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() {
	int64_t A;
	int N, ans;
	cin >> N;
	ans = 10000;
	for(int i = 0; i < N; i++) {
		cin >> A;
		int j = 0;
		for(; !(A & 1); j++) {
			A >>= 1;
		}
		ans = min(ans, j);
	}
	cout << ans << endl;
	return 0;
}