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

int main() {
  int64_t N;
  cin>>N;
  int64_t A=1;
  for(int64_t i=2;i*i<=N;i++){
    if(N%i==0){
      A=i;
    }
  }
  int64_t X=N/A,Z=0;
  while(X!=0||A!=0){
    Z++;
    X/=10;
    A/=10;
  }
  cout<<Z<<endl;
}


### 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>
using namespace std;

int main() {
  int64_t N;
  cin>>N;
  int64_t A=1;
  for(int64_t i=2;i*i<=N;i++){
    if(N%i==0){
      A=i;
    }
  }
  int64_t X=N/A,Z=0;
  while(X!=0||A!=0){
    Z++;
    X/=10;
    A/=10;
  }
  cout<<Z<<endl;
}


```