// SPDX-License-Identifier: MIT

import "../libraries/math/SafeMath.sol";

import "./interfaces/ISecondaryPriceFeed.sol";
import "./interfaces/IFastPriceFeed.sol";
import "./interfaces/IFastPriceEvents.sol";
import "../core/interfaces/IVaultPriceFeed.sol";
import "../core/interfaces/IPositionRouter.sol";
import "../access/Governable.sol";

pragma solidity 0.6.12;

contract FastPriceFeed is ISecondaryPriceFeed, IFastPriceFeed, Governable {
    using SafeMath for uint256;

    // fit data in a uint256 slot to save gas costs
    struct PriceDataItem {
        uint160 refPrice; // Chainlink price
        uint32 refTime; // last updated at time
        uint32 cumulativeRefDelta; // cumulative Chainlink price delta
        uint32 cumulativeFastDelta; // cumulative fast price delta
    }

    uint256 public constant PRICE_PRECISION = 10 ** 30;

    uint256 public constant CUMULATIVE_DELTA_PRECISION = 10 * 1000 * 1000;

    uint256 public constant MAX_REF_PRICE = type(uint160).max;
    uint256 public constant MAX_CUMULATIVE_REF_DELTA = type(uint32).max;
    uint256 public constant MAX_CUMULATIVE_FAST_DELTA = type(uint32).max;

    // uint256(~0) is 256 bits of 1s
    // shift the 1s by (256 - 32) to get (256 - 32) 0s followed by 32 1s
    uint256 constant public BITMASK_32 = uint256(~0) >> (256 - 32);

    uint256 public constant BASIS_POINTS_DIVISOR = 10000;

    uint256 public constant MAX_PRICE_DURATION = 30 minutes;

    bool public isInitialized;
    bool public isSpreadEnabled = false;

    address public vaultPriceFeed;
    address public fastPriceEvents;

    address public tokenManager;

    address public positionRouter;

    uint256 public override lastUpdatedAt;
    uint256 public override lastUpdatedBlock;

    uint256 public priceDuration;
    uint256 public maxPriceUpdateDelay;
    uint256 public spreadBasisPointsIfInactive;
    uint256 public spreadBasisPointsIfChainError;
    uint256 public minBlockInterval;
    uint256 public maxTimeDeviation;

    uint256 public priceDataInterval;

    // allowed deviation from primary price
    uint256 public maxDeviationBasisPoints;

    uint256 public minAuthorizations;
    uint256 public disableFastPriceVoteCount = 0;

    mapping (address => bool) public isUpdater;

    mapping (address => uint256) public prices;
    mapping (address => PriceDataItem) public priceData;
    mapping (address => uint256) public maxCumulativeDeltaDiffs;

    mapping (address => bool) public isSigner;
    mapping (address => bool) public disableFastPriceVotes;

    // array of tokens used in setCompactedPrices, saves L1 calldata gas costs
    address[] public tokens;
    // array of tokenPrecisions used in setCompactedPrices, saves L1 calldata gas costs
    // if the token price will be sent with 3 decimals, then tokenPrecision for that token
    // should be 10 ** 3
    uint256[] public tokenPrecisions;

    event DisableFastPrice(address signer);
    event EnableFastPrice(address signer);
    event PriceData(address token, uint256 refPrice, uint256 fastPrice, uint256 cumulativeRefDelta, uint256 cumulativeFastDelta);
    event MaxCumulativeDeltaDiffExceeded(address token, uint256 refPrice, uint256 fastPrice, uint256 cumulativeRefDelta, uint256 cumulativeFastDelta);

    modifier onlySigner() {
        require(isSigner[msg.sender], "FastPriceFeed: forbidden");
        _;
    }

    modifier onlyUpdater() {
        require(isUpdater[msg.sender], "FastPriceFeed: forbidden");
        _;
    }

    modifier onlyTokenManager() {
        require(msg.sender == tokenManager, "FastPriceFeed: forbidden");
        _;
    }

