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:
//package sept;

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


public class Rnd486
{
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    //boolean codechef=false;
    boolean codechef=true;
    
	void solve()
	{
		int n=ni();
		long[] a=new long[n];
		for(int i=0;i<n;i++)
		{
			a[i]=ni();
		}
		radixSort(a);
		ArrayList<Long> pow=new ArrayList<>();
		long curr=1;
		while(curr<2000000000)
		{
			pow.add(curr);
			curr*=2;
		}
		for(int i=0;i<n;i++)
		{
			int l=pow.size();
			for(int j=0;j<l;j++)
			{
				long l1=pow.get(j);
				int f1=Arrays.binarySearch(a, a[i]+l1);
				int f2=Arrays.binarySearch(a, a[i]+2*l1);
				if(f1>=0 && f2>=0)
				{
					out.println(3);
					out.println(a[i]+" "+(a[i]+l1)+" "+(a[i]+2*l1));
					return;
				}
			}
		}
		for(int i=0;i<n;i++)
		{
			int l=pow.size();
			for(int j=0;j<l;j++)
			{
				long l1=pow.get(j);
				int f1=Arrays.binarySearch(a, a[i]+l1);
				//int f2=Arrays.binarySearch(a, a[i]+2*l);
				if(f1>=0)
				{
					out.println(2);
					out.println(a[i]+" "+(a[i]+l1));
					return;
				}
			}
		}
		
		out.println(1);
		out.println(a[0]);
		
	}
	
	public static long[] radixSort(long[] f){ return radixSort(f, f.length); }
	public static long[] radixSort(long[] f, int n)
	{
		long[] to = new long[n];
		{
			int[] b = new int[65537];
			for(int i = 0;i < n;i++)b[1+(int)(f[i]&0xffff)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < n;i++)to[b[(int)(f[i]&0xffff)]++] = f[i];
			long[] d = f; f = to;to = d;
		}
		{
			int[] b = new int[65537];
			for(int i = 0;i < n;i++)b[1+(int)(f[i]>>>16&0xffff)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < n;i++)to[b[(int)(f[i]>>>16&0xffff)]++] = f[i];
			long[] d = f; f = to;to = d;
		}
		{
			int[] b = new int[65537];
			for(int i = 0;i < n;i++)b[1+(int)(f[i]>>>32&0xffff)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < n;i++)to[b[(int)(f[i]>>>32&0xffff)]++] = f[i];
			long[] d = f; f = to;to = d;
		}
		{
			int[] b = new int[65537];
			for(int i = 0;i < n;i++)b[1+(int)(f[i]>>>48&0xffff)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < n;i++)to[b[(int)(f[i]>>>48&0xffff)]++] = f[i];
			long[] d = f; f = to;to = d;
		}
		return f;
	}
	
	void solveC()
	{
		int k=ni();
		int[][] a=new int[k][];
		//Pair[][] arr=new Pair[k][];
		long[] sum=new long[k];
		int tot=0;
		for(int i=0;i<k;i++)
		{
			int len=ni();
			tot+=len;
			a[i]=new int[len];
			//arr[i]=new Pair[len];
			for(int j=0;j<len;j++)
			{
				a[i][j]=ni();
				sum[i]+=a[i][j];
			}
			
			
			//Arrays.sort(a[i]);
		}
		Pair[] arr=new Pair[tot];
		int ind=0;
		for(int i=0;i<k;i++)
		{
			int len=a[i].length;
			//arr[i]=new Pair[len];
			for(int j=0;j<len;j++)
			{
				arr[ind++]=new Pair(sum[i]-a[i][j],i,j);
			}
			
			
			//Arrays.sort(a[i]);
		}
		Arrays.sort(arr,new Comparator<Pair>() {

			@Override
			public int compare(Pair o1, Pair o2) {
				// TODO Auto-generated method stub
				long diff=o1.a-o2.a;
				if(diff<0)return -1;
				else if(diff==0)
				{
					return o1.b-o2.b;
				}
				return 1;
			}
		});
		for(int i=1;i<tot;i++)
		{
			if(arr[i].a==arr[i-1].a && arr[i].b!=arr[i-1].b)
			{
				out.println("YES");
				out.println((arr[i-1].b+1)+" "+(arr[i-1].c+1));
				out.println((arr[i].b+1)+" "+(arr[i].c+1));
				return;
			}
		}
		out.println("NO");
	}
	
	static void dfs(int[][] g,int u,int[] vis,int p)
	{
		vis[u]=p;
		for(int v:g[u])
		{
			if(vis[v]==0)dfs(g,v,vis,u);			
		}
	}
	
	static long fnc(long a,long b)
	{
		return a+(1000000007)*b;
	}
	
	static int[][] packD(int n, int[] from, int[] to) {
		int[][] g = new int[n][];
		int[] p = new int[n];
		for (int f : from)
			p[f]++;
		for (int i = 0; i < n; i++)
			g[i] = new int[p[i]];
		for (int i = 0; i < from.length; i++) {
			g[from[i]][--p[from[i]]] = to[i];
		}
		return g;
	}
	
    static class Pair
    {
    	long a;
        int b,c;
        public Pair(long a,int b,int c)
        {
            this.a=a;
            this.b=b;
            this.c=c;
        }
    }
    
    static long lcm(int a,int b)
    {
        long val=a;
        val*=b;
        return (val/gcd(a,b));
    }
    
    static long gcd(long a,long b)
    {
        if(a==0)return b;
        return gcd(b%a,a);
    }
    
    static int pow(int a, int b, int p)
    {
        long ans = 1, base = a;
        while (b!=0)
        {
            if ((b & 1)!=0)
            {
                ans *= base;
                ans%= p;
            }
            base *= base;
            base%= p;
            b >>= 1;
        }
        return (int)ans;
    }

    static int inv(int x, int p)
    {
        return pow(x, p - 2, p);
    }

    void run() throws Exception
    {
        if(codechef)oj=true;
        is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception {new Rnd486().run();}
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}