.
    /// (e.g. from 29th Feb to 28th Feb)
    function subMonths(uint256 timestamp, uint256 numMonths)
        internal
        pure
        returns (uint256 result)
    {
        (uint256 year, uint256 month, uint256 day) = epochDayToDate(timestamp / 86400);
        uint256 yearMonth = _totalMonths(year, month) - _add(numMonths, 1);
        result = _offsetted(yearMonth / 12, _add(yearMonth % 12, 1), day, timestamp);
    }

    /// @dev Subtracts `numDays` from the unix timestamp, and returns the result.
    function subDays(uint256 timestamp, uint256 numDays) internal pure returns (uint256 result) {
        result = timestamp - numDays * 86400;
    }

    /// @dev Subtracts `numHours` from the unix timestamp, and returns the result.
    function subHours(uint256 timestamp, uint256 numHours) internal pure returns (uint256 result) {
        result = timestamp - numHours * 3600;
    }

    /// @dev Subtracts `numMinutes` from the unix timestamp, and returns the result.
    function subMinutes(uint256 timestamp, uint256 numMinutes)
        internal
        pure
        returns (uint256 result)
    {
        result = timestamp - numMinutes * 60;
    }

    /// @dev Subtracts `numSeconds` from the unix timestamp, and returns the result.
    function subSeconds(uint256 timestamp, uint256 numSeconds)
        internal
        pure
        returns (uint256 result)
    {
        result = timestamp - numSeconds;
    }

    /// @dev Returns the difference in Gregorian calendar years
    /// between `fromTimestamp` and `toTimestamp`.
    /// Note: Even if the true time difference is less than a year,
    /// the difference can be non-zero is the timestamps are
    /// from diffrent Gregorian calendar years
    function diffYears(uint256 fromTimestamp, uint256 toTimestamp)
        internal
        pure
        returns (uint256 result)
    {
        toTimestamp - fromTimestamp;
        (uint256 fromYear,,) = epochDayToDate(fromTimestamp / 86400);
        (uint256 toYear,,) = epochDayToDate(toTimestamp / 86400);
        result = _sub(toYear, fromYear);
    }

    /// @dev Returns the difference in Gregorian calendar months
    /// between `fromTimestamp` and `toTimestamp`.
    /// Note: Even if the true time difference is less than a month,
    /// the difference can be non-zero is the timestamps are
    /// from diffrent Gregorian calendar months.
    function diffMonths(uint256 fromTimestamp, uint256 toTimestamp)
        internal
        pure
        returns (uint256 result)
    {
        toTimestamp - fromTimestamp;
        (uint256 fromYear, uint256 fromMonth,) = epochDayToDate(fromTimestamp / 86400);
        (uint256 toYear, uint256 toMonth,) = epochDayToDate(toTimestamp / 86400);
        result = _sub(_totalMonths(toYear, toMonth), _totalMonths(fromYear, fromMonth));
    }

    /// @dev Returns the difference in days between `fromTimestamp` and `toTimestamp`.
    function diffDays(uint256 fromTimestamp, uint256 toTimestamp)
        internal
        pure
        returns (uint256 result)
    {
        result = (toTimestamp - fromTimestamp) / 86400;
    }

    /// @dev Returns the difference in hours between `fromTimestamp` and `toTimestamp`.
    function diffHours(uint256 fromTimestamp, uint256 toTimestamp)
        internal
        pure
        returns (uint256 result)
    {
        result = (toTimestamp - fromTimestamp) / 3600;
    }

    /// @dev Returns the difference in minutes between `fromTimestamp` and `toTimestamp`.
    function diffMinutes(uint256 fromTimestamp, uint256 toTimestamp)
        internal
        pure
        returns (uint256 result)
    {
        result = (toTimestamp - fromTimestamp) / 60;
    }

    /// @dev Returns the difference in seconds between `fromTimestamp` and `toTimestamp`.
    function diffSeconds(uint256 fromTimestamp, uint256 toTimestamp)
        internal
        pure
        returns (uint256 result)
    {
        result = toTimestamp - fromTimestamp;
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                      PRIVATE HELPERS                       */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Unchecked arithmetic for computing the total number of months.
    function _totalMonths(uint256 numYears, uint256 numMonths)
        private
        pure
        returns (uint256 total)
    {
        unchecked {
            total = numYears * 12 + numMonths;
        }
    }

    /// @dev Unchecked arithmetic for adding two numbers.
    function _add(uint256 a, uint256 b) private pure returns (uint256 c) {
        unchecked {
            c = a + b;
        }
    }

    /// @dev Unchecked arithmetic for subtracting two numbers.
    function _sub(uint256 a, uint256 b) private pure returns (uint256 c) {
        unchecked {
            c = a - b;
        }
    }

    /// @dev Returns the offsetted timestamp.
    function _offsetted(uint256 year, uint256 month, uint256 day, uint256 timestamp)
        private
        pure
        returns (uint256 result)
    {
        uint256 dm = daysInMonth(year, month);
        if (day >= dm) {
            day = dm;
        }
        result = dateToEpochDay(year, month, day) * 86400 + (timestamp % 86400);
    }
}

// File: lib/solady/src/auth/Ownable.sol



// 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 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();

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                           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: `not(_OWNER_SLOT_NOT)`.
    /// It is intentionally choosen 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.
    uint256 private constant _OWNER_SLOT_NOT = 0x8b78c6d8;

    /// 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 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 {
        /// @solidity memory-safe-assembly
        assembly {
            // Clean the upper 96 bits.
            newOwner := shr(96, shl(96, newOwner))
            // Store the new value.
            sstore(not(_OWNER_SLOT_NOT), 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 {
        /// @solidity memory-safe-assembly
        assembly {
            let ownerSlot := not(_OWNER_SLOT_NOT)
            // 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(not(_OWNER_SLOT_NOT)))) {
                mstore(0x00, 0x82b42900) // `Unauthorized()`.
                revert(0x1c, 0x04)
            }
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  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 be 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(not(_OWNER_SLOT_NOT))
        }
    }

    /// @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))
        }
    }

    /// @dev Returns how long a two-step ownership handover is valid for in seconds.
    function ownershipHandoverValidFor() public view virtual returns (uint64) {
        return 48 * 3600;
    }

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

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

// File: lib/solady/src/utils/LibBitmap.sol



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

import "./LibBit.sol";

/// @notice Library for storage of packed unsigned booleans.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/LibBitmap.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/LibBitmap.sol)
/// @author Modified from Solidity-Bits (https://github.com/estarriolvetch/solidity-bits/blob/main/contracts/BitMaps.sol)
library LibBitmap {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The constant returned when a bitmap scan does not find a result.
    uint256 internal constant NOT_FOUND = type(uint256).max;

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

    /// @dev A bitmap in storage.
    struct Bitmap {
        mapping(uint256 => uint256) map;
    }

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

    /// @dev Returns the boolean value of the bit at `index` in `bitmap`.
    function get(Bitmap storage bitmap, uint256 index) internal view returns (bool isSet) {
        // It is better to set `isSet` to either 0 or 1, than zero vs non-zero.
        // Both cost the same amount of gas, but the former allows the returned value
        // to be reused without cleaning the upper bits.
        uint256 b = (bitmap.map[index >> 8] >> (index & 0xff)) & 1;
        /// @solidity memory-safe-assembly
        assembly {
            isSet := b
        }
    }

    /// @dev Updates the bit at `index` in `bitmap` to true.
    function set(Bitmap storage bitmap, uint256 index) internal {
        bitmap.map[index >> 8] |= (1 << (index & 0xff));
    }

    /// @dev Updates the bit at `index` in `bitmap` to false.
    function unset(Bitmap storage bitmap, uint256 index) internal {
        bitmap.map[index >> 8] &= ~(1 << (index & 0xff));
    }

    /// @dev Flips the bit at `index` in `bitmap`.
    /// Returns the boolean result of the flipped bit.
    function toggle(Bitmap storage bitmap, uint256 index) internal returns (bool newIsSet) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, shr(8, index))
            mstore(0x20, bitmap.slot)
            let storageSlot := keccak256(0x00, 0x40)
            let shift := and(index, 0xff)
            let storageValue := sload(storageSlot)

            let mask := shl(shift, 1)
            storageValue := xor(storageValue, mask)
            // It makes sense to return the `newIsSet`,
            // as it allow us to skip an additional warm `sload`,
            // and it costs minimal gas (about 15),
            // which may be optimized away if the returned value is unused.
            newIsSet := iszero(iszero(and(storageValue, mask)))
            sstore(storageSlot, storageValue)
        }
    }

    /// @dev Updates the bit at `index` in `bitmap` to `shouldSet`.
    function setTo(Bitmap storage bitmap, uint256 index, bool shouldSet) internal {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x20, bitmap.slot)
            mstore(0x00, shr(8, index))
            let storageSlot := keccak256(0x00, 0x40)
            let storageValue := sload(storageSlot)
            let shift := and(index, 0xff)

            sstore(
                storageSlot,
                // Unsets the bit at `shift` via `and`, then sets its new value via `or`.
                or(and(storageValue, not(shl(shift, 1))), shl(shift, iszero(iszero(shouldSet))))
            )
        }
    }

    /// @dev Consecutively sets `amount` of bits starting from the bit at `start`.
    function setBatch(Bitmap storage bitmap, uint256 start, uint256 amount) internal {
        /// @solidity memory-safe-assembly
        assembly {
            let max := not(0)
            let shift := and(start, 0xff)
            mstore(0x20, bitmap.slot)
            mstore(0x00, shr(8, start))
            if iszero(lt(add(shift, amount), 257)) {
                let storageSlot := keccak256(0x00, 0x40)
                sstore(storageSlot, or(sload(storageSlot), shl(shift, max)))
                let bucket := add(mload(0x00), 1)
                let bucketEnd := add(mload(0x00), shr(8, add(amount, shift)))
                amount := and(add(amount, shift), 0xff)
                shift := 0
                for {} iszero(eq(bucket, bucketEnd)) { bucket := add(bucket, 1) } {
                    mstore(0x00, bucket)
                    sstore(keccak256(0x00, 0x40), max)
                }
                mstore(0x00, bucket)
            }
            let storageSlot := keccak256(0x00, 0x40)
            sstore(storageSlot, or(sload(storageSlot), shl(shift, shr(sub(256, amount), max))))
        }
    }

    /// @dev Consecutively unsets `amount` of bits starting from the bit at `start`.
    function unsetBatch(Bitmap storage bitmap, uint256 start, uint256 amount) internal {
        /// @solidity memory-safe-assembly
        assembly {
            let shift := and(start, 0xff)
            mstore(0x20, bitmap.slot)
            mstore(0x00, shr(8, start))
            if iszero(lt(add(shift, amount), 257)) {
                let storageSlot := keccak256(0x00, 0x40)
                sstore(storageSlot, and(sload(storageSlot), not(shl(shift, not(0)))))
                let bucket := add(mload(0x00), 1)
                let bucketEnd := add(mload(0x00), shr(8, add(amount, shift)))
                amount := and(add(amount, shift), 0xff)
                shift := 0
                for {} iszero(eq(bucket, bucketEnd)) { bucket := add(bucket, 1) } {
                    mstore(0x00, bucket)
                    sstore(keccak256(0x00, 0x40), 0)
                }
                mstore(0x00, bucket)
            }
            let storageSlot := keccak256(0x00, 0x40)
            sstore(
                storageSlot, and(sload(storageSlot), not(shl(shift, shr(sub(256, amount), not(0)))))
            )
        }
    }

    /// @dev Returns number of set bits within a range by
    /// scanning `amount` of bits starting from the bit at `start`.
    function popCount(Bitmap storage bitmap, uint256 start, uint256 amount)
        internal
        view
        returns (uint256 count)
    {
        unchecked {
            uint256 bucket = start >> 8;
            uint256 shift = start & 0xff;
            if (!(amount + shift < 257)) {
                count = LibBit.popCount(bitmap.map[bucket] >> shift);
                uint256 bucketEnd = bucket + ((amount + shift) >> 8);
                amount = (amount + shift) & 0xff;
                shift = 0;
                for (++bucket; bucket != bucketEnd; ++bucket) {
                    count += LibBit.popCount(bitmap.map[bucket]);
                }
            }
            count += LibBit.popCount((bitmap.map[bucket] >> shift) << (256 - amount));
        }
    }

    /// @dev Returns the index of the most significant set bit before the bit at `before`.
    /// If no set bit is found, returns `NOT_FOUND`.
    function findLastSet(Bitmap storage bitmap, uint256 before)
        internal
        view
        returns (uint256 setBitIndex)
    {
        uint256 bucket;
        uint256 bucketBits;
        /// @solidity memory-safe-assembly
        assembly {
            setBitIndex := not(0)
            bucket := shr(8, before)
            mstore(0x00, bucket)
            mstore(0x20, bitmap.slot)
            let offset := and(0xff, not(before)) // `256 - (255 & before) - 1`.
            bucketBits := shr(offset, shl(offset, sload(keccak256(0x00, 0x40))))
            if iszero(bucketBits) {
                for {} bucket {} {
                    bucket := add(bucket, setBitIndex) // `sub(bucket, 1)`.
                    mstore(0x00, bucket)
                    bucketBits := sload(keccak256(0x00, 0x40))
                    if bucketBits { break }
                }
            }
        }
        if (bucketBits != 0) {
            setBitIndex = (bucket << 8) | LibBit.fls(bucketBits);
            /// @solidity memory-safe-assembly
            assembly {
                setBitIndex := or(setBitIndex, sub(0, gt(setBitIndex, before)))
            }
        }
    }
}

// File: lib/solady/src/utils/MerkleProofLib.sol



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

/// @notice Gas optimized verification of proof of inclusion for a leaf in a Merkle tree.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/MerkleProofLib.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/MerkleProofLib.sol)
/// @author Modified from OpenZeppelin (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/utils/cryptography/MerkleProof.sol)
library MerkleProofLib {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*            MERKLE PROOF VERIFICATION OPERATIONS            */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns whether `leaf` exists in the Merkle tree with `root`, given `proof`.
    function verify(bytes32[] memory proof, bytes32 root, bytes32 leaf)
        internal
        pure
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            if mload(proof) {
                // Initialize `offset` to the offset of `proof` elements in memory.
                let offset := add(proof, 0x20)
                // Left shift by 5 is equivalent to multiplying by 0x20.
                let end := add(offset, shl(5, mload(proof)))
                // Iterate over proof elements to compute root hash.
                for {} 1 {} {
                    // Slot of `leaf` in scratch space.
                    // If the condition is true: 0x20, otherwise: 0x00.
                    let scratch := shl(5, gt(leaf, mload(offset)))
                    // Store elements to hash contiguously in scratch space.
                    // Scratch space is 64 bytes (0x00 - 0x3f) and both elements are 32 bytes.
                    mstore(scratch, leaf)
                    mstore(xor(scratch, 0x20), mload(offset))
                    // Reuse `leaf` to store the hash to reduce stack operations.
                    leaf := keccak256(0x00, 0x40)
                    offset := add(offset, 0x20)
                    if iszero(lt(offset, end)) { break }
                }
            }
            isValid := eq(leaf, root)
        }
    }

    /// @dev Returns whether `leaf` exists in the Merkle tree with `root`, given `proof`.
    function verifyCalldata(bytes32[] calldata proof, bytes32 root, bytes32 leaf)
        internal
        pure
        returns (bool isValid)
    {
        /// @solidity memory-safe-assembly
        assembly {
            if proof.length {
                // Left shift by 5 is equivalent to multiplying by 0x20.
                let end := add(proof.offset, shl(5, proof.length))
                // Initialize `offset` to the offset of `proof` in the calldata.
                let offset := proof.offset
                // Iterate over proof elements to compute root hash.
                for {} 1 {} {
                    // Slot of `leaf` in scratch space.
                    // If the condition is true: 0x20, otherwise: 0x00.
                    let scratch := shl(5, gt(leaf, calldataload(offset)))
                    // Store elements to hash contiguously in scratch space.
                    // Scratch space is 64 bytes (0x00 - 0x3f) and both elements are 32 bytes.
                    mstore(scratch, leaf)
                    mstore(xor(scratch, 0x20), calldataload(offset))
                    // Reuse `leaf` to store the hash to reduce stack operations.
                    leaf := keccak256(0x00, 0x40)
                    offset := add(offset, 0x20)
                    if iszero(lt(offset, end)) { break }
                }
            }
            isValid := eq(leaf, root)
        }
    }

    /// @dev Returns whether all `leafs` exist in the Merkle tree with `root`,
    /// given `proof` and `flags`.
    function verifyMultiProof(
        bytes32[] memory proof,
        bytes32 root,
        bytes32[] memory leafs,
        bool[] memory flags
    ) internal pure returns (bool isValid) {
        // Rebuilds the root by consuming and producing values on a queue.
        // The queue starts with the `leafs` array, and goes into a `hashes` array.
        // After the process, the last element on the queue is verified
        // to be equal to the `root`.
        //
        // The `flags` array denotes whether the sibling
        // should be popped from the queue (`flag == true`), or
        // should be popped from the `proof` (`flag == false`).
        /// @solidity memory-safe-assembly
        assembly {
            // Cache the lengths of the arrays.
            let leafsLength := mload(leafs)
            let proofLength := mload(proof)
            let flagsLength := mload(flags)

            // Advance the pointers of the arrays to point to the data.
            leafs := add(0x20, leafs)
            proof := add(0x20, proof)
            flags := add(0x20, flags)

            // If the number of flags is correct.
            for {} eq(add(leafsLength, proofLength), add(flagsLength, 1)) {} {
                // For the case where `proof.length + leafs.length == 1`.
                if iszero(flagsLength) {
                    // `isValid = (proof.length == 1 ? proof[0] : leafs[0]) == root`.
                    isValid := eq(mload(xor(leafs, mul(xor(proof, leafs), proofLength))), root)
                    break
                }

                // We can use the free memory space for the queue.
                // We don't need to allocate, since the queue is temporary.
                let hashesFront := mload(0x40)
                // Copy the leafs into the hashes.
                // Sometimes, a little memory expansion costs less than branching.
                // Should cost less, even with a high free memory offset of 0x7d00.
                // Left shift by 5 is equivalent to multiplying by 0x20.
                leafsLength := shl(5, leafsLength)
                for { let i := 0 } iszero(eq(i, leafsLength)) { i := add(i, 0x20) } {
                    mstore(add(hashesFront, i), mload(add(leafs, i)))
                }
                // Compute the back of the hashes.
                let hashesBack := add(hashesFront, leafsLength)
                // This is the end of the memory for the queue.
                // We recycle `flagsLength` to save on stack variables
                // (this trick may not always save gas).
                flagsLength := add(hashesBack, shl(5, flagsLength))

                for {} 1 {} {
                    // Pop from `hashes`.
                    let a := mload(hashesFront)
                    // Pop from `hashes`.
                    let b := mload(add(hashesFront, 0x20))
                    hashesFront := add(hashesFront, 0x40)

                    // If the flag is false, load the next proof,
                    // else, pops from the queue.
                    if iszero(mload(flags)) {
                        // Loads the next proof.
                        b := mload(proof)
                        proof := add(proof, 0x20)
                        // Unpop from `hashes`.
                        hashesFront := sub(hashesFront, 0x20)
                    }

                    // Advance to the next flag.
                    flags := add(flags, 0x20)

                    // Slot of `a` in scratch space.
                    // If the condition is true: 0x20, otherwise: 0x00.
                    let scratch := shl(5, gt(a, b))
                    // Hash the scratch space and push the result onto the queue.
                    mstore(scratch, a)
                    mstore(xor(scratch, 0x20), b)
                    mstore(hashesBack, keccak256(0x00, 0x40))
                    hashesBack := add(hashesBack, 0x20)
                    if iszero(lt(hashesBack, flagsLength)) { break }
                }
                // Checks if the last value in the queue is same as the root.
                isValid := eq(mload(sub(hashesBack, 0x20)), root)
                break
            }
        }
    }

