#include <iostream>
#include <string>

using namespace std;

int main() {
  int a, b;
  while (cin >> a >> b) {
    string s = to_string(a + b);
    cout << s.size() << endl;
  }
}
### Prompt

Your task is to create 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>
#include <string>

using namespace std;

int main() {
  int a, b;
  while (cin >> a >> b) {
    string s = to_string(a + b);
    cout << s.size() << endl;
  }
}
```