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.util.*;
import java.io.*;

public class Es4
{
    static IO io = new IO();
    public static void main(String[] args)
    {
		int n = io.getInt();
		long[] a = new long[n];
		HashMap<Long, Integer> map = new HashMap<>();
		for(int i=0; i<n; i++){
			a[i] = io.getLong();
			map.put(a[i], i);
		}
		UnionFind uf = new UnionFind(n);
		ArrayList<Integer> disjointSets = new ArrayList<Integer>();
		disjointSets.add(0);
		for(int i=1; i<n; i++){
			boolean hasFound = false;
			for(Integer j : disjointSets){
				//io.print(i+" "+j+":  ");
				long gcd = gcd(a[i], a[j]);
				long path = a[i]/gcd + a[j]/gcd;
				
				//io.print(gcd+" "+ path+"  ");
				if(path%2==0){
					//io.println("same set");
					uf.unionSets(i, j);
					hasFound = true;
					break;
				}
				
			}
			if(!hasFound)
				disjointSets.add(i);
		}
		int max = -1;
		int maxi = -1;
		for(Integer i : disjointSets){
			//io.println(i+" "+uf.sizeOfSet(i));
			if(uf.sizeOfSet(i) > max){
				max = uf.sizeOfSet(i);
				maxi = i;
			}
		}
		io.println(n-max);
		for(int i=0; i<n; i++){
			if(!uf.isSameSet(i, maxi))
				io.print(a[i]+" ");
		}
		
        io.close();
    }
	
	public static long gcd(long a, long b) {
		if (a == 0)
			return b;

		while (b != 0) {
			if (a > b)
				a = a - b;
			else
				b = b - a;
		}

		return a;
	}
}



class IO extends PrintWriter {
	public IO() {
        super(new BufferedOutputStream(System.out));
        r = new BufferedReader(new InputStreamReader(System.in));
    }

    public IO(String fileName) {
        super(new BufferedOutputStream(System.out));
        try{
            r = new BufferedReader(new FileReader(fileName));
        } catch (FileNotFoundException e) {
            this.println("File Not Found");
        }
    }

    public boolean hasMoreTokens() {
        return peekToken() != null;
    }

    public int getInt() {
        return Integer.parseInt(nextToken());
    }

    public double getDouble() {
        return Double.parseDouble(nextToken());
    }

    public long getLong() {
        return Long.parseLong(nextToken());
    }

    public String getWord() {
        return nextToken();
    }

	public String getLine(){
        try{
            st = null;
            return r.readLine();
        }
        catch(IOException ex){}
        return null;
    }
	

    private BufferedReader r;
    private String line;
    private StringTokenizer st;
    private String token;

    private String peekToken() {
        if (token == null)
            try {
                while (st == null || !st.hasMoreTokens()) {
                    line = r.readLine();
                    if (line == null) return null;
                    st = new StringTokenizer(line);
                }
                token = st.nextToken();
            } catch (IOException e) { }
        return token;
    }

    private String nextToken() {
        String ans = peekToken();
        token = null;
        return ans;
    }
}

class UnionFind {
    public UnionFind(int N)
    {
        p = new ArrayList<Integer>(N);
        rank = new ArrayList<Integer>(N);
        setSize = new ArrayList<Integer>(N);
        numSets = N;
        for(int i=0; i<N; i++)
        {
            p.add(i);
            rank.add(0);
            setSize.add(1);
        }
    }
    
    public int findSet(int i)
    {
        if(p.get(i)==i)
            return i;
        else
        {
            int ret = findSet(p.get(i));
            p.set(i, ret);
            return ret;
        }
    }
    
    public boolean isSameSet(int i, int j)
    {
        return findSet(i)==findSet(j);
    }
    
    public void unionSets(int i, int j)
    {
        int x = findSet(i);
        int y = findSet(j);
        if(x!=y)
        {
            numSets--;
            if(rank.get(x) > rank.get(y))
            {
                p.set(y, x);
                setSize.set(x, setSize.get(x)+setSize.get(y));
            }
            else
            {
                p.set(x, y);
                setSize.set(y, setSize.get(y)+setSize.get(x));
                if(rank.get(x)==rank.get(y))
                    rank.set(y, rank.get(y)+1);
            }
        }
    }
    
    public int numDisjointSets()
    {
        return numSets;
    }
    
    public int sizeOfSet(int i)
    {
        return setSize.get(findSet(i));
    }
    
    private ArrayList<Integer> p, rank, setSize;
    private int numSets;
}