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 read(bool out = 0) {}
long long a[100009];
vector<vector<long long> > ad;
long long num[100009] = {};
void dfs(long long u, long long p) {
  num[u] = 1;
  for (auto v : ad[u]) {
    if (v == p) continue;
    dfs(v, u);
    num[u] += num[v];
  }
}
long long cont[100009] = {};
long long mx = -1;
long long buffer = 0;
long long ans[100009];
void add(long long u, long long p, long long big) {
  cont[a[u]]++;
  if (cont[a[u]] > mx) {
    mx = cont[a[u]];
    buffer = a[u];
  } else if (cont[a[u]] == mx) {
    buffer += a[u];
  }
  for (auto v : ad[u]) {
    if (v == p || v == big) continue;
    add(v, u, big);
  }
}
void del(long long u, long long p) {
  mx = -1;
  cont[a[u]]--;
  for (auto v : ad[u]) {
    if (v == p) continue;
    del(v, u);
  }
}
void dsu(long long u, long long p, long long heavy) {
  long long mx = -1;
  long long big;
  for (auto v : ad[u]) {
    if (v == p) continue;
    if (num[v] > mx) {
      mx = num[v];
      big = v;
    }
  }
  for (auto v : ad[u]) {
    if (v == p || v == big) continue;
    dsu(v, u, 0);
  }
  if (mx != -1) {
    dsu(big, u, 1);
  }
  add(u, p, big);
  ans[u] = buffer;
  if (!heavy) del(u, p);
}
int main() {
  read();
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  long long n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  ad = vector<vector<long long> >(n + 1);
  for (int i = 0; i < n - 1; i++) {
    long long x, y;
    cin >> x >> y;
    x--, y--;
    ad[x].push_back(y);
    ad[y].push_back(x);
  }
  dfs(0, -1);
  dsu(0, -1, 0);
  for (int i = 0; i < n; i++) cout << ans[i] << " ";
}
