library SafeMath {

  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;
  }

 
 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;
  }

 
 function sub(uint256 a, uint256 b) internal pure returns (uint256) {
    require(b <= a);
    uint256 c = a - b;

    return c;
  }

  
  function add(uint256 a, uint256 b) internal pure returns (uint256) {
    uint256 c = a + b;
    require(c >= a);

    return c;
  }
  
  function ceil(uint256 a, uint256 m) internal pure returns (uint256) {
    uint256 c = add(a,m);
    uint256 d = sub(c,1);
    return mul(div(d,m),m);
  }

  /**
  * @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;
  }
  
  function divRound(uint256 x, uint256 y) internal pure returns (uint256) {
        require(y != 0, "Div by zero");
        uint256 r = x / y;
        if (x % y != 0) {
            r = r + 1;
        }

        return r;
    }
}
function mod(uint256 a, uint256 b) internal pure returns (uint256) {
  require(b != 0);
  return a % b;
}

/**
 * @dev Divides two numbers and returns the remainder (unsigned integer modulo),
 * reverts when dividing by zero.
 */