#include <iostream>
int a,b,c,d;int main(){while(std::cin>>a>>b){if(d=a+b){c=0;while(d){c++;d/=10;}}else c=1;std::cout<<c<<"\n";}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 <iostream>
int a,b,c,d;int main(){while(std::cin>>a>>b){if(d=a+b){c=0;while(d){c++;d/=10;}}else c=1;std::cout<<c<<"\n";}return 0;}
```