// File: contracts/DfxSgdTWAP.sol



// SPDX-License-Identifier: MIT
// https://github.com/Uniswap/v2-periphery/blob/master/contracts/examples/ExampleOracleSimple.sol

pragma solidity ^0.8.10;
pragma experimental ABIEncoderV2;

import "./IDfxOracle.sol";
import "./IChainLinkOracle.sol";

import "./UniswapV2Oracle.sol";

import "./AccessControl.sol";

contract DfxSgdTWAP is AccessControl, UniswapV2Oracle, IDfxOracle {
    // **** Roles **** //
    bytes32 public constant SUDO = keccak256("dfxsgd.twap.sudo");
    bytes32 public constant SUDO_ADMIN = keccak256("dfxsgd.twap.sudo.admin");

    // **** Constants **** //
    address internal constant SUSHI_FACTORY =
        0xC0AEe478e3658e2610c5F7A4A2E1777cE9e4f2Ac;
    address internal constant WETH = 0xC02aaA39b223FE8D0A0e5C4F27eAD9083C756Cc2;
    address internal constant DFX = 0x888888435FDe8e7d4c54cAb67f206e4199454c60;

    IChainLinkOracle ETH_USD_ORACLE =
        IChainLinkOracle(0x5f4eC3Df9cbd43714FE2740f5E3616155c5b8419);
    IChainLinkOracle SGD_USD_ORACLE =
        IChainLinkOracle(0xe25277fF4bbF9081C75Ab0EB13B4A13a721f3E13);

    constructor(address _admin)
        UniswapV2Oracle(SUSHI_FACTORY, DFX, WETH, 6 hours)
    {
        _setRoleAdmin(SUDO, SUDO_ADMIN);
        _setupRole(SUDO_ADMIN, _admin);
        _setupRole(SUDO, _admin);
    }

    // **** Restricted functions **** //

    /// @notice Reads the price feed and updates internal TWAP state
    function update() public override onlyRole(SUDO) {
        super.update();
        emit Updated(price0CumulativeLast, price1CumulativeLast, blockTimestampLast);
    }

    /// @notice Changes the TWAP period
    function setPeriod(uint256 _period) public onlyRole(SUDO) {
        period = _period;
        emit PeriodSet(period);
    }

    // **** Public functions **** //

    /// @notice Returns price of DFX in SGD, e.g. 1 DFX = X SGD
    ///         Will assume 1 XSGD = 1 SGD in this case
    function read() public view override returns (uint256) {
        // 18 dec
        uint256 wethPerDfx18 = consult(DFX, 1e18);

        // in256, 8 dec -> uint256 18 dec
        (, int256 usdPerEth8, , , ) = ETH_USD_ORACLE.latestRoundData();
        (, int256 usdPerSgd8, , , ) = SGD_USD_ORACLE.latestRoundData();
        uint256 usdPerEth18 = uint256(usdPerEth8) * 1e10;
        uint256 usdPerSgd18 = uint256(usdPerSgd8) * 1e10;

        // (eth/dfx) * (usd/eth) = usd/dfx
        uint256 usdPerDfx = (wethPerDfx18 * usdPerEth18) / 1e18;

        // (usd/dfx) / (usd/sgd) = sgd/dfx
        uint256 sgdPerDfx = (usdPerDfx * 1e18) / usdPerSgd18;

        return sgdPerDfx;
    }

    /* ========== EVENTS ========== */
    event Updated(uint256 price0CumulativeLast, uint256 price1CumulativeLast, uint32 blockTimestampLast);
    event PeriodSet(uint256 period);
}

// File: contracts/AccessControl.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (access/AccessControl.sol)

pragma solidity ^0.8.0;

import "./IAccessControl.sol";
import "./Context.sol";
import "./Strings.sol";
import "./ERC165.sol";

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

    mapping(bytes32 => RoleData) private _roles;

    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;

    /**
     * @dev Modifier that checks that an account has a specific role. Reverts
     * with a standardized message including the required role.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     *
     * _Available since v4.1._
     */
    modifier onlyRole(bytes32 role) {
        _checkRole(role);
        _;
    }

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

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

    /**
     * @dev Revert with a standard message if `_msgSender()` is missing `role`.
     * Overriding this function changes the behavior of the {onlyRole} modifier.
     *
     * Format of the revert message is described in {_checkRole}.
     *
     * _Available since v4.6._
     */
    function _checkRole(bytes32 role) internal view virtual {
        _checkRole(role, _msgSender());
    }

