Problem: An exam for n students will take place in a long and narrow room, so the students will sit in a line in some order. The teacher suspects that students with adjacent numbers (i and i + 1) always studied side by side and became friends and if they take an exam sitting next to each other, they will help each other for sure.

Your task is to choose the maximum number of students and make such an arrangement of students in the room that no two students with adjacent numbers sit side by side.

Input

A single line contains integer n (1 ≤ n ≤ 5000) — the number of students at an exam.

Output

In the first line print integer k — the maximum number of students who can be seated so that no two students with adjacent numbers sit next to each other.

In the second line print k distinct integers a1, a2, ..., ak (1 ≤ ai ≤ n), where ai is the number of the student on the i-th position. The students on adjacent positions mustn't have adjacent numbers. Formally, the following should be true: |ai - ai + 1| ≠ 1 for all i from 1 to k - 1.

If there are several possible answers, output any of them.

Examples

Input

6

Output

6
1 5 3 6 2 4

Input

3


Output

2
1 3

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

/**
 * @author master_j
 * @version 0.4.1
 * @since Mar 22, 2015
 */
public class Solution {
    private void solve() throws IOException {
        int n = io.nI();
        if (n == 1) {
            io.wln(1);
            io.wln(1);
        } else if (n == 2) {
            io.wln(1);
            io.wln(1);
        } else if (n == 3) {
            io.wln(2);
            io.wln("1 3");
        } else {
            io.wln(n);

            if (n % 4 == 2)
                io.wf("%d ", n);
            else if (n % 4 == 3)
                io.wf("%d %d ", n, n - 2);

            for (int i = 1; 3 + i <= n; i += 4)
                io.wf("%d %d %d %d ", 1 + i, 3 + i, i, 2 + i);

            if (n % 4 == 1)
                io.wln(n);
            else if (n % 4 == 2)
                io.wln(n - 1);
            else if (n % 4 == 3)
                io.wln(n - 1);

        }
    }//2.2250738585072012e-308

    public static void main(String[] args) throws IOException {
        IO.launchSolution(args);
    }

    Solution(IO io) throws IOException {
        this.io = io;
        solve();
    }

    private final IO io;
}

class IO {
    static final String _localArg = "master_j";
    private static final String _problemName = "";
    private static final Mode _inMode = Mode.STD_;
    private static final Mode _outMode = Mode.STD_;
    private static final boolean _autoFlush = false;

    enum Mode {STD_, _PUT_TXT, PROBNAME_}

    private final StreamTokenizer st;
    private final BufferedReader br;
    private final Reader reader;

    private final PrintWriter pw;
    private final Writer writer;

    static void launchSolution(String[] args) throws IOException {
        boolean local = (args.length == 1 && args[0].equals(IO._localArg));
        IO io = new IO(local);

        long nanoTime = 0;
        if (local) {
            nanoTime -= System.nanoTime();
            io.wln("<output>");
        }

        io.flush();
        new Solution(io);
        io.flush();

        if (local) {
            io.wln("</output>");
            nanoTime += System.nanoTime();
            final long D9 = 1000000000, D6 = 1000000, D3 = 1000;
            if (nanoTime >= D9)
                io.wf("%d.%d seconds\n", nanoTime / D9, nanoTime % D9);
            else if (nanoTime >= D6)
                io.wf("%d.%d millis\n", nanoTime / D6, nanoTime % D6);
            else if (nanoTime >= D3)
                io.wf("%d.%d micros\n", nanoTime / D3, nanoTime % D3);
            else
                io.wf("%d nanos\n", nanoTime);
        }

        io.close();
    }

    IO(boolean local) throws IOException {
        if (_inMode == Mode.PROBNAME_ || _outMode == Mode.PROBNAME_)
            if (_problemName.length() == 0)
                throw new IllegalStateException("You imbecile. Where's my <_problemName>?");

        if (_problemName.length() > 0)
            if (_inMode != Mode.PROBNAME_ && _outMode != Mode.PROBNAME_)
                throw new IllegalStateException("You imbecile. What's the <_problemName> for?");

        Locale.setDefault(Locale.US);

        if (local) {
            reader = new FileReader("input.txt");
            writer = new OutputStreamWriter(System.out);
        } else {
            switch (_inMode) {
                case STD_:
                    reader = new InputStreamReader(System.in);
                    break;
                case PROBNAME_:
                    reader = new FileReader(_problemName + ".in");
                    break;
                case _PUT_TXT:
                    reader = new FileReader("input.txt");
                    break;
                default:
                    throw new NullPointerException("You imbecile. Gimme _inMode.");
            }
            switch (_outMode) {
                case STD_:
                    writer = new OutputStreamWriter(System.out);
                    break;
                case PROBNAME_:
                    writer = new FileWriter(_problemName + ".out");
                    break;
                case _PUT_TXT:
                    writer = new FileWriter("output.txt");
                    break;
                default:
                    throw new NullPointerException("You imbecile. Gimme _outMode.");
            }
        }

        br = new BufferedReader(reader);
        st = new StreamTokenizer(br);

        pw = new PrintWriter(writer, _autoFlush);

        if (local && _autoFlush)
            wln("Note: auto-flush is on.");
    }

    //@formatter:off
    void wln()          {pw.println(); }
    void wln(boolean x) {pw.println(x);}
    void wln(char x)    {pw.println(x);}
    void wln(char x[])  {pw.println(x);}
    void wln(double x)  {pw.println(x);}
    void wln(float x)   {pw.println(x);}
    void wln(int x)     {pw.println(x);}
    void wln(long x)    {pw.println(x);}
    void wln(Object x)  {pw.println(x);}
    void wln(String x)  {pw.println(x);}

    void wf(String f, Object... o) {pw.printf(f, o);}

    void w(boolean x)   {pw.print(x);}
    void w(char x) {pw.print(x);}
    void w(char x[]) {pw.print(x);}
    void w(double x)    {pw.print(x);}
    void w(float x)     {pw.print(x);}
    void w(int x)       {pw.print(x);}
    void w(long x)      {pw.print(x);}
    void w(Object x)    {pw.print(x);}
    void w(String x)    {pw.print(x);}

    int nI() throws IOException {st.nextToken(); return (int)st.nval;}
    double nD() throws IOException {st.nextToken(); return st.nval;}
    float nF() throws IOException {st.nextToken(); return (float)st.nval;}
    long nL() throws IOException   {st.nextToken(); return (long)st.nval;}
    String nS() throws IOException {st.nextToken(); return st.sval;}

    int[] nIa(int n) throws IOException {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nI();
        return a;
    }
    double[] nDa(int n) throws IOException {
        double[] a = new double[n];
        for (int i = 0; i < n; i++)
            a[i] = nD();
        return a;
    }
    String[] nSa(int n) throws IOException {
        String[] a = new String[n];
        for (int i = 0; i < n; i++)
            a[i] = nS();
        return a;
    }

    void wc(String x)         {wc(x.toCharArray());}
    void wc(char c1, char c2) {for (char c = c1; c<=c2; c++) wc(c);}
    void wc(char x[])         {for (char c : x) wc(c); }
    void wc(char x)           {st.ordinaryChar(x); st.wordChars(x, x);}

    public boolean eof() {return st.ttype == StreamTokenizer.TT_EOF;}
    public boolean eol() {return st.ttype == StreamTokenizer.TT_EOL;}

    void flush() {pw.flush();}
    void close() throws IOException {reader.close(); br.close(); flush(); pw.close();}
    //@formatter:on
}