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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 5000;
struct point {
  int x;
  int y;
};
int n;
long long S;
point p[MAXN + 1];
vector<point> convexHull;
long long crossProduct(point a, point b, point c) {
  long long x1 = a.x, y1 = a.y, x2 = b.x, y2 = b.y, x3 = c.x, y3 = c.y;
  return x1 * y2 + x2 * y3 + x3 * y1 - x3 * y2 - x1 * y3 - x2 * y1;
}
double dist(point a, point b) {
  long long dx = a.x - b.x, dy = a.y - b.y;
  return sqrt(dx * dx + dy * dy);
}
double area(int i, int j, int k) {
  point a = convexHull[i], b = convexHull[j], c = convexHull[k];
  double l1 = dist(a, b);
  double l2 = dist(b, c);
  double l3 = dist(a, c);
  double p = (l1 + l2 + l3) / 2;
  return sqrt(p * (p - l1) * (p - l2) * (p - l3));
}
void readData() {
  cin >> n >> S;
  for (int i = 1; i <= n; i++) cin >> p[i].x >> p[i].y;
}
bool cmp(point a, point b) { return crossProduct(p[1], a, b) < 0; }
void findConvexHull() {
  int pos = 1;
  for (int i = 2; i <= n; i++)
    if (p[i].y < p[pos].y)
      pos = i;
    else if (p[i].y == p[pos].y && p[i].x < p[pos].x)
      pos == i;
  swap(p[pos], p[1]);
  sort(p + 2, p + n + 1, cmp);
  convexHull.push_back(p[1]);
  convexHull.push_back(p[2]);
  for (int i = 3; i <= n; i++) {
    int last = convexHull.size() - 1, pen = convexHull.size() - 2;
    while (convexHull.size() >= 2 &&
           crossProduct(convexHull[pen], convexHull[last], p[i]) > 0) {
      convexHull.pop_back();
      last = convexHull.size() - 1, pen = convexHull.size() - 2;
    }
    convexHull.push_back(p[i]);
  }
}
int i1 = 0, i2 = 1, i3 = 2;
int computeCircularDistance(int p1, int p2, int n) {
  if (p1 >= p2)
    return p1 - p2;
  else
    return p1 + n - p2;
}
bool searchPosition(int left, int right, int p1, int p2, int &p3) {
  bool found = false;
  while (computeCircularDistance(right, left, convexHull.size()) > 1) {
    int d = computeCircularDistance(right, left, convexHull.size());
    int m = d / 2;
    if (area(p1, p2, p3) <= area(p1, p2, (p3 + m) % n)) {
      found = true;
      p3 = (p3 + m) % convexHull.size();
      left = p3;
    } else
      right = (p3 + m - 1) % convexHull.size();
  }
  if (computeCircularDistance(right, left, convexHull.size()))
    if (area(p1, p2, p3) <= area(p1, p2, (p3 + 1) % n)) {
      found = true;
      p3 = (p3 + 1) % convexHull.size();
    }
  return found;
}
void findMaxAreaTriangleWithTernary() {
  int p1 = 0, p2 = 1, p3 = 2;
  i1 = 0, i2 = 1, i3 = 2;
  int n = convexHull.size();
  for (p1 = 0; p1 <= n - 1; p1++) {
    if (p1 == p2) p2 = (p2 + 1) % n;
    if (p2 == p3) p3 = (p3 + 1) % n;
    while (1) {
      bool ok1 = searchPosition(p3, p1, p1, p2, p3);
      bool ok2 = searchPosition(p2, p3, p1, p3, p2);
      if (ok1 == false && ok2 == false) break;
    }
    if (area(p1, p2, p3) > area(i1, i2, i3)) i1 = p1, i2 = p2, i3 = p3;
  }
}
void findMaxAreaTriangle() {
  int p1 = 0, p2 = 1, p3 = 2;
  i1 = 0, i2 = 1, i3 = 2;
  int n = convexHull.size();
  while (1) {
    while (1) {
      while (area(p1, p2, p3) <= area(p1, p2, (p3 + 1) % n)) p3 = (p3 + 1) % n;
      if (area(p1, p2, p3) > area(p1, (p2 + 1) % n, p3))
        break;
      else
        p2 = (p2 + 1) % n;
    }
    if (area(p1, p2, p3) > area(i1, i2, i3)) i1 = p1, i2 = p2, i3 = p3;
    p1 = (p1 + 1) % n;
    if (p1 == 0) break;
    if (p1 == p2) p2 = (p2 + 1) % n;
    if (p2 == p3) p3 = (p3 + 1) % n;
  }
}
void printSolution() {
  point a = convexHull[i1], b = convexHull[i2], c = convexHull[i3];
  cout << a.x + c.x - b.x << ' ' << a.y + c.y - b.y << endl;
  cout << b.x + c.x - a.x << ' ' << b.y + c.y - a.y << endl;
  cout << a.x + b.x - c.x << ' ' << a.y + b.y - c.y << endl;
}
int main() {
  readData();
  findConvexHull();
  findMaxAreaTriangle();
  printSolution();
  return 0;
}