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;

public class Main {

	public static void main(String[] args) {

		int ans = 0;

		Scanner scan = new Scanner(System.in);

		int n = Integer.parseInt(scan.next());

		for(int i = 0; i < n; i++){
			int count = 0;
			String s2 = scan.next();
			int youso = Integer.parseInt(s2);

			while (0 == (youso % 2)) {
				youso = youso / 2;
				count++;
			}

			if(i == 0){
				ans = count;
			}else{
				if(ans > count){
					ans = count;
				}
			}
		}

		System.out.println(ans);
	}

}
