We call a cuboid regular if:
There is given a set of points of space, which coordinates are integers from the interval
. We try to find a regular cuboid of maximal volume, which does not contain any of the points from the set
. A point belongs to the cuboid if it belongs to the inside of the cuboid, i.e. it is a point of the cuboid, but not of its wall.
Write a program which:
In the first line of the standard input one non-negative integer ,
, is written. It is the number of elements in the set
. In the following
lines of the input there are triples of integers from the interval
, which are coordinates (respectively
,
and
) of points from
. Numbers in each line are separated by single spaces.
In the only line of the standard output there should be three integers separated by single spaces. These are coordinates (respectively ,
and
) of the vertex of the regular cuboid of maximal volume. We require that coordinates are positive.
For the input data:
4 3 3 300000 2 200000 5 90000 3 2000 2 2 1000
the correct result is:
1000000 200000 1000
Task author: Bogdan S. Chlebus.
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