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],count=0;
  	cin>>N;
	while(1){for(int i=0;i<N;++i){
      cin>>a[i];
      if(a[i]%2!=0){cout<<count<<endl;return 0;}
      else a[i]/=2;
    }++count;
            }return 0;
}