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.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;


public class E358 {
	static int N;
	static long time;
	public static void main(String[] args) {
		MyScanner scan = new MyScanner();
		PrintWriter out = new PrintWriter(System.out);
		time = System.nanoTime();
		N = scan.nextInt(); long S = scan.nextLong();
		Point[] list = new Point[N];
		for(int i=0;i<N;i++)list[i] = new Point(scan.nextLong(), scan.nextLong());
		
		Point[] T = new MaxTriangle(list).solve();
		long x1 = T[0].x-T[1].x+T[2].x, y1 = T[0].y-T[1].y+T[2].y;
		long x2 = T[1].x-T[2].x+T[0].x, y2 = T[1].y-T[2].y+T[0].y;
		long x3 = T[2].x-T[0].x+T[1].x, y3 = T[2].y-T[0].y+T[1].y;
		
		out.println(x1+" "+y1);
		out.println(x2+" "+y2);
		out.println(x3+" "+y3);
		out.close();
	}
	
	public static long cross(Point O, Point A, Point B){
		return (long) ((A.x-O.x)*(B.y-O.y)-(A.y-O.y)*(B.x-O.x));
	}
	
	private static class MaxTriangle {
		Point[] hull;
		static int M;
		int a = 0, b = 1, c = 2;
	    Point[] sol;
		long max;
		public MaxTriangle(Point[] list){
			ConvexHull ch = new ConvexHull(list);
			hull = ch.getHull();
			M = hull.length;
			sol = new Point[3];
			sol[0] = hull[a];sol[1] = hull[b];sol[2] = hull[c];
		}
		//assume at least 3 points
		public Point[] solve() {
			long cur, temp;
			max = cur = cross(sol[0],sol[1],sol[2]);
			while(a<M){
				while(a!=b&&(temp = cross(hull[a],hull[b],hull[(c+1)%M])) >= cur){
					c++;c%=M;
					cur = temp;
					if(max < temp)update(temp);
				}
				if((temp = cross(hull[a], hull[(b+1)%M], hull[c])) >= cur) {
					b++;b%=M;
					cur = temp;
					if(max < temp) update(temp);
				}else{
					a++;
					if(a==M)continue;
					cur = cross(hull[a],hull[b],hull[c]);
					if(max < cur)update(cur);
				}
			}
			return sol;
		}
		private void update(long temp) {
			sol[0] = hull[a];sol[1] = hull[b];sol[2] = hull[c];
			max = temp;
		}
	}
	private static class ConvexHull {
		Point[] hull;
		public Point[] getHull(){
			return hull;
		}
		public ConvexHull(Point[] p){
			if(p.length>1){
				int n = p.length, k=0;
				hull=new Point[2*n];
				Arrays.sort(p, new Comparator<Point>(){
					public int compare(Point p1, Point p2) {
						if(p1.x<p2.x)return -1;
						else if(p1.x>p2.x)return 1;
						else{
							if(p1.y<p2.y)return -1;
							else if(p1.y>p2.y)return 1;
							else return 0;
						}
					}
				});
				for(int i=0;i<n;++i){
					while(k>=2&&cross(hull[k-2],hull[k-1], p[i])<=0)
						k--;
					hull[k++]=p[i];
				}
				for(int i=n-2,t=k+1;i>=0;i--){
					while(k>=t&&cross(hull[k-2],hull[k-1],p[i])<=0)
						k--;
					hull[k++]=p[i];
				}
				if(k>1)hull=Arrays.copyOfRange(hull,0,k-1);
			}
			else if(p.length<=1)hull=p;
			else hull=null;
		}
		
	}
	private static class Point {
		long x, y; 
		public Point(long x, long y) {this.x = x;this.y=y;}
		public String toString() { return "( "+x+" , "+y+" )"; }
	}
	private static class MyScanner {
		BufferedReader br;
		StringTokenizer st;
		public MyScanner() {br = new BufferedReader(new InputStreamReader(System.in));}
		String next(){
			while(st==null||!st.hasMoreElements()){
				try{st = new StringTokenizer(br.readLine());}
				catch(IOException e){e.printStackTrace();}
			}return st.nextToken();
		}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong(){return Long.parseLong(next());}
	}
}