C1. Balanced Removals (Easier)time limit per test1 secondmemory limit per test512 megabytesinputstandard inputoutputstandard outputThis is an easier version of the problem. In this version, n \le 2000.There are n distinct points in three-dimensional space numbered from 1 to n. The i-th point has coordinates (x_i, y_i, z_i). The number of points n is even.You'd like to remove all n points using a sequence of \frac{n}{2} snaps. In one snap, you can remove any two points a and b that have not been removed yet and form a perfectly balanced pair. A pair of points a and b is perfectly balanced if no other point c (that has not been removed yet) lies within the axis-aligned minimum bounding box of points a and b.Formally, point c lies within the axis-aligned minimum bounding box of points a and b if and only if \min(x_a, x_b) \le x_c \le \max(x_a, x_b), \min(y_a, y_b) \le y_c \le \max(y_a, y_b), and \min(z_a, z_b) \le z_c \le \max(z_a, z_b). Note that the bounding box might be degenerate. Find a way to remove all points in \frac{n}{2} snaps.InputThe first line contains a single integer n (2 \le n \le 2000; n is even), denoting the number of points.Each of the next n lines contains three integers x_i, y_i, z_i (-10^8 \le x_i, y_i, z_i \le 10^8), denoting the coordinates of the i-th point.No two points coincide.OutputOutput \frac{n}{2} pairs of integers a_i, b_i (1 \le a_i, b_i \le n), denoting the indices of points removed on snap i. Every integer between 1 and n, inclusive, must appear in your output exactly once.We can show that it is always possible to remove all points. If there are many solutions, output any of them.ExamplesInput
6
3 1 0
0 3 0
2 2 0
1 0 0
1 3 0
0 1 0
Output
3 6
5 1
2 4
Input
8
0 1 1
1 0 1
1 1 0
1 1 1
2 2 2
3 2 2
2 3 2
2 2 3
Output
4 5
1 6
2 7
3 8
NoteIn the first example, here is what points and their corresponding bounding boxes look like (drawn in two dimensions for simplicity, as all points lie on z = 0 plane). Note that order of removing matters: for example, points 5 and 1 don't form a perfectly balanced pair initially, but they do after point 3 is removed.   
6
3 1 0
0 3 0
2 2 0
1 0 0
1 3 0
0 1 0

3 6 5 1 2 4 
['constructive algorithms', 'geometry', 'greedy', '*1700']