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.*;
import java.io.*;

public class Main{
  public static void main(String[] args){
    Scanner scan = new Scanner(System.in);
    int n = scan.nextInt();
    int[] a = new int[n];
    int cnt = 0;
    int min = 1000000000;

    for(int i = 0; i < n; i++){
      a[i] = scan.nextInt();
      while(a[i] % 2 == 0){
        a[i] /= 2;
        cnt++;
      }
      min = Math.min(min, cnt);
      cnt = 0;
    }

    System.out.println(min);
  }
}
