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() {
	int sum=0,xsum=100000000,N;
	cin>>N;
	for(;N>0;N--){
		int A;
		cin>>A;
		sum=0;
		while(A%2==0){
		A/=2;
		sum++;
		}
		if(xsum>sum)
		xsum=sum;
 
		if(N==1)
		cout<<xsum<<endl;
	}
}