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 a,i,c,d=0,e=0;
  cin>>a;
  for(i=0;i<a;i++){
    cin>>c;
    d=0;
  while(c%2==0){
    
    d++;
    
    c=c/2;
  }
    if(e>d||i==0)
    e=d;
  }
cout<<e<<endl;
}
