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 a,b[300],i,cnt=0;
	scanf("%d",&a);
	for(i=0;i<a;i++){
		scanf("%d",&b[i]);
	}
	i=0;
	while(1){
		if(b[i]%2!=0) break;
		else b[i]/=2;
		i++;
		if(i==a){
				i=0;
				cnt++;
		}
	}
	printf("%d\n",cnt);
}