    /**
     * @dev Revert with a standard message if `account` is missing `role`.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     */
    function _checkRole(bytes32 role, address account) internal view virtual {
        if (!hasRole(role, account)) {
            revert(
                string(
                    abi.encodePacked(
                        "AccessControl: account ",
                        Strings.toHexString(uint160(account), 20),
                        " is missing role ",
                        Strings.toHexString(uint256(role), 32)
                    )
                )
            );
        }
    }

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

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

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

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

        _revokeRole(role, account);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event. Note that unlike {grantRole}, this function doesn't perform any
     * checks on the calling account.
     *
     * [WARNING]
     * ====
     * This function should only be called from the constructor when setting
     * up the initial roles for the system.
     *
     * Using this function in any other way is effectively circumventing the admin
     * system imposed by {AccessControl}.
     * ====
     *
     * NOTE: This function is deprecated in favor of {_grantRole}.
     */
    function _setupRole(bytes32 role, address account) internal virtual {
        _grantRole(role, account);
    }

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

    /**
     * @dev Grants `role` to `account`.
     *
     * Internal function without access restriction.
     */
    function _grantRole(bytes32 role, address account) internal virtual {
        if (!hasRole(role, account)) {
            _roles[role].members[account] = true;
            emit RoleGranted(role, account, _msgSender());
        }
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * Internal function without access restriction.
     */
    function _revokeRole(bytes32 role, address account) internal virtual {
        if (hasRole(role, account)) {
            _roles[role].members[account] = false;
            emit RoleRevoked(role, account, _msgSender());
        }
    }
}

// File: contracts/UniswapV2Oracle.sol



// SPDX-License-Identifier: MIT
// https://github.com/Uniswap/v2-periphery/blob/master/contracts/examples/ExampleOracleSimple.sol

pragma solidity ^0.8.10;
pragma experimental ABIEncoderV2;

import "./IUniswapV2.sol";
import "./FixedPoint.sol";
import "./UniswapV2.sol";

contract UniswapV2Oracle {
    using FixedPoint for *;

    uint256 public period;

    uint256 public price0CumulativeLast;
    uint256 public price1CumulativeLast;
    uint32 public blockTimestampLast;

    FixedPoint.uq112x112 public price0Average;
    FixedPoint.uq112x112 public price1Average;

    IUniswapV2Pair public immutable pair;
    address public immutable token0;
    address public immutable token1;

    constructor(
        address factory,
        address tokenA,
        address tokenB,
        uint256 _period
    ) {
        period = _period;

        pair = IUniswapV2Pair(
            IUniswapV2Factory(factory).getPair(tokenA, tokenB)
        );

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

        price0CumulativeLast = pair.price0CumulativeLast();
        price1CumulativeLast = pair.price1CumulativeLast();
        
        (uint112 reserve0,uint112 reserve1,) = pair.getReserves();
        
        price0Average = FixedPoint.fraction(reserve1, reserve0);
        price1Average = FixedPoint.fraction(reserve0, reserve1);

        (reserve0, reserve1, blockTimestampLast) = pair.getReserves();
        require(reserve0 > 0 && reserve1 > 0, "empty-pair");
    }

    function update() public virtual {
        (
            uint256 price0Cumulative,
            uint256 price1Cumulative,
            uint32 blockTimestamp
        ) = UniswapV2OracleLibrary.currentCumulativePrices(address(pair));
        unchecked { 
            uint32 timeElapsed = blockTimestamp - blockTimestampLast; // overflow is desired

            // ensure that at least one full period has passed since the last update
            require(timeElapsed >= period, "UNIV2ORACLE: PERIOD_NOT_ELAPSED");

            // overflow is desired, casting never truncates
            // cumulative price is in (uq112x112 price * seconds) units so we simply wrap it after division by time elapsed
            price0Average = FixedPoint.uq112x112(
                uint224((price0Cumulative - price0CumulativeLast) / timeElapsed)
            );
            price1Average = FixedPoint.uq112x112(
                uint224((price1Cumulative - price1CumulativeLast) / timeElapsed)
            );
        }

        price0CumulativeLast = price0Cumulative;
        price1CumulativeLast = price1Cumulative;
        blockTimestampLast = blockTimestamp;
    }

