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) {
		// TODO Auto-generated method stub
	Scanner sc = new Scanner(System.in);
	int n = sc.nextInt();
	int [] k = new int [n];
	int a = 0;
	int cnt = 0;
	for(int i = 0;i < n;i++) {
		k[i] = sc.nextInt();
	}
out:	for(int i = 0;;i++){
		for(int j = 0;j < n;j++) {
			if(k[j] % 2 == 1) {
				break out;
			}
			k[j] = k[j] / 2;
		}
		cnt ++;
	}
	System.out.println(cnt);
	}
}

