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.*;
import java.lang.*;

public class Main {
  public static void main(String[] args) {
  	Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int a[] = new int[n];
    for (int i = 0; i < n; i++) {
		a[i] = sc.nextInt();
    }

	int cnt = 0;
	boolean f = true;
	while (f) {
		cnt++;
		for (int i = 0; i < n; i++) {
			if (a[i] % 2 != 0) {
				f = false;
				cnt--;
				break;
			}
			a[i] /= 2;
		}
	}
    System.out.println(cnt);
  }
}