    constructor(
      uint256 _priceDuration,
      uint256 _maxPriceUpdateDelay,
      uint256 _minBlockInterval,
      uint256 _maxDeviationBasisPoints,
      address _fastPriceEvents,
      address _tokenManager,
      address _positionRouter
    ) public {
        require(_priceDuration <= MAX_PRICE_DURATION, "FastPriceFeed: invalid _priceDuration");
        priceDuration = _priceDuration;
        maxPriceUpdateDelay = _maxPriceUpdateDelay;
        minBlockInterval = _minBlockInterval;
        maxDeviationBasisPoints = _maxDeviationBasisPoints;
        fastPriceEvents = _fastPriceEvents;
        tokenManager = _tokenManager;
        positionRouter = _positionRouter;
    }

    function initialize(uint256 _minAuthorizations, address[] memory _signers, address[] memory _updaters) public onlyGov {
        require(!isInitialized, "FastPriceFeed: already initialized");
        isInitialized = true;

        minAuthorizations = _minAuthorizations;

        for (uint256 i = 0; i < _signers.length; i++) {
            address signer = _signers[i];
            isSigner[signer] = true;
        }

        for (uint256 i = 0; i < _updaters.length; i++) {
            address updater = _updaters[i];
            isUpdater[updater] = true;
        }
    }

    function setSigner(address _account, bool _isActive) external override onlyGov {
        isSigner[_account] = _isActive;
    }

    function setUpdater(address _account, bool _isActive) external override onlyGov {
        isUpdater[_account] = _isActive;
    }

    function setFastPriceEvents(address _fastPriceEvents) external onlyGov {
      fastPriceEvents = _fastPriceEvents;
    }

    function setVaultPriceFeed(address _vaultPriceFeed) external override onlyGov {
      vaultPriceFeed = _vaultPriceFeed;
    }

    function setMaxTimeDeviation(uint256 _maxTimeDeviation) external onlyGov {
        maxTimeDeviation = _maxTimeDeviation;
    }

    function setPriceDuration(uint256 _priceDuration) external override onlyGov {
        require(_priceDuration <= MAX_PRICE_DURATION, "FastPriceFeed: invalid _priceDuration");
        priceDuration = _priceDuration;
    }

    function setMaxPriceUpdateDelay(uint256 _maxPriceUpdateDelay) external override onlyGov {
        maxPriceUpdateDelay = _maxPriceUpdateDelay;
    }

    function setSpreadBasisPointsIfInactive(uint256 _spreadBasisPointsIfInactive) external override onlyGov {
        spreadBasisPointsIfInactive = _spreadBasisPointsIfInactive;
    }

    function setSpreadBasisPointsIfChainError(uint256 _spreadBasisPointsIfChainError) external override onlyGov {
        spreadBasisPointsIfChainError = _spreadBasisPointsIfChainError;
    }

    function setMinBlockInterval(uint256 _minBlockInterval) external override onlyGov {
        minBlockInterval = _minBlockInterval;
    }

    function setIsSpreadEnabled(bool _isSpreadEnabled) external override onlyGov {
        isSpreadEnabled = _isSpreadEnabled;
    }

    function setLastUpdatedAt(uint256 _lastUpdatedAt) external onlyGov {
        lastUpdatedAt = _lastUpdatedAt;
    }

    function setTokenManager(address _tokenManager) external onlyTokenManager {
        tokenManager = _tokenManager;
    }

    function setMaxDeviationBasisPoints(uint256 _maxDeviationBasisPoints) external override onlyTokenManager {
        maxDeviationBasisPoints = _maxDeviationBasisPoints;
    }

    function setMaxCumulativeDeltaDiffs(address[] memory _tokens,  uint256[] memory _maxCumulativeDeltaDiffs) external override onlyTokenManager {
        for (uint256 i = 0; i < _tokens.length; i++) {
            address token = _tokens[i];
            maxCumulativeDeltaDiffs[token] = _maxCumulativeDeltaDiffs[i];
        }
    }

    function setPriceDataInterval(uint256 _priceDataInterval) external override onlyTokenManager {
        priceDataInterval = _priceDataInterval;
    }

    function setMinAuthorizations(uint256 _minAuthorizations) external onlyTokenManager {
        minAuthorizations = _minAuthorizations;
    }

