Contract Address Details

// SPDX-License-Identifier: GPLv3

pragma solidity 0.8.19;
pragma experimental ABIEncoderV2;

import "../libraries/SafeMath.sol";
import "@openzeppelin/contracts/access/Ownable.sol";
import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import "@openzeppelin/contracts/security/ReentrancyGuard.sol";

/// @notice The (older) MasterChef contract gives out a constant number of BBC tokens per block.
/// It is the only address with minting rights for BBC.
/// The idea for this MasterChef V2 (MCV2) contract is therefore to be the owner of a dummy token
/// that is deposited into the MasterChef V1 (MCV1) contract.
/// The allocation point for this pool on MCV1 is the total allocation point for all pools that receive incentives.
contract MasterChefV2 is Ownable, ReentrancyGuard {
    using SafeMath for uint256;
    using SafeERC20 for IERC20;

    /// @notice Info of each MCV2 user.
    /// `amount` LP token amount the user has provided.
    /// `rewardDebt` Used to calculate the correct amount of rewards. See explanation below.
    ///
    /// We do some fancy math here. Basically, any point in time, the amount of BBCs
    /// entitled to a user but is pending to be distributed is:
    ///
    ///   pending reward = (user share * pool.accBBCPerShare) - user.rewardDebt
    ///
    ///   Whenever a user deposits or withdraws LP tokens to a pool. Here's what happens:
    ///   1. The pool's `accBBCPerShare` (and `lastRewardBlock`) gets updated.
    ///   2. User receives the pending reward sent to his/her address.
    ///   3. User's `amount` gets updated. Pool's `totalBoostedShare` gets updated.
    ///   4. User's `rewardDebt` gets updated.
    struct UserInfo {
        uint256 amount;
        uint256 rewardDebt;
        uint256 boostMultiplier;
    }

    /// @notice Info of each MCV2 pool.
    /// `allocPoint` The amount of allocation points assigned to the pool.
    ///     Also known as the amount of "multipliers". Combined with `totalXAllocPoint`, it defines the % of
    ///     BBC rewards each pool gets.
    /// `accBBCPerShare` Accumulated BBCs per share, times 1e12.
    /// `lastRewardBlock` Last block number that pool update action is executed.
    /// `isRegular` The flag to set pool is regular or special. See below:
    ///     In MasterChef V2 farms are "regular pools". "special pools", which use a different sets of
    ///     `allocPoint` and their own `totalSpecialAllocPoint` are designed to handle the distribution of
    ///     the BBC rewards to all the 9inchSwap products.
    /// `totalBoostedShare` The total amount of user shares in each pool. After considering the share boosts.
    struct PoolInfo {
        uint256 accBBCPerShare;
        uint256 lastRewardBlock;
        uint256 allocPoint;
        uint256 totalBoostedShare;
        bool isRegular;
    }

    /// @notice Address of BBC contract.
    IERC20 public immutable BBC;

    /// @notice The only address can withdraw all the burn BBC.
    address public burnAdmin;
    /// @notice The contract handles the share boosts.
    address public boostContract;

    /// @notice Info of each MCV2 pool.
    PoolInfo[] public poolInfo;
    /// @notice Address of the LP token for each MCV2 pool.
    IERC20[] public lpToken;

    /// @notice Info of each pool user.
    mapping(uint256 => mapping(address => UserInfo)) public userInfo;
    /// @notice The whitelist of addresses allowed to deposit in special pools.
    mapping(address => bool) public whiteList;

    /// @notice

    /// @notice Total regular allocation points. Must be the sum of all regular pools' allocation points.
    uint256 public totalRegularAllocPoint;
    /// @notice Total special allocation points. Must be the sum of all special pools' allocation points.
    uint256 public totalSpecialAllocPoint;
    ///  @notice 40 BBCs per block in MCV1
    uint256 public constant MASTERCHEF_BBC_PER_BLOCK = 10 * 1e18;
    uint256 public constant ACC_BBC_PRECISION = 1e18;

