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:
// package cf.contest682.e;

import java.io.PrintWriter;

// Trick CF: public
class Scanner {

    private java.io.BufferedReader bufferedReader;
    private java.util.StringTokenizer stringTokenizer;

    public Scanner(java.io.InputStream inputStream) {
        bufferedReader = new java.io.BufferedReader(
                new java.io.InputStreamReader(inputStream));
    }

    public String next() {
        for (; null == stringTokenizer || !stringTokenizer.hasMoreTokens();) {
            try {
                stringTokenizer = new java.util.StringTokenizer(
                        bufferedReader.readLine());
            }
            catch (java.io.IOException ioException) {
                ioException.printStackTrace();
            }
        }
        return stringTokenizer.nextToken();
    }

    public String nextLine() {
        String result;
        stringTokenizer = null;
        try {
            result = bufferedReader.readLine();
        }
        catch (java.io.IOException ioException) {
            ioException.printStackTrace();
            result = "";
        }
        return result;
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

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

    public void close() {
        try {
            bufferedReader.close();
        }
        catch (java.io.IOException e) {
            e.printStackTrace();
        }
    }
}

class Task {

    private Scanner stdin;
    private PrintWriter stdout;

    public Task() {
        stdin = new Scanner(System.in);
        stdout = new PrintWriter(System.out);
    }

    public void close() {
        stdin.close();
        stdout.flush();
        stdout.close();
    }

    int[] x, y;

    public void run() {
        int n = stdin.nextInt();
        stdin.nextLong();
        x = new int[n];
        y = new int[n];
        for (int i = 0; i < n; ++i) {
            x[i] = stdin.nextInt();
            y[i] = stdin.nextInt();
        }
        int a = 0;
        int b = 1;
        int c = 2;
        for (;;) {
            boolean bigEnough = true;
            for (int i = 0; i < n; ++i) {
                if (calc(i, b, c) > calc(a, b, c)) {
                    a = i;
                    bigEnough = false;
                }
                if (calc(a, i, c) > calc(a, b, c)) {
                    b = i;
                    bigEnough = false;
                }
                if (calc(a, b, i) > calc(a, b, c)) {
                    c = i;
                    bigEnough = false;
                }
            }
            if (bigEnough) {
                break;
            }
        }
        append(a, b, c);
        append(b, c, a);
        append(c, a, b);
    }

    void append(int a, int b, int c) {
        stdout.append((x[a] + x[b] - x[c]) + " " + (y[a] + y[b] - y[c]) + "\n");
    }

    long calc(int a, int b, int c) {
        int[] dx = new int[] { x[a] - x[b], x[a] - x[c] };
        int[] dy = new int[] { y[a] - y[b], y[a] - y[c] };
        return (long) dx[0] * dy[1] - (long) dx[1] * dy[0];
    }
}

public class Main {
    public static void main(String[] args) {
        Task task = new Task();
        task.run();
        task.close();
    }
}