#include<iostream>
#include<math.h>
int main(){
	using namespace std;
	int a,b;

	while(cin>>a>>b){
		cout<<int(log10(a+b))+1<<endl;
	}
    return 0;
}
### Prompt

Please formulate 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<math.h>
int main(){
	using namespace std;
	int a,b;

	while(cin>>a>>b){
		cout<<int(log10(a+b))+1<<endl;
	}
    return 0;
}
```