#import<iostream>
int main(){for(int a,b;std::cin>>a>>b;std::cout<<b<<"\n")for(a+=b,b=0;a,++b,a/=10;);}
### Prompt

Create a solution in CPP for 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
#import<iostream>
int main(){for(int a,b;std::cin>>a>>b;std::cout<<b<<"\n")for(a+=b,b=0;a,++b,a/=10;);}
```