Codeforces 196 C. Paint Tree - c++编程基础

分治，选最左上的点分给根，剩下的极角排序后递归

C. Paint Tree time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output

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.

Input

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 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 thei-th point on the plane. No three points lie on one straight line.

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

Output

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.

Sample test(s) input

output

1 3 2

input

output

4 2 1 3

Note

The possible solutions for the sample are given below.

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