library SafeMath {

    //multiply
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a * b;
        assert(a == 0 || c / a == b);
        return c;
    }
    //divide
    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 c;
    }

    //subtract
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        assert(b <= a);
        return a - b;
    }

    //addition
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        assert(c >= a);
        return c;
    }
}
//Math operations with safety checks that throw on error
function mul(uint256 a, uint256 b) internal pure returns (uint256) {
    uint256 c = a * b;
    assert(a == 0 || c / a == b);
    return c;
}

//multiply