    function setTokens(address[] memory _tokens, uint256[] memory _tokenPrecisions) external onlyGov {
        require(_tokens.length == _tokenPrecisions.length, "FastPriceFeed: invalid lengths");
        tokens = _tokens;
        tokenPrecisions = _tokenPrecisions;
    }

    function setPrices(address[] memory _tokens, uint256[] memory _prices, uint256 _timestamp) external onlyUpdater {
        bool shouldUpdate = _setLastUpdatedValues(_timestamp);

        if (shouldUpdate) {
            address _fastPriceEvents = fastPriceEvents;
            address _vaultPriceFeed = vaultPriceFeed;

            for (uint256 i = 0; i < _tokens.length; i++) {
                address token = _tokens[i];
                _setPrice(token, _prices[i], _vaultPriceFeed, _fastPriceEvents);
            }
        }
    }

    function setCompactedPrices(uint256[] memory _priceBitArray, uint256 _timestamp) external onlyUpdater {
        bool shouldUpdate = _setLastUpdatedValues(_timestamp);

        if (shouldUpdate) {
            address _fastPriceEvents = fastPriceEvents;
            address _vaultPriceFeed = vaultPriceFeed;

            for (uint256 i = 0; i < _priceBitArray.length; i++) {
                uint256 priceBits = _priceBitArray[i];

                for (uint256 j = 0; j < 8; j++) {
                    uint256 index = i * 8 + j;
                    if (index >= tokens.length) { return; }

                    uint256 startBit = 32 * j;
                    uint256 price = (priceBits >> startBit) & BITMASK_32;

                    address token = tokens[i * 8 + j];
                    uint256 tokenPrecision = tokenPrecisions[i * 8 + j];
                    uint256 adjustedPrice = price.mul(PRICE_PRECISION).div(tokenPrecision);

                    _setPrice(token, adjustedPrice, _vaultPriceFeed, _fastPriceEvents);
                }
            }
        }
    }

    function setPricesWithBits(uint256 _priceBits, uint256 _timestamp) external onlyUpdater {
        _setPricesWithBits(_priceBits, _timestamp);
    }

    function setPricesWithBitsAndExecute(
        uint256 _priceBits,
        uint256 _timestamp,
        uint256 _endIndexForIncreasePositions,
        uint256 _endIndexForDecreasePositions,
        uint256 _maxIncreasePositions,
        uint256 _maxDecreasePositions
    ) external onlyUpdater {
        _setPricesWithBits(_priceBits, _timestamp);

        IPositionRouter _positionRouter = IPositionRouter(positionRouter);
        uint256 maxEndIndexForIncrease = _positionRouter.increasePositionRequestKeysStart().add(_maxIncreasePositions);
        uint256 maxEndIndexForDecrease = _positionRouter.increasePositionRequestKeysStart().add(_maxDecreasePositions);

        if (_endIndexForIncreasePositions > maxEndIndexForIncrease) {
            _endIndexForIncreasePositions = maxEndIndexForIncrease;
        }

        if (_endIndexForDecreasePositions > maxEndIndexForDecrease) {
            _endIndexForDecreasePositions = maxEndIndexForDecrease;
        }

        _positionRouter.executeIncreasePositions(_endIndexForIncreasePositions, payable(msg.sender));
        _positionRouter.executeDecreasePositions(_endIndexForDecreasePositions, payable(msg.sender));
    }

    function disableFastPrice() external onlySigner {
        require(!disableFastPriceVotes[msg.sender], "FastPriceFeed: already voted");
        disableFastPriceVotes[msg.sender] = true;
        disableFastPriceVoteCount = disableFastPriceVoteCount.add(1);

        emit DisableFastPrice(msg.sender);
    }

    function enableFastPrice() external onlySigner {
        require(disableFastPriceVotes[msg.sender], "FastPriceFeed: already enabled");
        disableFastPriceVotes[msg.sender] = false;
        disableFastPriceVoteCount = disableFastPriceVoteCount.sub(1);

