Petya has n integers: 1, 2, 3, ..., n. He wants to split these integers in two non-empty groups in such a way that the absolute difference of sums of integers in each group is as small as possible. 

Help Petya to split the integers. Each of n integers should be exactly in one group.

Input

The first line contains a single integer n (2 ≤ n ≤ 60 000) — the number of integers Petya has.

Output

Print the smallest possible absolute difference in the first line.

In the second line print the size of the first group, followed by the integers in that group. You can print these integers in arbitrary order. If there are multiple answers, print any of them.

Examples

Input

4


Output

0
2 1 4 


Input

2


Output

1
1 1 

Note

In the first example you have to put integers 1 and 4 in the first group, and 2 and 3 in the second. This way the sum in each group is 5, and the absolute difference is 0.

In the second example there are only two integers, and since both groups should be non-empty, you have to put one integer in the first group and one in the second. This way the absolute difference of sums of integers in each group is 1.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.Reader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Ruins He
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    OutputWriter out = new OutputWriter(outputStream);
    TaskC solver = new TaskC();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskC {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
      int n = in.nextInt();
      out.println(n % 4 == 1 || n % 4 == 2 ? 1 : 0);
      int offset = n % 4;
      int count = (n - n % 4) / 2;
      out.print(count + (n % 4 != 0 ? 1 : 0));
      if (n % 4 == 1 || n % 4 == 2) out.print(" 1");
      else if (n % 4 == 3) out.println(" 3");
      for (int i = 0; i < count; i += 2) {
        out.print(' ');
        out.print(i + 1 + offset);
        out.print(' ');
        out.print(n - i);
      }
      out.println();
    }

  }

  static class OutputWriter {
    private final PrintWriter writer;

    private OutputWriter(Writer writer, boolean autoFlush) {
      this.writer = new PrintWriter(new BufferedWriter(writer, 32767), autoFlush);
    }

    public OutputWriter(Writer writer) {
      this(writer, true);
    }

    public OutputWriter(OutputStream outputStream) {
      this(new OutputStreamWriter(outputStream), false);
    }

    public OutputWriter println() {
      writer.println();
      return this;
    }

    public OutputWriter println(String string) {
      writer.println(string);
      return this;
    }

    public OutputWriter println(int value) {
      writer.println(value);
      return this;
    }

    public OutputWriter print(char value) {
      writer.print(value);
      return this;
    }

    public OutputWriter print(int value) {
      writer.print(value);
      return this;
    }

    public OutputWriter print(Object object) {
      writer.print(object);
      return this;
    }

    public void close() {
      writer.close();
    }

  }

  static class InputReader {
    public final BufferedReader reader;
    public StringTokenizer tokenizer = null;

    public InputReader(Reader reader) {
      this.reader = new BufferedReader(reader, 32767);
    }

    public InputReader(InputStream inputStream) {
      this(new InputStreamReader(inputStream));
    }

    public String next() {
      if (hasNext()) return tokenizer.nextToken();
      else throw new NoSuchElementException();
    }

    public int nextInt() {
      return Integer.parseInt(next());
    }

    public boolean hasNext() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          String nextLine = reader.readLine();
          if (nextLine == null) return false;
          tokenizer = new StringTokenizer(nextLine);
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.hasMoreTokens();
    }

  }
}

