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;
const long long MAXN = 1e5 + 10;
vector<long long> adj[MAXN];
map<long long, long long> c_subtree[MAXN];
long long c[MAXN];
long long ans[MAXN];
long long vis[MAXN];
long long cont[MAXN];
void dfs(long long v) {
  vis[v] = 1;
  vector<long long> children;
  for (auto u : adj[v]) {
    if (!vis[u]) {
      dfs(u);
      children.push_back(u);
    }
  }
  if (children.size() == 0) {
    c_subtree[v][c[v]] = 1;
    ans[v] = c[v];
    cont[v] = 1;
  } else {
    long long large = 0;
    for (long long child : children) {
      if (c_subtree[child].size() > c_subtree[large].size()) large = child;
    }
    set<long long> candidates;
    for (long long child : children) {
      if (child != large) {
        for (auto p : c_subtree[child]) {
          c_subtree[large][p.first] += p.second;
          candidates.insert(p.first);
        }
        c_subtree[child].clear();
      }
    }
    swap(c_subtree[large], c_subtree[v]);
    c_subtree[v][c[v]]++;
    candidates.insert(c[v]);
    long long maxi = 0;
    vector<long long> topados;
    for (long long candidate : candidates) {
      if (c_subtree[v][candidate] > maxi) {
        topados.clear();
        maxi = c_subtree[v][candidate];
        topados.push_back(candidate);
      } else if (c_subtree[v][candidate] == maxi) {
        topados.push_back(candidate);
      }
    }
    if (maxi < cont[large]) {
      ans[v] = ans[large];
      cont[v] = cont[large];
    } else {
      for (auto t : topados) ans[v] += t;
      if (maxi == cont[large]) ans[v] += ans[large];
      cont[v] = maxi;
    }
  }
}
int32_t main() {
  memset(vis, 0, sizeof vis);
  long long n;
  cin >> n;
  for (long long i = 1; i < n + 1; i++) cin >> c[i];
  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);
  for (long long i = 1; i < n + 1; i++) cout << ans[i] << " ";
  cout << endl;
}
