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> c;
vector<long long> ans;
vector<vector<int>> g;
vector<map<int, int>> m;
vector<set<pair<int, int>>> s;
void dfs(int v, int pr) {
  m[v][c[v]] = 1;
  ans[v] = c[v];
  s[v].insert({1, c[v]});
  for (auto to : g[v]) {
    if (to != pr) {
      dfs(to, v);
      bool swaped = false;
      if (m[v].size() < m[to].size()) {
        swaped = true;
        swap(m[v], m[to]);
        swap(s[v], s[to]);
      }
      if (swaped) {
        if (s[v].rbegin()->first >= s[to].rbegin()->first) ans[v] = ans[to];
      }
      for (auto it : m[to]) {
        int col = it.first;
        int count = it.second;
        int oldcount = m[v][col];
        if (oldcount + count > s[v].rbegin()->first)
          ans[v] = col;
        else if (oldcount + count == s[v].rbegin()->first)
          ans[v] += col;
        m[v][col] += count;
        s[v].erase({oldcount, col});
        s[v].insert({oldcount + count, col});
      }
    }
  }
}
int main() {
  ios::sync_with_stdio(0);
  int n;
  cin >> n;
  c.resize(n);
  ans.resize(n);
  g.resize(n);
  s.resize(n);
  m.resize(n);
  for (int i = 0; i < n; i++) {
    cin >> c[i];
  }
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    a--, b--;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  dfs(0, -1);
  for (auto it : ans) cout << it << " ";
}
