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 scan = new Scanner(System.in);
    int n = scan.nextInt();
    int min = 0;
    for (int i = 0; i < n; i++) {
      int a = scan.nextInt();
      int count = findMin(a, 0);
      if (i == 0 || count < min) {
        min = count;
      }
    }
    System.out.println(min);
  }
  
  private static int findMin(int n, int count) {
    if (n % 2 != 0) {
      return count;
    }
    return findMin(n / 2, ++count);
  }
}