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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.HashSet;
import java.util.StringTokenizer;

public class e {

    static long MOD = 1_000_000_007;

    public static void main(String[] args) {
        FS in = new FS(System.in);
        PrintWriter out = new PrintWriter(System.out);
        
        int n = in.nextInt();
        long S = in.nextLong();
        VecL[] vecs = new VecL[n];
        for(int i = 0; i < n; i++) vecs[i] = new VecL(in.nextLong(), in.nextLong());
        VecL[] conv = ConvexHull.getHull(vecs);
        
        int[] points = new int[3];
        points[0] = 0;
        points[1] = 1;
        points[2] = 2;
        
        n = conv.length;
        
        int ind = 2;
        int num = 0;
        while(true) {
            int dist = 0;
            while(true) {
                long curr = area(conv[points[0]], conv[points[1]], conv[points[2]]);
                points[ind] = (points[ind]+1)%n;
                if(area(conv[points[0]], conv[points[1]], conv[points[2]]) <= curr) break;
                dist++;
            }
            points[ind] = (points[ind]+n-1)%n;
            while(true) {
                long curr = area(conv[points[0]], conv[points[1]], conv[points[2]]);
                points[ind] = (points[ind]+n-1)%n;
                if(area(conv[points[0]], conv[points[1]], conv[points[2]]) <= curr) break;
                dist++;
            }
            points[ind] = (points[ind]+1)%n;
            ind = (ind+1)%3;
            if(dist == 0) {
                num++;
                if(num == 4) break;
            } else {
                num = 0;
            }
        }
        
        out.println(conv[points[0]].x+conv[points[2]].x-conv[points[1]].x+" "+(conv[points[0]].y+conv[points[2]].y-conv[points[1]].y));
        out.println(conv[points[1]].x+conv[points[0]].x-conv[points[2]].x+" "+(conv[points[1]].y+conv[points[0]].y-conv[points[2]].y));
        out.println(conv[points[1]].x+conv[points[2]].x-conv[points[0]].x+" "+(conv[points[1]].y+conv[points[2]].y-conv[points[0]].y));
        out.close();
    }
    
    static long area(VecL a, VecL b, VecL c) {
        return Math.abs(a.cross(b)+b.cross(c)+c.cross(a));
    }

    static class ConvexHull {

        static VecL[] upperHull, lowerHull;

        public static VecL[] removeDupes(VecL[] points) {
            HashSet<VecL> set = new HashSet<>();
            for (VecL v : points) {
                set.add(v);
            }
            int counter = 0;
            points = new VecL[set.size()];
            for (VecL v : set) {
                points[counter++] = v;
            }
            return points;
        }

        // returns the hull in CCW order
        public static VecL[] getHull(VecL[] points) {
            points = points.clone();
            Arrays.sort(points);
            if (points.length < 3) {
                return upperHull = lowerHull = points;
            }
            int n = points.length, j = 2, k = 2;
            VecL[] lo = new VecL[n], up = new VecL[n];
            lo[0] = points[0];
            lo[1] = points[1];
            for (int i = 2; i < n; i++) {
                VecL p = points[i];
                while (j > 1 && !right(lo[j - 2], lo[j - 1], p)) {
                    j--;
                }
                lo[j++] = p;
            }
            up[0] = points[n - 1];
            up[1] = points[n - 2];
            for (int i = n - 3; i >= 0; i--) {
                VecL p = points[i];
                while (k > 1 && !right(up[k - 2], up[k - 1], p)) {
                    k--;
                }
                up[k++] = p;
            }

            VecL[] res = new VecL[j + k - 2];
            for (int i = 0; i < k; i++) {
                res[i] = up[i];
            }
            for (int i = 1; i < j - 1; i++) {
                res[k + i - 1] = lo[i];
            }

            // if you need upper and lower hulls
            upperHull = new VecL[k];
            for (int i = 0; i < k; i++) {
                upperHull[i] = up[k - i - 1];
            }
            lowerHull = new VecL[j];
            for (int i = 0; i < j; i++) {
                lowerHull[i] = lo[i];
            }

            return res;
        }

        // check if a->b->c are in the right order
        static boolean right(VecL a, VecL b, VecL c) {
            return b.sub(a).cross(c.sub(a)) > 0;
        }

    }

    static class VecL implements Comparable<VecL> {

        long x, y;

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

        public VecL add(VecL o) {
            return new VecL(x + o.x, y + o.y);
        }

        public VecL sub(VecL o) {
            return new VecL(x - o.x, y - o.y);
        }

        public VecL scale(long s) {
            return new VecL(x * s, y * s);
        }

        public long dot(VecL o) {
            return x * o.x + y * o.y;
        }

        public long cross(VecL o) {
            return x * o.y - y * o.x;
        }

        public long mag2() {
            return dot(this);
        }

        public VecL rot90() {
            return new VecL(-y, x);
        }

        public VecL rot270() {
            return new VecL(y, -x);
        }

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

        public int hashCode() {
            return Long.hashCode(x << 13 ^ (y * 57));
        }

        public boolean equals(Object oo) {
            VecL o = (VecL) oo;
            return x == o.x && y == o.y;
        }

        public int compareTo(VecL o) {
            if (x != o.x) {
                return Long.compare(x, o.x);
            }
            return Long.compare(y, o.y);
        }

        //origin->q1, axes-> quadrant in ccw direction
        public int quadrant() {
            if (x == 0 || y == 0) {
                if (y == 0) {
                    if (x >= 0) {
                        return 1;
                    } else {
                        return 3;
                    }
                } else if (y >= 0) {
                    return 2;
                } else {
                    return 4;
                }
            }
            if (x > 0) {
                if (y > 0) {
                    return 1;
                } else {
                    return 4;
                }
            } else if (y > 0) {
                return 2;
            } else {
                return 3;
            }
        }

        public int radialCompare(VecL o) {
            if (quadrant() == o.quadrant()) {
                return -Long.signum(cross(o));
            }
            return Integer.compare(quadrant(), o.quadrant());
        }
    }

    static class FS {

        BufferedReader in;
        StringTokenizer token;

        public FS(InputStream str) {
            in = new BufferedReader(new InputStreamReader(str));
        }

        public String next() {
            if (token == null || !token.hasMoreElements()) {
                try {
                    token = new StringTokenizer(in.readLine());
                } catch (IOException ex) {
                }
                return next();
            }
            return token.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        
        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}