        emit EnableFastPrice(msg.sender);
    }

    // under regular operation, the fastPrice (prices[token]) is returned and there is no spread returned from this function,
    // though VaultPriceFeed might apply its own spread
    //
    // if the fastPrice has not been updated within priceDuration then it is ignored and only _refPrice with a spread is used (spread: spreadBasisPointsIfInactive)
    // in case the fastPrice has not been updated for maxPriceUpdateDelay then the _refPrice with a larger spread is used (spread: spreadBasisPointsIfChainError)
    //
    // there will be a spread from the _refPrice to the fastPrice in the following cases:
    // - in case isSpreadEnabled is set to true
    // - in case the maxDeviationBasisPoints between _refPrice and fastPrice is exceeded
    // - in case watchers flag an issue
    // - in case the cumulativeFastDelta exceeds the cumulativeRefDelta by the maxCumulativeDeltaDiff
    function getPrice(address _token, uint256 _refPrice, bool _maximise) external override view returns (uint256) {
        if (block.timestamp > lastUpdatedAt.add(maxPriceUpdateDelay)) {
            if (_maximise) {
                return _refPrice.mul(BASIS_POINTS_DIVISOR.add(spreadBasisPointsIfChainError)).div(BASIS_POINTS_DIVISOR);
            }

            return _refPrice.mul(BASIS_POINTS_DIVISOR.sub(spreadBasisPointsIfChainError)).div(BASIS_POINTS_DIVISOR);
        }

        if (block.timestamp > lastUpdatedAt.add(priceDuration)) {
            if (_maximise) {
                return _refPrice.mul(BASIS_POINTS_DIVISOR.add(spreadBasisPointsIfInactive)).div(BASIS_POINTS_DIVISOR);
            }

            return _refPrice.mul(BASIS_POINTS_DIVISOR.sub(spreadBasisPointsIfInactive)).div(BASIS_POINTS_DIVISOR);
        }

        uint256 fastPrice = prices[_token];
        if (fastPrice == 0) { return _refPrice; }

        uint256 diffBasisPoints = _refPrice > fastPrice ? _refPrice.sub(fastPrice) : fastPrice.sub(_refPrice);
        diffBasisPoints = diffBasisPoints.mul(BASIS_POINTS_DIVISOR).div(_refPrice);

        // create a spread between the _refPrice and the fastPrice if the maxDeviationBasisPoints is exceeded
        // or if watchers have flagged an issue with the fast price
        bool hasSpread = !favorFastPrice(_token) || diffBasisPoints > maxDeviationBasisPoints;

        if (hasSpread) {
            // return the higher of the two prices
            if (_maximise) {
                return _refPrice > fastPrice ? _refPrice : fastPrice;
            }

            // return the lower of the two prices
            return _refPrice < fastPrice ? _refPrice : fastPrice;
        }

        return fastPrice;
    }

    function favorFastPrice(address _token) public view returns (bool) {
        if (isSpreadEnabled) {
            return false;
        }

        if (disableFastPriceVoteCount >= minAuthorizations) {
            // force a spread if watchers have flagged an issue with the fast price
            return false;
        }

        (/* uint256 prevRefPrice */, /* uint256 refTime */, uint256 cumulativeRefDelta, uint256 cumulativeFastDelta) = getPriceData(_token);
        if (cumulativeFastDelta > cumulativeRefDelta && cumulativeFastDelta.sub(cumulativeRefDelta) > maxCumulativeDeltaDiffs[_token]) {
            // force a spread if the cumulative delta for the fast price feed exceeds the cumulative delta
            // for the Chainlink price feed by the maxCumulativeDeltaDiff allowed
            return false;
        }

        return true;
    }

    function getPriceData(address _token) public view returns (uint256, uint256, uint256, uint256) {
        PriceDataItem memory data = priceData[_token];
        return (uint256(data.refPrice), uint256(data.refTime), uint256(data.cumulativeRefDelta), uint256(data.cumulativeFastDelta));
    }

    function _setPricesWithBits(uint256 _priceBits, uint256 _timestamp) private {
        bool shouldUpdate = _setLastUpdatedValues(_timestamp);

        if (shouldUpdate) {
            address _fastPriceEvents = fastPriceEvents;
            address _vaultPriceFeed = vaultPriceFeed;

            for (uint256 j = 0; j < 8; j++) {
                uint256 index = j;
                if (index >= tokens.length) { return; }

                uint256 startBit = 32 * j;
                uint256 price = (_priceBits >> startBit) & BITMASK_32;

                address token = tokens[j];
                uint256 tokenPrecision = tokenPrecisions[j];
                uint256 adjustedPrice = price.mul(PRICE_PRECISION).div(tokenPrecision);

