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.*;

/**
 * Created on 4/12/15.
 *
 * @author Mike Sorokin
 */
public class A {
    private static final BufferedReader reader;
    private static final StreamTokenizer in;
    private static final PrintWriter out;
    private static final boolean STDIO = true;

    static {
        if (STDIO) {
            in = new StreamTokenizer(reader = new BufferedReader(new InputStreamReader(System.in)));
            out = new PrintWriter(System.out);
        } else {
            BufferedReader tmpReader = null;
            StreamTokenizer tmpIn = null;
            PrintWriter tmpOut = null;
            try {
                tmpIn = new StreamTokenizer(tmpReader = new BufferedReader(new FileReader("input.txt")));
                tmpOut = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
            } catch (IOException e) {
                e.printStackTrace();
            }
            reader = tmpReader;
            in = tmpIn;
            out = tmpOut;
        }
    }

    private static int nextInt() throws IOException {
        in.nextToken();
        return (int) in.nval;
    }

    private static long nextLong() throws IOException {
        in.nextToken();
        return (long) in.nval;
    }

    private static double nextDouble() throws IOException {
        in.nextToken();
        return in.nval;
    }

    private static String next() throws IOException {
        in.nextToken();
        return in.sval;
    }

    public static void main(String[] args) throws IOException {
        int n = nextInt();
        if (n < 3) {
            out.printf("1\n1\n");
        } else if (n == 3) {
            out.printf("2\n1 3\n");
        } else if (n == 4) {
            out.printf("4\n2 4 1 3\n");
        } else{
            out.printf("%d\n", n);
            for (int i = 1; i <= n; i += 2) {
                out.printf("%d ", i);
            }
            for (int i = 2; i <= n; i += 2) {
                out.printf("%d ", i);
            }
            out.printf("\n");
        }

        out.close();
    }
}