#include <stdio.h>
int fuego(int val) {int ans=0;while (val) ans++,val/=10;return ans;}
int main() {int a,b;while (scanf("%d %d",&a,&b)!=EOF) printf("%d\n",fuego(a+b));return 0;}
### Prompt

Construct a CPP code solution to the problem outlined:

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 <stdio.h>
int fuego(int val) {int ans=0;while (val) ans++,val/=10;return ans;}
int main() {int a,b;while (scanf("%d %d",&a,&b)!=EOF) printf("%d\n",fuego(a+b));return 0;}
```