Alyona and Triangles

Description:

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: i^th of them consists of two integers x_i and y_i ( - 10⁸ ≤ x_i, y_i ≤ 10⁸) — coordinates of i^th 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.

Sample Input:

4 1
0 0
1 0
0 1
1 1

Sample Output:

-1 0
2 0
0 2

Note: