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;
namespace Geometry {
const double eps = 1e-8;
inline int Cmp(const double x) {
  if (fabs(x) < eps) return 0;
  return x < 0 ? -1 : 1;
}
class Point {
 public:
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
  inline std::istream friend &operator>>(std::istream &cin, Point &a) {
    return cin >> a.x >> a.y;
  }
  inline std::ostream friend &operator<<(std::ostream &cout, Point a) {
    return cout << (long long)a.x << ' ' << (long long)a.y;
  }
  bool friend operator<(const Point a, const Point b) {
    return a.x != b.x ? a.x < b.x : a.y < b.y;
  }
};
class Line {
 public:
  Point p;
  Point v;
  double ang;
  Line() {}
  Line(Point p, Point v) : p(p), v(v) { ang = atan2(v.y, v.x); }
  inline bool friend operator<(const Line a, const Line b) {
    return a.ang < b.ang;
  }
};
Point operator+(Point a, Point b) { return Point(a.x + b.x, a.y + b.y); }
Point operator-(Point a, Point b) { return Point(a.x - b.x, a.y - b.y); }
Point operator*(Point a, double b) { return Point(a.x * b, a.y * b); }
Point operator/(Point a, double b) { return Point(a.x / b, a.y / b); }
bool operator==(Point a, Point b) {
  return (fabs(a.x - b.x) < eps && fabs(a.y - b.y) < eps);
}
inline double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }
inline double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }
inline double length(Point a) { return sqrt(dot(a, a)); }
inline double angle(Point a, Point b) {
  return acos(dot(a, b) / (length(a) * length(b)));
}
inline bool onleft(Line l, Point p) { return Cmp(cross(l.v, p - l.p)) > 0; }
inline bool onsegment(Point p, Point a1, Point a2) {
  return (Cmp(cross(a1 - p, a2 - p) == 0) && Cmp(dot(a1 - p, a2 - p)) < 0);
}
inline Point rotate(const Point a, const double rad) {
  double c = cos(rad), s = sin(rad);
  return Point(a.x * c - a.y * s, a.x * s + a.y * c);
}
inline Point normal(const Point a) {
  double l = length(a);
  return Point(-a.y / l, a.x / l);
}
inline bool segmentprointersection(Point a, Point b, Point c, Point d) {
  double c1 = cross(b - a, c - a), c2 = cross(b - a, d - a);
  double d1 = cross(d - c, a - c), d2 = cross(d - c, b - c);
  return (Cmp(c1) * Cmp(c2) < 0 && Cmp(d1) * Cmp(d2) < 0);
}
inline Point LineIntersection(Point a, Point a0, Point b, Point b0) {
  double a1, b1, c1, a2, b2, c2;
  a1 = a.y - a0.y;
  b1 = a0.x - a.x;
  c1 = cross(a, a0);
  a2 = b.y - b0.y;
  b2 = b0.x - b.x;
  c2 = cross(b, b0);
  double d = a1 * a2 - a2 * b1;
  return Point((b1 * c2 - b2 * c1) / d, (c1 * a2 - c2 * a1) / d);
}
inline Point LineIntersection(Line a, Line b) {
  return LineIntersection(a.p, a.p + a.v, b.p, b.p + b.v);
}
inline double distancetoline(Point p, Point a, Point b) {
  Point v = p - a, u = b - a;
  return fabs(cross(v, u)) / length(u);
}
inline double distancetosegment(Point p, Point a, Point b) {
  if (a == b) return length(p - a);
  Point v1 = b - a, v2 = p - a, v3 = p - b;
  if (Cmp(dot(v1, v2)) < 0) return length(v2);
  if (Cmp(dot(v1, v3)) > 0) return length(v3);
  return fabs(cross(v1, v2)) / length(v1);
}
inline std::vector<Point> Convex(std::vector<Point> e) {
  sort(e.begin(), e.end());
  e.erase(unique(e.begin(), e.end()), e.end());
  int m = 0, n = e.size();
  std::vector<Point> ch(n + 1);
  for (int i = 0; i < n; ++i) {
    while (m > 1 && cross(ch[m - 1] - ch[m - 2], e[i] - ch[m - 2]) <= 0) m--;
    ch[m++] = e[i];
  }
  int k = m;
  for (int i = n - 2; i >= 0; --i) {
    while (m > k && cross(ch[m - 1] - ch[m - 2], e[i] - ch[m - 2]) <= 0) m--;
    ch[m++] = e[i];
  }
  if (n > 1) m--;
  ch.resize(m);
  return ch;
}
}  // namespace Geometry
using namespace Geometry;
int n;
long long SS;
Point p, A, B, C;
std::vector<Point> poly, Con;
double Max;
int main() {
  ios::sync_with_stdio(0);
  cin >> n >> SS;
  for (int i = 1; i <= n; ++i) {
    cin >> p;
    poly.push_back(p);
  }
  Con = Convex(poly);
  int siz = Con.size();
  for (int i = 0; i < siz; ++i) {
    for (int j = i + 1, k = ((j == siz - 1) ? 0 : j + 1); j < siz && k != i;
         ++j) {
      while (Cmp(cross(Con[j] - Con[i], Con[k] - Con[i]) -
                 cross(Con[j] - Con[i], Con[k + 1] - Con[i])) < 0)
        k = ((k == siz - 1) ? 0 : (k + 1));
      if (k != i && k != j) {
        double S = cross(Con[j] - Con[i], Con[k] - Con[i]);
        if (S > Max) Max = S, A = Con[i], B = Con[j], C = Con[k];
      }
    }
  }
  cout << (A - C + B) << endl << (B - A + C) << endl << (C - B + A) << endl;
  return 0;
}