    /// @dev Returns whether all `leafs` exist in the Merkle tree with `root`,
    /// given `proof` and `flags`.
    function verifyMultiProofCalldata(
        bytes32[] calldata proof,
        bytes32 root,
        bytes32[] calldata leafs,
        bool[] calldata flags
    ) internal pure returns (bool isValid) {
        // Rebuilds the root by consuming and producing values on a queue.
        // The queue starts with the `leafs` array, and goes into a `hashes` array.
        // After the process, the last element on the queue is verified
        // to be equal to the `root`.
        //
        // The `flags` array denotes whether the sibling
        // should be popped from the queue (`flag == true`), or
        // should be popped from the `proof` (`flag == false`).
        /// @solidity memory-safe-assembly
        assembly {
            // If the number of flags is correct.
            for {} eq(add(leafs.length, proof.length), add(flags.length, 1)) {} {
                // For the case where `proof.length + leafs.length == 1`.
                if iszero(flags.length) {
                    // `isValid = (proof.length == 1 ? proof[0] : leafs[0]) == root`.
                    // forgefmt: disable-next-item
                    isValid := eq(
                        calldataload(
                            xor(leafs.offset, mul(xor(proof.offset, leafs.offset), proof.length))
                        ),
                        root
                    )
                    break
                }

                // We can use the free memory space for the queue.
                // We don't need to allocate, since the queue is temporary.
                let hashesFront := mload(0x40)
                // Copy the leafs into the hashes.
                // Sometimes, a little memory expansion costs less than branching.
                // Should cost less, even with a high free memory offset of 0x7d00.
                // Left shift by 5 is equivalent to multiplying by 0x20.
                calldatacopy(hashesFront, leafs.offset, shl(5, leafs.length))
                // Compute the back of the hashes.
                let hashesBack := add(hashesFront, shl(5, leafs.length))
                // This is the end of the memory for the queue.
                // We recycle `flags.length` to save on stack variables
                // (this trick may not always save gas).
                flags.length := add(hashesBack, shl(5, flags.length))

                // We don't need to make a copy of `proof.offset` or `flags.offset`,
                // as they are pass-by-value (this trick may not always save gas).

                for {} 1 {} {
                    // Pop from `hashes`.
                    let a := mload(hashesFront)
                    // Pop from `hashes`.
                    let b := mload(add(hashesFront, 0x20))
                    hashesFront := add(hashesFront, 0x40)

                    // If the flag is false, load the next proof,
                    // else, pops from the queue.
                    if iszero(calldataload(flags.offset)) {
                        // Loads the next proof.
                        b := calldataload(proof.offset)
                        proof.offset := add(proof.offset, 0x20)
                        // Unpop from `hashes`.
                        hashesFront := sub(hashesFront, 0x20)
                    }

                    // Advance to the next flag offset.
                    flags.offset := add(flags.offset, 0x20)

                    // Slot of `a` in scratch space.
                    // If the condition is true: 0x20, otherwise: 0x00.
                    let scratch := shl(5, gt(a, b))
                    // Hash the scratch space and push the result onto the queue.
                    mstore(scratch, a)
                    mstore(xor(scratch, 0x20), b)
                    mstore(hashesBack, keccak256(0x00, 0x40))
                    hashesBack := add(hashesBack, 0x20)
                    if iszero(lt(hashesBack, flags.length)) { break }
                }
                // Checks if the last value in the queue is same as the root.
                isValid := eq(mload(sub(hashesBack, 0x20)), root)
                break
            }
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   EMPTY CALLDATA HELPERS                   */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns an empty calldata bytes32 array.
    function emptyProof() internal pure returns (bytes32[] calldata proof) {
        /// @solidity memory-safe-assembly
        assembly {
            proof.length := 0
        }
    }

    /// @dev Returns an empty calldata bytes32 array.
    function emptyLeafs() internal pure returns (bytes32[] calldata leafs) {
        /// @solidity memory-safe-assembly
        assembly {
            leafs.length := 0
        }
    }

    /// @dev Returns an empty calldata bool array.
    function emptyFlags() internal pure returns (bool[] calldata flags) {
        /// @solidity memory-safe-assembly
        assembly {
            flags.length := 0
        }
    }
}

// File: lib/VRGDAs/src/LinearVRGDA.sol



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

import {unsafeWadDiv} from "solmate/utils/SignedWadMath.sol";

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

/// @title Linear Variable Rate Gradual Dutch Auction
/// @author transmissions11 <t11s@paradigm.xyz>
/// @author FrankieIsLost <frankie@paradigm.xyz>
/// @notice VRGDA with a linear issuance curve.
abstract contract LinearVRGDA is VRGDA {
    /*//////////////////////////////////////////////////////////////
                           PRICING PARAMETERS
    //////////////////////////////////////////////////////////////*/

    /// @dev The total number of tokens to target selling every full unit of time.
    /// @dev Represented as an 18 decimal fixed point number.
    int256 internal immutable perTimeUnit;

    /// @notice Sets pricing parameters for the VRGDA.
    /// @param _targetPrice The target price for a token if sold on pace, scaled by 1e18.
    /// @param _priceDecayPercent The percent price decays per unit of time with no sales, scaled by 1e18.
    /// @param _perTimeUnit The number of tokens to target selling in 1 full unit of time, scaled by 1e18.
    constructor(
        int256 _targetPrice,
        int256 _priceDecayPercent,
        int256 _perTimeUnit
    ) VRGDA(_targetPrice, _priceDecayPercent) {
        perTimeUnit = _perTimeUnit;
    }

    /*//////////////////////////////////////////////////////////////
                              PRICING LOGIC
    //////////////////////////////////////////////////////////////*/

    /// @dev Given a number of tokens sold, return the target time that number of tokens should be sold by.
    /// @param sold A number of tokens sold, scaled by 1e18, to get the corresponding target sale time for.
    /// @return The target time the tokens should be sold by, scaled by 1e18, where the time is
    /// relative, such that 0 means the tokens should be sold immediately when the VRGDA begins.
    function getTargetSaleTime(int256 sold) public view virtual override returns (int256) {
        return unsafeWadDiv(sold, perTimeUnit);
    }
}

// File: src/Staking.sol



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

import {ERC20} from "solady/tokens/ERC20.sol";
import {Ownable} from "solady/auth/Ownable.sol";
import {SafeTransferLib} from "solady/utils/SafeTransferLib.sol";

contract Staking {
    ERC20 public token;

    uint256 public totalStaked;
    uint256 public totalShares;
    mapping(address => uint256) public shares;

    event Staked(address indexed user, uint256 share, uint256 amount);
    event Withdrawn(address indexed user, uint256 share, uint256 amount);

    constructor() {
        token = ERC20(msg.sender);
    }

    function stake(uint256 amount) public {
        uint256 tokensHeld = token.balanceOf(address(this));
        uint256 _totalShares = totalShares;
        uint256 sharesToMint = amount;
        if (_totalShares != 0 && tokensHeld != 0) {
            sharesToMint = (amount * _totalShares) / tokensHeld;
        }
        totalStaked += amount;
        totalShares += sharesToMint;
        shares[msg.sender] += sharesToMint;
        token.transferFrom(msg.sender, address(this), amount);
        emit Staked(msg.sender, sharesToMint, amount);
    }

    function withdraw(uint256 share) public {
        uint256 tokenAmount = (share * token.balanceOf(address(this))) / totalShares;
        shares[msg.sender] -= share;
        totalStaked -= tokenAmount;
        totalShares -= share;
        token.transfer(msg.sender, tokenAmount);
        emit Withdrawn(msg.sender, share, tokenAmount);
    }
}

// File: lib/forge-std/src/console.sol



// SPDX-License-Identifier: MIT
pragma solidity >=0.4.22 <0.9.0;

library console {
    address constant CONSOLE_ADDRESS = address(0x000000000000000000636F6e736F6c652e6c6f67);

    function _sendLogPayload(bytes memory payload) private view {
        uint256 payloadLength = payload.length;
        address consoleAddress = CONSOLE_ADDRESS;
        /// @solidity memory-safe-assembly
        assembly {
            let payloadStart := add(payload, 32)
            let r := staticcall(gas(), consoleAddress, payloadStart, payloadLength, 0, 0)
        }
    }

    function log() internal view {
        _sendLogPayload(abi.encodeWithSignature("log()"));
    }

    function logInt(int p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(int)", p0));
    }

    function logUint(uint p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint)", p0));
    }

    function logString(string memory p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string)", p0));
    }

    function logBool(bool p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool)", p0));
    }

    function logAddress(address p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address)", p0));
    }

    function logBytes(bytes memory p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes)", p0));
    }

    function logBytes1(bytes1 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes1)", p0));
    }

    function logBytes2(bytes2 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes2)", p0));
    }

    function logBytes3(bytes3 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes3)", p0));
    }

    function logBytes4(bytes4 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes4)", p0));
    }

    function logBytes5(bytes5 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes5)", p0));
    }

    function logBytes6(bytes6 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes6)", p0));
    }

    function logBytes7(bytes7 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes7)", p0));
    }

    function logBytes8(bytes8 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes8)", p0));
    }

    function logBytes9(bytes9 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes9)", p0));
    }

    function logBytes10(bytes10 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes10)", p0));
    }

    function logBytes11(bytes11 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes11)", p0));
    }

    function logBytes12(bytes12 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes12)", p0));
    }

    function logBytes13(bytes13 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes13)", p0));
    }

    function logBytes14(bytes14 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes14)", p0));
    }

    function logBytes15(bytes15 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes15)", p0));
    }

    function logBytes16(bytes16 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes16)", p0));
    }

    function logBytes17(bytes17 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes17)", p0));
    }

    function logBytes18(bytes18 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes18)", p0));
    }

    function logBytes19(bytes19 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes19)", p0));
    }

    function logBytes20(bytes20 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes20)", p0));
    }

    function logBytes21(bytes21 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes21)", p0));
    }

    function logBytes22(bytes22 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes22)", p0));
    }

    function logBytes23(bytes23 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes23)", p0));
    }

    function logBytes24(bytes24 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes24)", p0));
    }

    function logBytes25(bytes25 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes25)", p0));
    }

    function logBytes26(bytes26 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes26)", p0));
    }

    function logBytes27(bytes27 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes27)", p0));
    }

    function logBytes28(bytes28 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes28)", p0));
    }

    function logBytes29(bytes29 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes29)", p0));
    }

    function logBytes30(bytes30 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes30)", p0));
    }

    function logBytes31(bytes31 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes31)", p0));
    }

    function logBytes32(bytes32 p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bytes32)", p0));
    }

    function log(uint p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint)", p0));
    }

    function log(string memory p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string)", p0));
    }

    function log(bool p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool)", p0));
    }

    function log(address p0) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address)", p0));
    }

    function log(uint p0, uint p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint)", p0, p1));
    }

    function log(uint p0, string memory p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string)", p0, p1));
    }

