#include<iostream>
#include<algorithm>
#include<vector>
#include<cmath>
using namespace std;
int main(){
    int a,b;
    while(cin>>a>>b)
        cout<<(int)log10(a+b)+1<<endl;

}
### 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
#include<iostream>
#include<algorithm>
#include<vector>
#include<cmath>
using namespace std;
int main(){
    int a,b;
    while(cin>>a>>b)
        cout<<(int)log10(a+b)+1<<endl;

}
```