#include <stdio.h>
int main(void){
  int ans=0;
  long n,i=1,a,b,e=1;
  scanf("%ld",&n);
  while (i*i<=n){
    if (n%i==0) a=i;
    i++;
  }
  b=n/a;
  while (e<=b){
    e*=10;
    ans++;
  }
  printf("%d\n",ans);
  return 0;
}
### Prompt

Create a solution in CPP for 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 <stdio.h>
int main(void){
  int ans=0;
  long n,i=1,a,b,e=1;
  scanf("%ld",&n);
  while (i*i<=n){
    if (n%i==0) a=i;
    i++;
  }
  b=n/a;
  while (e<=b){
    e*=10;
    ans++;
  }
  printf("%d\n",ans);
  return 0;
}
```