    function log(uint p0, bool p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool)", p0, p1));
    }

    function log(uint p0, address p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address)", p0, p1));
    }

    function log(string memory p0, uint p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint)", p0, p1));
    }

    function log(string memory p0, string memory p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string)", p0, p1));
    }

    function log(string memory p0, bool p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool)", p0, p1));
    }

    function log(string memory p0, address p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address)", p0, p1));
    }

    function log(bool p0, uint p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint)", p0, p1));
    }

    function log(bool p0, string memory p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string)", p0, p1));
    }

    function log(bool p0, bool p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool)", p0, p1));
    }

    function log(bool p0, address p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address)", p0, p1));
    }

    function log(address p0, uint p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint)", p0, p1));
    }

    function log(address p0, string memory p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string)", p0, p1));
    }

    function log(address p0, bool p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool)", p0, p1));
    }

    function log(address p0, address p1) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address)", p0, p1));
    }

    function log(uint p0, uint p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,uint)", p0, p1, p2));
    }

    function log(uint p0, uint p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,string)", p0, p1, p2));
    }

    function log(uint p0, uint p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,bool)", p0, p1, p2));
    }

    function log(uint p0, uint p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,address)", p0, p1, p2));
    }

    function log(uint p0, string memory p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,uint)", p0, p1, p2));
    }

    function log(uint p0, string memory p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,string)", p0, p1, p2));
    }

    function log(uint p0, string memory p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,bool)", p0, p1, p2));
    }

    function log(uint p0, string memory p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,address)", p0, p1, p2));
    }

    function log(uint p0, bool p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,uint)", p0, p1, p2));
    }

    function log(uint p0, bool p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,string)", p0, p1, p2));
    }

    function log(uint p0, bool p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,bool)", p0, p1, p2));
    }

    function log(uint p0, bool p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,address)", p0, p1, p2));
    }

    function log(uint p0, address p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,uint)", p0, p1, p2));
    }

    function log(uint p0, address p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,string)", p0, p1, p2));
    }

    function log(uint p0, address p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,bool)", p0, p1, p2));
    }

    function log(uint p0, address p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,address)", p0, p1, p2));
    }

    function log(string memory p0, uint p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,uint)", p0, p1, p2));
    }

    function log(string memory p0, uint p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,string)", p0, p1, p2));
    }

    function log(string memory p0, uint p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,bool)", p0, p1, p2));
    }

    function log(string memory p0, uint p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,address)", p0, p1, p2));
    }

    function log(string memory p0, string memory p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,uint)", p0, p1, p2));
    }

    function log(string memory p0, string memory p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,string)", p0, p1, p2));
    }

    function log(string memory p0, string memory p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,bool)", p0, p1, p2));
    }

    function log(string memory p0, string memory p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,address)", p0, p1, p2));
    }

    function log(string memory p0, bool p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint)", p0, p1, p2));
    }

    function log(string memory p0, bool p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,string)", p0, p1, p2));
    }

    function log(string memory p0, bool p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool)", p0, p1, p2));
    }

    function log(string memory p0, bool p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,address)", p0, p1, p2));
    }

    function log(string memory p0, address p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,uint)", p0, p1, p2));
    }

    function log(string memory p0, address p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,string)", p0, p1, p2));
    }

    function log(string memory p0, address p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,bool)", p0, p1, p2));
    }

    function log(string memory p0, address p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,address)", p0, p1, p2));
    }

    function log(bool p0, uint p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,uint)", p0, p1, p2));
    }

    function log(bool p0, uint p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,string)", p0, p1, p2));
    }

    function log(bool p0, uint p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,bool)", p0, p1, p2));
    }

    function log(bool p0, uint p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,address)", p0, p1, p2));
    }

    function log(bool p0, string memory p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint)", p0, p1, p2));
    }

    function log(bool p0, string memory p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,string)", p0, p1, p2));
    }

    function log(bool p0, string memory p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool)", p0, p1, p2));
    }

    function log(bool p0, string memory p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,address)", p0, p1, p2));
    }

    function log(bool p0, bool p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint)", p0, p1, p2));
    }

    function log(bool p0, bool p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string)", p0, p1, p2));
    }

    function log(bool p0, bool p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool)", p0, p1, p2));
    }

    function log(bool p0, bool p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address)", p0, p1, p2));
    }

    function log(bool p0, address p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint)", p0, p1, p2));
    }

    function log(bool p0, address p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,string)", p0, p1, p2));
    }

    function log(bool p0, address p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool)", p0, p1, p2));
    }

    function log(bool p0, address p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,address)", p0, p1, p2));
    }

    function log(address p0, uint p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,uint)", p0, p1, p2));
    }

    function log(address p0, uint p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,string)", p0, p1, p2));
    }

    function log(address p0, uint p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,bool)", p0, p1, p2));
    }

    function log(address p0, uint p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,address)", p0, p1, p2));
    }

    function log(address p0, string memory p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,uint)", p0, p1, p2));
    }

    function log(address p0, string memory p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,string)", p0, p1, p2));
    }

    function log(address p0, string memory p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,bool)", p0, p1, p2));
    }

    function log(address p0, string memory p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,address)", p0, p1, p2));
    }

    function log(address p0, bool p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint)", p0, p1, p2));
    }

    function log(address p0, bool p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,string)", p0, p1, p2));
    }

    function log(address p0, bool p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool)", p0, p1, p2));
    }

    function log(address p0, bool p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,address)", p0, p1, p2));
    }

    function log(address p0, address p1, uint p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,uint)", p0, p1, p2));
    }

    function log(address p0, address p1, string memory p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,string)", p0, p1, p2));
    }

    function log(address p0, address p1, bool p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,bool)", p0, p1, p2));
    }

    function log(address p0, address p1, address p2) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,address)", p0, p1, p2));
    }

    function log(uint p0, uint p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,uint,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,uint,string)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,uint,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,uint,address)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,string,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,string,string)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,string,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,string,address)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,bool,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,bool,string)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,bool,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,bool,address)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,address,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,address,string)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,address,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, uint p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,uint,address,address)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,uint,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,uint,string)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,uint,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,uint,address)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,string,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,string,string)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,string,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,string,address)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,bool,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,bool,string)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,bool,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,bool,address)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,address,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,address,string)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,address,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, string memory p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,string,address,address)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,uint,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,uint,string)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,uint,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,uint,address)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,string,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,string,string)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,string,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,string,address)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,bool,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,bool,string)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,bool,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,bool,address)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,address,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,address,string)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,address,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, bool p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,bool,address,address)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,uint,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,uint,string)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,uint,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,uint,address)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,string,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,string,string)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,string,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,string,address)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,bool,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,bool,string)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,bool,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,bool,address)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,address,uint)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,address,string)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,address,bool)", p0, p1, p2, p3));
    }

    function log(uint p0, address p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(uint,address,address,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,uint,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,uint,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,uint,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,uint,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,string,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,string,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,string,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,string,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,bool,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,bool,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,bool,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,bool,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,address,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,address,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,address,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint,address,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,uint,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,uint,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,uint,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,uint,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,string,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,string,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,string,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,string,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,bool,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,bool,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,bool,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,bool,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,address,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,address,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,address,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,address,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,string,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,string,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,string,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,string,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,address,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,address,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,address,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,address,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,uint,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,uint,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,uint,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,uint,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,string,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,string,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,string,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,string,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,bool,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,bool,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,bool,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,bool,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,address,uint)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,address,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,address,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,address,address)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,uint,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,uint,string)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,uint,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,uint,address)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,string,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,string,string)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,string,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,string,address)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,bool,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,bool,string)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,bool,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,bool,address)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,address,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,address,string)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,address,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, uint p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint,address,address)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint,string)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint,address)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,string,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,string,string)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,string,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,string,address)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool,string)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool,address)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,address,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,address,string)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,address,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,address,address)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint,string)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint,address)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string,string)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string,address)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool,string)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool,address)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address,string)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address,address)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint,string)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint,address)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,string,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,string,string)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,string,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,string,address)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool,string)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool,address)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,address,uint)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,address,string)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,address,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,address,address)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,uint,uint)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,uint,string)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,uint,bool)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,uint,address)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,string,uint)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,string,string)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,string,bool)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,string,address)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,bool,uint)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,bool,string)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,bool,bool)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,bool,address)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,address,uint)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,address,string)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,address,bool)", p0, p1, p2, p3));
    }

    function log(address p0, uint p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint,address,address)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,uint,uint)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,uint,string)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,uint,bool)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,uint,address)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,string,uint)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,string,string)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,string,bool)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,string,address)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,bool,uint)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,bool,string)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,bool,bool)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,bool,address)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,address,uint)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,address,string)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,address,bool)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,address,address)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint,uint)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint,string)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint,bool)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint,address)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,string,uint)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,string,string)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,string,bool)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,string,address)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool,uint)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool,string)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool,bool)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool,address)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,address,uint)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,address,string)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,address,bool)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,address,address)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, uint p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,uint,uint)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, uint p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,uint,string)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, uint p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,uint,bool)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, uint p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,uint,address)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, string memory p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,string,uint)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, string memory p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,string,string)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, string memory p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,string,bool)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, string memory p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,string,address)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, bool p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,bool,uint)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, bool p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,bool,string)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, bool p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,bool,bool)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, bool p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,bool,address)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, address p2, uint p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,address,uint)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, address p2, string memory p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,address,string)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, address p2, bool p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,address,bool)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, address p2, address p3) internal view {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,address,address)", p0, p1, p2, p3));
    }

}
// File: src/bonding/Power.sol



/* Apache License
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APPENDIX: How to apply the Apache License to your work.

