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
#include<iostream>
using namespace std;
int main() {
long long n;
cin >> n;
int ans = 10;
for(long long i = 1; i*i <= n; i++) {
if(n%i != 0) continue;
if(to_string(n/i).size() < ans) ans = to_string(n/i).size();
}
cout << ans << endl;
return 0;
}