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;
class Problem {
 public:
  struct NodeData {
    map<int, long long> subtree_colors;
    long long res;
    int max_count;
    NodeData() : res(0), max_count(0) {}
  };
  int n;
  vector<int> c;
  vector<vector<int>> adj_list;
  vector<bool> touched;
  vector<long long> res;
  vector<int> map_id;
  vector<NodeData> nodes_datas;
  void solve() {
    cin >> n;
    c.resize(n);
    adj_list.resize(n);
    touched.resize(n, false);
    res.resize(n);
    map_id.resize(n);
    nodes_datas.resize(n);
    for (int i = 0; i < n; i++) cin >> c[i];
    for (int i = 1; i < n; i++) {
      int x, y;
      cin >> x >> y;
      x--;
      y--;
      adj_list[x].push_back(y);
      adj_list[y].push_back(x);
    }
    parse_collect_efficient(0);
    for (int i = 0; i < n; i++) {
      cout << res[i] << " ";
    }
  }
  void parse_collect_efficient(int p) {
    map_id[p] = p;
    touched[p] = true;
    std::vector<int> childs_ids(adj_list[p].size() + 1);
    int c_ = c[p];
    nodes_datas[p].subtree_colors[c_]++;
    nodes_datas[p].res = c_;
    nodes_datas[p].max_count = 1;
    int v_max = p;
    childs_ids[0] = p;
    int k = 1;
    for (int v : adj_list[p]) {
      if (touched[v]) continue;
      childs_ids[k] = v;
      parse_collect_efficient(v);
      int mv = map_id[v];
      if (nodes_datas[mv].subtree_colors.size() >
          nodes_datas[map_id[v_max]].subtree_colors.size())
        v_max = v;
      k++;
    }
    int mvmax = map_id[v_max];
    auto& node_data = nodes_datas[mvmax];
    for (int i = 0; i < k; i++) {
      int v = childs_ids[i];
      if (v == v_max) continue;
      int mv = map_id[v];
      for (auto e : nodes_datas[mv].subtree_colors) {
        long long count = node_data.subtree_colors[e.first] +=
            nodes_datas[mv].subtree_colors[e.first];
        if (count > node_data.max_count) {
          node_data.max_count = count;
          node_data.res = e.first;
        } else if (count == node_data.max_count) {
          node_data.res += e.first;
        }
      }
      nodes_datas[mv].subtree_colors.clear();
    }
    map_id[p] = mvmax;
    res[p] = node_data.res;
  }
};
int main() {
  Problem p;
  p.solve();
  return 0;
}
