#include<iostream>
using namespace std;
int main(){
  int a,b;
  while(cin >>a>>b){
    int ans = 1,c = a+b;
    for(;c>9; ans++,c/=10);
    cout <<ans<<endl;
  }
  return 0;
}
### Prompt

Your challenge is to write a Cpp solution to the following problem:

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

Constraints

* 0 ≤ a, b ≤ 1,000,000
* The number of datasets ≤ 200

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.

Output

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

Example

Input

5 7
1 99
1000 999


Output

2
3
4

### Response

```cpp
#include<iostream>
using namespace std;
int main(){
  int a,b;
  while(cin >>a>>b){
    int ans = 1,c = a+b;
    for(;c>9; ans++,c/=10);
    cout <<ans<<endl;
  }
  return 0;
}
```