    // note this will always return 0 before update has been called successfully for the first time.
    function consult(address token, uint256 amountIn)
        public
        view
        returns (uint256)
    {
        if (token == token0) {
            return price0Average.mul(amountIn).decode144();
        } else if (token == token1) {
            return price1Average.mul(amountIn).decode144();
        }

        revert("UNIV2ORACLE: INVALID_TOKEN");
    }
}
// File: contracts/IChainLinkOracle.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.5.0;

interface IChainLinkOracle {
    function acceptOwnership() external;

    function accessController() external view returns (address);

    function aggregator() external view returns (address);

    function confirmAggregator(address _aggregator) external;

    function decimals() external view returns (uint8);

    function description() external view returns (string memory);

    function getAnswer(uint256 _roundId) external view returns (int256);

    function getRoundData(uint80 _roundId)
        external
        view
        returns (
            uint80 roundId,
            int256 answer,
            uint256 startedAt,
            uint256 updatedAt,
            uint80 answeredInRound
        );

    function getTimestamp(uint256 _roundId) external view returns (uint256);

    function latestAnswer() external view returns (int256);

    function latestRound() external view returns (uint256);

    function latestRoundData()
        external
        view
        returns (
            uint80 roundId,
            int256 answer,
            uint256 startedAt,
            uint256 updatedAt,
            uint80 answeredInRound
        );

    function latestTimestamp() external view returns (uint256);

    function owner() external view returns (address);

    function phaseAggregators(uint16) external view returns (address);

    function phaseId() external view returns (uint16);

    function proposeAggregator(address _aggregator) external;

    function proposedAggregator() external view returns (address);

    function proposedGetRoundData(uint80 _roundId)
        external
        view
        returns (
            uint80 roundId,
            int256 answer,
            uint256 startedAt,
            uint256 updatedAt,
            uint80 answeredInRound
        );

    function proposedLatestRoundData()
        external
        view
        returns (
            uint80 roundId,
            int256 answer,
            uint256 startedAt,
            uint256 updatedAt,
            uint80 answeredInRound
        );

    function setController(address _accessController) external;

    function transferOwnership(address _to) external;

    function version() external view returns (uint256);
}

// File: contracts/IDfxOracle.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.8.0;

abstract contract IDfxOracle {
    function read() public virtual view returns (uint256);
}
// File: contracts/UniswapV2.sol



// SPDX-License-Identifier: GPL-3.0-or-later

pragma solidity >=0.5.0;

import "./IUniswapV2.sol";
import "./FixedPoint.sol";

// library with helper methods for oracles that are concerned with computing average prices
library UniswapV2OracleLibrary {
    using FixedPoint for *;

    // helper function that returns the current block timestamp within the range of uint32, i.e. [0, 2**32 - 1]
    function currentBlockTimestamp() internal view returns (uint32) {
        return uint32(block.timestamp % 2 ** 32);
    }

    // produces the cumulative price using counterfactuals to save gas and avoid a call to sync.
    function currentCumulativePrices(
        address pair
    ) internal view returns (uint price0Cumulative, uint price1Cumulative, uint32 blockTimestamp) {
        blockTimestamp = currentBlockTimestamp();
        price0Cumulative = IUniswapV2Pair(pair).price0CumulativeLast();
        price1Cumulative = IUniswapV2Pair(pair).price1CumulativeLast();

        // if time has elapsed since the last update on the pair, mock the accumulated price values
        (uint112 reserve0, uint112 reserve1, uint32 blockTimestampLast) = IUniswapV2Pair(pair).getReserves();
        if (blockTimestampLast != blockTimestamp) {
            unchecked { 
                // subtraction overflow is desired
                uint32 timeElapsed = blockTimestamp - blockTimestampLast; 
                // addition overflow is desired
                // counterfactual
                price0Cumulative += uint(FixedPoint.fraction(reserve1, reserve0)._x) * timeElapsed;
                // counterfactual
                price1Cumulative += uint(FixedPoint.fraction(reserve0, reserve1)._x) * timeElapsed;
            }
        }
    }
}
// File: contracts/FixedPoint.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.4.0;

import './FullMath.sol';
import './Babylonian.sol';
import './BitMath.sol';

// a library for handling binary fixed point numbers (https://en.wikipedia.org/wiki/Q_(number_format))
library FixedPoint {
    // range: [0, 2**112 - 1]
    // resolution: 1 / 2**112
    struct uq112x112 {
        uint224 _x;
    }

    // range: [0, 2**144 - 1]
    // resolution: 1 / 2**112
    struct uq144x112 {
        uint256 _x;
    }

    uint8 public constant RESOLUTION = 112;
    uint256 public constant Q112 = 0x10000000000000000000000000000; // 2**112
    uint256 private constant Q224 = 0x100000000000000000000000000000000000000000000000000000000; // 2**224
    uint256 private constant LOWER_MASK = 0xffffffffffffffffffffffffffff; // decimal of UQ*x112 (lower 112 bits)

