#include <iostream>
#include <cmath>

long long int n;

int main() {
    std::cin>>n;
    int i;
    for(i=sqrt(n);i>=1&&n%i!=0;--i);
    i=n/i;
    int cnt=0;
    while(i>0){
        i/=10;
        ++cnt;
    }
    std::cout<<cnt<<std::endl;
    return 0;
}
### Prompt

Develop a solution in Cpp 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 <iostream>
#include <cmath>

long long int n;

int main() {
    std::cin>>n;
    int i;
    for(i=sqrt(n);i>=1&&n%i!=0;--i);
    i=n/i;
    int cnt=0;
    while(i>0){
        i/=10;
        ++cnt;
    }
    std::cout<<cnt<<std::endl;
    return 0;
}
```