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,i=0,r,x,draw=30;	//10^9⇒2^30
  cin >> N;
  while(i<N)
  {
    r=0;
    cin >> x;
    while(x%2==0)
    {x/=2;r++;}
    if(draw>r){draw=r;}
    i++;
  }
  cout << draw << endl;
}