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:

import java.io.*;
import java.util.*;
import java.math.*;
import java.util.stream.Collectors;
import java.util.stream.*;


public class Main { 
    
    public static void main(String[] args) throws java.lang.Exception { 
        Reader pm =new Reader(); 
        //Scanner pm = new Scanner(new BufferedReader(new InputStreamReader(System.in)));

        int n = pm.nextInt();
        Long[] a = new Long[n];
        
        ArrayList<Long> al = new ArrayList();
        HashSet<Long> set = new HashSet<>();
        for(int i=0;i<n;i++){
            a[i] = pm.nextLong();
            set.add(a[i]);   
        }
            
        Arrays.sort(a);
        int alg = 0;  
        int go = 0;
        for(int i=0;i<n;i++){
            go = 0;
            for(int j=0;j<=30;j++){
                long f1 = a[i] - (long)Math.pow(2,j);
                long f2 = a[i] + (long)Math.pow(2,j);
                // int ind1 = Arrays.binarySearch(a,f1);
                // int ind2 = Arrays.binarySearch(a,f2);
                boolean ind1 = set.contains(f1);
                boolean ind2 = set.contains(f2);
                if(ind1 && ind2){
                    al.add(a[i]);
                    al.add(f1);
                    al.add(f2);
                    go = 1;
                    
                    break;
                } 
            }
            if(go == 1){
                alg = 1;
                break;
            }
        }
        if(alg == 1){
            System.out.println(al.size());
            for(int i=0;i<al.size();i++)
                System.out.print(al.get(i)+" ");
            return;
        }
        
        int flag = 0;
        int fl = 0;
        for(int i=0;i<n;i++){
            fl = 0;
            for(int j=0;j<=30;j++){
                long f1 = a[i] - (long)Math.pow(2,j);
                long f2 = a[i] + (long)Math.pow(2,j);
                boolean ind1 = set.contains(f1);
                boolean ind2 = set.contains(f2);
                // int ind1 = Arrays.binarySearch(a,f1);
                // int ind2 = Arrays.binarySearch(a,f2);
                if(ind1 && !ind2 ){
                    al.add(a[i]);
                    al.add(f1);
                    fl = 1;
                    break;
                } else if(ind2  && !ind1 ){
                    al.add(a[i]);
                    al.add(f2);
                    fl = 1;
                    break;
                }
            }
            if(fl == 1){
                flag = 1;
                break;
            }
        }
        if(flag == 1) {
            System.out.println(al.size());
            for(int i=0;i<al.size();i++)
                System.out.print(al.get(i)+" ");
        }
        else if(flag == 0){
            System.out.println(1);
            System.out.println(a[0]);
        } 
        
    }
    
    public static StringBuilder dec_to_bin(long n) {
        // decimal to binary upto 30 binaries
        if(n==0) {
            StringBuilder str=new StringBuilder("");
            for(int i=0;i<30;i++) {
                str.append("0");
            }
            return str;
        }
        StringBuilder str=new StringBuilder("");
        while(n!=0) {
            str.append(n%2L);
            n/=2L;
        }
        str=str.reverse();
        StringBuilder tmp_str=new StringBuilder("");
        int len=str.length();
        while(len!=30) {
            tmp_str.append("0");
            len++;
        }
        tmp_str.append(str);
        return tmp_str;
    }
    
    private static int binarySearchPM(int[] arr, int key){
        int n = arr.length;
        int mid = -1;
        int begin = 0,end=n;
        while(begin <= end){
            mid = (begin+end) / 2;
            if(mid == n){
                return n;
            }
            if(key < arr[mid]){
                end = mid-1;
            } else if(key > arr[mid]){
                begin = mid+1;
            } else {
                return mid;
            }
        }
        //System.out.println(begin+" "+end);
        return -begin; //expected Index
    }
    
    private static List<Integer> setToList(Set<Integer> s){
        List<Integer> al = s.stream().collect(Collectors.toList());
        return al;
    }
    
    private static List<Integer> mapValToList(HashMap<Integer,Integer> map){
        return map.values().stream().collect(Collectors.toList());
    }
    
    private static List<Integer> mapKeyToList(HashMap<Integer,Integer> map){
        return map.keySet().stream().collect(Collectors.toList());
    }
    
    private static HashMap<Integer, Integer> sortByKey(HashMap<Integer,Integer> map){
        return map
                .entrySet()
                .stream()
                .sorted(Map.Entry.comparingByValue())
                .collect(Collectors.toMap(
                    Map.Entry::getKey, 
                    Map.Entry::getValue, 
                    (oldValue, newValue) -> oldValue, LinkedHashMap::new));
    }
    
    static class Reader { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    }
}