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Copyright 2017 Bprotocol Foundation

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
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pragma solidity ^0.8.17;

/**
 * @title Power function by Bancor
 * @dev https://github.com/bancorprotocol/contracts
 *
 * Modified from the original by Slava Balasanov & Tarrence van As
 *
 * Split Power.sol out from BancorFormula.sol
 * https://github.com/bancorprotocol/contracts/blob/c9adc95e82fdfb3a0ada102514beb8ae00147f5d/solidity/contracts/converter/BancorFormula.sol
 */
contract Power {
    string public version = "0.3";

    uint256 private constant ONE = 1;
    uint8 private constant MIN_PRECISION = 32;
    uint8 private constant MAX_PRECISION = 127;

    /**
     * The values below depend on MAX_PRECISION. If you choose to change it:
     * Apply the same change in file 'PrintIntScalingFactors.py', run it and paste the results below.
     */
    uint256 private constant FIXED_1 = 0x080000000000000000000000000000000;
    uint256 private constant FIXED_2 = 0x100000000000000000000000000000000;
    uint256 private constant MAX_NUM = 0x200000000000000000000000000000000;

    /**
     * Auto-generated via 'PrintLn2ScalingFactors.py'
     */
    uint256 private constant LN2_NUMERATOR = 0x3f80fe03f80fe03f80fe03f80fe03f8;
    uint256 private constant LN2_DENOMINATOR = 0x5b9de1d10bf4103d647b0955897ba80;

    /**
     * Auto-generated via 'PrintFunctionOptimalLog.py' and 'PrintFunctionOptimalExp.py'
     */
    uint256 private constant OPT_LOG_MAX_VAL = 0x15bf0a8b1457695355fb8ac404e7a79e3;
    uint256 private constant OPT_EXP_MAX_VAL = 0x800000000000000000000000000000000;

    /**
     * The values below depend on MIN_PRECISION and MAX_PRECISION. If you choose to change either one of them:
     * Apply the same change in file 'PrintFunctionBancorFormula.py', run it and paste the results below.
     */
    uint256[128] private maxExpArray;

    constructor() public {
        //  maxExpArray[0] = 0x6bffffffffffffffffffffffffffffffff;
        //  maxExpArray[1] = 0x67ffffffffffffffffffffffffffffffff;
        //  maxExpArray[2] = 0x637fffffffffffffffffffffffffffffff;
        //  maxExpArray[3] = 0x5f6fffffffffffffffffffffffffffffff;
        //  maxExpArray[4] = 0x5b77ffffffffffffffffffffffffffffff;
        //  maxExpArray[5] = 0x57b3ffffffffffffffffffffffffffffff;
        //  maxExpArray[6] = 0x5419ffffffffffffffffffffffffffffff;
        //  maxExpArray[7] = 0x50a2ffffffffffffffffffffffffffffff;
        //  maxExpArray[8] = 0x4d517fffffffffffffffffffffffffffff;
        //  maxExpArray[9] = 0x4a233fffffffffffffffffffffffffffff;
        //  maxExpArray[10] = 0x47165fffffffffffffffffffffffffffff;
        //  maxExpArray[11] = 0x4429afffffffffffffffffffffffffffff;
        //  maxExpArray[12] = 0x415bc7ffffffffffffffffffffffffffff;
        //  maxExpArray[13] = 0x3eab73ffffffffffffffffffffffffffff;
        //  maxExpArray[14] = 0x3c1771ffffffffffffffffffffffffffff;
        //  maxExpArray[15] = 0x399e96ffffffffffffffffffffffffffff;
        //  maxExpArray[16] = 0x373fc47fffffffffffffffffffffffffff;
        //  maxExpArray[17] = 0x34f9e8ffffffffffffffffffffffffffff;
        //  maxExpArray[18] = 0x32cbfd5fffffffffffffffffffffffffff;
        //  maxExpArray[19] = 0x30b5057fffffffffffffffffffffffffff;
        //  maxExpArray[20] = 0x2eb40f9fffffffffffffffffffffffffff;
        //  maxExpArray[21] = 0x2cc8340fffffffffffffffffffffffffff;
        //  maxExpArray[22] = 0x2af09481ffffffffffffffffffffffffff;
        //  maxExpArray[23] = 0x292c5bddffffffffffffffffffffffffff;
        //  maxExpArray[24] = 0x277abdcdffffffffffffffffffffffffff;
        //  maxExpArray[25] = 0x25daf6657fffffffffffffffffffffffff;
        //  maxExpArray[26] = 0x244c49c65fffffffffffffffffffffffff;
        //  maxExpArray[27] = 0x22ce03cd5fffffffffffffffffffffffff;
        //  maxExpArray[28] = 0x215f77c047ffffffffffffffffffffffff;
        //  maxExpArray[29] = 0x1fffffffffffffffffffffffffffffffff;
        //  maxExpArray[30] = 0x1eaefdbdabffffffffffffffffffffffff;
        //  maxExpArray[31] = 0x1d6bd8b2ebffffffffffffffffffffffff;
        maxExpArray[32] = 0x1c35fedd14ffffffffffffffffffffffff;
        maxExpArray[33] = 0x1b0ce43b323fffffffffffffffffffffff;
        maxExpArray[34] = 0x19f0028ec1ffffffffffffffffffffffff;
        maxExpArray[35] = 0x18ded91f0e7fffffffffffffffffffffff;
        maxExpArray[36] = 0x17d8ec7f0417ffffffffffffffffffffff;
        maxExpArray[37] = 0x16ddc6556cdbffffffffffffffffffffff;
        maxExpArray[38] = 0x15ecf52776a1ffffffffffffffffffffff;
        maxExpArray[39] = 0x15060c256cb2ffffffffffffffffffffff;
        maxExpArray[40] = 0x1428a2f98d72ffffffffffffffffffffff;
        maxExpArray[41] = 0x13545598e5c23fffffffffffffffffffff;
        maxExpArray[42] = 0x1288c4161ce1dfffffffffffffffffffff;
        maxExpArray[43] = 0x11c592761c666fffffffffffffffffffff;
        maxExpArray[44] = 0x110a688680a757ffffffffffffffffffff;
        maxExpArray[45] = 0x1056f1b5bedf77ffffffffffffffffffff;
        maxExpArray[46] = 0x0faadceceeff8bffffffffffffffffffff;
        maxExpArray[47] = 0x0f05dc6b27edadffffffffffffffffffff;
        maxExpArray[48] = 0x0e67a5a25da4107fffffffffffffffffff;
        maxExpArray[49] = 0x0dcff115b14eedffffffffffffffffffff;
        maxExpArray[50] = 0x0d3e7a392431239fffffffffffffffffff;
        maxExpArray[51] = 0x0cb2ff529eb71e4fffffffffffffffffff;
        maxExpArray[52] = 0x0c2d415c3db974afffffffffffffffffff;
        maxExpArray[53] = 0x0bad03e7d883f69bffffffffffffffffff;
        maxExpArray[54] = 0x0b320d03b2c343d5ffffffffffffffffff;
        maxExpArray[55] = 0x0abc25204e02828dffffffffffffffffff;
        maxExpArray[56] = 0x0a4b16f74ee4bb207fffffffffffffffff;
        maxExpArray[57] = 0x09deaf736ac1f569ffffffffffffffffff;
        maxExpArray[58] = 0x0976bd9952c7aa957fffffffffffffffff;
        maxExpArray[59] = 0x09131271922eaa606fffffffffffffffff;
        maxExpArray[60] = 0x08b380f3558668c46fffffffffffffffff;
        maxExpArray[61] = 0x0857ddf0117efa215bffffffffffffffff;
        maxExpArray[62] = 0x07ffffffffffffffffffffffffffffffff;
        maxExpArray[63] = 0x07abbf6f6abb9d087fffffffffffffffff;
        maxExpArray[64] = 0x075af62cbac95f7dfa7fffffffffffffff;
        maxExpArray[65] = 0x070d7fb7452e187ac13fffffffffffffff;
        maxExpArray[66] = 0x06c3390ecc8af379295fffffffffffffff;
        maxExpArray[67] = 0x067c00a3b07ffc01fd6fffffffffffffff;
        maxExpArray[68] = 0x0637b647c39cbb9d3d27ffffffffffffff;
        maxExpArray[69] = 0x05f63b1fc104dbd39587ffffffffffffff;
        maxExpArray[70] = 0x05b771955b36e12f7235ffffffffffffff;
        maxExpArray[71] = 0x057b3d49dda84556d6f6ffffffffffffff;
        maxExpArray[72] = 0x054183095b2c8ececf30ffffffffffffff;
        maxExpArray[73] = 0x050a28be635ca2b888f77fffffffffffff;
        maxExpArray[74] = 0x04d5156639708c9db33c3fffffffffffff;
        maxExpArray[75] = 0x04a23105873875bd52dfdfffffffffffff;
        maxExpArray[76] = 0x0471649d87199aa990756fffffffffffff;
        maxExpArray[77] = 0x04429a21a029d4c1457cfbffffffffffff;
        maxExpArray[78] = 0x0415bc6d6fb7dd71af2cb3ffffffffffff;
        maxExpArray[79] = 0x03eab73b3bbfe282243ce1ffffffffffff;
        maxExpArray[80] = 0x03c1771ac9fb6b4c18e229ffffffffffff;
        maxExpArray[81] = 0x0399e96897690418f785257fffffffffff;
        maxExpArray[82] = 0x0373fc456c53bb779bf0ea9fffffffffff;
        maxExpArray[83] = 0x034f9e8e490c48e67e6ab8bfffffffffff;
        maxExpArray[84] = 0x032cbfd4a7adc790560b3337ffffffffff;
        maxExpArray[85] = 0x030b50570f6e5d2acca94613ffffffffff;
        maxExpArray[86] = 0x02eb40f9f620fda6b56c2861ffffffffff;
        maxExpArray[87] = 0x02cc8340ecb0d0f520a6af58ffffffffff;
        maxExpArray[88] = 0x02af09481380a0a35cf1ba02ffffffffff;
        maxExpArray[89] = 0x0292c5bdd3b92ec810287b1b3fffffffff;
        maxExpArray[90] = 0x0277abdcdab07d5a77ac6d6b9fffffffff;
        maxExpArray[91] = 0x025daf6654b1eaa55fd64df5efffffffff;
        maxExpArray[92] = 0x0244c49c648baa98192dce88b7ffffffff;
        maxExpArray[93] = 0x022ce03cd5619a311b2471268bffffffff;
        maxExpArray[94] = 0x0215f77c045fbe885654a44a0fffffffff;
        maxExpArray[95] = 0x01ffffffffffffffffffffffffffffffff;
        maxExpArray[96] = 0x01eaefdbdaaee7421fc4d3ede5ffffffff;
        maxExpArray[97] = 0x01d6bd8b2eb257df7e8ca57b09bfffffff;
        maxExpArray[98] = 0x01c35fedd14b861eb0443f7f133fffffff;
        maxExpArray[99] = 0x01b0ce43b322bcde4a56e8ada5afffffff;
        maxExpArray[100] = 0x019f0028ec1fff007f5a195a39dfffffff;
        maxExpArray[101] = 0x018ded91f0e72ee74f49b15ba527ffffff;
        maxExpArray[102] = 0x017d8ec7f04136f4e5615fd41a63ffffff;
        maxExpArray[103] = 0x016ddc6556cdb84bdc8d12d22e6fffffff;
        maxExpArray[104] = 0x015ecf52776a1155b5bd8395814f7fffff;
        maxExpArray[105] = 0x015060c256cb23b3b3cc3754cf40ffffff;
        maxExpArray[106] = 0x01428a2f98d728ae223ddab715be3fffff;
        maxExpArray[107] = 0x013545598e5c23276ccf0ede68034fffff;
        maxExpArray[108] = 0x01288c4161ce1d6f54b7f61081194fffff;
        maxExpArray[109] = 0x011c592761c666aa641d5a01a40f17ffff;
        maxExpArray[110] = 0x0110a688680a7530515f3e6e6cfdcdffff;
        maxExpArray[111] = 0x01056f1b5bedf75c6bcb2ce8aed428ffff;
        maxExpArray[112] = 0x00faadceceeff8a0890f3875f008277fff;
        maxExpArray[113] = 0x00f05dc6b27edad306388a600f6ba0bfff;
        maxExpArray[114] = 0x00e67a5a25da41063de1495d5b18cdbfff;
        maxExpArray[115] = 0x00dcff115b14eedde6fc3aa5353f2e4fff;
        maxExpArray[116] = 0x00d3e7a3924312399f9aae2e0f868f8fff;
        maxExpArray[117] = 0x00cb2ff529eb71e41582cccd5a1ee26fff;
        maxExpArray[118] = 0x00c2d415c3db974ab32a51840c0b67edff;
        maxExpArray[119] = 0x00bad03e7d883f69ad5b0a186184e06bff;
        maxExpArray[120] = 0x00b320d03b2c343d4829abd6075f0cc5ff;
        maxExpArray[121] = 0x00abc25204e02828d73c6e80bcdb1a95bf;
        maxExpArray[122] = 0x00a4b16f74ee4bb2040a1ec6c15fbbf2df;
        maxExpArray[123] = 0x009deaf736ac1f569deb1b5ae3f36c130f;
        maxExpArray[124] = 0x00976bd9952c7aa957f5937d790ef65037;
        maxExpArray[125] = 0x009131271922eaa6064b73a22d0bd4f2bf;
        maxExpArray[126] = 0x008b380f3558668c46c91c49a2f8e967b9;
        maxExpArray[127] = 0x00857ddf0117efa215952912839f6473e6;
    }

