#include<iostream>

using namespace std;

int main(){
	int a,b,c,i;
	i=0;
	while(cin>>a>>b){
	c=a+b;
	while(c>0){
	c /= 10;
	i += 1;
	}
	cout<<i<<endl;
	i=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>

using namespace std;

int main(){
	int a,b,c,i;
	i=0;
	while(cin>>a>>b){
	c=a+b;
	while(c>0){
	c /= 10;
	i += 1;
	}
	cout<<i<<endl;
	i=0;
	}
}
```