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;
int color[100005], sz[100005], mapa[100005], bigboy[100005], cnt[100005];
long long maxi, sum, res[100005];
vector<vector<int> > adj;
void dfs(int u, int p) {
  sz[u] = 1;
  for (int v : adj[u])
    if (v != p) {
      dfs(v, u);
      sz[u] += sz[v];
    }
}
void add(int u, int p) {
  cnt[color[u]]++;
  if (cnt[color[u]] > maxi)
    sum = color[u], maxi = cnt[color[u]];
  else if (cnt[color[u]] == maxi)
    sum += color[u];
  for (int v : adj[u])
    if (v != p and !bigboy[v]) add(v, u);
}
void rem(int u, int p) {
  cnt[color[u]]--;
  for (int v : adj[u])
    if (v != p and !bigboy[v]) rem(v, u);
}
void solve(int u, int p, int keep) {
  int bigChild = -1;
  for (int v : adj[u])
    if (v != p) {
      if (bigChild == -1 || sz[v] > sz[bigChild]) bigChild = v;
    }
  for (int v : adj[u])
    if (v != p and v != bigChild) solve(v, u, 0);
  if (bigChild != -1) solve(bigChild, u, 1), bigboy[bigChild] = 1;
  add(u, p);
  res[u] = sum;
  if (bigChild != -1) bigboy[bigChild] = 0;
  if (!keep) rem(u, p), maxi = sum = 0;
}
int main() {
  int n;
  scanf("%d", &n);
  adj.assign(n + 5, vector<int>());
  for (int i = 1; i <= n; i++) scanf("%d", &color[i]);
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    scanf("%d %d", &u, &v);
    adj[u].push_back(v);
    adj[v].push_back(u);
  }
  dfs(1, -1);
  solve(1, -1, 0);
  for (int i = 1; i <= n; i++) printf("%lld ", res[i]);
  printf("\n");
  return 0;
}
