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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.Scanner;
public class Main {
	public static void main(String[] args) {
		ABC057CCSolve solve = new ABC057CCSolve();
		solve.main();
	}
}

class ABC057CCSolve {
	
	long N;
	
	ABC057CCSolve() {
		Scanner cin = new Scanner(System.in);
		this.N = cin.nextLong();
	}
	
	void main() {
		int min = Integer.MAX_VALUE;
		for (int i = 1; i <= Math.sqrt(N); i++) {
			if (N % i != 0) continue;
						
			long a = i;
			long b = N / a;
			min = Math.min(min, F(a, b));
		}
		System.out.println(min);
	}
	
	int F(long A, long B) {
		return Math.min(String.valueOf(B).length(), String.valueOf(B).length());
	}
	
}