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 = Integer.parseInt(sc.next());
    	int[] a = new int[n];
    	int min = Integer.MAX_VALUE;
    	for(int i=0; i<n; i++) {
    	    a[i] = Integer.parseInt(sc.next());
    	    int count = 0;
    	    while(a[i] % 2 == 0) {
    	        a[i] /= 2;
    	        count++;
    	    }
    	    if(min > count) min = count;
    	}
    	System.out.println(min);
    }
}