CF196C 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.

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The possible solutions for the sample are given below.