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.math.BigInteger;
import java.security.KeyStore;
import java.util.*;


public class A {

    long b = 31;
    String fileName = "";


    //////////////////////    SOLUTION   SOLUTION  SOLUTION    //////////////////////////////
    Long INF = Long.MAX_VALUE / 7;
    long MODULO = 1000*1000*1000+7;
    int[][] graph;
    class Edge{
        int from, to;
        Edge(int from, int to){
            this.from = from;
            this.to = to;
        }
    }
    void solve() throws IOException {


        int n = readInt();
        long[] coords = new long[n];
        Set<Long> mp = new HashSet<>();
        for (int i=0; i<n; ++i) {
            coords[i] = readInt();
            mp.add(coords[i]);
        }
        int indForTwo = Integer.MAX_VALUE;
        long pow2 = -1;
        for (int i=0; i<n; ++i){
            for (int pow=0;pow<=30;++pow){
                long cur = 1l<<pow;
                if (mp.contains(coords[i] + cur)){
                    if (mp.contains(coords[i] - cur)){
                        out.println(3);
                        out.println(coords[i] - cur +" "+(coords[i])+" "+(coords[i]+cur));
                        return;
                    }else{
                        indForTwo = i;
                        pow2 = cur;
                    }
                }
                if (mp.contains(coords[i] - cur)){
                    indForTwo = i;
                    pow2 = - cur;
                }
            }

        }
        if (indForTwo == Integer.MAX_VALUE){
            out.println(1);
            out.println(coords[0]);
        }else{
            out.println(2);
            out.println(coords[indForTwo] + " "+(coords[indForTwo] + pow2));
        }
    }
    class TaskVals implements Comparable<TaskVals>{
        int ind, elem;
        TaskVals(int ind, int elem){
            this.ind = ind;
            this.elem = elem;
        }

        @Override
        public int compareTo(TaskVals o) {
            return Integer.compare(this.ind, o.ind);
        }
    }
    class Participant implements Comparable<Participant>{
        int a, b, ind;
        Participant(int a, int b, int ind){
            this.a = a;
            this.b = b;
            this.ind = ind;
        }

        @Override
        public int compareTo(Participant o) {
            if (this.a == o.a) return Integer.compare(this.b, o.b);
            return Integer.compare(this.a, o. a);
        }
    }
    class Vertex{
        int dist, from;
        Vertex(int b, int c){
            this.dist = b;
            this.from = c;
        }
    }
    ///////////////////////////////////////////////////////////////////////////////////////////

    class SparseTable{
        int[][] rmq;
        int[] logTable;
        int n;
        SparseTable(int[] a){
            n = a.length;
            logTable = new int[n+1];
            for(int i = 2; i <= n; ++i){
                logTable[i] = logTable[i >> 1] + 1;
            }
            rmq = new int[logTable[n] + 1][n];
            for(int i=0; i<n; ++i){
                rmq[0][i] = a[i];
            }

            for(int k=1; (1 << k) < n; ++k){
                for(int i=0; i + (1 << k) <= n; ++i){
                    int max1 = rmq[k - 1][i];
                    int max2 = rmq[k-1][i + (1 << (k-1))];
                    rmq[k][i] = Math.max(max1, max2);
                }
            }
        }

        int max(int l, int r){
            int k = logTable[r - l];
            int max1 = rmq[k][l];
            int max2 = rmq[k][r - (1 << k) + 1];
            return Math.max(max1, max2);
        }
    }
    long checkBit(long mask, int bit){
        return (mask >> bit) & 1;
    }
    class Dsu{
        int[] parent;
        int countSets;
        Dsu(int n){
            countSets = n;
            parent = new int[n];
            for(int i=0; i<n; ++i){
                parent[i] = i;
            }
        }
        int findSet(int a){
            if(parent[a] == a) return a;
            parent[a] = findSet(parent[a]);
            return parent[a];
        }
        void unionSets(int a, int b){
            a = findSet(a);
            b = findSet(b);
            if(a!=b){
                countSets--;
                parent[a] = b;
            }
        }
    }
    static int checkBit(int mask, int bit) {
        return (mask >> bit) & 1;
    }
    boolean isLower(char c){
        return c >= 'a' && c <= 'z';
    }

