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 n=sc.nextInt();
  int num[]=new int[n];
  boolean b=true;
  int count=0;
  for(int i=0;i<n;i++){
  num[i]=sc.nextInt();
    if(((num[i]/=2)%2)==1)b=false;
  }
  
  while(b){
    if(count==0)
    count++;
  for(int i=0;i<n;i++){
    if(((num[i]/=2)%2)==1)b=false;
  }
    count++;
  }
  System.out.println(count);
}
}