Rockets

A two dimensional map holds two sets of $n$ points each, $R$ and $W$. No three points of $R \cup W$ lie on one line. Surface to surface rockets stand on the points of $R$, and the targets to destroy stand on the points of $W$. A rocket flies only in a straight line, every rocket destroys exactly one target, and every target is hit by exactly one rocket.

No two trajectories may cross. Among the assignments that respect this, find the one whose total flight distance $\sum_{i=1}^{n} |r_i w_{k_i}|$ is the smallest. Here $|pq|$ is the Euclidean distance between $p$ and $q$, and $w_{k_i}$ is the target destroyed by rocket $r_i$. The input guarantees that exactly one of the $n!$ assignments reaches the smallest total flight distance, so the answer is unique.

The first line contains the size $n$ of both $R$ and $W$ ($1 \le n \le 200$).

Each of the next $2n$ lines contains the coordinates $x$ and $y$ of one point of the map, separated by a single space ($-10000 \le x, y \le 10000$). The first $n$ of those lines are the points of $R$, the last $n$ are the points of $W$. Line $i+1$ holds $r_i$ and line $i+n+1$ holds $w_i$ ($1 \le i \le n$). All $2n$ points are distinct and no three of them lie on one line.

Print $n$ lines. Line $i$ contains the index $k_i$ of the target that rocket $r_i$ destroys.