                _setPrice(token, adjustedPrice, _vaultPriceFeed, _fastPriceEvents);
            }
        }
    }

    function _setPrice(address _token, uint256 _price, address _vaultPriceFeed, address _fastPriceEvents) private {
        if (_vaultPriceFeed != address(0)) {
            uint256 refPrice = IVaultPriceFeed(_vaultPriceFeed).getLatestPrimaryPrice(_token);
            uint256 fastPrice = prices[_token];

            (uint256 prevRefPrice, uint256 refTime, uint256 cumulativeRefDelta, uint256 cumulativeFastDelta) = getPriceData(_token);

            if (prevRefPrice > 0) {
                uint256 refDeltaAmount = refPrice > prevRefPrice ? refPrice.sub(prevRefPrice) : prevRefPrice.sub(refPrice);
                uint256 fastDeltaAmount = fastPrice > _price ? fastPrice.sub(_price) : _price.sub(fastPrice);

                // reset cumulative delta values if it is a new time window
                if (refTime.div(priceDataInterval) != block.timestamp.div(priceDataInterval)) {
                    cumulativeRefDelta = 0;
                    cumulativeFastDelta = 0;
                }

                cumulativeRefDelta = cumulativeRefDelta.add(refDeltaAmount.mul(CUMULATIVE_DELTA_PRECISION).div(prevRefPrice));
                cumulativeFastDelta = cumulativeFastDelta.add(fastDeltaAmount.mul(CUMULATIVE_DELTA_PRECISION).div(fastPrice));
            }

            if (cumulativeFastDelta > cumulativeRefDelta && cumulativeFastDelta.sub(cumulativeRefDelta) > maxCumulativeDeltaDiffs[_token]) {
                emit MaxCumulativeDeltaDiffExceeded(_token, refPrice, fastPrice, cumulativeRefDelta, cumulativeFastDelta);
            }

            _setPriceData(_token, refPrice, cumulativeRefDelta, cumulativeFastDelta);
            emit PriceData(_token, refPrice, fastPrice, cumulativeRefDelta, cumulativeFastDelta);
        }

        prices[_token] = _price;
        _emitPriceEvent(_fastPriceEvents, _token, _price);
    }

    function _setPriceData(address _token, uint256 _refPrice, uint256 _cumulativeRefDelta, uint256 _cumulativeFastDelta) private {
        require(_refPrice < MAX_REF_PRICE, "FastPriceFeed: invalid refPrice");
        // skip validation of block.timestamp, it should only be out of range after the year 2100
        require(_cumulativeRefDelta < MAX_CUMULATIVE_REF_DELTA, "FastPriceFeed: invalid cumulativeRefDelta");
        require(_cumulativeFastDelta < MAX_CUMULATIVE_FAST_DELTA, "FastPriceFeed: invalid cumulativeFastDelta");

        priceData[_token] = PriceDataItem(
            uint160(_refPrice),
            uint32(block.timestamp),
            uint32(_cumulativeRefDelta),
            uint32(_cumulativeFastDelta)
        );
    }

    function _emitPriceEvent(address _fastPriceEvents, address _token, uint256 _price) private {
        if (_fastPriceEvents == address(0)) {
            return;
        }

        IFastPriceEvents(_fastPriceEvents).emitPriceEvent(_token, _price);
    }

    function _setLastUpdatedValues(uint256 _timestamp) private returns (bool) {
        if (minBlockInterval > 0) {
            require(block.number.sub(lastUpdatedBlock) >= minBlockInterval, "FastPriceFeed: minBlockInterval not yet passed");
        }

        uint256 _maxTimeDeviation = maxTimeDeviation;
        require(_timestamp > block.timestamp.sub(_maxTimeDeviation), "FastPriceFeed: _timestamp below allowed range");
        require(_timestamp < block.timestamp.add(_maxTimeDeviation), "FastPriceFeed: _timestamp exceeds allowed range");

