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.ArrayList;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		int count = 0;
		Scanner sc = new Scanner(System.in);
		int i = sc.nextInt();
		ArrayList<Integer> al = new ArrayList<Integer>(i);
		for(int j = 0; j < i; j++) {
			al.add(sc.nextInt());
		}
		me: while(true) {
			for(int t = 0; t < i; t++) {
				if(al.get(t) % 2 == 0) {
					al.set(t, al.get(t) / 2);
				}else {
					System.out.println(count);
					break me;
				}
			}
			count++;
		}
	}

}