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;
vector<int> sub, color, cnt, mx;
vector<long long> sum;
vector<vector<int> *> tree;
vector<vector<int> > adj;
int dfs(int u, int w) {
  sub[u] = 1;
  for (auto v : (adj[u])) {
    if (v != w) {
      sub[u] += dfs(v, u);
    }
  }
  return sub[u];
}
void merge(int u, int first) {
  tree[u]->push_back(first);
  cnt[color[first]]++;
  if (cnt[color[first]] > mx[u]) {
    mx[u] = cnt[color[first]];
    sum[u] = color[first] + 1;
  } else if (mx[u] == cnt[color[first]]) {
    sum[u] += color[first] + 1;
  }
}
void calc(int u, int w, bool f) {
  int r = -1;
  for (auto v : (adj[u])) {
    if (v == w) {
      continue;
    }
    if (r == -1 || sub[r] < sub[v]) {
      r = v;
    }
  }
  for (auto v : (adj[u])) {
    if (v != w && v != r) {
      calc(v, u, false);
    }
  }
  if (r != -1) {
    calc(r, u, 1);
    tree[u] = tree[r];
    mx[u] = mx[r];
    sum[u] = sum[r];
  }
  merge(u, u);
  for (auto v : (adj[u])) {
    if (v == w || v == r) {
      continue;
    }
    for (auto first : (*tree[v])) {
      merge(u, first);
    }
  }
  if (!f) {
    for (auto first : (*tree[u])) {
      cnt[color[first]]--;
    }
  }
}
int main() {
  std::ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  sub = color = mx = cnt = vector<int>(n);
  sum.resize(n);
  tree.resize(n);
  adj.resize(n);
  for (int i = 0; i < int(n); i++) {
    tree[i] = new vector<int>();
  }
  for (auto &e : (color)) {
    cin >> e;
    e--;
  }
  for (int i = 0; i < int(n - 1); i++) {
    int u, v;
    cin >> u >> v;
    adj[u - 1].push_back(v - 1);
    adj[v - 1].push_back(u - 1);
  }
  dfs(0, 0);
  calc(0, 0, 0);
  for (int i = 0; i < int(n); i++) {
    cout << sum[i] << " ";
  }
  return 0;
}
