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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

class Main {
	public static void main(String args[]) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		Solver solver = new Solver();
		solver.init();
		solver.readHead(in.readLine());
		// for (; solver.hasNextN();) {
		// solver.readN(in.readLine());
		// }
		// for (; solver.hasNextM();) {
		// solver.readM(in.readLine());
		// }
		// solver.solve();
	}
}

class Solver {
	public void init() {
	}

	public void readHead(String str) {
		String[] strArr = str.split(" ");
		long N = Long.parseLong(strArr[0]);
		int ans = 0;
		for (long i = N; i > 0; i /= 10) {
			ans++;
		}
		for (long d = 1; d <= N; d++) {
			if (N % d == 0) {
				// System.out.println(d);
				if (N / d < d)
					break;
				int dig = 0;
				for (long i = N / d; i > 0; i /= 10) {
					dig++;
				}
				if (ans > dig)
					ans = dig;
			}
		}
		System.out.println(ans);
	}

}