CF682E.Alyona and Triangles

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 4_S_, 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.

给你平面上的 $n$ 个整数坐标点。这些点满足如下条件：任意三个点构成的三角形的面积均不超过 $S$。

Alyona 尝试构造一个顶点坐标均为整数的三角形，使其包含全部 $n$ 个点，且面积不超过 $4S$；但显然她未能成功。请帮助 Alyona 构造出这样的三角形。注意：所构造三角形的顶点不一定来自给定的 $n$ 个点。

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.

输入的第一行包含两个整数 $n$ 和 $S$（$3 \leq n \leq 5000$，$1 \leq S \leq 10^{18}$）—— 分别表示给定的点的数量，以及由其中任意三个点所构成的三角形面积的上界值。

接下来的 $n$ 行描述了给定的点：第 $i$ 行包含两个整数 $x_i$ 和 $y_i$（$-10^8 \leq x_i, y_i \leq 10^8$）—— 表示第 $i$ 个点的坐标。

保证至少存在一组三点不共线。

Print the coordinates of three points — vertices of a triangle which contains all n points and which area doesn't exceed 4_S_.

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.

输出三个点的坐标——构成一个三角形的三个顶点，该三角形包含全部 n 个点，且其面积不超过 4_S_。

每个三角形顶点的坐标应单独占一行，每对坐标之间用一个空格分隔。所有坐标均为整数，且其绝对值不超过 10⁹。

保证至少存在一个满足条件的三角形。若存在多个答案，输出任意一个即可。