library SafeMath
{

//@dev Multiplies two numbers, throws on overflow.
function mul(uint256 a, uint256 b) internal pure returns (uint256) {
    if (a == 0) {
        return 0;
    }
    uint256 c = a * b;
    assert(c / a == b);
    return c;
}

//@dev Integer division of two numbers, 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 c;
}

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

//end library
}
//MATH OPERATIONS -- designed to avoid possibility of errors with built-in math functions
function mul(uint256 a, uint256 b) internal pure returns (uint256) {
    if (a == 0) {
        return 0;
    }
    uint256 c = a * b;
    assert(c / a == b);
    return c;
}
//@dev Multiplies two numbers, throws on overflow.