#include<iostream>
#include<cmath>

using namespace std;

int main(){
int a,b;
while(cin >> a >> b)
{
int x = a+b;
!x?cout << 1 << endl:cout << (int)log10(x)+1 << endl;
}
return 0;
}
### 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
#include<iostream>
#include<cmath>

using namespace std;

int main(){
int a,b;
while(cin >> a >> b)
{
int x = a+b;
!x?cout << 1 << endl:cout << (int)log10(x)+1 << endl;
}
return 0;
}
```