#include <bits/stdc++.h>
using namespace std;
const int N = 1500 + 5, INF = 2000 * 1000 * 1000;
vector<pair<int, int> > li[N];
vector<int> adj[N];
pair<pair<int, int>, int> po[N];
pair<int, int> J;
int d[N], out[N];
void dfs(const int &v, const int &pa) {
  d[v] = 1;
  for (int i = 0; i < (int)(adj[v]).size(); ++i) {
    if (adj[v][i] != pa) {
      dfs(adj[v][i], v);
      d[v] += d[adj[v][i]];
      li[v].push_back(make_pair(d[adj[v][i]], adj[v][i]));
    }
  }
}
bool cmp(const pair<pair<int, int>, int> &R,
         const pair<pair<int, int>, int> &T) {
  long long a1 = J.first - R.first.first, a2 = J.first - T.first.first;
  long long b1 = J.second - R.first.second, b2 = J.second - T.first.second;
  return a1 * b2 > a2 * b1;
}
void ass(int f, int s, int x) {
  pair<int, int> ans = make_pair(-INF, -INF);
  int no;
  for (int i = f; i <= s; ++i) {
    if (po[i].first.second > ans.second)
      ans = make_pair(po[i].first.first, po[i].first.second), no = i;
    else if (po[i].first.second == ans.second && po[i].first.first < ans.first)
      ans = make_pair(po[i].first.first, po[i].first.second), no = i;
  }
  J = ans;
  out[po[no].second] = x;
  swap(po[no], po[s]);
  sort(po + f, po + s, cmp);
  for (int i = 0; i < (int)(li[x]).size(); ++i) {
    ass(f, f + li[x][i].first - 1, li[x][i].second);
    f += li[x][i].first;
  }
}
int main() {
  ios::sync_with_stdio(false);
  srand(time(0));
  int n, a, b, root;
  int zero = 0;
  scanf("%d", &n);
  if (n >= 1300)
    root = 750;
  else
    root = rand() % n + 1;
  for (int i = 0; i < n - 1; ++i) {
    adj[i].reserve(N);
    li[i].reserve(N);
    scanf("%d%d", &a, &b);
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  dfs(root, zero);
  for (int i = 1; i <= n; ++i)
    scanf("%d%d", &po[i].first.first, &po[i].first.second), po[i].second = i;
  ass(1, n, root);
  for (int i = 1; i <= n; ++i) printf("%d ", out[i]);
  printf("\n");
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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 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.

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.

Examples

Input

3
1 3
2 3
0 0
1 1
2 0


Output

1 3 2


Input

4
1 2
2 3
1 4
-1 -2
3 5
-3 3
2 0


Output

4 2 1 3

Note

The possible solutions for the sample are given below.

<image> <image>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 1500 + 5, INF = 2000 * 1000 * 1000;
vector<pair<int, int> > li[N];
vector<int> adj[N];
pair<pair<int, int>, int> po[N];
pair<int, int> J;
int d[N], out[N];
void dfs(const int &v, const int &pa) {
  d[v] = 1;
  for (int i = 0; i < (int)(adj[v]).size(); ++i) {
    if (adj[v][i] != pa) {
      dfs(adj[v][i], v);
      d[v] += d[adj[v][i]];
      li[v].push_back(make_pair(d[adj[v][i]], adj[v][i]));
    }
  }
}
bool cmp(const pair<pair<int, int>, int> &R,
         const pair<pair<int, int>, int> &T) {
  long long a1 = J.first - R.first.first, a2 = J.first - T.first.first;
  long long b1 = J.second - R.first.second, b2 = J.second - T.first.second;
  return a1 * b2 > a2 * b1;
}
void ass(int f, int s, int x) {
  pair<int, int> ans = make_pair(-INF, -INF);
  int no;
  for (int i = f; i <= s; ++i) {
    if (po[i].first.second > ans.second)
      ans = make_pair(po[i].first.first, po[i].first.second), no = i;
    else if (po[i].first.second == ans.second && po[i].first.first < ans.first)
      ans = make_pair(po[i].first.first, po[i].first.second), no = i;
  }
  J = ans;
  out[po[no].second] = x;
  swap(po[no], po[s]);
  sort(po + f, po + s, cmp);
  for (int i = 0; i < (int)(li[x]).size(); ++i) {
    ass(f, f + li[x][i].first - 1, li[x][i].second);
    f += li[x][i].first;
  }
}
int main() {
  ios::sync_with_stdio(false);
  srand(time(0));
  int n, a, b, root;
  int zero = 0;
  scanf("%d", &n);
  if (n >= 1300)
    root = 750;
  else
    root = rand() % n + 1;
  for (int i = 0; i < n - 1; ++i) {
    adj[i].reserve(N);
    li[i].reserve(N);
    scanf("%d%d", &a, &b);
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  dfs(root, zero);
  for (int i = 1; i <= n; ++i)
    scanf("%d%d", &po[i].first.first, &po[i].first.second), po[i].second = i;
  ass(1, n, root);
  for (int i = 1; i <= n; ++i) printf("%d ", out[i]);
  printf("\n");
  return 0;
}

```