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()
{

	long long a,i,n,f,min;
	scanf("%lld",&n);
for(i=1;i<=n;i++)
	{
	scanf("%lld",&a);
f=0;
while(a)
{
	if(a%2==0)
	f++;
			else break;
			a=a/2;

}
if(i==1)
min=f;
else if(min>f)
min=f;


}
printf("%lld",min);
	return 0;
}