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 x = 0;
	int j = 0;
	int n = sc.nextInt();
	int[] table = new int[n];

	for(int i=0;i<n;i++){

	    table[i] = sc.nextInt();
	    
	}

	while(table[j]%2==0){
	    
	    table[j] = table[j]/2;
	    x++;
	    if(j==n-1){
		j=0;
	    }else{
		j++;
	    }
	}
       
	System.out.println(x/n);
    }
}
