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.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		// 整数の入力
		int n = sc.nextInt();
        List<Integer> list = new ArrayList<>();
		// スペース区切りの整数の入力
        for (int i = 0; i < n; i++) {
            int d = sc.nextInt();
            int x = 0;
            while (d % 2 == 0) {
                d /= 2;
                x++;
            }
            list.add(x);
        }
        Collections.sort(list);
		// 出力
		System.out.println(list.get(0));
	}
}