    // encode a uint112 as a UQ112x112
    function encode(uint112 x) internal pure returns (uq112x112 memory) {
        return uq112x112(uint224(x) << RESOLUTION);
    }

    // encodes a uint144 as a UQ144x112
    function encode144(uint144 x) internal pure returns (uq144x112 memory) {
        return uq144x112(uint256(x) << RESOLUTION);
    }

    // decode a UQ112x112 into a uint112 by truncating after the radix point
    function decode(uq112x112 memory self) internal pure returns (uint112) {
        return uint112(self._x >> RESOLUTION);
    }

    // decode a UQ144x112 into a uint144 by truncating after the radix point
    function decode144(uq144x112 memory self) internal pure returns (uint144) {
        return uint144(self._x >> RESOLUTION);
    }

    // multiply a UQ112x112 by a uint, returning a UQ144x112
    // reverts on overflow
    function mul(uq112x112 memory self, uint256 y) internal pure returns (uq144x112 memory) {
        uint256 z = 0;
        require(y == 0 || (z = self._x * y) / y == self._x, 'FixedPoint::mul: overflow');
        return uq144x112(z);
    }

    // multiply a UQ112x112 by an int and decode, returning an int
    // reverts on overflow
    function muli(uq112x112 memory self, int256 y) internal pure returns (int256) {
        uint256 z = FullMath.mulDiv(self._x, uint256(y < 0 ? -y : y), Q112);
        require(z < 2**255, 'FixedPoint::muli: overflow');
        return y < 0 ? -int256(z) : int256(z);
    }

    // multiply a UQ112x112 by a UQ112x112, returning a UQ112x112
    // lossy
    function muluq(uq112x112 memory self, uq112x112 memory other) internal pure returns (uq112x112 memory) {
        if (self._x == 0 || other._x == 0) {
            return uq112x112(0);
        }
        uint112 upper_self = uint112(self._x >> RESOLUTION); // * 2^0
        uint112 lower_self = uint112(self._x & LOWER_MASK); // * 2^-112
        uint112 upper_other = uint112(other._x >> RESOLUTION); // * 2^0
        uint112 lower_other = uint112(other._x & LOWER_MASK); // * 2^-112

        // partial products
        uint224 upper = uint224(upper_self) * upper_other; // * 2^0
        uint224 lower = uint224(lower_self) * lower_other; // * 2^-224
        uint224 uppers_lowero = uint224(upper_self) * lower_other; // * 2^-112
        uint224 uppero_lowers = uint224(upper_other) * lower_self; // * 2^-112

        // so the bit shift does not overflow
        require(upper <= type(uint112).max, 'FixedPoint::muluq: upper overflow');

        // this cannot exceed 256 bits, all values are 224 bits
        uint256 sum = uint256(upper << RESOLUTION) + uppers_lowero + uppero_lowers + (lower >> RESOLUTION);

        // so the cast does not overflow
        require(sum <= type(uint224).max, 'FixedPoint::muluq: sum overflow');

        return uq112x112(uint224(sum));
    }

    // divide a UQ112x112 by a UQ112x112, returning a UQ112x112
    function divuq(uq112x112 memory self, uq112x112 memory other) internal pure returns (uq112x112 memory) {
        require(other._x > 0, 'FixedPoint::divuq: division by zero');
        if (self._x == other._x) {
            return uq112x112(uint224(Q112));
        }
        if (self._x <= type(uint144).max) {
            uint256 value = (uint256(self._x) << RESOLUTION) / other._x;
            require(value <= type(uint224).max, 'FixedPoint::divuq: overflow');
            return uq112x112(uint224(value));
        }

        uint256 result = FullMath.mulDiv(Q112, self._x, other._x);
        require(result <= type(uint224).max, 'FixedPoint::divuq: overflow');
        return uq112x112(uint224(result));
    }

    // returns a UQ112x112 which represents the ratio of the numerator to the denominator
    // can be lossy
    function fraction(uint256 numerator, uint256 denominator) internal pure returns (uq112x112 memory) {
        require(denominator > 0, 'FixedPoint::fraction: division by zero');
        if (numerator == 0) return FixedPoint.uq112x112(0);

        if (numerator <= type(uint144).max) {
            uint256 result = (numerator << RESOLUTION) / denominator;
            require(result <= type(uint224).max, 'FixedPoint::fraction: overflow');
            return uq112x112(uint224(result));
        } else {
            uint256 result = FullMath.mulDiv(numerator, Q112, denominator);
            require(result <= type(uint224).max, 'FixedPoint::fraction: overflow');
            return uq112x112(uint224(result));
        }
    }

