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.Scanner;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner((System.in));
		BigInteger n = new BigInteger(sc.next());
		int a = 0, b = 0;
		int ans = String.valueOf(n).length();

		for (int i = 1; n.compareTo(new BigInteger(String.valueOf(i))) > 0; i++) {
			if (n.mod(new BigInteger(String.valueOf(i))).compareTo(BigInteger.ZERO) == 0) {
				a = String.valueOf(i).length();
				b = String.valueOf(n.divide(new BigInteger(String.valueOf(i)))).length();
				if (a >= b) {
					ans = a;
					break;
				}
			}
		}

		System.out.println(ans);

		sc.close();
	}
}