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;
template <typename T>
void sci(T& t) {
  cin >> t;
}
template <typename T, typename... Ts>
void sci(T& t, Ts&... ts) {
  sci(t);
  sci(ts...);
}
int c[111111];
vector<int> g[111111];
long long ans[111111];
map<int, int>* cnt[111111];
set<pair<int, int>>* cs[111111];
long long ca[111111];
void dfs(int v, int p) {
  cnt[v] = new map<int, int>;
  cnt[v]->operator[](c[v])++;
  cs[v] = new set<pair<int, int>>;
  cs[v]->insert({1, c[v]});
  ca[v] = c[v];
  for (int i : g[v]) {
    if (i == p) {
      continue;
    }
    dfs(i, v);
    if (cnt[v]->size() < cnt[i]->size()) {
      swap(cnt[v], cnt[i]);
      swap(cs[v], cs[i]);
      swap(ca[v], ca[i]);
    }
    for (auto p : (*cnt[i])) {
      auto it = cnt[v]->find(p.first);
      int omx = cs[v]->rbegin()->first;
      if (it != cnt[v]->end()) {
        cs[v]->erase({it->second, it->first});
      }
      cnt[v]->operator[](p.first) += p.second;
      it = cnt[v]->find(p.first);
      cs[v]->insert({it->second, it->first});
      if (omx < cs[v]->rbegin()->first) {
        ca[v] = 0;
      }
      if (it->second == cs[v]->rbegin()->first) {
        ca[v] += 1LL * it->first;
      }
    }
  }
  ans[v] = ca[v];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n;
  sci(n);
  for (int i = 0; i < n; i++) {
    sci(c[i]);
  }
  for (int i = 1; i < n; i++) {
    int x, y;
    sci(x, y);
    --x;
    --y;
    g[x].push_back(y);
    g[y].push_back(x);
  }
  dfs(0, -1);
  for (int i = 0; i < n; i++) {
    cout << ans[i] << " ";
  }
  return 0;
}
