#import<cstdio>
int main(){int a,b,s;while(scanf("%d%d",&a,&b)!=EOF){a+=b,s=0;while(a>0,s++,a/=10);printf("%d\n",s);}}
### Prompt

Please provide a cpp coded solution to the problem described below:

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