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>
namespace IO {
inline char read() {
  static const int IN_LEN = 100000;
  static char buf[IN_LEN], *s, *t;
  s == t ? t = (s = buf) + fread(buf, 1, IN_LEN, stdin) : 0;
  return s == t ? -1 : *s++;
}
template <typename T>
inline void read(T &x) {
  static char c;
  static bool iosig;
  for (c = read(), iosig = false; !isdigit(c); c = read()) {
    if (c == -1) return;
    c == '-' ? iosig = true : 0;
  }
  for (x = 0; isdigit(c); c = read()) x = x * 10 + (c ^ '0');
  iosig ? x = -x : 0;
}
inline int read(char *buf) {
  register int s = 0;
  register char c;
  while (c = read(), isspace(c) && c != -1)
    ;
  if (c == -1) {
    *buf = 0;
    return -1;
  }
  do buf[s++] = c;
  while (c = read(), !isspace(c) && c != -1);
  buf[s] = 0;
  return s;
}
inline void read(char &x) {
  while (x = read(), isspace(x) && x != -1)
    ;
}
const int OUT_LEN = 100000;
char obuf[OUT_LEN], *oh = obuf;
inline void print(char c) {
  oh == obuf + OUT_LEN ? (fwrite(obuf, 1, oh - obuf, stdout), oh = obuf) : 0;
  *oh++ = c;
}
template <typename T>
inline void print(T x) {
  static int buf[30], cnt;
  if (x == 0) {
    print('0');
  } else {
    x < 0 ? (print('-'), x = -x) : 0;
    for (cnt = 0; x; x /= 10) buf[++cnt] = x % 10 | 48;
    while (cnt) print((char)buf[cnt--]);
  }
}
inline void flush() { fwrite(obuf, 1, oh - obuf, stdout); }
struct InputOutputStream {
  template <typename T>
  inline InputOutputStream &operator<<(const T &x) {
    print(x);
    return *this;
  }
  template <typename T>
  inline InputOutputStream &operator>>(T &x) {
    read(x);
    return *this;
  }
  ~InputOutputStream() { flush(); }
} io;
}  // namespace IO
namespace {
using IO::io;
const int MAXN = 5010;
struct Point {
  long long x, y;
  Point(long long x = 0, long long y = 0) : x(x), y(y) {}
  inline Point operator+(const Point &p) const {
    return Point(x + p.x, y + p.y);
  }
  inline Point operator-(const Point &p) const {
    return Point(x - p.x, y - p.y);
  }
  inline long long operator*(const Point &p) const { return x * p.y - y * p.x; }
  inline bool operator<(const Point &p) const {
    return x < p.x || (x == p.x && y < p.y);
  }
  inline friend IO::InputOutputStream &operator>>(IO::InputOutputStream &io,
                                                  Point &p) {
    io >> p.x >> p.y;
    return io;
  }
  inline friend IO::InputOutputStream &operator<<(IO::InputOutputStream &io,
                                                  const Point &p) {
    io << p.x << ' ' << p.y << '\n';
    return io;
  }
} p[MAXN + 1], con[MAXN + 1];
inline int andrew(Point *p, Point *con, const int n) {
  std::sort(p, p + n);
  register int top = 0, k;
  for (register int i = 0; i < n; i++) {
    while (top > 1 && (con[top - 1] - con[top - 2]) * (p[i] - con[top - 2]) < 0)
      top--;
    con[top++] = p[i];
  }
  k = top;
  for (register int i = n - 2; i >= 0; i--) {
    while (top > k && (con[top - 1] - con[top - 2]) * (p[i] - con[top - 2]) < 0)
      top--;
    con[top++] = p[i];
  }
  return n > 1 ? --top : top;
}
inline bool check(const Point &p1, const Point &p2, const Point &p) {
  return p * p2 >= 0 && p * p1 <= 0;
}
int n, m;
long long S;
inline void rotatingCalispers() {
  for (register int i = 0, k; i < m; i++) {
    k = i + 2;
    for (register int j = i + 1; j < m - 1; ++j) {
      while (k <= j || (con[i] - con[j]) * (con[(k + 1) % m] - con[k]) < 0) k++;
      if (check(con[j] - con[(j + m - 1) % m], con[(j + 1) % m] - con[j],
                con[k] - con[i]) &&
          check(con[i] - con[(i + m - 1) % m], con[(i + 1) % m] - con[i],
                con[j] - con[k])) {
        Point a = con[i], b = con[j], c = con[k];
        io << (a + (b - c)) << (a + (c - b)) << (b + (c - a));
        return;
      }
    }
  }
}
inline void solve() {
  io >> n >> S;
  for (register int i = 0; i < n; i++) io >> p[i];
  m = andrew(p, con, n);
  rotatingCalispers();
}
}  // namespace
int main() {
  solve();
  return 0;
}