#include <math.h>
#include <iostream>

using namespace std;

int main()
{
	int a, b;
	while(cin >> a >> b)
	{
		cout << (int)log10(a + b) + 1 << endl;
	}

	return 0;
}
### 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 <math.h>
#include <iostream>

using namespace std;

int main()
{
	int a, b;
	while(cin >> a >> b)
	{
		cout << (int)log10(a + b) + 1 << endl;
	}

	return 0;
}
```