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

Generate 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;
	while(cin>>a>>b)
	{ 
		int x=a+b;
		int n=0; 
		while(x) 
		{ 
			n++;
			x/=10;
		}
		cout<<n<<endl;
	} 
	return 0;
}
```