#include<bits/stdc++.h> 
using namespace std;
long long a,b,i,n,ans;
int main(){
    cin>>n;
    for( i=sqrt(n);i>=1;i--)
    {
        if(n%i==0) 
		break;  	
	}
	b=n/i;
	while(b>0)
	{
	   b=b/10;
	   ans++;
	}
	cout<<ans;
  return 0;
} 
### Prompt

In Cpp, your task is to solve 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;
long long a,b,i,n,ans;
int main(){
    cin>>n;
    for( i=sqrt(n);i>=1;i--)
    {
        if(n%i==0) 
		break;  	
	}
	b=n/i;
	while(b>0)
	{
	   b=b/10;
	   ans++;
	}
	cout<<ans;
  return 0;
} 
```