#include<iostream>
using namespace std;
int main(){
int a,b,c;
int C=0;
int d=0;
while(cin>>a>>b){
c=a+b;
C=0;
d=1;
while(c>=d)
{
	C++;
	d*=10;
}
cout<<C<<endl;
}
}
### Prompt

Please create a solution in cpp 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,c;
int C=0;
int d=0;
while(cin>>a>>b){
c=a+b;
C=0;
d=1;
while(c>=d)
{
	C++;
	d*=10;
}
cout<<C<<endl;
}
}
```