    // take the reciprocal of a UQ112x112
    // reverts on overflow
    // lossy
    function reciprocal(uq112x112 memory self) internal pure returns (uq112x112 memory) {
        require(self._x != 0, 'FixedPoint::reciprocal: reciprocal of zero');
        require(self._x != 1, 'FixedPoint::reciprocal: overflow');
        return uq112x112(uint224(Q224 / self._x));
    }

    // square root of a UQ112x112
    // lossy between 0/1 and 40 bits
    function sqrt(uq112x112 memory self) internal pure returns (uq112x112 memory) {
        if (self._x <= type(uint144).max) {
            return uq112x112(uint224(Babylonian.sqrt(uint256(self._x) << 112)));
        }

        uint8 safeShiftBits = 255 - BitMath.mostSignificantBit(self._x);
        safeShiftBits -= safeShiftBits % 2;
        return uq112x112(uint224(Babylonian.sqrt(uint256(self._x) << safeShiftBits) << ((112 - safeShiftBits) / 2)));
    }
}

// File: contracts/IUniswapV2.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.5.0;

interface IUniswapV2Factory {
    event PairCreated(address indexed token0, address indexed token1, address pair, uint256);

    function feeTo() external view returns (address);

    function feeToSetter() external view returns (address);

    function migrator() external view returns (address);

    function getPair(address tokenA, address tokenB) external view returns (address pair);

    function allPairs(uint256) external view returns (address pair);

    function allPairsLength() external view returns (uint256);

    function createPair(address tokenA, address tokenB) external returns (address pair);

    function setFeeTo(address) external;

    function setFeeToSetter(address) external;

    function setMigrator(address) external;
}

interface IUniswapV2Pair {
    event Approval(address indexed owner, address indexed spender, uint256 value);
    event Transfer(address indexed from, address indexed to, uint256 value);

    function name() external pure returns (string memory);

    function symbol() external pure returns (string memory);

    function decimals() external pure returns (uint8);

    function totalSupply() external view returns (uint256);

    function balanceOf(address owner) external view returns (uint256);

    function allowance(address owner, address spender) external view returns (uint256);

    function approve(address spender, uint256 value) external returns (bool);

    function transfer(address to, uint256 value) external returns (bool);

    function transferFrom(
        address from,
        address to,
        uint256 value
    ) external returns (bool);

    function DOMAIN_SEPARATOR() external view returns (bytes32);

    function PERMIT_TYPEHASH() external pure returns (bytes32);

    function nonces(address owner) external view returns (uint256);

    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    event Mint(address indexed sender, uint256 amount0, uint256 amount1);
    event Burn(address indexed sender, uint256 amount0, uint256 amount1, address indexed to);
    event Swap(
        address indexed sender,
        uint256 amount0In,
        uint256 amount1In,
        uint256 amount0Out,
        uint256 amount1Out,
        address indexed to
    );
    event Sync(uint112 reserve0, uint112 reserve1);

    function MINIMUM_LIQUIDITY() external pure returns (uint256);

    function factory() external view returns (address);

    function token0() external view returns (address);

    function token1() external view returns (address);

    function getReserves()
        external
        view
        returns (
            uint112 reserve0,
            uint112 reserve1,
            uint32 blockTimestampLast
        );

    function price0CumulativeLast() external view returns (uint256);

    function price1CumulativeLast() external view returns (uint256);

    function kLast() external view returns (uint256);

    function mint(address to) external returns (uint256 liquidity);

    function burn(address to) external returns (uint256 amount0, uint256 amount1);

    function swap(
        uint256 amount0Out,
        uint256 amount1Out,
        address to,
        bytes calldata data
    ) external;

    function skim(address to) external;

    function sync() external;

    function initialize(address, address) external;
}

interface IUniswapV2Router01 {
    function factory() external pure returns (address);

    function WETH() external pure returns (address);

    function addLiquidity(
        address tokenA,
        address tokenB,
        uint256 amountADesired,
        uint256 amountBDesired,
        uint256 amountAMin,
        uint256 amountBMin,
        address to,
        uint256 deadline
    )
        external
        returns (
            uint256 amountA,
            uint256 amountB,
            uint256 liquidity
        );

    function addLiquidityETH(
        address token,
        uint256 amountTokenDesired,
        uint256 amountTokenMin,
        uint256 amountETHMin,
        address to,
        uint256 deadline
    )
        external
        payable
        returns (
            uint256 amountToken,
            uint256 amountETH,
            uint256 liquidity
        );

