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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;
import java.util.HashSet;
import java.util.Set;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long N = sc.nextLong();

		Set<Long> x = new HashSet<>();
		
		for(long i = 1; i * i <= N; i++) {
			if(N % i == 0) {
				x.add(i);
				x.add(N / i);
			}
		}
		
		int min = 100;
		
		for(Long i : x) {
			String a = String.valueOf(i);
			String b = String.valueOf(N / i);
			int temp = Math.max(a.length(), b.length());
			min = Math.min(min, temp);
		}
		System.out.println(min);
	}
}