    /// @notice Basic boost factor, none boosted user's boost factor
    uint256 public constant BOOST_PRECISION = 100 * 1e10;
    /// @notice Hard limit for maxmium boost factor, it must greater than BOOST_PRECISION
    uint256 public constant MAX_BOOST_PRECISION = 200 * 1e10;
    /// @notice total BBC rate = toBurn + toRegular + toSpecial
    uint256 public constant BBC_RATE_TOTAL_PRECISION = 1e12;
    /// @notice The last block number of BBC burn action being executed.
    /// @notice BBC distribute % for burn
    uint256 public bbcRateToBurn = 0; // 643750000000;
    /// @notice BBC distribute % for regular farm pool
    uint256 public bbcRateToRegularFarm = 9000000000000; // 62847222222
    /// @notice BBC distribute % for special pools
    uint256 public bbcRateToSpecialFarm = 1000000000000; // 293402777778

    uint256 public lastBurnedBlock;

    event Init();
    event AddPool(
        uint256 indexed pid,
        uint256 allocPoint,
        IERC20 indexed lpToken,
        bool isRegular
    );
    event SetPool(uint256 indexed pid, uint256 allocPoint);
    event UpdatePool(
        uint256 indexed pid,
        uint256 lastRewardBlock,
        uint256 lpSupply,
        uint256 accBBCPerShare
    );
    event Deposit(address indexed user, uint256 indexed pid, uint256 amount);
    event Withdraw(address indexed user, uint256 indexed pid, uint256 amount);
    event EmergencyWithdraw(
        address indexed user,
        uint256 indexed pid,
        uint256 amount
    );

    event UpdateBBCRate(
        uint256 burnRate,
        uint256 regularFarmRate,
        uint256 specialFarmRate
    );
    event UpdateBurnAdmin(address indexed oldAdmin, address indexed newAdmin);
    event UpdateWhiteList(address indexed user, bool isValid);
    event UpdateBoostContract(address indexed boostContract);
    event UpdateBoostMultiplier(
        address indexed user,
        uint256 pid,
        uint256 oldMultiplier,
        uint256 newMultiplier
    );

    /// @param _BBC The BBC token contract address.
    /// @param _burnAdmin The address of burn admin.
    constructor(IERC20 _BBC, address _burnAdmin) {
        require(
            address(_BBC) != address(0),
            "MasterChefV2: _BBC address cannot be 0"
        );
        require(
            _burnAdmin != address(0),
            "MasterChefV2: _burnAdmin address cannot be 0"
        );
        BBC = _BBC;
        burnAdmin = _burnAdmin;
    }

    /**
     * @dev Throws if caller is not the boost contract.
     */
    modifier onlyBoostContract() {
        require(
            boostContract == msg.sender,
            "Ownable: caller is not the boost contract"
        );
        _;
    }

    /// @notice Deposits a dummy token to `MASTER_CHEF` MCV1. This is required because MCV1 holds the minting permission of BBC.
    /// It will transfer all the `dummyToken` in the tx sender address.
    /// The allocation point for the dummy pool on MCV1 should be equal to the total amount of allocPoint.
    function init() external onlyOwner {
        lastBurnedBlock = block.number;
        emit Init();
    }

    /// @notice Returns the number of MCV2 pools.
    function poolLength() public view returns (uint256 pools) {
        pools = poolInfo.length;
    }

    /// @notice Add a new pool. Can only be called by the owner.
    /// DO NOT add the same LP token more than once. Rewards will be messed up if you do.
    /// @param _allocPoint Number of allocation points for the new pool.
    /// @param _lpToken Address of the LP BEP-20 token.
    /// @param _isRegular Whether the pool is regular or special. LP farms are always "regular". "Special" pools are
    /// @param _withUpdate Whether call "massUpdatePools" operation.
    /// only for BBC distributions within 9inchSwap products.
    function add(
        uint256 _allocPoint,
        IERC20 _lpToken,
        bool _isRegular,
        bool _withUpdate
    ) external onlyOwner {
        require(address(_lpToken) != address(0), "MCV2: _lpToken is zero");
        require(_lpToken.balanceOf(address(this)) >= 0, "None BEP20 tokens");
        // stake BBC token will cause staked token and reward token mixed up,
        // may cause staked tokens withdraw as reward token,never do it.
        require(_lpToken != BBC, "BBC token can't be added to farm pools");

