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 n,m=0,p=1,f=1;
int a[205];
int main(){
	cin>>n;
	for(int i=1;i<=n;i++)cin>>a[i];
	while (f){
		m++;p*=2;
		for(int i=1;i<=n and f;i++)
			if(a[i]%p!=0)f=0;
	}
	cout<<m-1<<endl;
	
}