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 N = sc.nextInt();
    int[] ans = new int[N];
    for (int i=0; i<N; i++) {
      ans[i] = sc.nextInt();
    }
    int count =0;
    int end =0;
    while (true) {
      for (int i=0; i<N; i++) {
        if (ans[i] % 2 == 0) {
          ans[i] /= 2;
        } else {
          end++;
          break;
        }
      }
      if (end != 0) break;
      count++;
    }
    System.out.println(count);
  }
}