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.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class Main {
	public static class Point implements Comparable<Point>{
		double x;
		double y;
		double t;
		public Point(double x, double y){
			this.x = x;
			this.y = y;
		}
		
		@Override
		public int compareTo(Point p){
			return Double.compare(this.t, p.t);
		}
	}
	public static double computeAngle(Point p1, Point p2){
		if(p1.x == p2.x){
			return 90;
		}
		double tan = (p1.y - p2.y) / (p1.x - p2.x);
		double angle = Math.toDegrees(Math.atan(Math.abs(tan)));
		return tan < 0 ? 180 - angle : angle;
	}
	public static double zComponent(Point p1, Point p2, Point p3){
		double zComponent = ((p3.x - p2.x) * (p1.y - p2.y)) - ((p3.y - p2.y) * (p1.x - p2.x));
		return zComponent;
	}
	public static ArrayList<Point> computeConvexHull(Point[] points){
		int n = points.length;
		int min = 0;
		for(int i=0;i<n;i++){
			if(points[i].y < points[min].y){
				min = i;
			}
			else if(points[i].y == points[min].y){
				if(points[i].x < points[min].x){
					min = i;
				}
			}
		}
		for(int i=0;i<n;i++){
			points[i].t = computeAngle(points[i], points[min]);
		}
		points[min].t = -1;
		ArrayList<Point> sorted = new ArrayList<Point>();
		for(int i=0;i<n;i++){
			sorted.add(points[i]);
		}
		Collections.sort(sorted);
		sorted.add(sorted.get(0));
		ArrayList<Point> hull = new ArrayList<Point>();
		hull.add(sorted.get(0));
		hull.add(sorted.get(1));
		int i = 2;
		while(i < n + 1){
			int last = hull.size() - 1;
			if(zComponent(hull.get(last - 1), hull.get(last), sorted.get(i)) >= 0){
				hull.add(sorted.get(i));
				i++;
			}
			else{
				hull.remove(last);
				if(hull.size() == 1){
					hull.add(sorted.get(i));
					i++;
				}
			}
		}
		hull.remove(hull.size() - 1);
		return hull;
	}
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long s = sc.nextLong();
		Point[] points = new Point[n];
		for(int i=0;i<n;i++){
			points[i] = new Point(sc.nextDouble(), sc.nextDouble());
		}
		ArrayList<Point> convexHull = computeConvexHull(points);
		int p1 = 0, p2 = 0, p3 = 0;
		double MAX = 0;
		int A = 0, B = 1, C = 2;
		while(true){
			double area = 0.0;
			while(true){
				area = 0.5 * Math.abs(zComponent(convexHull.get(A), convexHull.get(B)
						, convexHull.get(C)));
				while(area <= 0.5 * Math.abs(zComponent(convexHull.get(A), convexHull.get(B)
						, convexHull.get((C + 1) % convexHull.size())))){
					C = (C + 1) % convexHull.size();
					area = 0.5 * Math.abs(zComponent(convexHull.get(A), convexHull.get(B)
							, convexHull.get(C)));
				}
				if(area <= 0.5 * Math.abs(zComponent(convexHull.get(A), 
						convexHull.get((B + 1) % convexHull.size()), convexHull.get(C)))){
					B = (B + 1) % convexHull.size();
					continue;
				}
				else{
					break;
				}
			}
			if(area > MAX){
				p1 = A;
				p2 = B;
				p3 = C;
				MAX = area;
			}
			A = (A + 1) % convexHull.size();
			if(A == B){
				B = (B + 1) % convexHull.size();
			}
			if(B == C){
				C = (C + 1) % convexHull.size();
 			}
			if(A == 0)break;
		}
		
		Point point1 = convexHull.get(p1);
		Point point2 = convexHull.get(p2);
		Point point3 = convexHull.get(p3);
		if(point1.x - point2.x == 0){
			double m1 = (point1.y - point3.y) / ((point1.x - point3.x));
			double m2 = (point2.y - point3.y) / ((point2.x - point3.x));
			double c1 = point2.y - (m1 * point2.x);
			double c2 = point1.y - (m2 * point1.x);
			double x1 = (c2 - c1) / (m1 - m2);
			double y1 = (m1 * x1) + c1;
			double x2 = point3.x;
			double x3 = point3.x;
			double y2 = (m1 * x2) + c1;
			double y3 = (m2 * x3) + c2;
			x1 = (x1 - Math.floor(x1)) < 0.5 ? Math.floor(x1) : Math.ceil(x1);
