Adding large numbers in C++

Just wrote a C++ snippet to add huge numbers using strings -

#include <iostream>
using namespace std;

string add (string &s1, string &s2){
int carry=0,sum,i;

string  min=s1,
 max=s2,
 result = "";

// Finds the bigger string
if (s1.length()>s2.length()){
 max = s1;
 min = s2;
} else {
 max = s2;
 min = s1;
}

// Fills the result for overlapping regions of sum
for (i = min.length()-1; i>=0; i--){
 sum = min[i] + max[i + max.length() - min.length()] + carry - 2*'0';

 carry = sum/10;
 sum %=10;

 result = (char)(sum + '0') + result;
}

// Summates the previous carry and the remaining digits of bigger string
i = max.length() - min.length()-1;

while (i>=0){
 sum = max[i] + carry - '0';
 carry = sum/10;
 sum%=10;

 result = (char)(sum + '0') + result;
 i--;
}

// Adds the carry if remaining to the last digit e.g 999+1=1000
if (carry!=0){
 result = (char)(carry + '0') + result;
}

return result;
}

int main (){
// implementation
string a,b;
cin >> a >> b;
cout << add (a,b)<<endl;
return 0;
}

Output :

32485689234981709712094710984091842358764876328746187648716462938589273589723895789237587238947189748917894718973891728937189478913277893257891749817984719287439812789473289475328975981723894718927489127894712894

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

32485689234981709712094710984091842358764876328746187648716462938589273599723895789237587238947189748917894718973891728937189478913277893257891749817984719287439812789473289475328975981723894718927489127894712893