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-8;
const long double inf = 1e30;
struct point {
  long double x;
  long double y;
  point(long double _x = 0, long double _y = 0) {
    x = _x;
    y = _y;
  }
  point operator+(const point &o) const { return point(x + o.x, y + o.y); }
  point operator-(const point &o) const { return point(x - o.x, y - o.y); }
  point operator*(const long double c) const { return point(x * c, y * c); }
  point operator/(const long double c) const { return point(x / c, y / c); }
  bool operator<(const point &o) const {
    return make_pair(x, y) < make_pair(o.x, o.y);
  }
  bool operator==(const point &o) const {
    return (abs(x - o.x) < eps) && (abs(y - o.y) < eps);
  }
  void read() {
    int xx, yy;
    scanf("%d %d", &xx, &yy);
    x = xx;
    y = yy;
  }
  void print() { cout << fixed << setprecision(9) << x << " " << y << "\n"; }
};
long double dot(point a, point b) { return a.x * b.x + a.y * b.y; }
long double cross(point a, point b) { return a.x * b.y - a.y * b.x; }
long double dist(point a, point b) { return dot(a - b, a - b); }
bool colinear(point a, point b, point c) {
  return abs(cross(b - a, c - a)) < eps;
}
bool clockwise(point a, point b, point c) { return cross(b - a, c - a) < eps; }
bool anticlock(point a, point b, point c) { return cross(b - a, c - a) >= eps; }
point meet(point a, point b) {
  if (abs(a.x) < abs(b.x)) {
    swap(a, b);
  }
  point ret;
  if (abs(a.x) + 10.0 >= inf) {
    ret.x = a.y;
  } else {
    ret.x = (b.y - a.y) / (a.x - b.x);
  }
  ret.y = b.x * ret.x + b.y;
  return ret;
}
long double getc(long double slope, point a) {
  if (slope + 10.0 >= inf) {
    return a.x;
  }
  return a.y - slope * a.x;
}
point move(point base, long double angle, long double len) {
  return point(base.x + cos(angle) * len, base.y + sin(angle) * len);
}
point rotatecw(point a, long double angle) {
  return point(a.x * cos(angle) + a.y * sin(angle),
               a.y * cos(angle) - a.x * sin(angle));
}
point bottom;
bool cmp(point a, point b) {
  long double x = cross(a - bottom, b - bottom);
  if (abs(x) < eps) {
    return dist(bottom, a) < dist(bottom, b);
  }
  return x < 0;
}
double area(const point &a, const point &b, const point &c) {
  return abs(cross(b - a, c - a)) / 2.0;
}
long double slope(point a, point b) {
  if (abs(a.x - b.x) < eps) {
    return inf;
  }
  return (b.y - a.y) / (b.x - a.x);
}
vector<point> convexhull(vector<point> &v) {
  sort(v.begin(), v.end());
  v.resize(unique(v.begin(), v.end()) - v.begin());
  v.shrink_to_fit();
  if (v.size() <= 2) {
    return v;
  }
  int idx = 0;
  for (int i = 1; i < v.size(); ++i) {
    if (v[i].y < v[idx].y) {
      idx = i;
    }
  }
  swap(v[idx], v[0]);
  bottom = v[0];
  sort(v.begin() + 1, v.end(), cmp);
  vector<point> hull;
  hull.clear();
  for (int i = 0; i < v.size(); ++i) {
    while (hull.size() >= 2 &&
           cross(hull[hull.size() - 1] - hull[hull.size() - 2],
                 v[i] - hull[hull.size() - 1]) >= 0) {
      hull.pop_back();
    }
    hull.emplace_back(v[i]);
  }
  return hull;
}
bool inside(vector<point> &polygon, point p) {
  int n = polygon.size();
  for (int i = 0; i < n; ++i) {
    if (anticlock(polygon[i], polygon[(i + 1) % n], p)) {
      return 0;
    }
  }
  return 1;
}
int n;
long long s;
vector<point> arr;
void solve() {
  int a = 0, b = 1, c = 2;
  int k = 2;
  n = arr.size();
  for (int i = 0; i < n; ++i) {
    k = (i + 2) % n;
    for (int j = i + 1; j != i; j = (j + 1) % n) {
      while (area(arr[i], arr[j], arr[(k + 1) % n]) >
             area(arr[i], arr[j], arr[k])) {
        k = (k + 1) % n;
      }
      if (area(arr[i], arr[j], arr[k]) > area(arr[a], arr[b], arr[c])) {
        a = i;
        b = j;
        c = k;
      }
    }
  }
  point p1, p2, p3;
  p1.x = slope(arr[a], arr[b]);
  p2.x = slope(arr[b], arr[c]);
  p3.x = slope(arr[c], arr[a]);
  p1.y = getc(p1.x, arr[c]);
  p2.y = getc(p2.x, arr[a]);
  p3.y = getc(p3.x, arr[b]);
  point ans1 = meet(p1, p2);
  point ans2 = meet(p2, p3);
  point ans3 = meet(p3, p1);
  printf("%lld %lld\n", (long long)round(ans1.x), (long long)round(ans1.y));
  printf("%lld %lld\n", (long long)round(ans2.x), (long long)round(ans2.y));
  printf("%lld %lld\n", (long long)round(ans3.x), (long long)round(ans3.y));
}
int main() {
  scanf("%d %lld", &n, &s);
  arr.resize(n);
  arr.shrink_to_fit();
  for (int i = 1; i <= n; ++i) {
    arr[i - 1].read();
  }
  arr = convexhull(arr);
  solve();
}