        // do not update prices if _timestamp is before the current lastUpdatedAt value
        if (_timestamp < lastUpdatedAt) {
            return false;
        }

        lastUpdatedAt = _timestamp;
        lastUpdatedBlock = block.number;

        return true;
    }
}

// SPDX-License-Identifier: MIT

pragma solidity 0.6.12;

contract Governable {
    address public gov;

    constructor() public {
        gov = msg.sender;
    }

    modifier onlyGov() {
        require(msg.sender == gov, "Governable: forbidden");
        _;
    }

    function setGov(address _gov) external onlyGov {
        gov = _gov;
    }
}

// SPDX-License-Identifier: MIT

pragma solidity 0.6.12;

interface IFastPriceEvents {
    function emitPriceEvent(address _token, uint256 _price) external;
}

// SPDX-License-Identifier: MIT

pragma solidity 0.6.12;

interface IFastPriceFeed {
    function lastUpdatedAt() external view returns (uint256);
    function lastUpdatedBlock() external view returns (uint256);
    function setSigner(address _account, bool _isActive) external;
    function setUpdater(address _account, bool _isActive) external;
    function setPriceDuration(uint256 _priceDuration) external;
    function setMaxPriceUpdateDelay(uint256 _maxPriceUpdateDelay) external;
    function setSpreadBasisPointsIfInactive(uint256 _spreadBasisPointsIfInactive) external;
    function setSpreadBasisPointsIfChainError(uint256 _spreadBasisPointsIfChainError) external;
    function setMinBlockInterval(uint256 _minBlockInterval) external;
    function setIsSpreadEnabled(bool _isSpreadEnabled) external;
    function setMaxDeviationBasisPoints(uint256 _maxDeviationBasisPoints) external;
    function setMaxCumulativeDeltaDiffs(address[] memory _tokens,  uint256[] memory _maxCumulativeDeltaDiffs) external;
    function setPriceDataInterval(uint256 _priceDataInterval) external;
    function setVaultPriceFeed(address _vaultPriceFeed) external;
}

// SPDX-License-Identifier: MIT

pragma solidity 0.6.12;

interface IPositionRouter {
    function increasePositionRequestKeysStart() external returns (uint256);
    function decreasePositionRequestKeysStart() external returns (uint256);
    function executeIncreasePositions(uint256 _count, address payable _executionFeeReceiver) external;
    function executeDecreasePositions(uint256 _count, address payable _executionFeeReceiver) external;
}

// SPDX-License-Identifier: MIT

pragma solidity 0.6.12;

interface ISecondaryPriceFeed {
    function getPrice(address _token, uint256 _referencePrice, bool _maximise) external view returns (uint256);
}

// SPDX-License-Identifier: MIT

pragma solidity 0.6.12;

interface IVaultPriceFeed {
    function adjustmentBasisPoints(address _token) external view returns (uint256);
    function isAdjustmentAdditive(address _token) external view returns (bool);
    function setAdjustment(address _token, bool _isAdditive, uint256 _adjustmentBps) external;
    function setUseV2Pricing(bool _useV2Pricing) external;
    function setIsAmmEnabled(bool _isEnabled) external;
    function setIsSecondaryPriceEnabled(bool _isEnabled) external;
    function setSpreadBasisPoints(address _token, uint256 _spreadBasisPoints) external;
    function setSpreadThresholdBasisPoints(uint256 _spreadThresholdBasisPoints) external;
    function setFavorPrimaryPrice(bool _favorPrimaryPrice) external;
    function setPriceSampleSpace(uint256 _priceSampleSpace) external;
    function setMaxStrictPriceDeviation(uint256 _maxStrictPriceDeviation) external;
    function getPrice(address _token, bool _maximise, bool _includeAmmPrice, bool _useSwapPricing) external view returns (uint256);
    function getAmmPrice(address _token) external view returns (uint256);
    function getLatestPrimaryPrice(address _token) external view returns (uint256);
    function getPrimaryPrice(address _token, bool _maximise) external view returns (uint256);
    function setTokenConfig(
        address _token,
        address _priceFeed,
        uint256 _priceDecimals,
        bool _isStrictStable
    ) external;
}

// SPDX-License-Identifier: MIT

pragma solidity 0.6.12;

/**
 * @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;
    }
}

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