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.*;
class Main{
    public static void main(String[] args){
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int A[]=new int[n];
        int ans=0;
        boolean flag=true;
    for(int i=0;i<n;i++){
        A[i]=Integer.parseInt(sc.next());
    }
    while(flag){
        for(int i=0;i<n;i++){
            if(A[i]%2==0){A[i]/=2;}
            else{flag=false;}
            }
        if(flag){ans++;}
        }
    System.out.print(ans);
    }
}