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 long double eps = 1e-6;
inline int dcmp(long double first) {
  if (fabs(first) < eps)
    return 0;
  else
    return first < 0 ? -1 : 1;
}
struct Point {
  long double first, second;
  Point(long double first = 0, long double second = 0)
      : first(first), second(second) {}
  void read() { cin >> first >> second; }
  void write() { cout << first << ' ' << second << endl; }
  bool operator==(const Point& u) const {
    return dcmp(first - u.first) == 0 && dcmp(second - u.second) == 0;
  }
  bool operator!=(const Point& u) const { return !(*this == u); }
  bool operator<(const Point& u) const {
    return dcmp(first - u.first) < 0 ||
           (dcmp(first - u.first) == 0 && dcmp(second - u.second) < 0);
  }
  bool operator>(const Point& u) const { return u < *this; }
  bool operator<=(const Point& u) const { return *this < u || *this == u; }
  bool operator>=(const Point& u) const { return *this > u || *this == u; }
  Point operator+(const Point& u) {
    return Point(first + u.first, second + u.second);
  }
  Point operator-(const Point& u) {
    return Point(first - u.first, second - u.second);
  }
  Point operator*(const long double u) { return Point(first * u, second * u); }
  Point operator/(const long double u) { return Point(first / u, second / u); }
  long double operator*(const Point& u) {
    return first * u.second - second * u.first;
  }
};
long double getDistance(Point a, Point b) {
  long double first = a.first - b.first, second = a.second - b.second;
  return sqrt(first * first + second * second);
}
long double getDot(Point a, Point b) {
  return a.first * b.first + a.second * b.second;
}
long double getCross(Point a, Point b) {
  return a.first * b.second - a.second * b.first;
}
long double getLength(Point a) { return sqrt(getDot(a, a)); }
long double getPLength(Point a) { return getDot(a, a); }
long double getAngle(Point u) { return atan2(u.second, u.first); }
long double getAngle(Point a, Point b) {
  return acos(getDot(a, b) / getLength(a) / getLength(b));
}
Point rotate(Point a, long double rad) {
  return Point(a.first * cos(rad) - a.second * sin(rad),
               a.first * sin(rad) + a.second * cos(rad));
}
Point getNormal(Point a) {
  long double l = getLength(a);
  return Point(-a.second / l, a.first / l);
}
int getConvexHull(Point* p, int n, Point* ch) {
  sort(p, p + n);
  int m = 0;
  for (int i = 0; i < n; i++) {
    while (m > 1 &&
           dcmp(getCross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 1])) <= 0)
      m--;
    ch[m++] = p[i];
  }
  int k = m;
  for (int i = n - 2; i >= 0; i--) {
    while (m > k &&
           dcmp(getCross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2])) <= 0)
      m--;
    ch[m++] = p[i];
  }
  if (n > 1) m--;
  return m;
}
bool onSegment(Point p, Point a, Point b) {
  return dcmp(getCross(a - p, b - p)) == 0 && dcmp(getDot(a - p, b - p)) < 0;
}
Point ComputeLineIntersection(Point a, Point b, Point c, Point d) {
  b = b - a;
  d = c - d;
  c = c - a;
  return a + b * getCross(c, d) / getCross(b, d);
}
long double getArea2(Point a, Point b, Point c) {
  return fabs(getCross(b - a, c - a));
}
Point p[100007], ch[100007];
int main() {
  long long n;
  long double s;
  cin >> n >> s;
  for (int i = (0); i < (n); i++) {
    p[i].read();
  }
  n = getConvexHull(p, n, ch);
  for (int i = (0); i < (n); i++) ch[n + i] = ch[i];
  long long p1, p2, p3;
  long double A = 0;
  for (int i = (0); i < (n); i++) {
    long long k = i + 1;
    for (int j = (i + 1); j < (n); j++) {
      while (k < (i + n) &&
             getArea2(ch[i], ch[j], ch[k + 1]) > getArea2(ch[i], ch[j], ch[k]))
        k++;
      long double A_ = getArea2(ch[i], ch[j], ch[k]);
      if (A_ > A) {
        p1 = i, p2 = j, p3 = k;
        A = A_;
      }
    }
  }
  Point P1, P2, P3;
  P1 = ch[p1] + ch[p2] - ch[p3];
  P2 = ch[p2] + ch[p3] - ch[p1];
  P3 = ch[p3] + ch[p1] - ch[p2];
  cout << (long long)P1.first << ' ' << (long long)P1.second << endl;
  cout << (long long)P2.first << ' ' << (long long)P2.second << endl;
  cout << (long long)P3.first << ' ' << (long long)P3.second << endl;
}