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

Construct a CPP code solution to the problem outlined:

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,temp,i;
while(scanf("%d%d",&a,&b)!=EOF){
temp=a+b;
i=0;
while(temp){
i++;
temp/=10;
}
printf("%d\n",i);
}
}
```