    function removeLiquidity(
        address tokenA,
        address tokenB,
        uint256 liquidity,
        uint256 amountAMin,
        uint256 amountBMin,
        address to,
        uint256 deadline
    ) external returns (uint256 amountA, uint256 amountB);

    function removeLiquidityETH(
        address token,
        uint256 liquidity,
        uint256 amountTokenMin,
        uint256 amountETHMin,
        address to,
        uint256 deadline
    ) external returns (uint256 amountToken, uint256 amountETH);

    function removeLiquidityWithPermit(
        address tokenA,
        address tokenB,
        uint256 liquidity,
        uint256 amountAMin,
        uint256 amountBMin,
        address to,
        uint256 deadline,
        bool approveMax,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external returns (uint256 amountA, uint256 amountB);

    function removeLiquidityETHWithPermit(
        address token,
        uint256 liquidity,
        uint256 amountTokenMin,
        uint256 amountETHMin,
        address to,
        uint256 deadline,
        bool approveMax,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external returns (uint256 amountToken, uint256 amountETH);

    function swapExactTokensForTokens(
        uint256 amountIn,
        uint256 amountOutMin,
        address[] calldata path,
        address to,
        uint256 deadline
    ) external returns (uint256[] memory amounts);

    function swapTokensForExactTokens(
        uint256 amountOut,
        uint256 amountInMax,
        address[] calldata path,
        address to,
        uint256 deadline
    ) external returns (uint256[] memory amounts);

    function swapExactETHForTokens(
        uint256 amountOutMin,
        address[] calldata path,
        address to,
        uint256 deadline
    ) external payable returns (uint256[] memory amounts);

    function swapTokensForExactETH(
        uint256 amountOut,
        uint256 amountInMax,
        address[] calldata path,
        address to,
        uint256 deadline
    ) external returns (uint256[] memory amounts);

    function swapExactTokensForETH(
        uint256 amountIn,
        uint256 amountOutMin,
        address[] calldata path,
        address to,
        uint256 deadline
    ) external returns (uint256[] memory amounts);

    function swapETHForExactTokens(
        uint256 amountOut,
        address[] calldata path,
        address to,
        uint256 deadline
    ) external payable returns (uint256[] memory amounts);

    function quote(
        uint256 amountA,
        uint256 reserveA,
        uint256 reserveB
    ) external pure returns (uint256 amountB);

    function getAmountOut(
        uint256 amountIn,
        uint256 reserveIn,
        uint256 reserveOut
    ) external pure returns (uint256 amountOut);

    function getAmountIn(
        uint256 amountOut,
        uint256 reserveIn,
        uint256 reserveOut
    ) external pure returns (uint256 amountIn);

    function getAmountsOut(uint256 amountIn, address[] calldata path) external view returns (uint256[] memory amounts);

    function getAmountsIn(uint256 amountOut, address[] calldata path) external view returns (uint256[] memory amounts);
}

interface IUniswapV2Router02 is IUniswapV2Router01 {
    function removeLiquidityETHSupportingFeeOnTransferTokens(
        address token,
        uint256 liquidity,
        uint256 amountTokenMin,
        uint256 amountETHMin,
        address to,
        uint256 deadline
    ) external returns (uint256 amountETH);

    function removeLiquidityETHWithPermitSupportingFeeOnTransferTokens(
        address token,
        uint256 liquidity,
        uint256 amountTokenMin,
        uint256 amountETHMin,
        address to,
        uint256 deadline,
        bool approveMax,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external returns (uint256 amountETH);

    function swapExactTokensForTokensSupportingFeeOnTransferTokens(
        uint256 amountIn,
        uint256 amountOutMin,
        address[] calldata path,
        address to,
        uint256 deadline
    ) external;

    function swapExactETHForTokensSupportingFeeOnTransferTokens(
        uint256 amountOutMin,
        address[] calldata path,
        address to,
        uint256 deadline
    ) external payable;

    function swapExactTokensForETHSupportingFeeOnTransferTokens(
        uint256 amountIn,
        uint256 amountOutMin,
        address[] calldata path,
        address to,
        uint256 deadline
    ) external;
}

// File: contracts/ERC165.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165.sol)

pragma solidity ^0.8.0;

import "./IERC165.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 *
 * Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
 */
abstract contract ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// File: contracts/Strings.sol



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

pragma solidity ^0.8.0;

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _HEX_SYMBOLS = "0123456789abcdef";

