#include <bits/stdc++.h>
using namespace std;
int ABS(int a) {
  if (a < 0) return (-a);
  return a;
}
void input() {}
void readInt(int &n) {
  n = 0;
  char ch = getchar();
  while (!isdigit(ch)) ch = getchar();
  while (isdigit(ch)) {
    n = n * 10 + ch - 48;
    ch = getchar();
  }
}
vector<int> v[1505];
pair<pair<int, int>, int> p[1505];
long double cross[1505];
bool cmp(pair<pair<int, int>, int> a, pair<pair<int, int>, int> b) {
  return cross[a.second] > cross[b.second];
}
long double dis(pair<pair<int, int>, int> a, pair<pair<int, int>, int> b) {
  long double x1 = a.first.first;
  long double y1 = a.first.second;
  long double x2 = b.first.first;
  long double y2 = b.first.second;
  long double dx = x1 - x2;
  long double dy = y1 - y2;
  return sqrt(dx * dx + dy * dy);
}
int n;
void updateDot(int from, int to) {
  int base = from;
  for (int i = (from); i < (to); ++i) {
    if (p[i].first.first < p[base].first.first) {
      base = i;
    } else if (p[i].first.first < p[base].first.first &&
               p[i].first.second < p[base].first.second) {
      base = i;
    }
  }
  swap(p[base], p[from]);
  pair<pair<int, int>, int> inf = pair<pair<int, int>, int>(
      pair<int, int>(p[from].first.first, 1000001000), 1500);
  for (int i = (from + 1); i < (to); ++i) {
    long double abx = p[from].first.first - p[i].first.first;
    long double aby = p[from].first.second - p[i].first.second;
    long double bcx = inf.first.first - p[from].first.first;
    long double bcy = inf.first.second - p[from].first.second;
    long double dot = abx * bcx + aby * bcy;
    cross[p[i].second] = dot / (dis(p[from], p[i]) * dis(p[from], inf));
  }
  sort(p + from + 1, p + to, cmp);
}
int ans[1505];
int cnt[1505];
void count(int whr, int par) {
  cnt[whr] = 1;
  for (int i = (0); i < (v[whr].size()); ++i) {
    int nxt = v[whr][i];
    if (nxt == par) continue;
    count(nxt, whr);
    cnt[whr] += cnt[nxt];
  }
}
void dfs(int whr, int par, int K) {
  updateDot(K, K + cnt[whr]);
  ans[p[K].second] = whr + 1;
  K++;
  for (int i = (0); i < (v[whr].size()); ++i) {
    int nxt = v[whr][i];
    if (nxt == par) continue;
    dfs(nxt, whr, K);
    K += cnt[nxt];
  }
}
int main() {
  input();
  cin >> n;
  if (n == 1) {
    cout << "1" << endl;
    return 0;
  }
  for (int i = (1); i < (n); ++i) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  for (int i = (0); i < (n); ++i) {
    int a, b;
    cin >> p[i].first.first >> p[i].first.second;
    p[i].second = i;
  }
  count(0, -1);
  dfs(0, -1, 0);
  for (int i = (0); i < (n); ++i) cout << ans[i] << " ";
  cout << endl;
  return 0;
}

### Prompt

Create a solution in cpp for the following problem:

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;
int ABS(int a) {
  if (a < 0) return (-a);
  return a;
}
void input() {}
void readInt(int &n) {
  n = 0;
  char ch = getchar();
  while (!isdigit(ch)) ch = getchar();
  while (isdigit(ch)) {
    n = n * 10 + ch - 48;
    ch = getchar();
  }
}
vector<int> v[1505];
pair<pair<int, int>, int> p[1505];
long double cross[1505];
bool cmp(pair<pair<int, int>, int> a, pair<pair<int, int>, int> b) {
  return cross[a.second] > cross[b.second];
}
long double dis(pair<pair<int, int>, int> a, pair<pair<int, int>, int> b) {
  long double x1 = a.first.first;
  long double y1 = a.first.second;
  long double x2 = b.first.first;
  long double y2 = b.first.second;
  long double dx = x1 - x2;
  long double dy = y1 - y2;
  return sqrt(dx * dx + dy * dy);
}
int n;
void updateDot(int from, int to) {
  int base = from;
  for (int i = (from); i < (to); ++i) {
    if (p[i].first.first < p[base].first.first) {
      base = i;
    } else if (p[i].first.first < p[base].first.first &&
               p[i].first.second < p[base].first.second) {
      base = i;
    }
  }
  swap(p[base], p[from]);
  pair<pair<int, int>, int> inf = pair<pair<int, int>, int>(
      pair<int, int>(p[from].first.first, 1000001000), 1500);
  for (int i = (from + 1); i < (to); ++i) {
    long double abx = p[from].first.first - p[i].first.first;
    long double aby = p[from].first.second - p[i].first.second;
    long double bcx = inf.first.first - p[from].first.first;
    long double bcy = inf.first.second - p[from].first.second;
    long double dot = abx * bcx + aby * bcy;
    cross[p[i].second] = dot / (dis(p[from], p[i]) * dis(p[from], inf));
  }
  sort(p + from + 1, p + to, cmp);
}
int ans[1505];
int cnt[1505];
void count(int whr, int par) {
  cnt[whr] = 1;
  for (int i = (0); i < (v[whr].size()); ++i) {
    int nxt = v[whr][i];
    if (nxt == par) continue;
    count(nxt, whr);
    cnt[whr] += cnt[nxt];
  }
}
void dfs(int whr, int par, int K) {
  updateDot(K, K + cnt[whr]);
  ans[p[K].second] = whr + 1;
  K++;
  for (int i = (0); i < (v[whr].size()); ++i) {
    int nxt = v[whr][i];
    if (nxt == par) continue;
    dfs(nxt, whr, K);
    K += cnt[nxt];
  }
}
int main() {
  input();
  cin >> n;
  if (n == 1) {
    cout << "1" << endl;
    return 0;
  }
  for (int i = (1); i < (n); ++i) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  for (int i = (0); i < (n); ++i) {
    int a, b;
    cin >> p[i].first.first >> p[i].first.second;
    p[i].second = i;
  }
  count(0, -1);
  dfs(0, -1, 0);
  for (int i = (0); i < (n); ++i) cout << ans[i] << " ";
  cout << endl;
  return 0;
}

```