#include <stdio.h>

int main(){

long a,b,i,n;

while(scanf("%ld",&a)!=EOF){

scanf("%ld",&b);

n = a+b;

for(i=1;i<10;i++){

 n = n/10;

if(n==0) break;

}

printf("%ld\n",i);

}


}
### Prompt

Your challenge is to write 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(){

long a,b,i,n;

while(scanf("%ld",&a)!=EOF){

scanf("%ld",&b);

n = a+b;

for(i=1;i<10;i++){

 n = n/10;

if(n==0) break;

}

printf("%ld\n",i);

}


}
```