library SafeMath {

  /**
  * @dev Multiplies two numbers, 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, "SafeMath failure");

        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, "SafeMath failure"); // 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, "SafeMath failure");
        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, "SafeMath failure");

        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, "SafeMath failure");
        return a % b;
    }
}
function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b != 0, "SafeMath failure");
        return a % b;
    }
/**
 * @dev Divides two numbers and returns the remainder (unsigned integer modulo),
 * reverts when dividing by zero.
 */