        if (_withUpdate) {
            massUpdatePools();
        }

        if (_isRegular) {
            totalRegularAllocPoint = totalRegularAllocPoint.add(_allocPoint);
        } else {
            totalSpecialAllocPoint = totalSpecialAllocPoint.add(_allocPoint);
        }
        lpToken.push(_lpToken);

        poolInfo.push(
            PoolInfo({
                allocPoint: _allocPoint,
                lastRewardBlock: block.number,
                accBBCPerShare: 0,
                isRegular: _isRegular,
                totalBoostedShare: 0
            })
        );
        emit AddPool(lpToken.length.sub(1), _allocPoint, _lpToken, _isRegular);
    }

    /// @notice Update the given pool's BBC allocation point. Can only be called by the owner.
    /// @param _pid The id of the pool. See `poolInfo`.
    /// @param _allocPoint New number of allocation points for the pool.
    /// @param _withUpdate Whether call "massUpdatePools" operation.
    function set(
        uint256 _pid,
        uint256 _allocPoint,
        bool _withUpdate
    ) external onlyOwner {
        // No matter _withUpdate is true or false, we need to execute updatePool once before set the pool parameters.
        updatePool(_pid);

        if (_withUpdate) {
            massUpdatePools();
        }

        if (poolInfo[_pid].isRegular) {
            totalRegularAllocPoint = totalRegularAllocPoint
                .sub(poolInfo[_pid].allocPoint)
                .add(_allocPoint);
        } else {
            totalSpecialAllocPoint = totalSpecialAllocPoint
                .sub(poolInfo[_pid].allocPoint)
                .add(_allocPoint);
        }
        poolInfo[_pid].allocPoint = _allocPoint;
        emit SetPool(_pid, _allocPoint);
    }

    /// @notice View function for checking pending BBC rewards.
    /// @param _pid The id of the pool. See `poolInfo`.
    /// @param _user Address of the user.
    function pendingBBC(
        uint256 _pid,
        address _user
    ) external view returns (uint256) {
        PoolInfo memory pool = poolInfo[_pid];
        UserInfo memory user = userInfo[_pid][_user];
        uint256 accBBCPerShare = pool.accBBCPerShare;
        uint256 lpSupply = pool.totalBoostedShare;

        if (block.number > pool.lastRewardBlock && lpSupply != 0) {
            uint256 multiplier = block.number.sub(pool.lastRewardBlock);

            uint256 bbcReward = multiplier
                .mul(bbcPerBlock(pool.isRegular))
                .mul(pool.allocPoint)
                .div(
                    (
                        pool.isRegular
                            ? totalRegularAllocPoint
                            : totalSpecialAllocPoint
                    )
                );
            accBBCPerShare = accBBCPerShare.add(
                bbcReward.mul(ACC_BBC_PRECISION).div(lpSupply)
            );
        }

        uint256 boostedAmount = user
            .amount
            .mul(getBoostMultiplier(_user, _pid))
            .div(BOOST_PRECISION);
        return
            boostedAmount.mul(accBBCPerShare).div(ACC_BBC_PRECISION).sub(
                user.rewardDebt
            );
    }

    /// @notice Update bbc reward for all the active pools. Be careful of gas spending!
    function massUpdatePools() public {
        uint256 length = poolInfo.length;
        for (uint256 pid = 0; pid < length; ++pid) {
            PoolInfo memory pool = poolInfo[pid];
            if (pool.allocPoint != 0) {
                updatePool(pid);
            }
        }
    }

    /// @notice Calculates and returns the `amount` of BBC per block.
    /// @param _isRegular If the pool belongs to regular or special.
    function bbcPerBlock(bool _isRegular) public view returns (uint256 amount) {
        if (_isRegular) {
            amount = MASTERCHEF_BBC_PER_BLOCK.mul(bbcRateToRegularFarm).div(
                BBC_RATE_TOTAL_PRECISION
            );
        } else {
            amount = MASTERCHEF_BBC_PER_BLOCK.mul(bbcRateToSpecialFarm).div(
                BBC_RATE_TOTAL_PRECISION
            );
        }
    }

