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>
using namespace std;

int main()
{
	int n,a[200];
	cin>>n;
	for(int i=0;i<n;i++) cin>>a[i];
	
	bool f=1;
	int v=-1;
	while(f){
		for(int i=0;i<n;i++){
			if(a[i]%2==1) f=0;
			a[i]/=2;
		}
		v++;
	}
	
	cout<<v<<endl;
	
	return 0;
}
