Unlimited rows sum SStream

#include <iostream>
#include <string>
#include <cstdlib>
#include <sstream>      // std::stringstream

using namespace std;

int main() {

string input;
string  word;
int sum =0;

    while(getline(cin, input)){
      stringstream stream(input);
      while(stream >> word!=0) {
      int number = atoi(word.c_str());
      sum += number;
     }
     if (input.empty())
       break;
     cout << sum << endl;

    }


}