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 = Integer.MAX_VALUE;
    for (int i = 0; i < N; i++) {
      int a = sc.nextInt();
      int count = 0;
      while (a % 2 == 0) {
        count++;
        a /= 2;
      }
      ans = Math.min(ans, count);
    }
    
    System.out.println(ans == Integer.MAX_VALUE ? 0 : ans);
  }
}