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 sc = new Scanner(System.in);
        long N = sc.nextLong();

        int answer = Integer.MAX_VALUE;
        long left = 1;
        long right = N;
        long divider = 2;
        while (left <= right) {
            if (right % divider == 0) {
                left *= divider;
                right /= divider;
            } else {
                divider += 1;
            }
            int diff = Math.max(digitLength(left), digitLength(right));
            if (answer > Math.max(digitLength(left), digitLength(right))) {
                answer = diff;
            }

        }

        System.out.println(answer);


    }

    private static int digitLength(long i) {
        return Long.toString(i).length();
    }

}