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.*;
import java.io.*;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();

		int[] arr = new int[n];
		int[] cnt = new int[n];
		for(int i = 0; i < n; ++i) {
			arr[i] = in.nextInt();
			while(arr[i] % 2 == 0) {
				++cnt[i];
				arr[i] /= 2;
			}
		}


		int ans = cnt[0];
		for(int i = 0; i< n; ++i)
			ans = Math.min(ans, cnt[i]);

		System.out.println(ans);
	}
}
