Problem:
Score : 200 points

Problem Statement

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.

Sample Input 1

3
8 12 40

Sample Output 1

2

Initially, [8, 12, 40] are written on the blackboard.
Since all those integers are even, Snuke can perform the operation.

After the operation is performed once, [4, 6, 20] are written on the blackboard.
Since all those integers are again even, he can perform the operation.

After the operation is performed twice, [2, 3, 10] are written on the blackboard.
Now, there is an odd number 3 on the blackboard, so he cannot perform the operation any more.

Thus, Snuke can perform the operation at most twice.

Sample Input 2

4
5 6 8 10

Sample Output 2

0

Since there is an odd number 5 on the blackboard already in the beginning, Snuke cannot perform the operation at all.

Sample Input 3

6
382253568 723152896 37802240 379425024 404894720 471526144

Sample Output 3

8

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;
import java.util.stream.Stream;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String s = scanner.nextLine();
        List<Integer> inputs = Stream.of(scanner.nextLine().split(" "))
                .map(Integer::parseInt)
                .collect(Collectors.toList());
        int cnt = 0;
        System.out.println(reduce(inputs, cnt));
    }

    private static int reduce(List<Integer> list, int cnt) {
        if (isEven(list)) {
            cnt++;
            reduce(division(list), cnt);
        }
        return cnt;
    }

    private static List<Integer> division(List<Integer> list) {
        return list.stream()
                .map(num -> num / 2)
                .collect(Collectors.toList());
    }

    private static boolean isEven(List<Integer> list) {
        return list.stream()
                .filter(s -> s % 2 != 0)
                .count() == 0;
    }
}