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;

public class Main{
  public static void main(String[] args){
    Scanner scanner = new Scanner(System.in);
    int a = Integer.parseInt(scanner.next());
    int[] b = new int [a];
    int count = 0;
    
    for(int i = 0; i < a; i++){
      b[i] = Integer.parseInt(scanner.next());
    }

    loop: for(count = 0; ; count++){
      for(int j = 0; j < a; j++){
        if(b[j] % 2 == 1){
          break loop;
        }
        b[j] /= 2;
      }
    }
    System.out.println(count);
    scanner.close();
  }
}