    ////////////////////////////////////////////////////////////

    class SegmentTree{
        int[] t;
        int n;
        SegmentTree(int n){
            t = new int[4*n];
            build(new int[n+1], 1, 1, n);
        }
        void build (int a[], int v, int tl, int tr) {
            if (tl == tr)
                t[v] = a[tl];
            else {
                int tm = (tl + tr) / 2;
                build (a, v*2, tl, tm);
                build (a, v*2+1, tm+1, tr);
            }
        }

        void update (int v, int tl, int tr, int l, int r, int add) {
            if (l > r)
                return;
            if (l == tl && tr == r)
                t[v] += add;
            else {
                int tm = (tl + tr) / 2;
                update (v*2, tl, tm, l, Math.min(r,tm), add);
                update (v*2+1, tm+1, tr, Math.max(l,tm+1), r, add);
            }
        }

        int get (int v, int tl, int tr, int pos) {
            if (tl == tr)
                return t[v];
            int tm = (tl + tr) / 2;
            if (pos <= tm)
                return t[v] + get (v*2, tl, tm, pos);
            else
                return t[v] + get (v*2+1, tm+1, tr, pos);
        }
    }
    class Fenwik {
        long[] t;
        int length;

        Fenwik(int[] a) {
            length = a.length + 100;
            t = new long[length];

            for (int i = 0; i < a.length; ++i) {
                inc(i, a[i]);
            }
        }

        void inc(int ind, int delta) {
            for (; ind < length; ind = ind | (ind + 1)) {
                t[ind] += delta;
            }
        }

        long getSum(int r) {
            long sum = 0;
            for (; r >= 0; r = (r & (r + 1)) - 1) {
                sum += t[r];
            }
            return sum;
        }
    }
    int gcd(int a, int b){
        return b == 0 ? a : gcd(b, a%b);
    }

    long binPow(long a, long b, long m) {
        if (b == 0) {
            return 1;
        }
        if (b % 2 == 1) {
            return ((a % m) * (binPow(a, b - 1, m) % m)) % m;
        } else {
            long c = binPow(a, b / 2, m);
            return (c * c) % m;
        }

    }
    int minInt(int... values) {
        int min = Integer.MAX_VALUE;
        for (int value : values) min = Math.min(min, value);
        return min;
    }

    int maxInt(int... values) {
        int max = Integer.MIN_VALUE;
        for (int value : values) max = Math.max(max, value);
        return max;
    }
    public static void main(String[] args) throws NumberFormatException, IOException {
        // TODO Auto-generated method stub
        new A().run();
    }

    void run() throws NumberFormatException, IOException {
        solve();
        out.close();
    };

    BufferedReader in;
    PrintWriter out;

    StringTokenizer tok;
    String delim = " ";
    Random rnd = new Random();

    A() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            if (fileName.isEmpty()) {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                in = new BufferedReader(new FileReader(fileName + ".in"));
                out = new PrintWriter(fileName + ".out");
            }

        }
        tok = new StringTokenizer("");
    }

    String readLine() throws IOException {
        return in.readLine();
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine) {
                return null;
            }

            tok = new StringTokenizer(nextLine);
        }
        return tok.nextToken();
    }

    int readInt() throws NumberFormatException, IOException {
        return Integer.parseInt(readString());
    }
    byte readByte() throws NumberFormatException, IOException {
        return Byte.parseByte(readString());
    }
    int[] readIntArray (int n) throws NumberFormatException, IOException {
        int[] a = new int[n];
        for(int i=0; i<n; ++i){
            a[i] = readInt();
        }
        return a;
    }

    Integer[] readIntegerArray (int n) throws NumberFormatException, IOException {
        Integer[] a = new Integer[n];
        for(int i=0; i<n; ++i){
            a[i] = readInt();
        }
        return a;
    }

    long readLong() throws NumberFormatException, IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(readString());
    }
}