    /// @notice Calculates and returns the `amount` of BBC per block to burn.
    function bbcPerBlockToBurn() public view returns (uint256 amount) {
        amount = MASTERCHEF_BBC_PER_BLOCK.mul(bbcRateToBurn).div(
            BBC_RATE_TOTAL_PRECISION
        );
    }

    /// @notice Update reward variables for the given pool.
    /// @param _pid The id of the pool. See `poolInfo`.
    /// @return pool Returns the pool that was updated.
    function updatePool(uint256 _pid) public returns (PoolInfo memory pool) {
        pool = poolInfo[_pid];
        if (block.number > pool.lastRewardBlock) {
            uint256 lpSupply = pool.totalBoostedShare;
            uint256 totalAllocPoint = (
                pool.isRegular ? totalRegularAllocPoint : totalSpecialAllocPoint
            );

            if (lpSupply > 0 && totalAllocPoint > 0) {
                uint256 multiplier = block.number.sub(pool.lastRewardBlock);
                uint256 bbcReward = multiplier
                    .mul(bbcPerBlock(pool.isRegular))
                    .mul(pool.allocPoint)
                    .div(totalAllocPoint);

                (bool success, bytes memory data) = address(BBC).call(
                    abi.encodeWithSelector(
                        bytes4(keccak256(bytes("mint(uint256)"))),
                        bbcReward
                    )
                );
                require(
                    success && (data.length == 0 || abi.decode(data, (bool))),
                    "NineInch: Mint failed"
                );
                //BBC.mint(bbcReward);
                pool.accBBCPerShare = pool.accBBCPerShare.add(
                    (bbcReward.mul(ACC_BBC_PRECISION).div(lpSupply))
                );
            }
            pool.lastRewardBlock = block.number;
            poolInfo[_pid] = pool;
            emit UpdatePool(
                _pid,
                pool.lastRewardBlock,
                lpSupply,
                pool.accBBCPerShare
            );
        }
    }

    /// @notice Deposit LP tokens to pool.
    /// @param _pid The id of the pool. See `poolInfo`.
    /// @param _amount Amount of LP tokens to deposit.
    function deposit(uint256 _pid, uint256 _amount) external nonReentrant {
        PoolInfo memory pool = updatePool(_pid);
        UserInfo storage user = userInfo[_pid][msg.sender];

        require(
            pool.isRegular || whiteList[msg.sender],
            "MasterChefV2: The address is not available to deposit in this pool"
        );

        uint256 multiplier = getBoostMultiplier(msg.sender, _pid);

        if (user.amount > 0) {
            settlePendingBBC(msg.sender, _pid, multiplier);
        }

        if (_amount > 0) {
            uint256 before = lpToken[_pid].balanceOf(address(this));
            lpToken[_pid].safeTransferFrom(msg.sender, address(this), _amount);
            _amount = lpToken[_pid].balanceOf(address(this)).sub(before);
            user.amount = user.amount.add(_amount);

            // Update total boosted share.
            pool.totalBoostedShare = pool.totalBoostedShare.add(
                _amount.mul(multiplier).div(BOOST_PRECISION)
            );
        }

        user.rewardDebt = user
            .amount
            .mul(multiplier)
            .div(BOOST_PRECISION)
            .mul(pool.accBBCPerShare)
            .div(ACC_BBC_PRECISION);
        poolInfo[_pid] = pool;

        emit Deposit(msg.sender, _pid, _amount);
    }

    /// @notice Withdraw LP tokens from pool.
    /// @param _pid The id of the pool. See `poolInfo`.
    /// @param _amount Amount of LP tokens to withdraw.
    function withdraw(uint256 _pid, uint256 _amount) external nonReentrant {
        PoolInfo memory pool = updatePool(_pid);
        UserInfo storage user = userInfo[_pid][msg.sender];

        require(user.amount >= _amount, "withdraw: Insufficient");

        uint256 multiplier = getBoostMultiplier(msg.sender, _pid);

