library SafeMathIntLib {
    int256 constant INT256_MIN = int256((uint256(1) << 255));
    int256 constant INT256_MAX = int256(~((uint256(1) << 255)));

    //
    //Functions below accept positive and negative integers and result must not overflow.
    //
    function div(int256 a, int256 b)
    internal
    pure
    returns (int256)
    {
        require(a != INT256_MIN || b != - 1);
        return a / b;
    }

    function mul(int256 a, int256 b)
    internal
    pure
    returns (int256)
    {
        require(a != - 1 || b != INT256_MIN);
        // overflow
        require(b != - 1 || a != INT256_MIN);
        // overflow
        int256 c = a * b;
        require((b == 0) || (c / b == a));
        return c;
    }

    function sub(int256 a, int256 b)
    internal
    pure
    returns (int256)
    {
        require((b >= 0 && a - b <= a) || (b < 0 && a - b > a));
        return a - b;
    }

    function add(int256 a, int256 b)
    internal
    pure
    returns (int256)
    {
        int256 c = a + b;
        require((b >= 0 && c >= a) || (b < 0 && c < a));
        return c;
    }

    //
    //Functions below only accept positive integers and result must be greater or equal to zero too.
    //
    function div_nn(int256 a, int256 b)
    internal
    pure
    returns (int256)
    {
        require(a >= 0 && b > 0);
        return a / b;
    }

    function mul_nn(int256 a, int256 b)
    internal
    pure
    returns (int256)
    {
        require(a >= 0 && b >= 0);
        int256 c = a * b;
        require(a == 0 || c / a == b);
        require(c >= 0);
        return c;
    }

    function sub_nn(int256 a, int256 b)
    internal
    pure
    returns (int256)
    {
        require(a >= 0 && b >= 0 && b <= a);
        return a - b;
    }

    function add_nn(int256 a, int256 b)
    internal
    pure
    returns (int256)
    {
        require(a >= 0 && b >= 0);
        int256 c = a + b;
        require(c >= a);
        return c;
    }

    //
    //Conversion and validation functions.
    //
    function abs(int256 a)
    public
    pure
    returns (int256)
    {
        return a < 0 ? neg(a) : a;
    }

    function neg(int256 a)
    public
    pure
    returns (int256)
    {
        return mul(a, - 1);
    }

    function toNonZeroInt256(uint256 a)
    public
    pure
    returns (int256)
    {
        require(a > 0 && a < (uint256(1) << 255));
        return int256(a);
    }

    function toInt256(uint256 a)
    public
    pure
    returns (int256)
    {
        require(a >= 0 && a < (uint256(1) << 255));
        return int256(a);
    }

    function toUInt256(int256 a)
    public
    pure
    returns (uint256)
    {
        require(a >= 0);
        return uint256(a);
    }

    function isNonZeroPositiveInt256(int256 a)
    public
    pure
    returns (bool)
    {
        return (a > 0);
    }

    function isPositiveInt256(int256 a)
    public
    pure
    returns (bool)
    {
        return (a >= 0);
    }

    function isNonZeroNegativeInt256(int256 a)
    public
    pure
    returns (bool)
    {
        return (a < 0);
    }

    function isNegativeInt256(int256 a)
    public
    pure
    returns (bool)
    {
        return (a <= 0);
    }

    //
    //Clamping functions.
    //
    function clamp(int256 a, int256 min, int256 max)
    public
    pure
    returns (int256)
    {
        if (a < min)
            return min;
        return (a > max) ? max : a;
    }

    function clampMin(int256 a, int256 min)
    public
    pure
    returns (int256)
    {
        return (a < min) ? min : a;
    }

    function clampMax(int256 a, int256 max)
    public
    pure
    returns (int256)
    {
        return (a > max) ? max : a;
    }
}
/**
 * @title     SafeMathIntLib
 * @dev       Math operations with safety checks that throw on error
 */
function div(int256 a, int256 b)
    internal
    pure
    returns (int256)
    {
        require(a != INT256_MIN || b != - 1);
        return a / b;
    }
//
//Functions below accept positive and negative integers and result must not overflow.
//