#include <iostream>
using namespace std;

int main(){
int cnt, a, b, tmp;

while(cin>>a>>b){
  cnt=0;
  tmp=a+b;
  while(tmp>0){
    cnt++;
    tmp/=10;
  }
  cout<<cnt<<endl;
 }
}
### Prompt

Generate 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>
using namespace std;

int main(){
int cnt, a, b, tmp;

while(cin>>a>>b){
  cnt=0;
  tmp=a+b;
  while(tmp>0){
    cnt++;
    tmp/=10;
  }
  cout<<cnt<<endl;
 }
}
```