1 \(s / 64\) \(MB / 140\) points

Recently, a new popular computer game has appeared, called “Parallelograms”. In the

beginning of the game, the computer draws N points on the screen whose coordinates are

integers betwe\(en -10\) and 10 (inclusive).

The only allowed move in the game is to take 3 n\(on-co\)llinear points A, B, C, and, instead of

point C, draw point D such that ACBD is a parallelogram whose one diagonal is segment

AB. Notice that such point D always exists and is unique.
In the beginning, all points are different, but during the game it is allowed for two or more

points to have identical coordinates. Additionally, all newly created points’ coordinates must

be at most 10 ^{9}{ } in absolute value.

The aim of the game is to, using a series of moves, bring all points to the first quadrant.

More precisely, at the end of the game, all points must have n\(on-ne\)gative coordinates.
Find a series of moves, consisting of at most 2 500 moves, that brings all points to the first

quadrant, or determine that such a series of moves does not exist.

The first line of input contains the number N from the task (\(3 \le N \le 400\)).
The i ^{th}{ } of the following N lines contains coordinates of the i ^{th}{ } point X {i}{ }, Y {i}{ } (-\(10 \le X\) {i}{ }, Y {i}{ } ≤ 10).
In the beginning, no two points have identical coordinates.

If the solution does not exist, the first and only line of output must conta\(in -1\).
Otherwise, the first line of output must contain the number of moves M (\(0 \le M \le 2\,500\)).
Each of the following M lines must contain 3 different numbers A, B, C (\(1 \le A\), B, \(C \le N\)) that
denote the indices of the points involved in the move. The point with index C changes
according to the described rule, and points with indices A and B do not change.

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출처 COCI 2016/2017 Contest 7