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

int main() {
  long long N, A, B;
  cin >> N;

  for (long long i = 1LL; i * i <= N; ++i) if (N % i == 0) A = i;

  int count = 0;
  B = N / A;
  while (B > 0) {
    B /= 10;
    count++;
  }
  cout << count << endl;
}

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

int main() {
  long long N, A, B;
  cin >> N;

  for (long long i = 1LL; i * i <= N; ++i) if (N % i == 0) A = i;

  int count = 0;
  B = N / A;
  while (B > 0) {
    B /= 10;
    count++;
  }
  cout << count << endl;
}

```