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:
/*
If you want to aim high, aim high
Don't let that studying and grades consume you
Just live life young
******************************
If I'm the sun, you're the moon
Because when I go up, you go down
*******************************
I'm working for the day I will surpass you
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class D2
   {
      public static void main(String omkar[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int N = Integer.parseInt(st.nextToken());
         long[] arr = readArr2(N, infile, st);
         ArrayList<Long>[] buckets = new ArrayList[64];
         for(int i=0; i < 64; i++)
            buckets[i] = new ArrayList<Long>();
         StringBuilder sb = new StringBuilder();
         //pray
         int max = 0;
         for(long x: arr)
         {
            int cnt = 0;
            long val = x;
            while(val%2 == 0)
            {
               val /= 2;
               cnt++;
            }
            buckets[cnt].add(x);
            max = Math.max(buckets[cnt].size(), max);
         }
         for(int i=0; i < 64; i++)
            if(max == buckets[i].size())
            {
               System.out.println(N-buckets[i].size());
               for(int a=0; a < 64; a++)
                  if(a != i)
                     for(long x: buckets[a])
                        sb.append(x+"\n");
               System.out.print(sb);
               return;
            }
      }
      public static long[] readArr2(int N, BufferedReader infile, StringTokenizer st) throws Exception
      {
         long[] arr = new long[N];
         st = new StringTokenizer(infile.readLine());
         for(int i=0; i < N; i++)
            arr[i] = Long.parseLong(st.nextToken());
         return arr;
      }
   }