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: Wrong Answer)


import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		long N = scan.nextLong();
		long min = (long)Math.pow(10,10);
		
		for(long i = 1; i < (long)Math.sqrt(N); i++) {
			if(N % i == 0) {
				if(getMax(i, N / i) < min) {
					min = getMax(i, N / i);
				}
			}
		}
		
		System.out.println(min);
		
		scan.close();

	}
	
	public static int getMax(long A, long B) {
		if(Long.toString(A).length() > Long.toString(B).length()) {
			return Long.toString(A).length();
		} else {
			return Long.toString(B).length();
		}
	}

}