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 a,b[201],c,d;
cin>>a;
for(int i=1;i<=a;i++){
cin>>b[i];}
for(int i=1;i<=10000000;i++){
for(int i1=1;i1<=a;i1++){
c=b[i1]%2;
if(c!=0){cout<<i-1;return 0;}
b[i1]/=2;
}}
}