#include<iostream>
#include<cmath>
using namespace std;
long n,i,a;
int main()
{
	for(cin>>n,i=1,a=99;i<=sqrt(n);i++)if(!(n%i))a=min(a,(long)max(to_string(i).size(),to_string(n/i).size()));cout<<a<<endl;
}
### 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<iostream>
#include<cmath>
using namespace std;
long n,i,a;
int main()
{
	for(cin>>n,i=1,a=99;i<=sqrt(n);i++)if(!(n%i))a=min(a,(long)max(to_string(i).size(),to_string(n/i).size()));cout<<a<<endl;
}
```