Patrick is a big fan of the bricks. He has been collecting the bricks of different colors, sizes,
and shapes, since he was little. Recently, he got a job in another city, and he planned to move next week. Since the new apartment is much smaller than the old one, Patrick decided to give away his bricks to the kids in his neighborhood. However, to receive the gift, the kid must play the bricks with Patrick and solve a brick game. The game is quite simple and the rules are as
follows:

1. The kid chooses a number N by casting lots.

2. Then, Patrick randomly selects N bricks from his collection.

3. The kid has to figure out the similar bricks from the N ones.

4. The kid will obtain the N bricks for free if he gives the correct answer.

    Note that the two bricks are considered similar if and only if their corresponding angles are all congruent and corresponding sides are all proportional with/without 180-degree flipping.

    For the ease of representation, we describe each brick by a sequence of vertices along the
border of the brick in clockwise order using the 2D Cartesian coordinate system. For instance, if N = 4, and the four bricks are B₁ = {(4,1) (4,7) (8,7) (8,5) (6,5) (6,1)}, B₂ = {(6,5) (6,3) (5,3) (5,4) (3,4) (3,5)}, B₃ = {(10,1) (1,1) (1,4) (7,4) (7,7) (10,7)}, and B₄ = {(6,3) (6,1) (4,1) (4,7) (8,7) (8,3)}. We know that B₁ and B₂ are similar, because their corresponding angles are all congruent and corresponding sides are all proportional. Moreover, B₂ and B₃ are similar, because, after flipping B₃ , their corresponding angles are all congruent and corresponding sides
are all proportional. Meanwhile, B₄ is not similar to any other bricks. Thus, we know the answer of this brick game is 3, and the three similar bricks are B₁ , B₂ , and B₃ .

    For simplicity, we assume N is an integer, and 3 ≤ N ≤ 10. Each polygon is simple (i.e., the boundary of the polygon does not cross itself) and represented by a list of P vertices in clockwise order. P is an integer, and 3 ≤ P ≤ 10. The X, Y coordinates of the i-th vertex of the polygon is (X_i , Y_i ). X_i and Y_i are positive real numbers to four decimal places; moreover,
0 < X_i ≤ 1, 000 and 0 < Y_i ≤ 1, 000. Finally, for each brick game, there is either none or only
one set of bricks that are similar. In addition, all bricks in a game have the same number of vertices.