#include <bits/stdc++.h>
#include <cmath>
using namespace std;
int main(){
  long N;
  cin>>N;
  double a;
  a=sqrt(N);
  int A=a;
  string s;
    for(int i=A;i>0;i--){
      if(N%i==0){
        s=to_string(N/i);
        cout<<s.size();
        break;
      }
  }
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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>
#include <cmath>
using namespace std;
int main(){
  long N;
  cin>>N;
  double a;
  a=sqrt(N);
  int A=a;
  string s;
    for(int i=A;i>0;i--){
      if(N%i==0){
        s=to_string(N/i);
        cout<<s.size();
        break;
      }
  }
}

```