A8644 | Paint Tree

You are given a tree with $n$ vertexes and $n$ points on a plane, no three points lie on one straight line.

Your task is to paint the given tree on a plane, using the given points as vertexes.

That is, you should correspond each vertex of the tree to exactly one point and each point should correspond to a vertex. If two vertexes of the tree are connected by an edge, then the corresponding points should have a segment painted between them. The segments that correspond to non-adjacent edges, should not have common points. The segments that correspond to adjacent edges should have exactly one common point.

The first line contains an integer $n$ ( $1<=n<=1500$ ) — the number of vertexes on a tree (as well as the number of chosen points on the plane).

Each of the next $n-1$ lines contains two space-separated integers $u_{i}$ and $v_{i}$ ( $1<=u_{i},v_{i}<=n$ , $u_{i}≠v_{i}$ ) — the numbers of tree vertexes connected by the $i$ -th edge.

Each of the next $n$ lines contain two space-separated integers $x_{i}$ and $y_{i}$ ( $-10^{9}<=x_{i},y_{i}<=10^{9}$ ) — the coordinates of the $i$ -th point on the plane. No three points lie on one straight line.

It is guaranteed that under given constraints problem has a solution.

Print $n$ distinct space-separated integers from $1$ to $n$ : the $i$ -th number must equal the number of the vertex to place at the $i$ -th point (the points are numbered in the order, in which they are listed in the input).

If there are several solutions, print any of them.