#include<iostream>
using namespace std;
int main()
{
int a,b,c;
while(cin>>a>>b)
{int k=0;
 c=a+b;

 while(c!=0) 
 {
 c=c/10;
 k++;

 }

 cout<<k<<endl;

}

return 0;

}
### Prompt

Please create a solution in CPP 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>
using namespace std;
int main()
{
int a,b,c;
while(cin>>a>>b)
{int k=0;
 c=a+b;

 while(c!=0) 
 {
 c=c/10;
 k++;

 }

 cout<<k<<endl;

}

return 0;

}
```