library SafeMath {

/**
* @dev Multiplies two numbers, reverts on overflow.
*/
function mul(uint256 _a, uint256 _b) internal pure returns (uint256) {
if (_a == 0) {
return 0;
}

uint256 c = _a * _b;
require(c / _a == _b);

return c;
}

/**
* @dev Integer division of two numbers truncating the quotient, reverts on division by zero.
*/
function div(uint256 _a, uint256 _b) internal pure returns (uint256) {
require(_b > 0); // Solidity only automatically asserts 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 Subtracts two numbers, 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 numbers, 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 numbers 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 Math operations with safety checks that revert on error
 */
function mul(uint256 _a, uint256 _b) internal pure returns (uint256) {
if (_a == 0) {
return 0;
}

uint256 c = _a * _b;
require(c / _a == _b);

return c;
}

/**
 * @dev Multiplies two numbers, reverts on overflow.
 */