#include<iostream>


using namespace std;


int main(){
	int a=0,b=0,c,i;

	while(cin >> a >> b){
		i=1;
		c = a+b;
	
		while(c>=10){
			c = c/10;
			i++;
		}
	cout << i << endl;

	}
}
### Prompt

In cpp, your task is to solve 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 a=0,b=0,c,i;

	while(cin >> a >> b){
		i=1;
		c = a+b;
	
		while(c>=10){
			c = c/10;
			i++;
		}
	cout << i << endl;

	}
}
```