You are given a rooted tree with root in vertex 1. Each vertex is coloured in some colour.

Let's call colour c dominating in the subtree of vertex v if there are no other colours that appear in the subtree of vertex v more times than colour c. So it's possible that two or more colours will be dominating in the subtree of some vertex.

The subtree of vertex v is the vertex v and all other vertices that contains vertex v in each path to the root.

For each vertex v find the sum of all dominating colours in the subtree of vertex v.

Input

The first line contains integer n (1 ≤ n ≤ 105) — the number of vertices in the tree.

The second line contains n integers ci (1 ≤ ci ≤ n), ci — the colour of the i-th vertex.

Each of the next n - 1 lines contains two integers xj, yj (1 ≤ xj, yj ≤ n) — the edge of the tree. The first vertex is the root of the tree.

Output

Print n integers — the sums of dominating colours for each vertex.

Examples

Input

4
1 2 3 4
1 2
2 3
2 4


Output

10 9 3 4


Input

15
1 2 3 1 2 3 3 1 1 3 2 2 1 2 3
1 2
1 3
1 4
1 14
1 15
2 5
2 6
2 7
3 8
3 9
3 10
4 11
4 12
4 13


Output

6 5 4 3 2 3 3 1 1 3 2 2 1 2 3
#include <bits/stdc++.h>
using namespace std;
const int NMAX = 100000 + 5;
const int MMAX = 2000 + 5;
const int INF = 1000000000;
const int BS = 1000000000 + 7;
const long long INFLL = 1000000000ll * 1000000000ll;
const long double eps = 1e-6;
map<int, int> colorsCount[NMAX];
set<pair<int, int> > colorsCountPairs[NMAX];
int where[NMAX];
long long dominatingSum[NMAX];
long long answer[NMAX];
int color[NMAX];
vector<int> e[NMAX];
void addColor(int u, int c, int cnt) {
  int currentCount = colorsCount[u][c];
  int currentMax =
      colorsCountPairs[u].empty() ? -1 : colorsCountPairs[u].rbegin()->first;
  if (currentCount > 0) {
    colorsCountPairs[u].erase(make_pair(currentCount, c));
    if (currentCount == currentMax) {
      dominatingSum[u] -= c;
    }
  }
  int newCount = currentCount + cnt;
  colorsCount[u][c] = newCount;
  colorsCountPairs[u].insert(make_pair(newCount, c));
  int newMax =
      colorsCountPairs[u].empty() ? -1 : colorsCountPairs[u].rbegin()->first;
  if (newMax != currentMax) {
    dominatingSum[u] = 0;
  }
  if (newCount == newMax) {
    dominatingSum[u] += c;
  }
}
void merge(int p, int v) {
  for (auto pair : colorsCount[v]) {
    int c = pair.first;
    int _count = pair.second;
    addColor(p, c, _count);
  }
}
void dfs(int u, int p) {
  for (auto v : e[u]) {
    if (v == p) continue;
    dfs(v, u);
  }
  vector<pair<int, int> > childIndexes;
  for (auto v : e[u]) {
    if (v == p) continue;
    childIndexes.push_back(make_pair(colorsCount[where[v]].size(), v));
  }
  sort(childIndexes.begin(), childIndexes.end());
  reverse(childIndexes.begin(), childIndexes.end());
  where[u] = u;
  bool isFirst = true;
  for (auto pair : childIndexes) {
    int index = pair.second;
    if (isFirst) {
      where[u] = where[index];
      isFirst = false;
    } else {
      merge(where[u], where[index]);
    }
  }
  addColor(where[u], color[u], 1);
  answer[u] = dominatingSum[where[u]];
}
int main(int argc, char** argv) {
  if (argc > 1 && strcmp(argv[1], "seland") == 0) {
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
  }
  ios::sync_with_stdio(false);
  cin.tie();
  cout.tie();
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> color[i];
  }
  for (int i = 1; i < n; i++) {
    int x, y;
    cin >> x >> y;
    e[x].push_back(y);
    e[y].push_back(x);
  }
  dfs(1, -1);
  for (int i = 1; i <= n; i++) {
    cout << answer[i] << " ";
  }
  return 0;
}
