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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main 
{
	public static void main(String[] args) throws IOException 
	{
		// TODO 自動生成されたメソッド・スタブ
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		long N = Long.parseLong(br.readLine());
		int i = 10000000;
		long O = 0;
		long T = 0;
		int o = 0;
		int t = 0;
		for(long l = 1; l < (long)Math.sqrt(N) + 10; l++)
		{
			if(N % l == 0)
			{
				O = l;
				T = N / l;
				o = (int) Math.log10(O) + 1;
				t = (int) Math.log10(T) + 1;
				if(i > (o > t ? o : t)) i = (o > t ? o : t);
			}
		}
		System.out.println(i);
	}
}