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.Scanner;
public class Main {

	public static void main(String args[]) {
		Scanner scan = new Scanner(System.in);
		int a = scan.nextInt();
		int ans = Integer.MAX_VALUE;
		for(int i = 0 ; i < a ; i++){
			long temp = scan.nextLong();
			int cnt = 0;
			while(true){
				if(temp % 2 == 0){
					temp = temp / 2;
					cnt ++;
				}else{
					break;
				}
			}
			if(cnt < ans){
				ans = cnt;
			}
		}
		System.out.println(ans);
	}
}