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 N = 1e5 + 4, INF = 2e18;
long long cnt[N], big[N], sz[N], col[N], lnt[N], n;
long long sum[N];
set<long long> s;
vector<int> g[N];
void dfs1(int v, int p) {
  sz[v] = 1;
  for (auto to : g[v]) {
    if (to == p) {
      continue;
    }
    dfs1(to, v);
    sz[v] += sz[to];
  }
}
void add(int v, int p, int x) {
  sum[cnt[col[v]]] -= col[v];
  if (sum[cnt[col[v]]] == 0) {
    s.erase(cnt[col[v]]);
  }
  cnt[col[v]] += x;
  sum[cnt[col[v]]] += col[v];
  s.insert(cnt[col[v]]);
  for (auto u : g[v]) {
    if (u != p && !big[u]) add(u, v, x);
  }
}
void dfs(int v, int p, int keep) {
  int mx = -1, bch = -1;
  for (auto u : g[v]) {
    if (sz[u] > mx && u != p) bch = u, mx = sz[u];
  }
  for (auto u : g[v]) {
    if (u != p && u != bch) dfs(u, v, 0);
  }
  if (bch != -1) dfs(bch, v, 1), big[bch] = 1;
  add(v, p, 1);
  lnt[v] = sum[*(--s.end())];
  if (bch > 0) big[bch] = 0;
  if (!keep) add(v, p, -1);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> col[i];
  for (int i = 1; i < n; i++) {
    int x, y;
    cin >> x >> y;
    g[x].push_back(y);
    g[y].push_back(x);
  }
  dfs1(1, 1);
  dfs(1, 1, 1);
  for (int i = 1; i <= n; i++) cout << lnt[i] << " ";
}
