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:
/*-
 * Codeforces problem :
 * http://codeforces.com/problemset/problem/682/E
 *
 * Print the coordinates of three points 
 * Vertices of a triangle which contains all n points and which area doesn't exceed 4S.
 */

import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

/**
 * @author Karthik Venkataraman
 * @email kafy83@gmail.com
 */
public class AlyonaTriangles {

    private int n;
    private long s;
    private Point[] points;
    private Point[] hull;
    private Point[] maxAreaTriangle;

    class Point implements Comparable {

        private long x;
        private long y;

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

        @Override
        public boolean equals(Object o) {
            if (o == null || !(o instanceof Point)) {
                return false;
            }
            Point other = (Point) o;
            return this.x == other.x && this.y == other.y;
        }

        @Override
        public int hashCode() {
            int hash = 7;
            hash = 89 * hash + (int) (this.x ^ (this.x >>> 32));
            hash = 89 * hash + (int) (this.y ^ (this.y >>> 32));
            return hash;
        }

        @Override
        public int compareTo(Object o) {
            Point other = (Point) o;
            if (this.x == other.x) {
                return Long.compare(this.y, other.y);
            }
            return Long.compare(this.x, other.x);
        }

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

    private static long area2(Point a, Point b, Point c) {
        return a.x * (b.y - c.y) - a.y * (b.x - c.x) + (b.x * c.y - b.y * c.x);
    }

    private static boolean isRightTurnOrCollinear(Point a, Point b, Point c) {
        return area2(a, b, c) <= 0;
    }

    private static long absArea2(Point a, Point b, Point c) {
        return Math.abs(area2(a, b, c));
    }

    private void compute() {
        InputReader sc = new InputReader(System.in);
        n = sc.nextInt();
        s = sc.nextLong();
        points = new Point[n];
        for (int i = 0; i < n; i++) {
            points[i] = new Point(sc.nextLong(), sc.nextLong());
        }
        computeConvexHull();
        findTrianglePointsWithMaxArea();
        printAnticomplimentaryTrianglePoints();
    }

    private void printAnticomplimentaryTrianglePoints() {
        System.out.println(new Point((-maxAreaTriangle[0].x + maxAreaTriangle[1].x + maxAreaTriangle[2].x),
                (-maxAreaTriangle[0].y + maxAreaTriangle[1].y + maxAreaTriangle[2].y)).toString());
        System.out.println(new Point((maxAreaTriangle[0].x - maxAreaTriangle[1].x + maxAreaTriangle[2].x),
                (maxAreaTriangle[0].y - maxAreaTriangle[1].y + maxAreaTriangle[2].y)).toString());
        System.out.println(new Point((maxAreaTriangle[0].x + maxAreaTriangle[1].x - maxAreaTriangle[2].x),
                (maxAreaTriangle[0].y + maxAreaTriangle[1].y - maxAreaTriangle[2].y)).toString());
    }

    private void findTrianglePointsWithMaxArea() {
        maxAreaTriangle = new Point[3];
        int m = hull.length;
        int a = 0, b = 1, c = 2;
        int ba = a, bb = b, bc = c;
        while (true) { //loop A
            while (true) { //loop B
                while (absArea2(hull[a], hull[b], hull[c])
                        <= absArea2(hull[a], hull[b], hull[(c + 1) % m])) { //loop C
                    c = (c + 1) % m;
                }
                if (absArea2(hull[a], hull[b], hull[c])
                        <= absArea2(hull[a], hull[(b + 1) % m], hull[c])) {
                    b = (b + 1) % m;
                } else {
                    break;
                }
            }
            if (absArea2(hull[a], hull[b], hull[c]) > absArea2(hull[ba], hull[bb], hull[bc])) {
                ba = a;
                bb = b;
                bc = c;
            }
            a = (a + 1) % m;
            if (a == b) {
                b = (b + 1) % m;
            }
            if (b == c) {
                c = (c + 1) % m;
            }
            if (a == 0) {
                break;
            }
        }
        maxAreaTriangle[0] = hull[ba];
        maxAreaTriangle[1] = hull[bb];
        maxAreaTriangle[2] = hull[bc];
    }

    private void computeConvexHull() {
        Arrays.sort(points);
        int[] hullIdx = new int[n + 1];
        int hullPtr = 0;
        for (int i = 0; i < n; i++) {
            while (hullPtr > 1 && isRightTurnOrCollinear(points[hullIdx[hullPtr - 2]], points[hullIdx[hullPtr - 1]], points[i])) {
                hullPtr--;
            }
            hullIdx[hullPtr++] = i;
        }

        for (int i = n - 2, t = hullPtr; i >= 0; i--) {
            while (hullPtr > t && isRightTurnOrCollinear(points[hullIdx[hullPtr - 2]], points[hullIdx[hullPtr - 1]], points[i])) {
                hullPtr--;
            }
            hullIdx[hullPtr++] = i;
        }

        hullPtr--;
        hull = new Point[hullPtr];
        for (int i = 0; i < hullPtr; i++) {
            hull[i] = points[hullIdx[i]];
        }
    }

    class InputReader {

        private static final int INPUT_KB = 1024;
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), INPUT_KB);
        }

        private String readNext() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException ex) {
                    throw new IllegalArgumentException(ex);
                }
            }
            return tokenizer.nextToken();
        }

        private Integer nextInt() {
            return Integer.parseInt(readNext());
        }

        private Long nextLong() {
            return Long.parseLong(readNext());
        }
    }

    public static void main(String... args) {
        AlyonaTriangles at = new AlyonaTriangles();
        at.compute();
    }
}