Drawing a Tree

There are $N$ points on a two-dimensional plane. Draw $N - 1$ line segments to form a tree. No two of the drawn segments may cross each other.

A segment crosses another when an endpoint of one lies on the other. Two segments that meet only at a shared endpoint do not cross.

The first line contains the number of points $N$. ($2 \le N \le 1\,000$)

The next $N$ lines each contain the coordinates of one point. The $i$-th line contains the integers $x_i$ and $y_i$, separated by a space. ($-10^9 \le x_i, y_i \le 10^9$)

All given points have distinct coordinates.

Print $N - 1$ lines that describe the segments forming the tree. Each line contains the numbers of the two endpoints, separated by a space.

If there are multiple valid trees, print any one of them.