Problem: Boy Dima gave Julian a birthday present — set B consisting of positive integers. However, he didn't know, that Julian hates sets, but enjoys bipartite graphs more than anything else!

Julian was almost upset, but her friend Alex said, that he can build an undirected graph using this set in such a way: let all integer numbers be vertices, then connect any two i and j with an edge if |i - j| belongs to B.

Unfortunately, Julian doesn't like the graph, that was built using B. Alex decided to rectify the situation, so he wants to erase some numbers from B, so that graph built using the new set is bipartite. The difficulty of this task is that the graph, Alex has to work with, has an infinite number of vertices and edges! It is impossible to solve this task alone, so Alex asks you for help. Write a program that erases a subset of minimum size from B so that graph constructed on the new set is bipartite.

Recall, that graph is bipartite if all its vertices can be divided into two disjoint sets such that every edge connects a vertex from different sets.

Input

First line contains an integer n ~ (1 ⩽ n ⩽ 200 000) — size of B

Second line contains n integers b_1, b_2, …, b_n ~ (1 ⩽ b_i ⩽ 10^{18}) — numbers of B, all b_i are unique

Output

In the first line print single integer k – the number of erased elements. In the second line print k integers — values of erased elements.

If there are multiple answers, print any of them.

Examples

Input


3
1 2 3


Output


1
2 

Input


2
2 6


Output


0

Solution (in JAVA):

Solution:
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Locale;
import java.util.Map;
import java.util.StringTokenizer;

public class Solution implements Runnable {
	
	public static final long MAXB = 1000000000000000000L;
	
	private PrintStream out;
	private BufferedReader in;
	private StringTokenizer st;
	
	public void solve() throws IOException {
		long time0 = System.currentTimeMillis();
		int n = nextInt();
		long[] b = new long[n];
		for (int i = 0; i < n; i++) {
			b[i] = nextLong();
		}
		long[] answer = solve(n, b);
		out.println(answer.length);
		for (int i = 0; i < answer.length; i++) {
			out.print(answer[i]);
			out.print(" ");
		}
		System.err.println("time: " + (System.currentTimeMillis() - time0));
	}
	
	private long[] solve(int n, long[] b) {
		Map<Long, List<Long>> t = new HashMap<>();
		for (long v = 1; v <= MAXB; v *= 2) {
			t.put(v, new ArrayList<>());
		}
		for (int i = 0; i < n; i++) {
			t.get(twos(b[i])).add(b[i]);
		}
		int max = 0;
		for (List<Long> a : t.values()) {
			max = Math.max(max, a.size());
		}
		long[] result = new long[n - max];
		int done = 0;
		boolean skipped = false;
		for (List<Long> a : t.values()) {
			if (a.size() == max && !skipped) {
				skipped = true;
			} else {
				for (Long v : a) {
					result[done++] = v;
				}
			}
		}
		return result;
	}

	private long twos(long v) {
		long result = 1;
		while (v % 2 == 0) {
			result *= 2;
			v /= 2;
		}
		return result;
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
	
	public long nextLong() throws IOException {
		return Long.parseLong(next());
	}
	
	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
	
	public String next() throws IOException {
		while (!st.hasMoreTokens()) {
			String line = in.readLine();
			if (line == null) {
				return null;
			}
			st = new StringTokenizer(line);
		}
		return st.nextToken();
	}
	
	@Override
	public void run() {
		try {
			solve();
			out.close();
		} catch (Throwable e) {
			throw new RuntimeException(e);
		}
	}
	
	public Solution(String name) throws IOException {
		Locale.setDefault(Locale.US);
		if (name == null) {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintStream(new BufferedOutputStream(System.out));
		} else {
			in = new BufferedReader(new InputStreamReader(new FileInputStream(name + ".in")));
			out = new PrintStream(new BufferedOutputStream(new FileOutputStream(name + ".out")));
		}
		st = new StringTokenizer("");
	}
	
	public static void main(String[] args) throws IOException {
		new Thread(new Solution(null)).start();
	}
}