#include <iostream>
using namespace std;

typedef long long ll;

int main(){
  ll n;
  cin >> n;
  ll val=0;
  for(ll i=1;i*i<=n;i++){
    if(n%i==0) val=i;
  }
  val=n/val;
  int ans=0;
  while(val>0){
    val/=10;
    ans++;
  }
  cout << ans << endl;
}
### Prompt

Your task is to create 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 <iostream>
using namespace std;

typedef long long ll;

int main(){
  ll n;
  cin >> n;
  ll val=0;
  for(ll i=1;i*i<=n;i++){
    if(n%i==0) val=i;
  }
  val=n/val;
  int ans=0;
  while(val>0){
    val/=10;
    ans++;
  }
  cout << ans << endl;
}
```