Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

10000

Sample Output 1

3

F(A,B) has a minimum value of 3 at (A,B)=(100,100).

Sample Input 2

1000003

Sample Output 2

7

There are two pairs (A,B) that satisfy the condition: (1,1000003) and (1000003,1). For these pairs, F(1,1000003)=F(1000003,1)=7.

Sample Input 3

9876543210

Sample Output 3

6

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main{
  public static void main(String[] args){
	  Scanner sc = new Scanner(System.in);
	  long n=sc.nextLong(),min=11;
	  String a="",b="";
	  for(int i=1;i<=Math.sqrt(n);i++) {
		  if(n%i==0) {
			 a=String.valueOf(i);
			 b=String.valueOf(n/i);
			 min=Math.min(min, Math.max(a.length(), b.length()));
		  }
	  }
	  System.out.println(min);
  }
	public static List<Long> divisorEnum(long n) {
		List<Long> l=new ArrayList<>();
		for(long i=1;i<=Math.sqrt(n);i++) {
			if(n%i==0) {
				l.add(i);
				if(i!=Math.sqrt(n))l.add(n/i);
			}
		}
		l.sort(null);
		return l;
	}
}