#include <stdio.h>

int main(){
 int a,b;
 while(scanf("%d %d ",&a,&b)>0){
  a+=b;
  b=0;
  while(a>0){
   b++;
   a/=10;
  }
  printf("%d\n",(b?b:1));
 }



 return 0;
}
### Prompt

Develop a solution in CPP to the problem described below:

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 <stdio.h>

int main(){
 int a,b;
 while(scanf("%d %d ",&a,&b)>0){
  a+=b;
  b=0;
  while(a>0){
   b++;
   a/=10;
  }
  printf("%d\n",(b?b:1));
 }



 return 0;
}
```