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: Time Limit Exceeded)

import java.util.Scanner;

public class Main
{
	public static void main(String[] args)
	{
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		sc.close();
		int ans = 11;
		for (long i=1; i<=n; i++) {
			if (n % i == 0) {
				long j = n / i;
				int buf = 0;
				int a = keta(i);
				int b = keta(j);
				if (a>=b) {
					buf = a;
				} else {
					buf = b;
				}
				if (ans > buf) ans = buf;
				if (i>=j) break;
			}
		}
		System.out.println(ans);
	}

	private static int keta(long n)
	{
		int ans = 1;
		long index = 10;
		for (int i=0; i<10; i++) {
			if (n <index) return ans;
			index *=10;
			ans +=1;
		}
		return ans;
	}
}