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 <bits/stdc++.h>
using namespace std;

int main()
{
	int n, x;
	
	scanf("%d", &n);
	int ans = 64;
	while (n--) {
		scanf("%d", &x);
		int tmp = 0;
		while (x % 2 == 0) {
			tmp++;
			x /= 2;
		} 
		ans = min(ans, tmp);
	}
	printf("%d\n", ans);
}