#include <iostream>
#include <cmath>

using namespace std;

typedef long long LL;

int main() {
  LL N;
  cin >> N;
  LL max = 1;
  for (LL i = 2; i * i <= N; ++i) {
    if (N % i == 0) {
      max = i;
    }
  }
  cout << (int)log10(N / max) + 1 << endl;

  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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>
#include <cmath>

using namespace std;

typedef long long LL;

int main() {
  LL N;
  cin >> N;
  LL max = 1;
  for (LL i = 2; i * i <= N; ++i) {
    if (N % i == 0) {
      max = i;
    }
  }
  cout << (int)log10(N / max) + 1 << endl;

  return 0;
}

```