        settlePendingBBC(msg.sender, _pid, multiplier);

        if (_amount > 0) {
            user.amount = user.amount.sub(_amount);
            lpToken[_pid].safeTransfer(msg.sender, _amount);
        }

        user.rewardDebt = user
            .amount
            .mul(multiplier)
            .div(BOOST_PRECISION)
            .mul(pool.accBBCPerShare)
            .div(ACC_BBC_PRECISION);
        poolInfo[_pid].totalBoostedShare = poolInfo[_pid].totalBoostedShare.sub(
            _amount.mul(multiplier).div(BOOST_PRECISION)
        );

        emit Withdraw(msg.sender, _pid, _amount);
    }

    /// @notice Withdraw without caring about the rewards. EMERGENCY ONLY.
    /// @param _pid The id of the pool. See `poolInfo`.
    function emergencyWithdraw(uint256 _pid) external nonReentrant {
        PoolInfo storage pool = poolInfo[_pid];
        UserInfo storage user = userInfo[_pid][msg.sender];

        uint256 amount = user.amount;
        user.amount = 0;
        user.rewardDebt = 0;
        uint256 boostedAmount = amount
            .mul(getBoostMultiplier(msg.sender, _pid))
            .div(BOOST_PRECISION);
        pool.totalBoostedShare = pool.totalBoostedShare > boostedAmount
            ? pool.totalBoostedShare.sub(boostedAmount)
            : 0;

        // Note: transfer can fail or succeed if `amount` is zero.
        lpToken[_pid].safeTransfer(msg.sender, amount);
        emit EmergencyWithdraw(msg.sender, _pid, amount);
    }

    /// @notice Send BBC pending for burn to `burnAdmin`.
    /// @param _withUpdate Whether call "massUpdatePools" operation.
    function burnBBC(bool _withUpdate) public onlyOwner {
        if (_withUpdate) {
            massUpdatePools();
        }

        uint256 multiplier = block.number.sub(lastBurnedBlock);
        uint256 pendingBBCToBurn = multiplier.mul(bbcPerBlockToBurn());

        // SafeTransfer BBC
        _safeTransfer(burnAdmin, pendingBBCToBurn);
        lastBurnedBlock = block.number;
    }

    /// @notice Update the % of BBC distributions for burn, regular pools and special pools.
    /// @param _burnRate The % of BBC to burn each block.
    /// @param _regularFarmRate The % of BBC to regular pools each block.
    /// @param _specialFarmRate The % of BBC to special pools each block.
    /// @param _withUpdate Whether call "massUpdatePools" operation.
    function updateBBCRate(
        uint256 _burnRate,
        uint256 _regularFarmRate,
        uint256 _specialFarmRate,
        bool _withUpdate
    ) external onlyOwner {
        require(
            _burnRate > 0 && _regularFarmRate > 0 && _specialFarmRate > 0,
            "MasterChefV2: BBC rate must be greater than 0"
        );
        require(
            _burnRate.add(_regularFarmRate).add(_specialFarmRate) ==
                BBC_RATE_TOTAL_PRECISION,
            "MasterChefV2: Total rate must be 1e12"
        );
        if (_withUpdate) {
            massUpdatePools();
        }
        // burn bbc base on old burn bbc rate
        burnBBC(false);

        bbcRateToBurn = _burnRate;
        bbcRateToRegularFarm = _regularFarmRate;
        bbcRateToSpecialFarm = _specialFarmRate;

        emit UpdateBBCRate(_burnRate, _regularFarmRate, _specialFarmRate);
    }

    /// @notice Update burn admin address.
    /// @param _newAdmin The new burn admin address.
    function updateBurnAdmin(address _newAdmin) external onlyOwner {
        require(
            _newAdmin != address(0),
            "MasterChefV2: Burn admin address must be valid"
        );
        require(
            _newAdmin != burnAdmin,
            "MasterChefV2: Burn admin address is the same with current address"
        );
        address _oldAdmin = burnAdmin;
        burnAdmin = _newAdmin;
        emit UpdateBurnAdmin(_oldAdmin, _newAdmin);
    }

