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;
inline long long getint() {
  long long _x = 0, _tmp = 1;
  char _tc = getchar();
  while ((_tc < '0' || _tc > '9') && _tc != '-') _tc = getchar();
  if (_tc == '-') _tc = getchar(), _tmp = -1;
  while (_tc >= '0' && _tc <= '9') _x *= 10, _x += (_tc - '0'), _tc = getchar();
  return _x * _tmp;
}
inline long long add(long long _x, long long _y,
                     long long _mod = 1000000007ll) {
  long long _ = _x + _y;
  if (_ >= _mod) _ -= _mod;
  return _;
}
inline long long sub(long long _x, long long _y,
                     long long _mod = 1000000007ll) {
  long long _ = _x - _y;
  if (_ < 0) _ += _mod;
  return _;
}
inline long long mul(long long _x, long long _y,
                     long long _mod = 1000000007ll) {
  long long _ = _x * _y;
  if (_ >= _mod) _ %= _mod;
  return _;
}
long long mypow(long long _a, long long _x, long long _mod) {
  if (_x == 0) return 1ll;
  long long _tmp = mypow(_a, _x / 2, _mod);
  _tmp = mul(_tmp, _tmp, _mod);
  if (_x & 1) _tmp = mul(_tmp, _a, _mod);
  return _tmp;
}
long long mymul(long long _a, long long _x, long long _mod) {
  if (_x == 0) return 0ll;
  long long _tmp = mymul(_a, _x / 2, _mod);
  _tmp = add(_tmp, _tmp, _mod);
  if (_x & 1) _tmp = add(_tmp, _a, _mod);
  return _tmp;
}
inline bool equal(double _x, double _y) {
  return _x > _y - 1e-3 && _x < _y + 1e-3;
}
int __ = 1, _cs;
inline pair<long long, long long> operator+(
    const pair<long long, long long>& p1,
    const pair<long long, long long>& p2) {
  return {p1.first + p2.first, p1.second + p2.second};
}
inline pair<long long, long long> operator-(
    const pair<long long, long long>& p1,
    const pair<long long, long long>& p2) {
  return {p1.first - p2.first, p1.second - p2.second};
}
inline long long operator^(const pair<long long, long long>& p1,
                           const pair<long long, long long>& p2) {
  return p1.first * p2.second - p1.second * p2.first;
}
inline long long area(const pair<long long, long long>& p1,
                      const pair<long long, long long>& p2,
                      const pair<long long, long long>& p3) {
  return abs((p1 ^ p2) + (p2 ^ p3) + (p3 ^ p1));
}
long long n, s;
vector<pair<long long, long long> > p, ch;
void build() {}
inline void convexHull() {
  sort((p).begin(), (p).end());
  size_t psz = 0, csz = 0;
  for (int _ = 0; _ < 2; _++) {
    for (size_t i = 0; i < p.size(); i++) {
      while (csz - psz > 1 &&
             ((ch[csz - 1] - ch[csz - 2]) ^ (p[i] - ch[csz - 2])) <= 0) {
        ch.pop_back();
        csz--;
      }
      ch.push_back(p[i]);
      csz++;
    }
    psz = ch.size() - 1;
    reverse((p).begin(), (p).end());
  }
}
void init() {
  n = getint();
  s = getint();
  for (int i = 0; i < n; i++) {
    long long tx = getint();
    long long ty = getint();
    p.push_back({tx, ty});
  }
  if (n == 3) {
    for (size_t i = 0; i < p.size(); i++)
      printf("%lld %lld\n", p[i].first, p[i].second);
    exit(0);
  }
  convexHull();
}
void solve() {
  ch.pop_back();
  size_t sz = ch.size();
  for (size_t i = 0; i < sz; i++) ch.push_back(ch[i]);
  for (size_t i = 0; i < sz; i++) ch.push_back(ch[i]);
  for (size_t i = 0; i < sz; i++) ch.push_back(ch[i]);
  int n1 = 0, n2 = 0, n3 = 0;
  long long bst = -1;
  for (size_t i = 0, j = 0, k = 0; i < sz; i++) {
    if (j <= i) j = i + 1;
    if (k <= j) k = j + 1;
    while (area(ch[i], ch[j], ch[k + 1]) > area(ch[i], ch[j], ch[k])) k++;
    while (area(ch[i], ch[k], ch[j + 1]) > area(ch[i], ch[k], ch[j])) j++;
    long long narea = area(ch[i], ch[j], ch[k]);
    if (narea > bst) {
      bst = narea;
      n1 = i;
      n2 = j;
      n3 = k;
    }
  }
  pair<long long, long long> a1 = ch[n1] + (ch[n3] - ch[n2]);
  pair<long long, long long> a2 = ch[n2] + (ch[n1] - ch[n3]);
  pair<long long, long long> a3 = ch[n3] + (ch[n2] - ch[n1]);
  printf("%lld %lld\n", a1.first, a1.second);
  printf("%lld %lld\n", a2.first, a2.second);
  printf("%lld %lld\n", a3.first, a3.second);
}
int main() {
  build();
  while (__--) {
    init();
    solve();
  }
}