Problem: There are n distinct points on a coordinate line, the coordinate of i-th point equals to x_i. Choose a subset of the given set of points such that the distance between each pair of points in a subset is an integral power of two. It is necessary to consider each pair of points, not only adjacent. Note that any subset containing one element satisfies the condition above. Among all these subsets, choose a subset with maximum possible size.

In other words, you have to choose the maximum possible number of points x_{i_1}, x_{i_2}, ..., x_{i_m} such that for each pair x_{i_j}, x_{i_k} it is true that |x_{i_j} - x_{i_k}| = 2^d where d is some non-negative integer number (not necessarily the same for each pair of points).

Input

The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of points.

The second line contains n pairwise distinct integers x_1, x_2, ..., x_n (-10^9 ≤ x_i ≤ 10^9) — the coordinates of points.

Output

In the first line print m — the maximum possible number of points in a subset that satisfies the conditions described above.

In the second line print m integers — the coordinates of points in the subset you have chosen.

If there are multiple answers, print any of them.

Examples

Input

6
3 5 4 7 10 12


Output

3
7 3 5

Input

5
-1 2 5 8 11


Output

1
8

Note

In the first example the answer is [7, 3, 5]. Note, that |7-3|=4=2^2, |7-5|=2=2^1 and |3-5|=2=2^1. You can't find a subset having more points satisfying the required property.

Solution (in JAVA):

Solution:
/* 
 * UMANG PANCHAL
 * DAIICT
 */

import java.util.*;
import java.io.*;
import java.math.*;
import java.util.Comparator;
public class Main
{
 
	private static final Comparator<? super Integer> Comparator = null;
	static LinkedList<Integer> adj[];
	static ArrayList<Integer> adj1[];
	static int[] color,visited1;
	static boolean b[],visited[],possible;
	static int level[];
	static Map<Integer,HashSet<Integer>> s;
	static int totalnodes,colored;
	static int count[];
	static long sum[];
	static int nodes;
	static long ans=0;
	static long[] as=new long[10001];
	static long c1=0,c2=0;
	static int[] a,d,k;
	static int max=100000000;
	static long MOD = 1000000007,sm=0,m=Long.MIN_VALUE;
	static boolean[] prime=new boolean[1000005];
	static int[] levl;
    static int[] eat;
    static int price[];
    static int res[],par[],co[];
    static int result=0;
    static int[] root,size,du,dv;
    static long p=Long.MAX_VALUE;
    static int start,end,r=0;
    static boolean[] vis1,vis2;
    static int to;
    static HashSet<Integer> hs;
    static boolean as1;
    static Node head;
  
	// --------------------My Code Starts Here----------------------
	
	public static void main(String[] args) throws IOException
	{
		in=new InputReader(System.in);
	    w=new PrintWriter(System.out);
 
	   int n=ni();
	   long[] a=new long[n];
	   ArrayList<Long> p=new ArrayList<Long>();
	   for(int i=0;i<n;i++)
		   p.add(nl());;
	   //shuffle(a,n);
	   Collections.sort(p);
	   for(int i=0;i<n;i++)
		   a[i]=p.get(i);
	   HashSet<Long> h=new HashSet<Long>();
	   for(int i=0;i<n;i++)
		   h.add(a[i]);
	   long x=-1,y=-1;
	   boolean ans=false;
	   for(int i=0;i<n;i++)
	   {
		   long dif=1L;
		   while(a[i]+dif<=a[n-1])
		   {
			   if(h.contains(a[i]+dif))
			   {
				   x=a[i];
				   y=a[i]+dif;
				   if(h.contains(a[i]+2L*dif))
				   {
					   w.println(3);
					   w.println(a[i]+" "+(a[i]+dif)+" "+(a[i]+2L*dif));
					   ans=true;
					   break;
				   }
			   }
			   dif=dif*2L;
		   }
		   if(ans)
			   break;
	   }
	   if(!ans)
	   {
		   if(x!=-1 && y!=-1)
		   {
			   w.println(2);
			   w.print(x+" "+y);
		   }
		   else
		   { 
			   w.println(1);
			   w.print(a[0]);
			   
		   }
	   }
    
   w.close();
   }
	 static class Pair implements Comparable<Pair>
	 {
		 Integer v;
		 Integer i;
	        Pair(int v,int i)
	        {
	            this.v=v;
	            this.i=i;
	    
	        }
	        public int compareTo(Pair p)
	        {
	            return Integer.compare(this.v,p.v);
	        }
		
