#include <bits/stdc++.h>
using namespace std;

int main() {
   long long N;
   cin >> N;
   int count;
   for (int i=1; i<=sqrt(N); i++) {
       if (N%i==0) {
           string s=to_string(N/i);
           count=s.size();
       }
   }
   cout << count << endl;
}
### Prompt

Generate a cpp solution to the following problem:

You are given an integer N.
For two positive integers A and B, we will define F(A,B) as the larger of the following: the number of digits in the decimal notation of A, and the number of digits in the decimal notation of B.
For example, F(3,11) = 2 since 3 has one digit and 11 has two digits.
Find the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Constraints

* 1 \leq N \leq 10^{10}
* N is an integer.

Input

The input is given from Standard Input in the following format:


N


Output

Print the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Examples

Input

10000


Output

3


Input

1000003


Output

7


Input

9876543210


Output

6

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

int main() {
   long long N;
   cin >> N;
   int count;
   for (int i=1; i<=sqrt(N); i++) {
       if (N%i==0) {
           string s=to_string(N/i);
           count=s.size();
       }
   }
   cout << count << endl;
}
```