#include<iostream>
#include<cmath>

int main(){
	int a,b;
	while (std::cin >> a >> b)
		std::cout << static_cast<int>(log10(a + b)) + 1 << std::endl;
	return 0;
}
### Prompt

Your task is to create 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>
#include<cmath>

int main(){
	int a,b;
	while (std::cin >> a >> b)
		std::cout << static_cast<int>(log10(a + b)) + 1 << std::endl;
	return 0;
}
```