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.Arrays;
import java.util.Scanner;
class Main{
	public static void main(String[]$){
		Scanner s=new Scanner(System.in);
		int n=s.nextInt(),a[]=new int[n];
		for(int i=0;i<n;++i)
			a[i]=s.nextInt();
		for(int i=0;i<32;++i) {
			int b=1<<i;
			if(Arrays.stream(a).anyMatch(o->o%b!=0)) {
				System.out.println(i-1);
				return;
			}
		}
	}
}