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.*;
import java.util.regex.Matcher;

/**
 * Created by Seiya on 2016/10/16.
 */

public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        long N = scanner.nextLong();

        ArrayList<Long> list = new ArrayList<Long>();
        long i = 1;
        while(true){
            if(N % i == 0){
                list.add(N / i);
                if(N / i < i)break;
            }
            i++;
        }

        long ans = 99999999;
        for (int j = 0; j < list.size(); j++) {
            int temp = Math.max(log10(list.get(j)), log10(N / list.get(j)));
            ans = Math.min(ans, temp);
        }
        System.out.println(ans);


    } // mainMethod

    public static int log10(long n){
        int ans = 0;
        while(n > 0){
            n /= 10;
            ans++;
        }

        return ans;
    }


} // MainClass