    /**
     * General Description:
     *     Determine a value of precision.
     *     Calculate an integer approximation of (_baseN / _baseD) ^ (_expN / _expD) * 2 ^ precision.
     *     Return the result along with the precision used.
     *  Detailed Description:
     *     Instead of calculating "base ^ exp", we calculate "e ^ (log(base) * exp)".
     *     The value of "log(base)" is represented with an integer slightly smaller than "log(base) * 2 ^ precision".
     *     The larger "precision" is, the more accurately this value represents the real value.
     *     However, the larger "precision" is, the more bits are required in order to store this value.
     *     And the exponentiation function, which takes "x" and calculates "e ^ x", is limited to a maximum exponent (maximum value of "x").
     *     This maximum exponent depends on the "precision" used, and it is given by "maxExpArray[precision] >> (MAX_PRECISION - precision)".
     *     Hence we need to determine the highest precision which can be used for the given input, before calling the exponentiation function.
     *     This allows us to compute "base ^ exp" with maximum accuracy and without exceeding 256 bits in any of the intermediate computations.
     *     This functions assumes that "_expN < 2 ^ 256 / log(MAX_NUM - 1)", otherwise the multiplication should be replaced with a "safeMul".
     */
    function power(uint256 _baseN, uint256 _baseD, uint32 _expN, uint32 _expD) internal view returns (uint256, uint8) {
        assert(_baseN < MAX_NUM);
        require(_baseN >= _baseD, "Bases < 1 are not supported.");

        uint256 baseLog;
        uint256 base = _baseN * FIXED_1 / _baseD;
        if (base < OPT_LOG_MAX_VAL) {
            baseLog = optimalLog(base);
        } else {
            baseLog = generalLog(base);
        }

        uint256 baseLogTimesExp = baseLog * _expN / _expD;
        if (baseLogTimesExp < OPT_EXP_MAX_VAL) {
            return (optimalExp(baseLogTimesExp), MAX_PRECISION);
        } else {
            uint8 precision = findPositionInMaxExpArray(baseLogTimesExp);
            return (generalExp(baseLogTimesExp >> (MAX_PRECISION - precision), precision), precision);
        }
    }

    /**
     * Compute log(x / FIXED_1) * FIXED_1.
     *   This functions assumes that "x >= FIXED_1", because the output would be negative otherwise.
     */
    function generalLog(uint256 _x) internal pure returns (uint256) {
        uint256 res = 0;
        uint256 x = _x;

        // If x >= 2, then we compute the integer part of log2(x), which is larger than 0.
        if (x >= FIXED_2) {
            uint8 count = floorLog2(x / FIXED_1);
            x >>= count; // now x < 2
            res = count * FIXED_1;
        }

        // If x > 1, then we compute the fraction part of log2(x), which is larger than 0.
        if (x > FIXED_1) {
            for (uint8 i = MAX_PRECISION; i > 0; --i) {
                x = (x * x) / FIXED_1; // now 1 < x < 4
                if (x >= FIXED_2) {
                    x >>= 1; // now 1 < x < 2
                    res += ONE << (i - 1);
                }
            }
        }

        return res * LN2_NUMERATOR / LN2_DENOMINATOR;
    }

    /**
     * Compute the largest integer smaller than or equal to the binary logarithm of the input.
     */
    function floorLog2(uint256 _n) internal pure returns (uint8) {
        uint8 res = 0;
        uint256 n = _n;

        if (n < 256) {
            // At most 8 iterations
            while (n > 1) {
                n >>= 1;
                res += 1;
            }
        } else {
            // Exactly 8 iterations
            for (uint8 s = 128; s > 0; s >>= 1) {
                if (n >= (ONE << s)) {
                    n >>= s;
                    res |= s;
                }
            }
        }

        return res;
    }

    /**
     * The global "maxExpArray" is sorted in descending order, and therefore the following statements are equivalent:
     *   - This function finds the position of [the smallest value in "maxExpArray" larger than or equal to "x"]
     *   - This function finds the highest position of [a value in "maxExpArray" larger than or equal to "x"]
     */
    function findPositionInMaxExpArray(uint256 _x) internal view returns (uint8) {
        uint8 lo = MIN_PRECISION;
        uint8 hi = MAX_PRECISION;

        while (lo + 1 < hi) {
            uint8 mid = (lo + hi) / 2;
            if (maxExpArray[mid] >= _x) {
                lo = mid;
            } else {
                hi = mid;
            }
        }

        if (maxExpArray[hi] >= _x) {
            return hi;
        }
        if (maxExpArray[lo] >= _x) {
            return lo;
        }

        assert(false);
        return 0;
    }

    /* solium-disable */
    /**
     * This function can be auto-generated by the script 'PrintFunctionGeneralExp.py'.
     *    It approximates "e ^ x" via maclaurin summation: "(x^0)/0! + (x^1)/1! + ... + (x^n)/n!".
     *    It returns "e ^ (x / 2 ^ precision) * 2 ^ precision", that is, the result is upshifted for accuracy.
     *    The global "maxExpArray" maps each "precision" to "((maximumExponent + 1) << (MAX_PRECISION - precision)) - 1".
     *    The maximum permitted value for "x" is therefore given by "maxExpArray[precision] >> (MAX_PRECISION - precision)".
     */
    function generalExp(uint256 _x, uint8 _precision) internal pure returns (uint256) {
        uint256 xi = _x;
        uint256 res = 0;

        xi = (xi * _x) >> _precision;
        res += xi * 0x3442c4e6074a82f1797f72ac0000000; // add x^02 * (33! / 02!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x116b96f757c380fb287fd0e40000000; // add x^03 * (33! / 03!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x045ae5bdd5f0e03eca1ff4390000000; // add x^04 * (33! / 04!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00defabf91302cd95b9ffda50000000; // add x^05 * (33! / 05!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x002529ca9832b22439efff9b8000000; // add x^06 * (33! / 06!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00054f1cf12bd04e516b6da88000000; // add x^07 * (33! / 07!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000a9e39e257a09ca2d6db51000000; // add x^08 * (33! / 08!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000012e066e7b839fa050c309000000; // add x^09 * (33! / 09!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000001e33d7d926c329a1ad1a800000; // add x^10 * (33! / 10!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000002bee513bdb4a6b19b5f800000; // add x^11 * (33! / 11!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000003a9316fa79b88eccf2a00000; // add x^12 * (33! / 12!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000048177ebe1fa812375200000; // add x^13 * (33! / 13!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000005263fe90242dcbacf00000; // add x^14 * (33! / 14!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000000000057e22099c030d94100000; // add x^15 * (33! / 15!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000057e22099c030d9410000; // add x^16 * (33! / 16!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000052b6b54569976310000; // add x^17 * (33! / 17!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000004985f67696bf748000; // add x^18 * (33! / 18!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000000000000003dea12ea99e498000; // add x^19 * (33! / 19!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000000031880f2214b6e000; // add x^20 * (33! / 20!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000000000000000025bcff56eb36000; // add x^21 * (33! / 21!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000000000000000001b722e10ab1000; // add x^22 * (33! / 22!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000000000001317c70077000; // add x^23 * (33! / 23!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000000000000cba84aafa00; // add x^24 * (33! / 24!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000000000000082573a0a00; // add x^25 * (33! / 25!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000000000000005035ad900; // add x^26 * (33! / 26!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x000000000000000000000002f881b00; // add x^27 * (33! / 27!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000000000000000001b29340; // add x^28 * (33! / 28!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x00000000000000000000000000efc40; // add x^29 * (33! / 29!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000000000000000000007fe0; // add x^30 * (33! / 30!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000000000000000000000420; // add x^31 * (33! / 31!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000000000000000000000021; // add x^32 * (33! / 32!)
        xi = (xi * _x) >> _precision;
        res += xi * 0x0000000000000000000000000000001; // add x^33 * (33! / 33!)

