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 N,B;
	B=100000000000000;
	cin>>N;
	for(int i=0; i<N; i++ ){
		int a,A=0;
		cin>>a;
		for(int j=0;a%2==0;j++){
		A++;
		a/=2;
		}
		if(A<B){
			B=A;
		}
	}
	cout<<B<<endl;
}
