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: Runtime Error)

import java.util.*;
class Main{
    public static void main(String[]args){
        Scanner cin=new Scanner(System.in);
        int input;
        int mini;
        int minj;
        ArrayList<Integer> value = new ArrayList<Integer>();
        input=cin.nextInt();
        for(int i=1;i*i<=input;i++){
            for(int j=1;j*j<=input;j++){
                if(i*j==input){
                    mini = String.valueOf(i).length();
                    minj = String.valueOf(j).length();
                    if(mini>minj){
                        value.add(mini);
                    }else{
                        value.add(minj);
                    }
                }
            }
        }
        Collections.sort(value);
        System.out.println(value.get(0));
        }
    }