Problem: You are given n points with integer coordinates on the plane. Points are given in a way such that there is no triangle, formed by any three of these n points, which area exceeds S.

Alyona tried to construct a triangle with integer coordinates, which contains all n points and which area doesn't exceed 4S, but, by obvious reason, had no success in that. Please help Alyona construct such triangle. Please note that vertices of resulting triangle are not necessarily chosen from n given points.

Input

In the first line of the input two integers n and S (3 ≤ n ≤ 5000, 1 ≤ S ≤ 1018) are given — the number of points given and the upper bound value of any triangle's area, formed by any three of given n points.

The next n lines describes given points: ith of them consists of two integers xi and yi ( - 108 ≤ xi, yi ≤ 108) — coordinates of ith point.

It is guaranteed that there is at least one triple of points not lying on the same line.

Output

Print the coordinates of three points — vertices of a triangle which contains all n points and which area doesn't exceed 4S.

Coordinates of every triangle's vertex should be printed on a separate line, every coordinate pair should be separated by a single space. Coordinates should be an integers not exceeding 109 by absolute value.

It is guaranteed that there is at least one desired triangle. If there is more than one answer, print any of them.

Example

Input

4 1
0 0
1 0
0 1
1 1


Output

-1 0
2 0
0 2

Note

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Solution (in JAVA):

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

public class E {

    FastScanner scanner;
    PrintWriter writer;

    static class Point implements Comparable<Point> {
        long x, y;

        public Point(long x, long y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Point o) {
            if (x < o.x || x == o.x && y < o.y)
                return -1;
            else if (x == o.x && y == o.y)
                return 0;
            else return 1;
        }
    }

    enum Or {
        L, R, C
    }

    long sq(Point p1, Point p2, Point p3) {
        return (p2.x - p1.x) * (p3.y - p1.y) - (p2.y - p1.y) * (p3.x - p1.x);
    }

    Or or(Point p1, Point p2, Point p3) {
        long s = sq(p1, p2, p3);
        if (s < 0)
            return Or.R;
        else if (s == 0)
            return Or.C;
        else return Or.L;
    }

    <T>
    void shuffle(List<T> l) {
        Random random = new Random(System.currentTimeMillis());
        for (int i = 1; i < l.size(); i++) {
            int j = random.nextInt(i + 1);
            T tmp = l.get(i);
            l.set(i, l.get(j));
            l.set(j, tmp);
        }
    }

    Point[] findTri(List<Point> pts) {
        Point[] tri = new Point[] {pts.get(0), pts.get(1), pts.get(2)};
        boolean change = true;
        long curS = Math.abs(sq(tri[0], tri[1], tri[2]));
        while (change) {
            change = false;
            for (Point p : pts) {
                for (int i = 0; i < 3; i++) {
                    Point a = tri[(i + 1) % 3];
                    Point b = tri[(i + 2) % 3];
                    long newS = Math.abs(sq(a, b, p));
                    if (newS > curS) {
                        tri[i] = p;
                        curS = newS;
                        change = true;
                        break;
                    }
                }
            }
        }
        if (or(tri[0], tri[1], tri[2]) == Or.R) {
            Point tmp = tri[1];
            tri[1] = tri[2];
            tri[2] = tmp;
        }
        return tri;
    }

    Point add(Point p, Point vb, Point ve) {
        long x = p.x + ve.x - vb.x;
        long y = p.y + ve.y - vb.y;
        return new Point(x, y);
    }

    void solve() throws IOException {
        scanner = new FastScanner(System.in);
        writer = new PrintWriter(System.out);
        int n = scanner.nextInt();
        long s = scanner.nextLong();
        List<Point> pts = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            long x = scanner.nextLong();
            long y = scanner.nextLong();
            Point p = new Point(x, y);
            pts.add(p);
        }
        Point[] tri = findTri(pts);
        Point a = add(tri[0], tri[1], tri[2]);
        Point b = add(tri[0], tri[2], tri[1]);
        Point c = add(tri[1], tri[0], tri[2]);
        writer.println(a.x + " " + a.y);
        writer.println(b.x + " " + b.y);
        writer.println(c.x + " " + c.y);
        writer.close();
    }

    public static void main(String... args) throws IOException {
        new E().solve();
    }

    static 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());
        }
    }
}