#include <stdio.h>
long long n, a, b;
int main() {
	scanf("%lld", &n);
	for (long long i = 1; i * i <= n; i++) {
		if (n % i == 0) {
			a = i;
			b = n / i;
		}
	}
	a = 0;
	while (b) {
		b /= 10;
		a++;
	}
	printf("%lld\n", a);
}
### 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 <stdio.h>
long long n, a, b;
int main() {
	scanf("%lld", &n);
	for (long long i = 1; i * i <= n; i++) {
		if (n % i == 0) {
			a = i;
			b = n / i;
		}
	}
	a = 0;
	while (b) {
		b /= 10;
		a++;
	}
	printf("%lld\n", a);
}
```