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