#include<stdio.h>
#include<math.h>
int main(){
int a,b;
while(scanf("%d %d",&a,&b)!=EOF){
a+=b;
printf("%d\n",(int)log10(a)+1);
}
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<stdio.h>
#include<math.h>
int main(){
int a,b;
while(scanf("%d %d",&a,&b)!=EOF){
a+=b;
printf("%d\n",(int)log10(a)+1);
}
return 0;
}
```