#include <cstdio>
int main(){
 int d,n,a,b; 
 while(true){
  d=0;
  if (scanf("%d %d",&a,&b)==EOF) break;
  n=a+b;
  while(n>0) { d++, n/=10;  };
  printf("%d\n",d);
 };
 return 0;
};
### Prompt

In Cpp, your task is to solve 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 <cstdio>
int main(){
 int d,n,a,b; 
 while(true){
  d=0;
  if (scanf("%d %d",&a,&b)==EOF) break;
  n=a+b;
  while(n>0) { d++, n/=10;  };
  printf("%d\n",d);
 };
 return 0;
};
```