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<stdio.h>
int main(){
int N,i;
long long int A[200],B[200],min=1000000000;
scanf("%d",&N);
for(i=0;i<N;i++){
scanf("%d",&A[i]);
for(B[i]=0;A[i]%2==0;B[i]++){
A[i]=A[i]/2;
}
if(min>B[i]){
min=B[i];}}
printf("%d",min);
return 0;

}