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>

#include<cmath>
using namespace std;
int main()
{int n,m[100000],a=0,b=0,i=0;
cin>>n;
for(i=0;i<n;i++)
cin>>m[i];
while(b==0){
for(i=0;i<n;i++){
	if(m[i]%2==1)b++;
	else m[i]=m[i]/2;
}
if(i==n)a++;
}
a--;
cout<<a;
    return 0;

}