	}
	   public static void removeDuplicates()
	    {
	         Node cur=head;
	         while(cur!=null)
	         {
	        	// w.println(1);
	             int k=cur.data;
	             Node p=cur.next;
	             Node pre=cur;
	             while(p!=null)
	             {
	            	// w.println(2);
	                 if(p.data==k)
	                 {
	                     pre.next=p.next;
	                     p=pre.next;
	                 }
	                 else
	                 {
	                     p=p.next;
	                     pre=pre.next;
	                 }
	             }
	             cur=cur.next;
	         }
	     
	    }

	public static void insert_front(int x)
	{
		Node f=new Node(x);
		f.next=head;
		head=f;
	}
	public static void insert_mid(Node x,int d)
	{
		if(x==null)
		{
			w.println("Nothing can be shown");
			return;
		}
		Node nex=x.next;
		Node ne=new Node(d);
		x.next=ne;
		ne.next=nex;
	}
	public static void insert_end(int x)
	{
		Node f=new Node(x);
		Node temp=head;
		while(temp.next!=null)
			temp=temp.next;
		temp.next=f;
			
	}
	public static class Node
	{
		int data;
		Node next;
		Node(int d)
		{
			this.data=d;
			this.next=null;
		}
	}

	// --------------------My Code Ends Here------------------------
     
	public static void dfs(int n,int p)
	{
		visited[n]=true;
		if(adj[n].size()!=2)
			as1=false;
		for(int i:adj[n])
		{
			if(!visited[i])
			{
				dfs(i,n);
			}
		}		
	}
	
	/*
	 *  PriorityQueue<Integer> pq = new PriorityQueue<Integer>(new Comparator<Integer>()
  			{
  				public int compare(Integer o1, Integer o2)
  				{
  					return Intege
  					r.compare(o2,o1);
  				}
  			});
	 * 
	 * 
	 */
	
	public static void shuffle(long[] a,int n)
	{
		Random r=new Random();
		for(int i=n-1;i>0;i--)
		{
			int j=r.nextInt(i);
			long t=a[j];
			a[j]=a[i];
			a[i]=t;
		}
	}
	public static void bfs1(int u)
	{
	    Queue<Integer> q=new LinkedList();
	    q.add(u);
	    visited[u]=true;
	    while(!q.isEmpty())
	    {
	    	//w.print(1);
	    	int p=q.poll();
	      for(int i=0;i<adj[p].size();i++)
	     { 
	    	  if(!visited[adj[p].get(i)])
	    	  {
	    	q.add(adj[p].get(i));
	    	visited[adj[p].get(i)]=true;
	    	  }
	    	  levl[adj[p].get(i)]=levl[p]+1;
	    	  }
	    }
	    
	}
	public static void bfs2(int u)
	{
	    Queue<Integer> q=new LinkedList();
	    q.add(u);
	    vis2[u]=true;
	    while(!q.isEmpty())
	    {
	    	int p=q.poll();
	      for(int i=0;i<adj[p].size();i++)
	     { 
	    	  if(!vis2[adj[p].get(i)])
	    	  {
	    	dv[adj[p].get(i)]=dv[p]+1;
	    	q.add(adj[p].get(i));
	    	  
	    	vis2[adj[p].get(i)]=true;
	    	  }
	    	  }
	    }
	    
	}
	 public static void buildgraph(int n)
	 {
         adj=new LinkedList[n+1];
         visited=new boolean[n];
         level=new int[n];
         par=new int[n];
         for(int i=0;i<=n;i++)
         	{
        	 adj[i]=new LinkedList<Integer>();
         	
         	}
      
	 }
	
	/*public static long kruskal(Pair[] p)
	{
		long ans=0;
		int w=0,x=0,y=0;
		for(int i=0;i<p.length;i++)
		{
			w=p[i].w;
			x=p[i].x;
			y=p[i].y;
			if(root(x)!=root(y))
			{
				ans+=w;
				union(x,y);
			}
		}
		return ans;
	}*/
	

	 static  class npair implements Comparable<npair>
	 {
	     int a,b;
	     
	
		npair(int a,int b)
		{
			this.a=a;
			this.b=b;
			//this.index=index;
		}


		public int compareTo(npair o) {
			// TODO Auto-generated method stub
			return Integer.compare(this.a,o.a);
		}


	
		
