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.*;
import java.util.*;

public class Main {
    static FastScanner in;
    static PrintWriter out;
    static final long MOD = 1000000007;
    static boolean[][] dp;
    static List<Integer> ans;

    public static void main(String[] args) throws IOException {
        //        Scanner in = new Scanner(new File("input.txt"));
        //        Scanner in = new Scanner(System.in);
        //        System.setOut(new PrintStream(new BufferedOutputStream(new FileOutputStream("output.txt")), true));
        out = new PrintWriter(System.out);
        in = new FastScanner(System.in);
        //        in = new FastScanner("input.txt");
        long n = in.nextLong();
        ans = new ArrayList<Integer>();
        List<Long> ans = new ArrayList<Long>();
        long ss = n * (n + 1) / 4;
        System.out.println(Math.abs(n * (n + 1) / 2 - 2 * ss));
        for (long i = n; i >= 1; i--) {
            if (ss - i > 0) {
                ans.add(i);
                ss -= i;
            } else {
                ans.add(ss);
                break;
            }
        }
        System.out.print(ans.size() + " ");
        for (int i = 0; i < ans.size(); i++) {
            System.out.print(ans.get(i) + " ");
        }
        out.close();
    }
}

class Pair {
    public int first; //first member of pair
    public int second; //second member of pair

    public Pair(int first, int second) {
        this.first = first;
        this.second = second;
    }

    public Pair() {

    }

    @Override
    public boolean equals(Object o) {
        if (this == o)
            return true;
        if (!(o instanceof Pair))
            return false;
        Pair p = (Pair) o;
        return first == p.first && second == p.second;
    }

    @Override
    public int hashCode() {
        int result = (int) first;
        result = 31 * result + (int) second;
        return result;
    }
}

class PairComparable implements Comparator<Pair> {

    @Override
    public int compare(Pair o1, Pair o2) {
        if (o1.second < o2.second)
            return -1;
        else if (o1.second > o2.second)
            return 1;
        else {
            return 0;
        }
    }
}

class FastScanner {

    BufferedReader br;
    StringTokenizer tokenizer;

    FastScanner(String fileName) throws FileNotFoundException {
        this(new FileInputStream(new File(fileName)));
    }

    FastScanner(InputStream is) {
        br = new BufferedReader(new InputStreamReader(is));
    }

    String nextLine() throws IOException {
        tokenizer = null;
        return br.readLine();
    }

    String next() throws IOException {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            String line = br.readLine();
            if (line == null) {
                return null;
            }
            tokenizer = new StringTokenizer(line);
        }
        return tokenizer.nextToken();
    }

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

    long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    char nextChar() throws IOException {
        return next().charAt(0);
    }
}