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;
double eps = 1e-8;
double INF = 1e100;
struct PT {
  double x, y;
  PT() {}
  PT(double x, double y) : x(x), y(y) {}
  PT(const PT &p) : x(p.x), y(p.y) {}
  PT operator+(const PT &p) const { return PT(x + p.x, y + p.y); }
  PT operator-(const PT &p) const { return PT(x - p.x, y - p.y); }
  PT operator*(double c) const { return PT(x * c, y * c); }
  PT operator/(double c) const { return PT(x / c, y / c); }
};
double dot(PT p, PT q) { return p.x * q.x + p.y * q.y; }
double dist2(PT p, PT q) { return dot(p - q, p - q); }
double cross(PT p, PT q) { return p.x * q.y - p.y * q.x; }
PT lower_left;
bool sorter(const PT &p, const PT &q) {
  double cpq = cross(p - lower_left, q - lower_left);
  if (abs(cpq) < eps) return dist2(p, lower_left) < dist2(q, lower_left);
  return (cpq > 0);
}
void convex_hull(vector<PT> &A, vector<PT> &hull) {
  for (int i = 1; i < A.size(); ++i) {
    if (A[i].y < A[0].y || (A[i].y <= A[0].y && A[i].x < A[0].x))
      swap(A[0], A[i]);
  }
  lower_left = A[0];
  sort(A.begin() + 1, A.end(), sorter);
  hull.clear();
  hull.push_back(A[0]);
  hull.push_back(A[1]);
  int hull_sz = 2;
  for (int i = 2; i < A.size(); ++i) {
    while (hull_sz > 1 && cross(hull[hull_sz - 1] - hull[hull_sz - 2],
                                A[i] - hull[hull_sz - 1]) <= 0) {
      hull.pop_back();
      hull_sz--;
    }
    hull.push_back(A[i]);
    hull_sz++;
  }
}
double tri_area(PT &a, PT &b, PT &c) { return (cross(b - a, c - a) / 2.0); }
double get_slope(PT &a, PT &b) {
  if (abs(b.x - a.x) < eps) return INF;
  return (b.y - a.y) / (b.x - a.x);
}
double get_intercept(PT &a, double m) {
  if (abs(m) > 1e50) return a.x;
  return (a.y - m * a.x);
}
PT intersection(double m1, double c1, double m2, double c2) {
  if (abs(m1) < abs(m2)) {
    swap(m1, m2);
    swap(c1, c2);
  }
  PT ret;
  if (abs(m1) > 1e50)
    ret.x = c1;
  else
    ret.x = (c2 - c1) / (m1 - m2);
  ret.y = m2 * ret.x + c2;
  return ret;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  long long int s;
  cin >> n >> s;
  vector<PT> A(n), hull;
  for (int i = 0; i < n; ++i) cin >> A[i].x >> A[i].y;
  convex_hull(A, hull);
  int sz = hull.size(), i = 0, j = 1, k = 2, ans[] = {0, 0, 0};
  for (i = 0; i < sz; ++i) {
    if (i == j) j = (j + 1) % sz;
    if (j == k) k = (k + 1) % sz;
    while (true) {
      while (tri_area(hull[i], hull[j], hull[k]) <=
             tri_area(hull[i], hull[j], hull[(k + 1) % sz]))
        k = (k + 1) % sz;
      if (tri_area(hull[i], hull[j], hull[k]) <=
          tri_area(hull[i], hull[(j + 1) % sz], hull[k]))
        j = (j + 1) % sz;
      else
        break;
    }
    if (tri_area(hull[i], hull[j], hull[k]) >
        tri_area(hull[ans[0]], hull[ans[1]], hull[ans[2]])) {
      ans[0] = i;
      ans[1] = j;
      ans[2] = k;
    }
  }
  double m[3], c[3];
  for (int i = 0; i < 3; ++i) {
    m[i] = get_slope(hull[ans[(i + 1) % 3]], hull[ans[(i + 2) % 3]]);
    c[i] = get_intercept(hull[ans[i]], m[i]);
  }
  for (int i = 0; i < 3; ++i)
    for (int j = i + 1; j < 3; ++j) {
      PT temp = intersection(m[i], c[i], m[j], c[j]);
      cout << (int)round(temp.x) << " " << (int)round(temp.y) << "\n";
    }
  return 0;
}