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);
        int num = Integer.parseInt(sc.next());
        int minDivideCount = Integer.MAX_VALUE;
        for (int i = 0; i < num; i++) {
            int count = Integer.numberOfTrailingZeros(sc.nextInt());
            if (minDivideCount > count) {
                minDivideCount = count;
            }
        }

        System.out.println(minDivideCount);
    }
}