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.Scanner;

class Main {
  public static void main(String[] args) {
    Scanner s = new Scanner(System.in);
    int n = s.nextInt();
    int min = Integer.MAX_VALUE;
    for (int i = 0; i < n; i++) {
      int num = s.nextInt();
      int cnt = count(num);
      if (cnt < min) min = cnt;
    }
    System.out.println(min);
  }

  private static int count(int num) {
    int cnt = 0;
    while (num > 0 && num % 2 == 0) {
      num /= 2;
      cnt++;
    }
    return cnt;
  }
}
