library SafeMath { 
    /**
    * @dev Multiplies two unsigned integers, reverts on overflow. 
    */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) { 
        // Gas optimization: this is cheaper than requiring '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;
        }
        uint256 c = a * b; 
        require(c / a == b); 
        return c; 
    }
    /**
    * @dev Integer division of two unsigned integers truncating the quotient, reverts on division by zero. 
    */
    function div(uint256 a, uint256 b) internal pure returns (uint256) 
    {
        // Solidity only automatically asserts when dividing by 0 
        require(b > 0); 
        uint256 c = a / b; 
        //assert(a == b * c + a % b); //There is no case in which this doesn't hold 
        return c; 
    }
    /**
    * @dev Subtracts two unsigned integers, reverts on overflow (i.e. if subtrahend is greater than minuend). 
    */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) 
    { 
        require(b <= a); 
        uint256 c = a - b; 
        return c; 
    }
    /**
    * @dev Adds two unsigned integers, reverts on overflow. 
    */
    function add(uint256 a, uint256 b) internal pure returns (uint256) 
    { 
        uint256 c = a + b; 
        require(c >= a); 
        return c; 
    }
    /**
    * @dev Divides two unsigned integers and returns the remainder (unsigned integer modulo), 
    * reverts when dividing by zero. 
    */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) 
    { 
        require(b != 0); 
        return a % b; 
    }
}
/**
 * @title SafeMath 
 * @dev Unsigned math operations with safety checks that revert on error
 */
function add(uint256 a, uint256 b) internal pure returns (uint256) 
{ 
    uint256 c = a + b; 
    require(c >= a); 
    return c; 
}

/**
 * @dev Adds two unsigned integers, reverts on overflow. 
 */