			y1 = (y1 - Math.floor(y1)) < 0.5 ? Math.floor(y1) : Math.ceil(y1);
			x2 = (x2 - Math.floor(x2)) < 0.5 ? Math.floor(x2) : Math.ceil(x2);
			y2 = (y2 - Math.floor(y2)) < 0.5 ? Math.floor(y2) : Math.ceil(y2);
			x3 = (x3 - Math.floor(x3)) < 0.5 ? Math.floor(x3) : Math.ceil(x3);
			y3 = (y3 - Math.floor(y3)) < 0.5 ? Math.floor(y3) : Math.ceil(y3);
			System.out.println((int)x1 + " " + (int)y1);
			System.out.println((int)x2 + " " + (int)y2);
			System.out.println((int)x3 + " " + (int)y3);
		}
		else if(point2.x - point3.x == 0){
			double m1 = (point1.y - point3.y) / ((point1.x - point3.x));
			double m2 = (point1.y - point2.y) / ((point1.x - point2.x));
			double c1 = point2.y - (m1 * point2.x);
			double c2 = point3.y - (m2 * point3.x);
			double x1 = (c2 - c1) / (m1 - m2);
			double y1 = (m1 * x1) + c1;
			double x2 = point1.x;
			double x3 = point1.x;
			double y2 = (m1 * x2) + c1;
			double y3 = (m2 * x3) + c2;
			x1 = (x1 - Math.floor(x1)) < 0.5 ? Math.floor(x1) : Math.ceil(x1);
			y1 = (y1 - Math.floor(y1)) < 0.5 ? Math.floor(y1) : Math.ceil(y1);
			x2 = (x2 - Math.floor(x2)) < 0.5 ? Math.floor(x2) : Math.ceil(x2);
			y2 = (y2 - Math.floor(y2)) < 0.5 ? Math.floor(y2) : Math.ceil(y2);
			x3 = (x3 - Math.floor(x3)) < 0.5 ? Math.floor(x3) : Math.ceil(x3);
			y3 = (y3 - Math.floor(y3)) < 0.5 ? Math.floor(y3) : Math.ceil(y3);
			System.out.println((int)x1 + " " + (int)y1);
			System.out.println((int)x2 + " " + (int)y2);
			System.out.println((int)x3 + " " + (int)y3);
		}
		else if(point1.x - point3.x == 0){
			double m1 = (point1.y - point2.y) / ((point1.x - point2.x));
			double m2 = (point2.y - point3.y) / ((point2.x - point3.x));
			double c1 = point3.y - (m1 * point3.x);
			double c2 = point1.y - (m2 * point1.x);
			double x1 = (c2 - c1) / (m1 - m2);
			double y1 = (m1 * x1) + c1;
			double x2 = point2.x;
			double x3 = point2.x;
			double y2 = (m1 * x2) + c1;
			double y3 = (m2 * x3) + c2;
			x1 = (x1 - Math.floor(x1)) < 0.5 ? Math.floor(x1) : Math.ceil(x1);
			y1 = (y1 - Math.floor(y1)) < 0.5 ? Math.floor(y1) : Math.ceil(y1);
			x2 = (x2 - Math.floor(x2)) < 0.5 ? Math.floor(x2) : Math.ceil(x2);
			y2 = (y2 - Math.floor(y2)) < 0.5 ? Math.floor(y2) : Math.ceil(y2);
			x3 = (x3 - Math.floor(x3)) < 0.5 ? Math.floor(x3) : Math.ceil(x3);
			y3 = (y3 - Math.floor(y3)) < 0.5 ? Math.floor(y3) : Math.ceil(y3);
			System.out.println((int)x1 + " " + (int)y1);
			System.out.println((int)x2 + " " + (int)y2);
			System.out.println((int)x3 + " " + (int)y3);
		}
		else{
			double m1 = (point1.y - point2.y) / ((point1.x - point2.x));
			double m2 = (point1.y - point3.y) / ((point1.x - point3.x));
			double m3 = (point2.y - point3.y) / ((point2.x - point3.x));
			double c1 = point3.y - (m1 * point3.x);
			double c2 = point2.y - (m2 * point2.x);
			double c3 = point1.y - (m3 * point1.x);
			double x1 = (c2 - c1) / (m1 - m2);
			double y1 = (m1 * x1) + c1;
			double x2 = (c3 - c1) / (m1 - m3);
			double y2 = (m1 * x2) + c1;
			double x3 = (c2 - c3) / (m3 - m2);
			double y3 = (m2 * x3) + c2;
			x1 = (x1 - Math.floor(x1)) < 0.5 ? Math.floor(x1) : Math.ceil(x1);
			y1 = (y1 - Math.floor(y1)) < 0.5 ? Math.floor(y1) : Math.ceil(y1);
			x2 = (x2 - Math.floor(x2)) < 0.5 ? Math.floor(x2) : Math.ceil(x2);
			y2 = (y2 - Math.floor(y2)) < 0.5 ? Math.floor(y2) : Math.ceil(y2);
			x3 = (x3 - Math.floor(x3)) < 0.5 ? Math.floor(x3) : Math.ceil(x3);
			y3 = (y3 - Math.floor(y3)) < 0.5 ? Math.floor(y3) : Math.ceil(y3);
			System.out.println((int)x1 + " " + (int)y1);
			System.out.println((int)x2 + " " + (int)y2);
			System.out.println((int)x3 + " " + (int)y3);
		}
	}
}