#include <iostream>
#include <cmath>
using namespace std;
long long weishu=0;
int main(){
	long long i,j,k,n,l=0;
	cin>>n;
	for(i=sqrt(n);i>=1;i--){
		if(n%i==0){
			k=n/i;
			while(k>0){
				k/=10;
				weishu++;
			}
			cout<<weishu<<endl;
			return 0;
		}
	}
}
### Prompt

Please provide a cpp coded solution 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>
using namespace std;
long long weishu=0;
int main(){
	long long i,j,k,n,l=0;
	cin>>n;
	for(i=sqrt(n);i>=1;i--){
		if(n%i==0){
			k=n/i;
			while(k>0){
				k/=10;
				weishu++;
			}
			cout<<weishu<<endl;
			return 0;
		}
	}
}
```