        return res / 0x688589cc0e9505e2f2fee5580000000 + _x + (ONE << _precision); // divide by 33! and then add x^1 / 1! + x^0 / 0!
    }

    /**
     * Return log(x / FIXED_1) * FIXED_1
     *    Input range: FIXED_1 <= x <= LOG_EXP_MAX_VAL - 1
     *    Auto-generated via 'PrintFunctionOptimalLog.py'
     */
    function optimalLog(uint256 x) internal pure returns (uint256) {
        uint256 res = 0;

        uint256 y;
        uint256 z;
        uint256 w;

        if (x >= 0xd3094c70f034de4b96ff7d5b6f99fcd8) {
            res += 0x40000000000000000000000000000000;
            x = x * FIXED_1 / 0xd3094c70f034de4b96ff7d5b6f99fcd8;
        }
        if (x >= 0xa45af1e1f40c333b3de1db4dd55f29a7) {
            res += 0x20000000000000000000000000000000;
            x = x * FIXED_1 / 0xa45af1e1f40c333b3de1db4dd55f29a7;
        }
        if (x >= 0x910b022db7ae67ce76b441c27035c6a1) {
            res += 0x10000000000000000000000000000000;
            x = x * FIXED_1 / 0x910b022db7ae67ce76b441c27035c6a1;
        }
        if (x >= 0x88415abbe9a76bead8d00cf112e4d4a8) {
            res += 0x08000000000000000000000000000000;
            x = x * FIXED_1 / 0x88415abbe9a76bead8d00cf112e4d4a8;
        }
        if (x >= 0x84102b00893f64c705e841d5d4064bd3) {
            res += 0x04000000000000000000000000000000;
            x = x * FIXED_1 / 0x84102b00893f64c705e841d5d4064bd3;
        }
        if (x >= 0x8204055aaef1c8bd5c3259f4822735a2) {
            res += 0x02000000000000000000000000000000;
            x = x * FIXED_1 / 0x8204055aaef1c8bd5c3259f4822735a2;
        }
        if (x >= 0x810100ab00222d861931c15e39b44e99) {
            res += 0x01000000000000000000000000000000;
            x = x * FIXED_1 / 0x810100ab00222d861931c15e39b44e99;
        }
        if (x >= 0x808040155aabbbe9451521693554f733) {
            res += 0x00800000000000000000000000000000;
            x = x * FIXED_1 / 0x808040155aabbbe9451521693554f733;
        }

        z = y = x - FIXED_1;
        w = y * y / FIXED_1;
        res += z * (0x100000000000000000000000000000000 - y) / 0x100000000000000000000000000000000;
        z = z * w / FIXED_1;
        res += z * (0x0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa - y) / 0x200000000000000000000000000000000;
        z = z * w / FIXED_1;
        res += z * (0x099999999999999999999999999999999 - y) / 0x300000000000000000000000000000000;
        z = z * w / FIXED_1;
        res += z * (0x092492492492492492492492492492492 - y) / 0x400000000000000000000000000000000;
        z = z * w / FIXED_1;
        res += z * (0x08e38e38e38e38e38e38e38e38e38e38e - y) / 0x500000000000000000000000000000000;
        z = z * w / FIXED_1;
        res += z * (0x08ba2e8ba2e8ba2e8ba2e8ba2e8ba2e8b - y) / 0x600000000000000000000000000000000;
        z = z * w / FIXED_1;
        res += z * (0x089d89d89d89d89d89d89d89d89d89d89 - y) / 0x700000000000000000000000000000000;
        z = z * w / FIXED_1;
        res += z * (0x088888888888888888888888888888888 - y) / 0x800000000000000000000000000000000;

        return res;
    }

    /**
     * Return e ^ (x / FIXED_1) * FIXED_1
     *    Input range: 0 <= x <= OPT_EXP_MAX_VAL - 1
     *    Auto-generated via 'PrintFunctionOptimalExp.py'
     */
    function optimalExp(uint256 x) internal pure returns (uint256) {
        uint256 res = 0;

        uint256 y;
        uint256 z;

        z = y = x % 0x10000000000000000000000000000000;
        z = z * y / FIXED_1;
        res += z * 0x10e1b3be415a0000; // add y^02 * (20! / 02!)
        z = z * y / FIXED_1;
        res += z * 0x05a0913f6b1e0000; // add y^03 * (20! / 03!)
        z = z * y / FIXED_1;
        res += z * 0x0168244fdac78000; // add y^04 * (20! / 04!)
        z = z * y / FIXED_1;
        res += z * 0x004807432bc18000; // add y^05 * (20! / 05!)
        z = z * y / FIXED_1;
        res += z * 0x000c0135dca04000; // add y^06 * (20! / 06!)
        z = z * y / FIXED_1;
        res += z * 0x0001b707b1cdc000; // add y^07 * (20! / 07!)
        z = z * y / FIXED_1;
        res += z * 0x000036e0f639b800; // add y^08 * (20! / 08!)
        z = z * y / FIXED_1;
        res += z * 0x00000618fee9f800; // add y^09 * (20! / 09!)
        z = z * y / FIXED_1;
        res += z * 0x0000009c197dcc00; // add y^10 * (20! / 10!)
        z = z * y / FIXED_1;
        res += z * 0x0000000e30dce400; // add y^11 * (20! / 11!)
        z = z * y / FIXED_1;
        res += z * 0x000000012ebd1300; // add y^12 * (20! / 12!)
        z = z * y / FIXED_1;
        res += z * 0x0000000017499f00; // add y^13 * (20! / 13!)
        z = z * y / FIXED_1;
        res += z * 0x0000000001a9d480; // add y^14 * (20! / 14!)
        z = z * y / FIXED_1;
        res += z * 0x00000000001c6380; // add y^15 * (20! / 15!)
        z = z * y / FIXED_1;
        res += z * 0x000000000001c638; // add y^16 * (20! / 16!)
        z = z * y / FIXED_1;
        res += z * 0x0000000000001ab8; // add y^17 * (20! / 17!)
        z = z * y / FIXED_1;
        res += z * 0x000000000000017c; // add y^18 * (20! / 18!)
        z = z * y / FIXED_1;
        res += z * 0x0000000000000014; // add y^19 * (20! / 19!)
        z = z * y / FIXED_1;
        res += z * 0x0000000000000001; // add y^20 * (20! / 20!)
        res = res / 0x21c3677c82b40000 + y + FIXED_1; // divide by 20! and then add y^1 / 1! + y^0 / 0!

        if ((x & 0x010000000000000000000000000000000) != 0) {
            res = res * 0x1c3d6a24ed82218787d624d3e5eba95f9 / 0x18ebef9eac820ae8682b9793ac6d1e776;
        }
        if ((x & 0x020000000000000000000000000000000) != 0) {
            res = res * 0x18ebef9eac820ae8682b9793ac6d1e778 / 0x1368b2fc6f9609fe7aceb46aa619baed4;
        }
        if ((x & 0x040000000000000000000000000000000) != 0) {
            res = res * 0x1368b2fc6f9609fe7aceb46aa619baed5 / 0x0bc5ab1b16779be3575bd8f0520a9f21f;
        }
        if ((x & 0x080000000000000000000000000000000) != 0) {
            res = res * 0x0bc5ab1b16779be3575bd8f0520a9f21e / 0x0454aaa8efe072e7f6ddbab84b40a55c9;
        }
        if ((x & 0x100000000000000000000000000000000) != 0) {
            res = res * 0x0454aaa8efe072e7f6ddbab84b40a55c5 / 0x00960aadc109e7a3bf4578099615711ea;
        }
        if ((x & 0x200000000000000000000000000000000) != 0) {
            res = res * 0x00960aadc109e7a3bf4578099615711d7 / 0x0002bf84208204f5977f9a8cf01fdce3d;
        }
        if ((x & 0x400000000000000000000000000000000) != 0) {
            res = res * 0x0002bf84208204f5977f9a8cf01fdc307 / 0x0000003c6ab775dd0b95b4cbee7e65d11;
        }

        return res;
    }
    /* solium-enable */
}

// File: lib/solady/src/utils/LibBit.sol



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

/// @notice Library for bit twiddling and boolean operations.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/LibBit.sol)
/// @author Inspired by (https://graphics.stanford.edu/~seander/bithacks.html)
library LibBit {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  BIT TWIDDLING OPERATIONS                  */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Find last set.
    /// Returns the index of the most significant bit of `x`,
    /// counting from the least significant bit position.
    /// If `x` is zero, returns 256.
    /// Equivalent to `log2(x)`, but without reverting for the zero case.
    function fls(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            r := shl(8, iszero(x))

            r := or(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))))

            // For the remaining 32 bits, use a De Bruijn lookup.
            x := shr(r, x)
            x := or(x, shr(1, x))
            x := or(x, shr(2, x))
            x := or(x, shr(4, x))
            x := or(x, shr(8, x))
            x := or(x, shr(16, x))

            // forgefmt: disable-next-item
            r := or(r, byte(shr(251, mul(x, shl(224, 0x07c4acdd))),
                0x0009010a0d15021d0b0e10121619031e080c141c0f111807131b17061a05041f))
        }
    }

    /// @dev Count leading zeros.
    /// Returns the number of zeros preceding the most significant one bit.
    /// If `x` is zero, returns 256.
    function clz(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            let t := add(iszero(x), 255)

            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))))

            // For the remaining 32 bits, use a De Bruijn lookup.
            x := shr(r, x)
            x := or(x, shr(1, x))
            x := or(x, shr(2, x))
            x := or(x, shr(4, x))
            x := or(x, shr(8, x))
            x := or(x, shr(16, x))

            // forgefmt: disable-next-item
            r := sub(t, or(r, byte(shr(251, mul(x, shl(224, 0x07c4acdd))),
                0x0009010a0d15021d0b0e10121619031e080c141c0f111807131b17061a05041f)))
        }
    }

    /// @dev Find first set.
    /// Returns the index of the least significant bit of `x`,
    /// counting from the least significant bit position.
    /// If `x` is zero, returns 256.
    /// Equivalent to `ctz` (count trailing zeros), which gives
    /// the number of zeros following the least significant one bit.
    function ffs(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            r := shl(8, iszero(x))

            // Isolate the least significant bit.
            x := and(x, add(not(x), 1))

            r := or(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))))

