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 NR = 5e5 + 10, oo = 1e18 + 10, MOD = 1e9 + 7;
const long double pi = 2 * acos(0.0);
vector<int> v[NR];
int n, m, sz[NR], big[NR];
long long ans[NR];
int c[NR];
void dfs1(int nod, int prt) {
  sz[nod] = 1;
  for (auto it : v[nod]) {
    if (it == prt) continue;
    dfs1(it, nod);
    sz[nod] += sz[it];
    big[nod] = max(big[nod], sz[it]);
  }
}
void dfs2(int nod, int prt, map<int, int>& mapp, int& l_max) {
  int nod_boss = -1, l = 0, max_ = 0;
  long long sum = 0;
  map<int, int> temp;
  for (auto it : v[nod]) {
    if (it == prt) continue;
    if (big[nod] == sz[it]) {
      nod_boss = it;
      dfs2(it, nod, mapp, l);
      sum = ans[it];
      max_ = l;
      break;
    }
  }
  mapp[c[nod]] = mapp[c[nod]] + 1;
  if (mapp[c[nod]] == max_) {
    sum += c[nod];
  }
  if (mapp[c[nod]] > max_) {
    max_ = mapp[c[nod]];
    sum = c[nod];
  }
  for (auto it : v[nod]) {
    if (it == prt || it == nod_boss) continue;
    dfs2(it, nod, temp, l);
    for (auto it2 : temp) {
      mapp[it2.first] = mapp[it2.first] + it2.second;
      if (mapp[it2.first] == max_) {
        sum += it2.first;
      }
      if (mapp[it2.first] > max_) {
        max_ = mapp[it2.first];
        sum = it2.first;
      }
    }
    temp.clear();
  }
  l_max = max_;
  ans[nod] = sum;
}
signed main() {
  int i, j, x, y;
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  map<int, int> temp;
  cin >> n;
  for (i = 1; i <= n; ++i) {
    cin >> c[i];
  }
  for (i = 1; i < n; ++i) {
    cin >> x >> y;
    v[x].push_back(y);
    v[y].push_back(x);
  }
  dfs1(1, 0);
  dfs2(1, 0, temp, x);
  for (i = 1; i <= n; ++i) cout << ans[i] << ' ';
  cout << '\n';
  return 0;
}
