#include <stdio.h>
int main() {
  int a,b,cnt;
  while(scanf("%d %d",&a,&b)!=EOF) {
    cnt=1;
    a += b;
    while(a/=10,a>0) cnt++;
    printf("%d\n",cnt);
  }
  
}
### Prompt

Please formulate 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 <stdio.h>
int main() {
  int a,b,cnt;
  while(scanf("%d %d",&a,&b)!=EOF) {
    cnt=1;
    a += b;
    while(a/=10,a>0) cnt++;
    printf("%d\n",cnt);
  }
  
}
```