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.math.BigInteger;
import java.util.Scanner;

class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		long N = sc.nextLong();
		
		double root_N = Math.sqrt((double)N);
		int root_N_kiriage;
		if((int)root_N==root_N){
			root_N_kiriage = (int)root_N;
		}else{
			root_N_kiriage = (int)root_N + 1;
		}
		//a<b
		int a = 1;
		int b = 1;
		for(int i = root_N_kiriage; i<=N; i++){
			if(N%i == 0){
				a = (int)(N/i);
				b =i;
				break;
			}
		}
		int b_keta = (int)Math.log10((double)b) + 1;
		System.out.println(b_keta);
		
	}

}