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:
// package codeforces.cf3xx.cf358.div2;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.List;

/**
 * Created by hama_du on 2016/07/12.
 */
public class E {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        in.nextLong();
        Point[] pt = new Point[n];
        for (int i = 0; i < n ; i++) {
            pt[i] = new Point(in.nextLong(), in.nextLong());
        }
        List<Point> hull = convexHull(pt);
        Point[] abc = null;
        long bestArea = -1;
        int hn = hull.size();
        for (int i = 0; i < hn ; i++) {
            Point a = hull.get(i);
            int k = -1;
            for (int j = i+1 ; j < hn ; j++) {
                Point b = hull.get(j);
                if (k <= j) {
                    k = j+1;
                }
                while (k+1 < hn && Point.area(a, b, hull.get(k+1)) >= Point.area(a, b, hull.get(k))) {
                    k++;
                }
                if (k < hn) {
                    Point c = hull.get(k);
                    long area = Point.area(a, b, c);
                    if (bestArea < area) {
                        bestArea = area;
                        abc = new Point[]{a, b, c};
                    }
                }
            }
        }
        if (abc == null) {
            throw new RuntimeException("wtf");
        }

        for (int i = 0; i < 3 ; i++) {
            int a = i;
            int b = (i+1)%3;
            int c = (i+2)%3;
            long x = abc[a].x + abc[b].x - abc[c].x;
            long y = abc[a].y + abc[b].y - abc[c].y;
            out.println(x + " " + y);
        }
        out.flush();
    }


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

        Point(long _x, long _y) {
            x = _x;
            y = _y;
        }

        Point(Point a, Point b) {
            x = b.x - a.x;
            y = b.y - a.y;
        }

        public int compareTo(Point o) {
            if (x != o.x) {
                return Long.signum(x - o.x);
            }
            return Long.signum(y - o.y);
        }

        public long dist2(Point to) {
            return (x-to.x)*(x-to.x)+(y-to.y)*(y-to.y);
        }


        public long det(Point other) {
            return x * other.y - y * other.x;
        }

        public String toString() {
            return "(" + x + "," + y + ")";
        }

        public static long area(Point a, Point b, Point c) {
            long dx1 = c.x - a.x;
            long dy1 = c.y - a.y;
            long dx2 = b.x - a.x;
            long dy2 = b.y - a.y;
            return Math.abs(dx1*dy2-dy1*dx2)/2;
        }
    }

    public static List<Point> convexHull(Point[] points) {
        int n = points.length;
        Arrays.sort(points);
        Point[] candidate = new Point[n*2];
        int k = 0;

        // downer
        for (int i = 0 ; i < n ; i++) {
            while (k > 1) {
                Point a = new Point(candidate[k-2], candidate[k-1]);
                Point b = new Point(candidate[k-1], points[i]);
                if (a.det(b) <= 0) {
                    k--;
                } else {
                    break;
                }
            }
            candidate[k++] = points[i];
        }

        // upper
        int t = k;
        for (int i = n-2 ; i >= 0 ; i--) {
            while (k > t) {
                Point a = new Point(candidate[k-2], candidate[k-1]);
                Point b = new Point(candidate[k-1], points[i]);
                if (a.det(b) <= 0) {
                    k--;
                } else {
                    break;
                }
            }
            candidate[k++] = points[i];
        }
        List<Point> ret = new ArrayList<Point>();
        for (int i = 0 ; i < k - 1 ; i++) {
            ret.add(candidate[i]);
        }
        return ret;
    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int next() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            if ('a' <= c && c <= 'z') {
                return (char) c;
            }
            if ('A' <= c && c <= 'Z') {
                return (char) c;
            }
            throw new InputMismatchException();
        }

        public String nextToken() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res*sgn;
        }

        public long nextLong() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res*sgn;
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}