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.*;
 
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		long a=0;
		boolean warikire = false;
		if( n%2 == 0 ){ a=2; warikire = true;}

		for(long i=3; i<=99999; i+=2){
			if( n%i == 0 ){
				a = i;
				warikire = true;
			}
		}

		if(warikire){
			if( keta((long)Math.sqrt(n)) > keta(a) ){
				System.out.println( keta((long)Math.sqrt(n)) );
			}else{
				System.out.println( keta(a) );
			}
		}else{
			System.out.println( keta(n) );
		}
		return;
	}

	public static int keta( long a ){
		int ans = 1;
		while( a/10 != 0 ){
			a /= 10;
			ans++;
		}
		return ans;
	}
}