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;
  cin >> n;
  int ans=1001001;
  for(int i=0; i<n; ++i){
    int x, nans=0;
    cin >> x;
    while(x%2==0){
      x/=2;
      ++nans;
    }
    ans = min(ans, nans);
  }
  cout << ans << endl;
}