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
#include<bits/stdc++.h>
using namespace std;
int main(){
	long n,x,y,s;
	s=0;
	cin>>n;
	for (int i=0;n>i;i++) {
		cin>>x;
		y=0;
		while (x%2==0){
			y++;
			x=x/2;
		}
		if (i==0){
			s=y;
		}
		else{
			if(s>y){
				s=y;
			}
		}

	}
	cout<<s<<endl;
}