library SafeMath {

    /**
    * @dev Multiplies two unsigned integers, throws on overflow.
    */
    function mul(uint256 a, uint256 b) internal pure returns (uint256 c) {
        // Gas optimization: this is cheaper than asserting 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-solidity/pull/522
        if (a == 0) {
            return 0;
        }

        c = a * b;
        assert(c / a == b);
        return c;
    }

    /**
    * @dev Multiplies two signed integers, throws on overflow.
    */
    function mul(int256 a, int256 b) internal pure returns (int256) {
        // Gas optimization: this is cheaper than asserting 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-solidity/pull/522
        if (a == 0) {
            return 0;
        }
        int256 c = a * b;
        assert(c / a == b);
        return c;
    }

    /**
    * @dev Integer division of two unsigned integers, truncating the quotient.
    */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        // assert(b > 0); // Solidity automatically throws when dividing by 0
        // uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold
        return a / b;
    }

    /**
    * @dev Integer division of two signed integers, truncating the quotient.
    */
    function div(int256 a, int256 b) internal pure returns (int256) {
        // assert(b > 0); // Solidity automatically throws when dividing by 0
        // Overflow only happens when the smallest negative int is multiplied by -1.
        int256 INT256_MIN = int256((uint256(1) << 255));
        assert(a != INT256_MIN || b != - 1);
        return a / b;
    }

    /**
    * @dev Subtracts two unsigned integers, throws on overflow (i.e. if subtrahend is greater than minuend).
    */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        assert(b <= a);
        return a - b;
    }

    /**
    * @dev Subtracts two signed integers, throws on overflow.
    */
    function sub(int256 a, int256 b) internal pure returns (int256) {
        int256 c = a - b;
        assert((b >= 0 && c <= a) || (b < 0 && c > a));
        return c;
    }

    /**
    * @dev Adds two unsigned integers, throws on overflow.
    */
    function add(uint256 a, uint256 b) internal pure returns (uint256 c) {
        c = a + b;
        assert(c >= a);
        return c;
    }

    /**
    * @dev Adds two signed integers, throws on overflow.
    */
    function add(int256 a, int256 b) internal pure returns (int256) {
        int256 c = a + b;
        assert((b >= 0 && c >= a) || (b < 0 && c < a));
        return c;
    }
}
/**
 * @title SafeMath
 * @dev Math operations with safety checks that throw on error.
 * From zeppelin-solidity
 */
function div(uint256 a, uint256 b) internal pure returns (uint256) {
    // assert(b > 0); // Solidity automatically throws when dividing by 0
    // uint256 c = a / b;
    // assert(a == b * c + a % b); // There is no case in which this doesn't hold
    return a / b;
}

/**
 * @dev Integer division of two unsigned integers, truncating the quotient.
 */