#include <iostream>
#include <cmath>

int main()
{
	long int N, max, num=0;
	scanf("%ld", &N);
	int mid = std::sqrt(N);
	for(int i=1; i<=mid; i++){
		if(N%i==0){
			max = N/i;
		}
	}
	while(max>=10){
		max = max/10;
		num++;
	}
	num++;
	printf("%ld\n", num);
	return 0;
}
### Prompt

Please create a solution in Cpp to 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>

int main()
{
	long int N, max, num=0;
	scanf("%ld", &N);
	int mid = std::sqrt(N);
	for(int i=1; i<=mid; i++){
		if(N%i==0){
			max = N/i;
		}
	}
	while(max>=10){
		max = max/10;
		num++;
	}
	num++;
	printf("%ld\n", num);
	return 0;
}
```