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 int MAXN = 1e5 + 10;
vector<int> adj[MAXN];
int col[MAXN];
long long sum[MAXN], pw[MAXN];
int sz[MAXN];
void getsz(int v, int pre) {
  sz[v] = 1;
  for (auto u : adj[v]) {
    if (u != pre) {
      getsz(u, v);
      sz[v] += sz[u];
    }
  }
}
vector<int> *vec[MAXN];
int cnt[MAXN];
void DFS(int v, int pre, bool type) {
  int mx = -1, bigChild = -1;
  for (auto u : adj[v])
    if (sz[u] > mx && u != pre) mx = sz[u], bigChild = u;
  for (auto u : adj[v])
    if (u != bigChild && u != pre) DFS(u, v, 0);
  if (bigChild != -1) {
    DFS(bigChild, v, 1), vec[v] = vec[bigChild];
    pw[v] = pw[bigChild];
    sum[v] = sum[bigChild];
  } else
    vec[v] = new vector<int>();
  vec[v]->push_back(v);
  cnt[col[v]]++;
  if (cnt[col[v]] == pw[v])
    sum[v] += col[v];
  else if (cnt[col[v]] > pw[v]) {
    pw[v] = cnt[col[v]];
    sum[v] = col[v];
  }
  for (auto u : adj[v])
    if (u != bigChild && u != pre)
      for (auto i : *vec[u]) {
        cnt[col[i]]++;
        vec[v]->push_back(i);
        if (cnt[col[i]] == pw[v])
          sum[v] += col[i];
        else if (cnt[col[i]] > pw[v]) {
          pw[v] = cnt[col[i]];
          sum[v] = col[i];
        }
      }
  if (!type)
    for (auto u : *vec[v]) cnt[col[u]]--;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) cin >> col[i];
  for (int i = 0; i < n - 1; ++i) {
    int x, y;
    scanf("%d%d", &x, &y);
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
  getsz(1, -1);
  DFS(1, -1, 1);
  for (int i = 1; i <= n; ++i) printf("%lld ", sum[i]);
}
