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{
	static int dfs(int a) {
		if(a%2==1 || a==0) {
			return 0;
		}
		return dfs(a/2)+1;
	}
    public  static void main(String[] args) {
    	try (Scanner sc = new Scanner(System.in)) {
    		int m=1000000000;
    		int N=sc.nextInt();
    		for(int i=0; i<N; i++) {
    			int A=sc.nextInt();
    			m=Math.min(m, dfs(A));
    		}
    		System.out.println(m);
    	}
    }
}