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> v[MAXN];
long long c[MAXN];
set<pair<long long, long long> > *s[MAXN];
map<long long, long long> *m[MAXN];
long long sum[MAXN];
void join(set<pair<long long, long long> > *set1,
          map<long long, long long> *map1, long long &sum1,
          set<pair<long long, long long> > *set2,
          map<long long, long long> *map2, long long &sum2) {
  for (map<long long, long long>::iterator it = map2->begin();
       it != map2->end(); it++) {
    long long n = it->first;
    long long add = it->second;
    long long old = (*map1)[n];
    (*map1)[n] = old + add;
    if (old != 0) set1->erase(pair<long long, long long>(old, n));
    set1->insert(pair<long long, long long>(old + add, n));
    set<pair<long long, long long> >::iterator pos2 =
        set1->find(pair<long long, long long>(old + add, n));
    if (pos2 == prev(set1->end())) {
      if (pos2 == set1->begin() || pos2->first != prev(pos2)->first) sum1 = 0;
      sum1 += pos2->second;
    } else if (pos2->first == prev(set1->end())->first) {
      sum1 += pos2->second;
    }
  }
}
long long dfs(long long cur, long long last) {
  if (v[cur].size() == 1 && cur != 1) {
    s[cur] = new set<pair<long long, long long> >;
    m[cur] = new map<long long, long long>;
    s[cur]->insert(pair<long long, long long>(1, c[cur]));
    (*m[cur])[c[cur]] = 1;
    sum[cur] = c[cur];
    return 1;
  }
  long long size = 1, ms = 0, mv = -1;
  for (long long i = 0; i < v[cur].size(); i++) {
    long long next = v[cur][i];
    if (next == last) continue;
    long long nsize = dfs(next, cur);
    if (nsize > ms) ms = nsize, mv = next;
    size += nsize;
  }
  s[cur] = s[mv];
  m[cur] = m[mv];
  sum[cur] = sum[mv];
  set<pair<long long, long long> > *ts = new set<pair<long long, long long> >;
  map<long long, long long> *tm = new map<long long, long long>;
  long long tsum = c[cur];
  ts->insert(pair<long long, long long>(1, c[cur]));
  (*tm)[c[cur]] = 1;
  join(s[cur], m[cur], sum[cur], ts, tm, tsum);
  for (long long i = 0; i < v[cur].size(); i++) {
    long long next = v[cur][i];
    if (next != last && next != mv) {
      join(s[cur], m[cur], sum[cur], s[next], m[next], sum[next]);
    }
  }
  return size;
}
int main() {
  long long n;
  scanf("%lld", &n);
  for (long long i = 1; i <= n; i++) scanf("%lld", &c[i]);
  for (long long i = 1, a, b; i < n; i++) {
    scanf("%lld %lld", &a, &b);
    v[a].push_back(b);
    v[b].push_back(a);
  }
  dfs(1, 0);
  printf("%lld", sum[1]);
  for (long long i = 2; i <= n; i++) printf(" %lld", sum[i]);
  printf("\n");
}
