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 number = sc.nextInt();
    int[] numbers = new int[number];
    for (int i = 0; i < number; i++) {
      numbers[i] = sc.nextInt();
    }
    int[] count = new int[number];
    for (int j = 0; j < number; j++) {
      while(numbers[j] % 2 == 0) {
        numbers[j] /= 2;
        count[j]++;
        }
      }
    Arrays.sort(count);
    System.out.println(count[0]);
    
  }
}