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E. Alyona and Triangles

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

Example

Input

4 1

0 0

1 0

0 1

1 1

Output

-1 0

2 0

0 2

Note

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