	}
	public static int root(int i)
	{
		while(root[i]!=i)
		{
			root[i]=root[root[i]];
			i=root[i];
		}
		return i;
	}
	
	public static void init(int n)
	{
		root=new int[n+1];
		for(int i=1;i<=n;i++)
			root[i]=i;
	}
	public static void union(int a,int b)
	{
	    int root_a=root(a);	
	    int root_b=root(b);
	    root[root_a]=root_b;
	   // size[root_b]+=size[root_a];
	}


	
	public static boolean isPrime(long n)
	{
	    // Corner cases
	    if (n <= 1)  return false;
	    if (n <= 3)  return true;
	 
	    // This is checked so that we can skip 
	    // middle five numbers in below loop
	    if (n%2 == 0 || n%3 == 0)
	    	return false;
	 
	    for (long i=5; i*i<=n; i=i+6)
	        if (n%i == 0 || n%(i+2) == 0)
	           return false;
	 
	    return true;
	}
	

	
	public static String ns()
	{
		return in.nextLine();
	}
	public static int ni()
	{
		return in.nextInt();
	}
	public static long nl()
	{
		return in.nextLong();
	}
	public static int[] na(int n)
	{
		int[] a=new int[n];
		for(int i=0;i<n;i++)
		a[i]=ni();
		return a;
	}
	public static long[] nla(int n)
	{
		long[] a=new long[n];
		for(int i=0;i<n;i++)
		a[i]=nl();
		return a;
	}
	public static void sieve()
	    {
	       int n=prime.length;
	        for(int i=0;i<n;i++)
	            prime[i] = true;
	         
	        for(int p = 2; p*p <=n; p++)
	        {
	            if(prime[p] == true)
	            {
	                for(int i = p*2; i <n; i += p)
	                    prime[i] = false;
	            }
	        }
	    }

  public static String rev(String s)
	{
		StringBuilder sb=new StringBuilder(s);
		sb.reverse();
		return sb.toString();
	}
	static long lcm(long a, long b)
	{
	    return a * (b / gcd(a, b));
	}
	static long gcd(long a, long b)
	{
	    while (b > 0)
	    {
	        long temp = b;
	        b = a % b; // % is remainder
	        a = temp;
	    }
	    return a;
	}
	static InputReader in;
	static PrintWriter w;
static class InputReader 
{
 
private final InputStream stream;
private final byte[] buf = new byte[8192];
private int curChar, snumChars;
private SpaceCharFilter filter;
 
public InputReader(InputStream stream)
{
  this.stream = stream;
}
 
public int snext()
{
  if (snumChars == -1)
    throw new InputMismatchException();
  if (curChar >= snumChars)
  {
    curChar = 0;
    try 
    {
      snumChars = stream.read(buf);
    }
    catch (IOException e)
    {
      throw new InputMismatchException();
    }
    if (snumChars <= 0)
      return -1;
  }
  return buf[curChar++];
}
 
public int nextInt() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  int sgn = 1;
  if (c == '-')
  {
    sgn = -1;
    c = snext();
  }
  int res = 0;
  do
  {
    if (c < '0' || c > '9')
      throw new InputMismatchException();
    res *= 10;
    res += c - '0';
    c = snext();
  }
  while (!isSpaceChar(c));
  return res * sgn;
}
 
public long nextLong() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  int sgn = 1;
  if (c == '-')
  {
    sgn = -1;
    c = snext();
  }
  long res = 0;
  do
  {
    if (c < '0' || c > '9')
      throw new InputMismatchException();
    res *= 10;
    res += c - '0';
    c = snext();
  }
  while (!isSpaceChar(c));
  return res * sgn;
}	    
public String readString() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  StringBuilder res = new StringBuilder();
  do
  {
    res.appendCodePoint(c);
    c = snext();
  }
  while (!isSpaceChar(c));
  return res.toString();
}
 
public String nextLine() 
{
  int c = snext();
  while (isSpaceChar(c))
    c = snext();
  StringBuilder res = new StringBuilder();
  do
  {
    res.appendCodePoint(c);
    c = snext();
  }
  while (!isEndOfLine(c));
  return res.toString();
}
 
public boolean isSpaceChar(int c)
{
  if (filter != null)
    return filter.isSpaceChar(c);
  return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
}
 
private boolean isEndOfLine(int c) 
{
  return c == '\n' || c == '\r' || c == -1;
}
 
public interface SpaceCharFilter
{
  public boolean isSpaceChar(int ch);
}
}
	
}