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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer buffer;

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

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Point point = (Point) o;

            if (x != point.x) return false;
            return y == point.y;

        }

        @Override
        public int hashCode() {
            int result = (int) (x ^ (x >>> 32));
            result = 31 * result + (int) (y ^ (y >>> 32));
            return result;
        }
    }

    /**
     * Points p1, p2, p3 are counter-clockwise oriented if ccw > 0,
     * clockwise oriented if ccw < 0 and collinear if ccw == 0
     */
    public static long ccw(Point p1, Point p2, Point p3) {
        return (p2.x - p1.x)*(p3.y - p1.y) - (p2.y - p1.y)*(p3.x - p1.x);
    }

    public static List<Point> getConvexHull (List<Point> points) {
        int n = points.size();
        if (n <= 1) return points;
        Collections.sort(points, new Comparator<Point>() {
            @Override
            public int compare(Point o1, Point o2) {
                if (o1.x != o2.x) return Long.compare(o1.x, o2.x);
                return Long.compare(o1.y, o2.y);
            }
        });

        int[] pos = new int[n+1];
        int p = 0;
        for (int i=0;i<n;i++) {
            if (p > 0 && points.get(i).equals(points.get(pos[p]))) continue;
            while ( p > 1 && ccw(points.get(pos[p-2]), points.get(pos[p-1]), points.get(i)) < 0) p--;
            pos[p++] = i;
        }

        int inf = p+1;
        for (int i=n-2;i>=0;i--) {
            if (points.get(pos[p-1]).equals(points.get(i))) continue;
            while (p>=inf && ccw(points.get(pos[p-2]), points.get(pos[p-1]), points.get(i)) < 0) p--;
            pos[p++] = i;
        }

        List<Point> res = new ArrayList<Point>(p-1);
        for (int i=0;i<p-1;i++) res.add(points.get(pos[i]));

        return res;
    }

    public static long area2(Point p1, Point p2, Point p3) {
        return Math.abs(ccw(p1, p2, p3));
    }

    public static void solve() throws IOException {
        int n = ni();
        long S = nl();

        List<Point> pts = new ArrayList<>();
        for (int i=0;i<n;i++) {
            pts.add(new Point(nl(), nl()));
        }

        List<Point>ch = getConvexHull(pts);

        long max = -1L;
        Point p1 = null, p2 = null, p3 = null;
        int m = ch.size();

        for (int i=0;i<m;i++) {
            int k = i;
            for (int j=i;j<m;j++) {
                if (k<j) k=j;
                long curA = area2(ch.get(i), ch.get(j), ch.get(k));
                while (k+1 < m) {
                    long nextA = area2(ch.get(i), ch.get(j), ch.get(k+1));
                    if (nextA > curA) {
                        curA = nextA;
                        k++;
                    } else {
                        break;
                    }
                }

                if (curA > max) {
                    max = curA;
                    p1 = ch.get(i);
                    p2 = ch.get(j);
                    p3 = ch.get(k);
                }
            }
        }


        out.println((p3.x - p2.x + p1.x) + " " + (p3.y - p2.y + p1.y));
        out.println((p2.x - p1.x + p3.x) + " " + (p2.y - p1.y + p3.y));
        out.println((p1.x - p3.x + p2.x) + " " + (p1.y - p3.y + p2.y));

    }

    public static void main(String[] args) throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }

    static String next() {
        while (buffer == null || !buffer.hasMoreElements()) {
            try {
                buffer = new StringTokenizer(in.readLine());
            } catch (IOException e) {
            }
        }
        return buffer.nextToken();
    }

    static int ni() {
        return Integer.parseInt(next());
    }

    static long nl() {
        return Long.parseLong(next());
    }

    static double nd() {
        return Double.parseDouble(next());
    }

    static String ns() {
        return next();
    }

    static int[] ni(int n) {
        int[] res = new int[n];
        for (int i = 0; i < n; i++)
            res[i] = Integer.parseInt(next());
        return res;
    }

    static long[] nl(int n) {
        long[] res = new long[n];
        for (int i = 0; i < n; i++)
            res[i] = Long.parseLong(next());
        return res;
    }

    static double[] nd(int n) {
        double[] res = new double[n];
        for (int i = 0; i < n; i++)
            res[i] = Double.parseDouble(next());
        return res;
    }

    static String[] ns(int n) {
        String[] res = new String[n];
        for (int i = 0; i < n; i++)
            res[i] = next();
        return res;
    }

}