    /// @notice Update whitelisted addresses for special pools.
    /// @param _user The address to be updated.
    /// @param _isValid The flag for valid or invalid.
    function updateWhiteList(address _user, bool _isValid) external onlyOwner {
        require(
            _user != address(0),
            "MasterChefV2: The white list address must be valid"
        );

        whiteList[_user] = _isValid;
        emit UpdateWhiteList(_user, _isValid);
    }

    /// @notice Update boost contract address and max boost factor.
    /// @param _newBoostContract The new address for handling all the share boosts.
    function updateBoostContract(address _newBoostContract) external onlyOwner {
        require(
            _newBoostContract != address(0) &&
                _newBoostContract != boostContract,
            "MasterChefV2: New boost contract address must be valid"
        );

        boostContract = _newBoostContract;
        emit UpdateBoostContract(_newBoostContract);
    }

    /// @notice Update user boost factor.
    /// @param _user The user address for boost factor updates.
    /// @param _pid The pool id for the boost factor updates.
    /// @param _newMultiplier New boost multiplier.
    function updateBoostMultiplier(
        address _user,
        uint256 _pid,
        uint256 _newMultiplier
    ) external onlyBoostContract nonReentrant {
        require(
            _user != address(0),
            "MasterChefV2: The user address must be valid"
        );
        require(
            poolInfo[_pid].isRegular,
            "MasterChefV2: Only regular farm could be boosted"
        );
        require(
            _newMultiplier >= BOOST_PRECISION &&
                _newMultiplier <= MAX_BOOST_PRECISION,
            "MasterChefV2: Invalid new boost multiplier"
        );

        PoolInfo memory pool = updatePool(_pid);
        UserInfo storage user = userInfo[_pid][_user];

        uint256 prevMultiplier = getBoostMultiplier(_user, _pid);
        settlePendingBBC(_user, _pid, prevMultiplier);

        user.rewardDebt = user
            .amount
            .mul(_newMultiplier)
            .div(BOOST_PRECISION)
            .mul(pool.accBBCPerShare)
            .div(ACC_BBC_PRECISION);
        pool.totalBoostedShare = pool
            .totalBoostedShare
            .sub(user.amount.mul(prevMultiplier).div(BOOST_PRECISION))
            .add(user.amount.mul(_newMultiplier).div(BOOST_PRECISION));
        poolInfo[_pid] = pool;
        userInfo[_pid][_user].boostMultiplier = _newMultiplier;

        emit UpdateBoostMultiplier(_user, _pid, prevMultiplier, _newMultiplier);
    }

    /// @notice Get user boost multiplier for specific pool id.
    /// @param _user The user address.
    /// @param _pid The pool id.
    function getBoostMultiplier(
        address _user,
        uint256 _pid
    ) public view returns (uint256) {
        uint256 multiplier = userInfo[_pid][_user].boostMultiplier;
        return multiplier > BOOST_PRECISION ? multiplier : BOOST_PRECISION;
    }

    /// @notice Settles, distribute the pending BBC rewards for given user.
    /// @param _user The user address for settling rewards.
    /// @param _pid The pool id.
    /// @param _boostMultiplier The user boost multiplier in specific pool id.
    function settlePendingBBC(
        address _user,
        uint256 _pid,
        uint256 _boostMultiplier
    ) internal {
        UserInfo memory user = userInfo[_pid][_user];

        uint256 boostedAmount = user.amount.mul(_boostMultiplier).div(
            BOOST_PRECISION
        );
        uint256 accBBC = boostedAmount.mul(poolInfo[_pid].accBBCPerShare).div(
            ACC_BBC_PRECISION
        );
        uint256 pending = accBBC.sub(user.rewardDebt);
        // SafeTransfer BBC
        _safeTransfer(_user, pending);
    }

    /// @notice Safe Transfer BBC.
    /// @param _to The BBC receiver address.
    /// @param _amount transfer BBC amounts.
    function _safeTransfer(address _to, uint256 _amount) internal {
        if (_amount > 0) {
            // Check whether MCV2 has enough BBC. If not, harvest from MCV1.
            /*
            if (BBC.balanceOf(address(this)) < _amount) {
                harvestFromMasterChef();
            }
            */
            uint256 balance = BBC.balanceOf(address(this));
            if (balance < _amount) {
                _amount = balance;
            }
            BBC.safeTransfer(_to, _amount);
        }
    }

    function transferOwnershipOfBBC(address _to) public onlyOwner {
        Ownable(address(BBC)).transferOwnership(_to);
    }
}
        

