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 min = get2times(sc.nextInt());
		
		for(int i=1; i<n; i++) {
			int k = sc.nextInt();
			if(get2times(k)<min) {
				min = get2times(k);
			}
		}
		
		System.out.println(min);
	}
	
	public static int get2times(int n) {
		int count = 0;
		while(n%2 == 0) {
			n = n/2;
			count ++;
		}
		
		return count;
	}
}