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        // Inspired by OraclizeAPI's implementation - MIT licence
        // https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol

        if (value == 0) {
            return "0";
        }
        uint256 temp = value;
        uint256 digits;
        while (temp != 0) {
            digits++;
            temp /= 10;
        }
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
            value /= 10;
        }
        return string(buffer);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        if (value == 0) {
            return "0x00";
        }
        uint256 temp = value;
        uint256 length = 0;
        while (temp != 0) {
            length++;
            temp >>= 8;
        }
        return toHexString(value, length);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _HEX_SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }
}

// File: contracts/Context.sol



// 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;
    }
}

// File: contracts/IAccessControl.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (access/IAccessControl.sol)

pragma solidity ^0.8.0;

/**
 * @dev External interface of AccessControl declared to support ERC165 detection.
 */
interface IAccessControl {
    /**
     * @dev Emitted when `newAdminRole` is set as ``role``'s admin role, replacing `previousAdminRole`
     *
     * `DEFAULT_ADMIN_ROLE` is the starting admin for all roles, despite
     * {RoleAdminChanged} not being emitted signaling this.
     *
     * _Available since v3.1._
     */
    event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);

    /**
     * @dev Emitted when `account` is granted `role`.
     *
     * `sender` is the account that originated the contract call, an admin role
     * bearer except when using {AccessControl-_setupRole}.
     */
    event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);

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

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

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

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

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

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

// File: contracts/BitMath.sol



// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.5.0;

library BitMath {
    // returns the 0 indexed position of the most significant bit of the input x
    // s.t. x >= 2**msb and x < 2**(msb+1)
    function mostSignificantBit(uint256 x) internal pure returns (uint8 r) {
        require(x > 0, 'BitMath::mostSignificantBit: zero');

        if (x >= 0x100000000000000000000000000000000) {
            x >>= 128;
            r += 128;
        }
        if (x >= 0x10000000000000000) {
            x >>= 64;
            r += 64;
        }
        if (x >= 0x100000000) {
            x >>= 32;
            r += 32;
        }
        if (x >= 0x10000) {
            x >>= 16;
            r += 16;
        }
        if (x >= 0x100) {
            x >>= 8;
            r += 8;
        }
        if (x >= 0x10) {
            x >>= 4;
            r += 4;
        }
        if (x >= 0x4) {
            x >>= 2;
            r += 2;
        }
        if (x >= 0x2) r += 1;
    }

    // returns the 0 indexed position of the least significant bit of the input x
    // s.t. (x & 2**lsb) != 0 and (x & (2**(lsb) - 1)) == 0)
    // i.e. the bit at the index is set and the mask of all lower bits is 0
    function leastSignificantBit(uint256 x) internal pure returns (uint8 r) {
        require(x > 0, 'BitMath::leastSignificantBit: zero');

        r = 255;
        if (x & type(uint128).max > 0) {
            r -= 128;
        } else {
            x >>= 128;
        }
        if (x & type(uint64).max > 0) {
            r -= 64;
        } else {
            x >>= 64;
        }
        if (x & type(uint32).max > 0) {
            r -= 32;
        } else {
            x >>= 32;
        }
        if (x & type(uint16).max > 0) {
            r -= 16;
        } else {
            x >>= 16;
        }
        if (x & type(uint8).max > 0) {
            r -= 8;
        } else {
            x >>= 8;
        }
        if (x & 0xf > 0) {
            r -= 4;
        } else {
            x >>= 4;
        }
        if (x & 0x3 > 0) {
            r -= 2;
        } else {
            x >>= 2;
        }
        if (x & 0x1 > 0) r -= 1;
    }
}

// File: contracts/Babylonian.sol



// SPDX-License-Identifier: GPL-3.0-or-later

pragma solidity >=0.4.0;

// computes square roots using the babylonian method
// https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
library Babylonian {
    // credit for this implementation goes to
    // https://github.com/abdk-consulting/abdk-libraries-solidity/blob/master/ABDKMath64x64.sol#L687
    function sqrt(uint256 x) internal pure returns (uint256) {
        if (x == 0) return 0;
        // this block is equivalent to r = uint256(1) << (BitMath.mostSignificantBit(x) / 2);
        // however that code costs significantly more gas
        uint256 xx = x;
        uint256 r = 1;
        if (xx >= 0x100000000000000000000000000000000) {
            xx >>= 128;
            r <<= 64;
        }
        if (xx >= 0x10000000000000000) {
            xx >>= 64;
            r <<= 32;
        }
        if (xx >= 0x100000000) {
            xx >>= 32;
            r <<= 16;
        }
        if (xx >= 0x10000) {
            xx >>= 16;
            r <<= 8;
        }
        if (xx >= 0x100) {
            xx >>= 8;
            r <<= 4;
        }
        if (xx >= 0x10) {
            xx >>= 4;
            r <<= 2;
        }
        if (xx >= 0x8) {
            r <<= 1;
        }
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1;
        r = (r + x / r) >> 1; // Seven iterations should be enough
        uint256 r1 = x / r;
        return (r < r1 ? r : r1);
    }
}

