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.

Input

In the first line of the input two integers $*n*$ and $*S*$ ($3 ≤ *n* ≤ 5000$, $1 ≤ *S* ≤ 10^{18}$) 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 $*y*_{*i*}$ $( - 10^{8} ≤ *x*_{*i*}, *y*_{*i*} ≤ 10^{8})$ — 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 $4*S*$.

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 $10^{9}$ 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.

Note