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.awt.geom.Point2D;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;

public class E {
  private static class Task {
    void solve(FastScanner in, PrintWriter out) {
      int N = in.nextInt();
      long S = in.nextLong();
      Long[][] xy = new Long[N][];
      for (int i = 0; i < N; i++) xy[i] = new Long[]{in.nextLong(), in.nextLong()};

      ArrayList<Point2D.Double> co = new ArrayList<>();
      {
        ArrayList<Long[]> hull = ConvexHull.run(xy);
        for (Long[] l : hull) {
          Point2D.Double p = new Point2D.Double();
          p.setLocation(l[0], l[1]);
          co.add(p);
        }
      }

      double max = -1.0;
      int bi = -1, bj = -1, bk = -1;
      int m = co.size();
      for (int i = 0; i < m; i++) {
        int k = i;
        for (int j = i; j < m; j++) {
          if (k < j) k = j;
          double curs = S(co.get(i), co.get(j), co.get(k));
          while (k + 1 < m) {
            double nexs = S(co.get(i), co.get(j), co.get(k + 1));
            if (nexs > curs) {
              curs = nexs;
              k++;
            } else {
              break;
            }
          }
          if (curs > max) {
            max = curs;
            bi = i;
            bj = j;
            bk = k;
          }
        }
      }
      Point2D pi = co.get(bi), pj = co.get(bj), pk = co.get(bk);

      double ax = pi.getX() + (pj.getX() - pi.getX()) + (pk.getX() - pi.getX());
      double ay = pi.getY() + (pj.getY() - pi.getY()) + (pk.getY() - pi.getY());
      double bx = pi.getX() + (pj.getX() - pi.getX()) - (pk.getX() - pi.getX());
      double by = pi.getY() + (pj.getY() - pi.getY()) - (pk.getY() - pi.getY());
      double cx = pi.getX() - (pj.getX() - pi.getX()) + (pk.getX() - pi.getX());
      double cy = pi.getY() - (pj.getY() - pi.getY()) + (pk.getY() - pi.getY());
      out.println((long) ax + " " + (long) ay);
      out.println((long) bx + " " + (long) by);
      out.println((long) cx + " " + (long) cy);
    }

    double S(Point2D a, Point2D b, Point2D c) {
      double vx = b.getX() - a.getX();
      double vy = b.getY() - a.getY();
      double wx = c.getX() - a.getX();
      double wy = c.getY() - a.getY();
      return Math.abs(vx * wy - vy * wx);
    }

  }

  static class ConvexHull {
    public static <T extends Number> ArrayList<T[]> run(T[][] xy) {
      int N = xy.length;
      if (N <= 1) {
        ArrayList<T[]> list = new ArrayList<>();
        Collections.addAll(list, xy);
        return list;
      }
      Arrays.sort(xy, new Comparator<T[]>() {
        @Override
        public int compare(T[] a, T[] b) {
          if (!a[0].equals(b[0])) return Double.compare(a[0].doubleValue(), b[0].doubleValue());
          return Double.compare(a[1].doubleValue(), b[1].doubleValue());
        }
      });

      int[] qs = new int[N * 2];//構築中の凸包
      int k = 0;//凸包の頂点数
      for (int i = 0; i < N; i++) {
        if (k >= 1 && xy[qs[k - 1]][0].equals(xy[i][0]) && xy[qs[k - 1]][1].equals(xy[i][1])) continue;
        while (k > 1 && ccw(xy[qs[k - 2]], xy[qs[k - 1]], xy[i]) > 0) k--;
        qs[k++] = i;
      }

      int inf = k + 1;
      for (int i = N - 2; i >= 0; i--) {
        if (xy[qs[k - 1]][0] == xy[i][0] && xy[qs[k - 1]][1] == xy[i][1]) continue;
        while (k >= inf && ccw(xy[qs[k - 2]], xy[qs[k - 1]], xy[i]) > 0) k--;
        qs[k++] = i;
      }

      ArrayList<T[]> ret = new ArrayList<>(k - 1);
      for (int i = 0; i < k - 1; i++) ret.add(xy[qs[i]]);
      return ret;
    }

    private static <T extends Number> double ccw(T[] a, T[] b, T[] t) {
      return (t[0].doubleValue() - a[0].doubleValue()) * (b[1].doubleValue()
        - a[1].doubleValue()) - (b[0].doubleValue() - a[0].doubleValue()) * (t[1].doubleValue() - a[1].doubleValue());
    }
  }

  // Template
  public static void main(String[] args) {
    OutputStream outputStream = System.out;
    FastScanner in = new FastScanner();
    PrintWriter out = new PrintWriter(outputStream);
    Task solver = new Task();
    solver.solve(in, out);
    out.close();
  }
  private static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int bufferLength = 0;

    private boolean hasNextByte() {
      if (ptr < bufferLength) {
        return true;
      } else {
        ptr = 0;
        try {
          bufferLength = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (bufferLength <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

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

    double[] nextDoubleArray(int n) {
      double[] array = new double[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextDouble();
      }
      return array;
    }

    double[][] nextDoubleMap(int n, int m) {
      double[][] map = new double[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextDoubleArray(m);
      }
      return map;
    }

    public int nextInt() {
      return (int) nextLong();
    }
  }
}