#include <iostream>

using namespace std;

int main (void){

	int a,b,i=0;

	while(cin>>a>>b){


		a+=b;
		b=0;
		while(a>0){
			a=a/10;
			i++;
		}

		cout<<i<<endl;
		i=0;
	}
}
### Prompt

Your challenge is to write 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 (void){

	int a,b,i=0;

	while(cin>>a>>b){


		a+=b;
		b=0;
		while(a>0){
			a=a/10;
			i++;
		}

		cout<<i<<endl;
		i=0;
	}
}
```