C. Paint Treetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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 ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi) — the numbers of tree vertexes connected by the i-th edge.Each of the next n lines contain two space-separated integers xi and yi ( - 109 ≤ xi, yi ≤ 109) — 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.OutputPrint 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.ExamplesInput31 32 30 01 12 0Output1 3 2Input41 22 31 4-1 -23 5-3 32 0Output4 2 1 3NoteThe possible solutions for the sample are given below.   
Input31 32 30 01 12 0
Output1 3 2
['constructive algorithms', 'divide and conquer', 'geometry', 'sortings', 'trees', '*2200']