// File: contracts/FullMath.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.8.0;

/// @notice Math library that facilitates multiplication and division that can have overflow of an intermediate value without any loss of precision.
/// @author Adapted from https://github.com/Uniswap/uniswap-v3-core/blob/main/contracts/libraries/FullMath.sol.
/// @dev Handles "phantom overflow", i.e., allows multiplication and division where an intermediate value overflows 256 bits.
library FullMath {
    /// @notice Calculates floor(a×b÷denominator) with full precision - throws if result overflows an uint256 or denominator == 0.
    /// @param a The multiplicand.
    /// @param b The multiplier.
    /// @param denominator The divisor.
    /// @return result The 256-bit result.
    /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
    function mulDiv(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
    unchecked {
        // 512-bit multiply [prod1 prod0] = a * b.
        // 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.
        uint256 prod0; // Least significant 256 bits of the product.
        uint256 prod1; // Most significant 256 bits of the product.
        assembly {
            let mm := mulmod(a, b, not(0))
            prod0 := mul(a, b)
            prod1 := sub(sub(mm, prod0), lt(mm, prod0))
        }
        // Handle non-overflow cases, 256 by 256 division.
        if (prod1 == 0) {
            require(denominator > 0);
            assembly {
                result := div(prod0, denominator)
            }
            return result;
        }
        // Make sure the result is less than 2**256 -
        // also prevents denominator == 0.
        require(denominator > prod1);
        ///////////////////////////////////////////////
        // 512 by 256 division.
        ///////////////////////////////////////////////
        // Make division exact by subtracting the remainder from [prod1 prod0] -
        // compute remainder using mulmod.
        uint256 remainder;
        assembly {
            remainder := mulmod(a, b, denominator)
        }
        // Subtract 256 bit number from 512 bit number.
        assembly {
            prod1 := sub(prod1, gt(remainder, prod0))
            prod0 := sub(prod0, remainder)
        }
        // Factor powers of two out of denominator -
        // compute largest power of two divisor of denominator
        // (always >= 1).
        uint256 twos = uint256(-int256(denominator)) & denominator;
        // Divide denominator by power of two.
        assembly {
            denominator := div(denominator, twos)
        }
        // Divide [prod1 prod0] by the factors of two.
        assembly {
            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.
        assembly {
            twos := add(div(sub(0, twos), twos), 1)
        }
        prod0 |= prod1 * twos;
        // Invert denominator mod 2**256 -
        // now that denominator is an odd number, it has an inverse
        // modulo 2**256 such that denominator * inv = 1 mod 2**256.
        // Compute the inverse by starting with a seed that is correct
        // for four bits. That is, denominator * inv = 1 mod 2**4.
        uint256 inv = (3 * denominator) ^ 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 *= 2 - denominator * inv; // Inverse mod 2**8.
        inv *= 2 - denominator * inv; // Inverse mod 2**16.
        inv *= 2 - denominator * inv; // Inverse mod 2**32.
        inv *= 2 - denominator * inv; // Inverse mod 2**64.
        inv *= 2 - denominator * inv; // Inverse mod 2**128.
        inv *= 2 - denominator * inv; // Inverse mod 2**256.
        // Because the division is now exact we can divide by multiplying
        // with the modular inverse of denominator. This will give us the
        // correct result modulo 2**256. Since the precoditions guarantee
        // that the outcome is less than 2**256, this is the final result.
        // We don't need to compute the high bits of the result and prod1
        // is no longer required.
        result = prod0 * inv;
        return result;
    }
    }

    /// @notice Calculates ceil(a×b÷denominator) with full precision - throws if result overflows an uint256 or denominator == 0.
    /// @param a The multiplicand.
    /// @param b The multiplier.
    /// @param denominator The divisor.
    /// @return result The 256-bit result.
    function mulDivRoundingUp(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        result = mulDiv(a, b, denominator);
    unchecked {
        if (mulmod(a, b, denominator) != 0) {
            require(result < type(uint256).max);
            result++;
        }
    }
    }
}
// File: contracts/IERC165.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

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