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 double eps = 1e-8;
const long long inf = 1e18;
struct pot {
  long long x, y;
  pot() {}
  pot(long long _x, long long _y) : x(_x), y(_y) {}
  inline friend pot operator-(const pot &a, const pot &b) {
    return (pot){a.x - b.x, a.y - b.y};
  }
  inline friend pot operator+(const pot &a, const pot &b) {
    return (pot){a.x + b.x, a.y + b.y};
  }
  inline friend long long operator*(const pot &a, const pot &b) {
    return a.x * b.y - a.y * b.x;
  }
  inline long long norm() { return x * x + y * y; }
  inline void print() { printf("%lld %lld\n", x, y); }
};
int n;
long long s;
pot p[5010], q[5010];
int id[5010], top;
pot ansa, ansb, ansc, da, db, dc;
inline bool cmp(int x, int y) {
  long long num = (p[x] - p[1]) * (p[y] - p[1]);
  if (num != 0) return num > 0;
  return (p[x] - p[1]).norm() < (p[y] - p[1]).norm();
}
void graham() {
  int dt = 1;
  for (int i = 2; i <= n; i++)
    if (p[i].x < p[dt].x || p[i].x == p[dt].x && p[i].y < p[dt].y) dt = i;
  if (dt != 1) swap(p[1], p[dt]);
  for (int i = 1; i <= n; i++) id[i] = i;
  sort(id + 2, id + n + 1, cmp);
  q[++top] = p[1];
  for (int i = 2; i <= n; i++) {
    int v = id[i];
    while (top >= 2 && (q[top] - q[top - 1]) * (p[v] - q[top - 1]) <= 0) top--;
    q[++top] = p[v];
  }
  q[0] = q[top];
}
void rotatefind() {
  long long maxn = 0;
  for (int i = 0; i < top; i++)
    for (int j = i + 1, num = i + 1; j < top; j++) {
      while ((q[j] - q[i]) * (q[num] - q[i]) <
             (q[j] - q[i]) * (q[num + 1] - q[i]))
        num = (num + 1) % top;
      if ((q[j] - q[i]) * (q[num] - q[i]) > maxn) {
        maxn = (q[j] - q[i]) * (q[num] - q[i]);
        da = q[i], db = q[j], dc = q[num];
      }
    }
}
int main() {
  scanf("%d%lld", &n, &s);
  for (int i = 1; i <= n; i++) scanf("%lld%lld", &p[i].x, &p[i].y);
  graham();
  rotatefind();
  ansa = da + (db - dc), ansb = db + (dc - da), ansc = dc + (da - db);
  ansa.print(), ansb.print(), ansc.print();
}