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.*;
import java.nio.charset.StandardCharsets;
// import java.math.BigInteger;

public class A {
    static Writer wr;

    public static void main(String[] args) throws Exception {
        // long startTime = System.nanoTime();

        // String testString = "";
        // InputStream stream = new ByteArrayInputStream(testString.getBytes(StandardCharsets.UTF_8));
        // Reader in = new Reader(stream);

        Reader in = new Reader();
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        
        wr = new Writer();

        /* Precomputation */


        // long elapsedTime = System.nanoTime() - startTime;
        // double seconds = (double)elapsedTime / 1000000000.0;
        // wr.writeRedLn(seconds);

        /* Input */
        int N = in.nextInt();

        int count = 0;
        StringBuilder sb = new StringBuilder();
        
        int last = 0;
        for(int i=1;i<=N;i+=2) {
            count++;
            sb.append(i + " ");
            last = i;
        }



        for(int i=2;i<=N;i+=2) {
            if(Math.abs(i-last)==1) continue;

            count++;
            sb.append(i + " ");
            last = i;
        }

        if(N==4) {
            count=4;
            sb = new StringBuilder("3 1 4 2");
        }

        out.write(count + "\n");
        out.write(sb.toString().trim() + "\n");

        out.flush();
    }
}



class Writer {
    public void writeRedLn(Object x) { writeRedLn(x+""); }
    public void writeBlueLn(Object x) { writeBlueLn(x+""); }
    public void writeGreenLn(Object x) { writeGreenLn(x+""); }
    public void writePinkLn(Object x) { writePinkLn(x+""); }
    public void writeRedLn(String x) { System.out.println((char)27 + "[31m" + (char)27 + "[40m" + x + (char)27 + "[0m"); }
    public void writeBlueLn(String x) { System.out.println((char)27 + "[34m" + (char)27 + "[3m" + x + (char)27 + "[0m"); }
    public void writeGreenLn(String x) { System.out.println((char)27 + "[32m" + (char)27 + "[3m" + x + (char)27 + "[0m"); }
    public void writePinkLn(String x) { System.out.println((char)27 + "[30m" + (char)27 + "[45m" + x + (char)27 + "[0m"); }
    public void writeRed(String x) { System.out.print((char)27 + "[31m" + (char)27 + "[40m" + x + (char)27 + "[0m"); }
    public void writeBlue(String x) { System.out.print((char)27 + "[34m" + (char)27 + "[3m" + x + (char)27 + "[0m"); }
    public void writeGreen(String x) { System.out.print((char)27 + "[32m" + (char)27 + "[3m" + x + (char)27 + "[0m"); }
    public void writePink(String x) { System.out.print((char)27 + "[30m" + (char)27 + "[45m" + x + (char)27 + "[0m"); }
}


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(InputStream stream){din=new DataInputStream(stream);buffer=new byte[BUFFER_SIZE];bufferPointer=bytesRead=0;}
    public String readLine()throws IOException{byte[] buf=new byte[1024];int cnt=0,c;
        while((c=read())!=-1){if(c=='\n')break;buf[cnt++]=(byte)c;}return new String(buf,0,cnt);}
    public char nextChar()throws IOException{byte c=read();while(c<=' ')c=read();return (char)c;}
    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();}
}