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