#include<iostream>
using namespace std;
int main(){
	int x,y,z,pre;
	while(cin>>x>>y){
		z=x+y;
		pre=0;
		while(z>0){
			z/=10;
			pre++;
		}
		cout<<pre<<endl;
	}
	return 0;
}
### Prompt

Please create a solution in cpp 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 x,y,z,pre;
	while(cin>>x>>y){
		z=x+y;
		pre=0;
		while(z>0){
			z/=10;
			pre++;
		}
		cout<<pre<<endl;
	}
	return 0;
}
```