The Life of Insects
In a cubic room with each side measuring 200 cm, there are N flies. Each fly claims ownership of the part of the room that is closer to it than to any other fly. The Wise Spider, observing from a corner, noted that the first fly controls A_1 cm(^3), the second fly controls A_2 cm(^3), and so on, up to the N-th fly, which controls A_N cm(^3).
What are the volumes that the Wise Spider mentioned?
Input
The first line of the input contains a natural number N (1 ≤ N ≤ 6), representing the number of flies in the room. The following N lines provide the positions of the flies at the time of their claim. Each position is given by a triplet of integers x_i, y_i, z_i (0 ≤ x_i, y_i, z_i ≤ 200), which are the coordinates of the flies in the space. No two flies share the same coordinates. The coordinate system is set such that one corner of the room is at (0, 0, 0) and the opposite corner is at (200, 200, 200).
Output
Output N real numbers A_1, A_2, ..., A_N.