#include <iostream>
#include <cmath>
using namespace std;

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

### Prompt

Create a solution in Cpp for 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>
using namespace std;

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

```