Problem:
Digit Number

Write a program which computes the digit number of sum of two integers a and b.

Input

There are several test cases. Each test case consists of two non-negative integers a and b which are separeted by a space in a line. The input terminates with EOF.

Constraints

0 ≤ a, b ≤ 1,000,000

The number of datasets ≤ 200

Output

Print the number of digits of a + b for each data set.

Sample Input

5 7
1 99
1000 999

Output for the Sample Input

2
3
4

Solution in C++ (judge verdict: Time Limit Exceeded)

#include <iostream>

int main(){
  int a, b, c;
  int i = 1;
  int num = 0;
  
  std::cin >> a;
  std::cin >> b;
  
  c = a + b;
  while(1){
    if(c/i!=0){
      num++;
    }else{
      break;
    }
  }
  std::cout << num << std::endl;
  
  return 0;
}