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 F(int x){
int count=0;
for(int i =0;i<31;i++){
if(x%2 != 0){
break;
}
x/=2;
count++;
}
return count;
}
int main() {
int N,x,ans=31;
cin >>N;
for(int i=0;i<N;i++){
cin>>x;
ans=min(ans,F(x));
}
cout<<ans<<endl;
}