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/Context.sol";

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

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

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor() {
        _transferOwnership(_msgSender());
    }

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

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

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }

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

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (security/ReentrancyGuard.sol)

pragma solidity ^0.8.0;

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

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

    uint256 private _status;

    constructor() {
        _status = _NOT_ENTERED;
    }

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

    function _nonReentrantBefore() private {
        // On the first call to nonReentrant, _status will be _NOT_ENTERED
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

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

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

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

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

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/extensions/IERC20Permit.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on {IERC20-approve}, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over ``owner``'s tokens,
     * given ``owner``'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) external view returns (uint256);

    /**
     * @dev Returns the domain separator used in the encoding of the signature for {permit}, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view returns (bytes32);
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";
import "../extensions/IERC20Permit.sol";
import "../../../utils/Address.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using Address for address;

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

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

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(IERC20 token, address spender, uint256 value) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        require(
            (value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

    /**
     * @dev Increase the calling contract's allowance toward `spender` by `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     */
    function safeIncreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 oldAllowance = token.allowance(address(this), spender);
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, oldAllowance + value));
    }

    /**
     * @dev Decrease the calling contract's allowance toward `spender` by `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     */
    function safeDecreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, oldAllowance - value));
        }
    }

    /**
     * @dev Set the calling contract's allowance toward `spender` to `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful. Compatible with tokens that require the approval to be set to
     * 0 before setting it to a non-zero value.
     */
    function forceApprove(IERC20 token, address spender, uint256 value) internal {
        bytes memory approvalCall = abi.encodeWithSelector(token.approve.selector, spender, value);

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

    /**
     * @dev Use a ERC-2612 signature to set the `owner` approval toward `spender` on `token`.
     * Revert on invalid signature.
     */
    function safePermit(
        IERC20Permit token,
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        uint256 nonceBefore = token.nonces(owner);
        token.permit(owner, spender, value, deadline, v, r, s);
        uint256 nonceAfter = token.nonces(owner);
        require(nonceAfter == nonceBefore + 1, "SafeERC20: permit did not succeed");
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address-functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

        bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
        require(returndata.length == 0 || abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     *
     * This is a variant of {_callOptionalReturn} that silents catches all reverts and returns a bool instead.
     */
    function _callOptionalReturnBool(IERC20 token, bytes memory data) private returns (bool) {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We cannot use {Address-functionCall} here since this should return false
        // and not revert is the subcall reverts.

        (bool success, bytes memory returndata) = address(token).call(data);
        return
            success && (returndata.length == 0 || abi.decode(returndata, (bool))) && Address.isContract(address(token));
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/Address.sol)

pragma solidity ^0.8.1;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     *
     * Furthermore, `isContract` will also return true if the target contract within
     * the same transaction is already scheduled for destruction by `SELFDESTRUCT`,
     * which only has an effect at the end of a transaction.
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.8.0/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

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

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

// SPDX-License-Identifier: GPLv3
pragma solidity 0.8.19;

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");

        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        return sub(a, b, "SafeMath: subtraction overflow");
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        uint256 c = a - b;

        return c;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) {
            return 0;
        }

        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");

        return c;
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        return div(a, b, "SafeMath: division by zero");
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold

        return c;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        return mod(a, b, "SafeMath: modulo by zero");
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts with custom message when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        require(b != 0, errorMessage);
        return a % b;
    }

    function min(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = x < y ? x : y;
    }

    // babylonian method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method)
    function sqrt(uint256 y) internal pure returns (uint256 z) {
        if (y > 3) {
            z = y;
            uint256 x = y / 2 + 1;
            while (x < z) {
                z = x;
                x = (y / x + x) / 2;
            }
        } else if (y != 0) {
            z = 1;
        }
    }
}