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;
void setIO(string s = "") {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  if ((long long)((s).size())) {
    freopen((s + ".in").c_str(), "r", stdin);
    freopen((s + ".out").c_str(), "w", stdout);
  }
}
const long long MOD = 1e9 + 7;
const long long MAXN = 1e5 + 1;
const long long INF = 1e18 + 5;
long long col[MAXN], ans[MAXN];
vector<long long> adj[MAXN];
vector<map<long long, long long>> v(MAXN);
pair<long long, long long> bes[MAXN];
void dfs(long long s, long long e) {
  if ((long long)((adj[s]).size()) == 1 && s != 1) {
    v[s][col[s]]++;
    ans[s] = col[s];
    bes[s] = {1, col[s]};
    return;
  }
  v[s][col[s]]++;
  bes[s] = {1, col[s]};
  for (auto u : adj[s]) {
    if (u != e) {
      dfs(u, s);
      if ((long long)((v[s]).size()) < (long long)((v[u]).size())) {
        swap(v[s], v[u]);
        swap(bes[u], bes[s]);
      }
      for (auto z : v[u]) {
        v[s][z.first] += z.second;
        if (v[s][z.first] > bes[s].first)
          bes[s] = {v[s][z.first], z.first};
        else if (v[s][z.first] == bes[s].first)
          bes[s].second += z.first;
      }
    }
  }
  ans[s] = bes[s].second;
}
signed main() {
  setIO();
  long long n;
  cin >> n;
  for (long long i = 0; i < n; i++) cin >> col[i + 1];
  for (long long i = 0; i < n - 1; i++) {
    long long a, b;
    cin >> a >> b;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  dfs(1, 0);
  for (long long i = 1; i <= n; i++) cout << ans[i] << " ";
  return 0;
}
