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 ) throws Exception {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    
    List<Integer> As = new ArrayList<>();
    
    int bit = 0;
    for (int i=0; i<N; i++) {
        bit = bit | sc.nextInt();
    }
    
    System.out.println(Integer.numberOfTrailingZeros(bit));
  }
}
