There are N positive integers written on a blackboard: A_1, ..., A_N.

Snuke can perform the following operation when all integers on the blackboard are even:

* Replace each integer X on the blackboard by X divided by 2.



Find the maximum possible number of operations that Snuke can perform.

Constraints

* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the maximum possible number of operations that Snuke can perform.

Examples

Input

3
8 12 40


Output

2


Input

4
5 6 8 10


Output

0


Input

6
382253568 723152896 37802240 379425024 404894720 471526144


Output

8
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			System.out.println(IntStream.range(0, n).map(i -> devide2Count(scanner.nextInt())).min().getAsInt());
		}
	}

	/**
	 * @param number
	 * @return numberが何回2で割れるか
	 */
	private static int devide2Count(int number) {
		int result = 0;
		while ((number & 1) == 0) {
			number >>= 1;
			result++;
		}
		return result;
	}
}
