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 <iostream>
#include <algorithm>
using namespace std;
int n, m[222],b[222];
int main(){
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>m[i];
	}
	for(int i=0;i<n;i++){
		while(m[i]%2==0){
			m[i]=m[i]/2;
			b[i]++;	
		}
	}
	sort(b,b+n);
	cout<<b[0];
	return 0;
}