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,f=1,s=0;
 cin>>n;
 int a[n+1];
 for(int i=1;i<=n;i++) cin>>a[i];
 while(f!=0)
 {
  s++;
  for(int i=1;i<=n;i++)
  {
   if(a[i]%2!=0)
   f=0;
   
   a[i]=a[i]/2;
  }
 }
 cout<<s-1;
 return 0;
}