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