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 int two(int a) {
		int tmp = a;
		int cnt = 0;
		while(tmp % 2 == 0) {
			tmp /= 2;
			++cnt;
		}
		return cnt;
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int a[] = new int[n];
		int min = 30;
		for(int i = 0; i < n; ++i) {
			a[i] = sc.nextInt();
			int tmp = two(a[i]);
			min = Math.min(min,  tmp);
		}
		sc.close();
		System.out.println(min);
	}

}
