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>
#include<string.h>
int main()
{
	int i,n,a,r,m=10000000;
	scanf("%d",&n);
	for(i=0;i<n;i++){
		scanf("%d",&a);
		r=0;
		while(a%2==0){
			a/=2;
			r++;
		}
		if(r<m)m=r;
	}
	printf("%d\n",m);
	return 0;
}