            // For the remaining 32 bits, use a De Bruijn lookup.
            // forgefmt: disable-next-item
            r := or(r, byte(shr(251, mul(shr(r, x), shl(224, 0x077cb531))), 
                0x00011c021d0e18031e16140f191104081f1b0d17151310071a0c12060b050a09))
        }
    }

    /// @dev Returns the number of set bits in `x`.
    function popCount(uint256 x) internal pure returns (uint256 c) {
        /// @solidity memory-safe-assembly
        assembly {
            let max := not(0)
            let isMax := eq(x, max)
            x := sub(x, and(shr(1, x), div(max, 3)))
            x := add(and(x, div(max, 5)), and(shr(2, x), div(max, 5)))
            x := and(add(x, shr(4, x)), div(max, 17))
            c := or(shl(8, isMax), shr(248, mul(x, div(max, 255))))
        }
    }

    /// @dev Returns whether `x` is a power of 2.
    function isPo2(uint256 x) internal pure returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `x && !(x & (x - 1))`.
            result := iszero(add(and(x, sub(x, 1)), iszero(x)))
        }
    }

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

    /// @dev Returns `x & y`.
    function and(bool x, bool y) internal pure returns (bool z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := and(x, y)
        }
    }

    /// @dev Returns `x | y`.
    function or(bool x, bool y) internal pure returns (bool z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := or(x, y)
        }
    }

    /// @dev Returns a non-zero number if `b` is true, else 0.
    /// If `b` is from plain Solidity, the non-zero number will be 1.
    function toUint(bool b) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := b
        }
    }
}

// File: lib/solmate/src/utils/SignedWadMath.sol



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

/// @notice Signed 18 decimal fixed point (wad) arithmetic library.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/SignedWadMath.sol)
/// @author Modified from Remco Bloemen (https://xn--2-umb.com/22/exp-ln/index.html)

/// @dev Will not revert on overflow, only use where overflow is not possible.
function toWadUnsafe(uint256 x) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Multiply x by 1e18.
        r := mul(x, 1000000000000000000)
    }
}

/// @dev Takes an integer amount of seconds and converts it to a wad amount of days.
/// @dev Will not revert on overflow, only use where overflow is not possible.
/// @dev Not meant for negative second amounts, it assumes x is positive.
function toDaysWadUnsafe(uint256 x) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Multiply x by 1e18 and then divide it by 86400.
        r := div(mul(x, 1000000000000000000), 86400)
    }
}

/// @dev Takes a wad amount of days and converts it to an integer amount of seconds.
/// @dev Will not revert on overflow, only use where overflow is not possible.
/// @dev Not meant for negative day amounts, it assumes x is positive.
function fromDaysWadUnsafe(int256 x) pure returns (uint256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Multiply x by 86400 and then divide it by 1e18.
        r := div(mul(x, 86400), 1000000000000000000)
    }
}

/// @dev Will not revert on overflow, only use where overflow is not possible.
function unsafeWadMul(int256 x, int256 y) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Multiply x by y and divide by 1e18.
        r := sdiv(mul(x, y), 1000000000000000000)
    }
}

/// @dev Will return 0 instead of reverting if y is zero and will
/// not revert on overflow, only use where overflow is not possible.
function unsafeWadDiv(int256 x, int256 y) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Multiply x by 1e18 and divide it by y.
        r := sdiv(mul(x, 1000000000000000000), y)
    }
}

function wadMul(int256 x, int256 y) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Store x * y in r for now.
        r := mul(x, y)

        // Equivalent to require(x == 0 || (x * y) / x == y)
        if iszero(or(iszero(x), eq(sdiv(r, x), y))) {
            revert(0, 0)
        }

        // Scale the result down by 1e18.
        r := sdiv(r, 1000000000000000000)
    }
}

function wadDiv(int256 x, int256 y) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Store x * 1e18 in r for now.
        r := mul(x, 1000000000000000000)

        // Equivalent to require(y != 0 && ((x * 1e18) / 1e18 == x))
        if iszero(and(iszero(iszero(y)), eq(sdiv(r, 1000000000000000000), x))) {
            revert(0, 0)
        }

        // Divide r by y.
        r := sdiv(r, y)
    }
}

/// @dev Will not work with negative bases, only use when x is positive.
function wadPow(int256 x, int256 y) pure returns (int256) {
    // Equivalent to x to the power of y because x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)
    return wadExp((wadLn(x) * y) / 1e18); // Using ln(x) means x must be greater than 0.
}

function wadExp(int256 x) pure returns (int256 r) {
    unchecked {
        // When the result is < 0.5 we return zero. This happens when
        // x <= floor(log(0.5e18) * 1e18) ~ -42e18
        if (x <= -42139678854452767551) return 0;

        // When the result is > (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 (x >= 135305999368893231589) revert("EXP_OVERFLOW");

        // 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));
    }
}

function wadLn(int256 x) pure returns (int256 r) {
    unchecked {
        require(x > 0, "UNDEFINED");

        // 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.

        /// @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))))
            r := or(r, shl(2, lt(0xf, shr(r, x))))
            r := or(r, shl(1, lt(0x3, shr(r, x))))
            r := or(r, lt(0x1, shr(r, x)))
        }

        // Reduce range of x to (1, 2) * 2**96
        // ln(2^k * x) = k * ln(2) + ln(x)
        int256 k = r - 96;
        x <<= uint256(159 - k);
        x = int256(uint256(x) >> 159);

        // Evaluate using a (8, 8)-term rational approximation.
        // p is made monic, we will multiply by a scale factor later.
        int256 p = x + 3273285459638523848632254066296;
        p = ((p * x) >> 96) + 24828157081833163892658089445524;
        p = ((p * x) >> 96) + 43456485725739037958740375743393;
        p = ((p * x) >> 96) - 11111509109440967052023855526967;
        p = ((p * x) >> 96) - 45023709667254063763336534515857;
        p = ((p * x) >> 96) - 14706773417378608786704636184526;
        p = p * x - (795164235651350426258249787498 << 96);

        // 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.
        int256 q = x + 5573035233440673466300451813936;
        q = ((q * x) >> 96) + 71694874799317883764090561454958;
        q = ((q * x) >> 96) + 283447036172924575727196451306956;
        q = ((q * x) >> 96) + 401686690394027663651624208769553;
        q = ((q * x) >> 96) + 204048457590392012362485061816622;
        q = ((q * x) >> 96) + 31853899698501571402653359427138;
        q = ((q * x) >> 96) + 909429971244387300277376558375;
        /// @solidity memory-safe-assembly
        assembly {
            // Div in assembly because solidity adds a zero check despite the unchecked.
            // The q polynomial is known not to have zeros in the domain.
            // No scaling required because p is already 2**96 too large.
            r := sdiv(p, q)
        }

        // r 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

        // mul s * 5e18 * 2**96, base is now 5**18 * 2**192
        r *= 1677202110996718588342820967067443963516166;
        // add ln(2) * k * 5e18 * 2**192
        r += 16597577552685614221487285958193947469193820559219878177908093499208371 * k;
        // add ln(2**96 / 10**18) * 5e18 * 2**192
        r += 600920179829731861736702779321621459595472258049074101567377883020018308;
        // base conversion: mul 2**18 / 2**192
        r >>= 174;
    }
}

/// @dev Will return 0 instead of reverting if y is zero.
function unsafeDiv(int256 x, int256 y) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Divide x by y.
        r := sdiv(x, y)
    }
}

// File: lib/VRGDAs/src/VRGDA.sol



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

import {wadExp, wadLn, wadMul, unsafeWadMul, toWadUnsafe} from "solmate/utils/SignedWadMath.sol";

/// @title Variable Rate Gradual Dutch Auction
/// @author transmissions11 <t11s@paradigm.xyz>
/// @author FrankieIsLost <frankie@paradigm.xyz>
/// @notice Sell tokens roughly according to an issuance schedule.
abstract contract VRGDA {
    /*//////////////////////////////////////////////////////////////
                            VRGDA PARAMETERS
    //////////////////////////////////////////////////////////////*/

    /// @notice Target price for a token, to be scaled according to sales pace.
    /// @dev Represented as an 18 decimal fixed point number.
    int256 public immutable targetPrice;

    /// @dev Precomputed constant that allows us to rewrite a pow() as an exp().
    /// @dev Represented as an 18 decimal fixed point number.
    int256 internal immutable decayConstant;

    /// @notice Sets target price and per time unit price decay for the VRGDA.
    /// @param _targetPrice The target price for a token if sold on pace, scaled by 1e18.
    /// @param _priceDecayPercent The percent price decays per unit of time with no sales, scaled by 1e18.
    constructor(int256 _targetPrice, int256 _priceDecayPercent) {
        targetPrice = _targetPrice;

        decayConstant = wadLn(1e18 - _priceDecayPercent);

        // The decay constant must be negative for VRGDAs to work.
        require(decayConstant < 0, "NON_NEGATIVE_DECAY_CONSTANT");
    }

    /*//////////////////////////////////////////////////////////////
                              PRICING LOGIC
    //////////////////////////////////////////////////////////////*/

    /// @notice Calculate the price of a token according to the VRGDA formula.
    /// @param timeSinceStart Time passed since the VRGDA began, scaled by 1e18.
    /// @param sold The total number of tokens that have been sold so far.
    /// @return The price of a token according to VRGDA, scaled by 1e18.
    function getVRGDAPrice(int256 timeSinceStart, uint256 sold) public view virtual returns (uint256) {
        unchecked {
            // prettier-ignore
            return uint256(wadMul(targetPrice, wadExp(unsafeWadMul(decayConstant,
                // Theoretically calling toWadUnsafe with sold can silently overflow but under
                // any reasonable circumstance it will never be large enough. We use sold + 1 as
                // the VRGDA formula's n param represents the nth token and sold is the n-1th token.
                timeSinceStart - getTargetSaleTime(toWadUnsafe(sold + 1))
            ))));
        }
    }

    /// @dev Given a number of tokens sold, return the target time that number of tokens should be sold by.
    /// @param sold A number of tokens sold, scaled by 1e18, to get the corresponding target sale time for.
    /// @return The target time the tokens should be sold by, scaled by 1e18, where the time is
    /// relative, such that 0 means the tokens should be sold immediately when the VRGDA begins.
    function getTargetSaleTime(int256 sold) public view virtual returns (int256);
}