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 = 100005;
const int MAXA = 1000005;
int N, C[MAXN], SZ[MAXN], CCNT[MAXN], HCH[MAXN];
map<int, int>* countMap[MAXN];
long long domCount[MAXN], domSum[MAXN];
vector<int> G[MAXN];
void find_subtree_size(int cur, int prev) {
  SZ[cur] = 1;
  HCH[cur] = -1;
  int heavySize = -1;
  for (int v : G[cur]) {
    if (v != prev) {
      find_subtree_size(v, cur);
      SZ[cur] += SZ[v];
      if (heavySize < SZ[v]) {
        heavySize = SZ[v];
        HCH[cur] = v;
      }
    }
  }
}
void find_dominating_color_sum(int cur, int prev) {
  for (int u : G[cur])
    if (u != prev && u != HCH[cur]) find_dominating_color_sum(u, cur);
  if (HCH[cur] != -1) {
    find_dominating_color_sum(HCH[cur], cur);
    countMap[cur] = countMap[HCH[cur]];
    domCount[cur] = domCount[HCH[cur]];
    domSum[cur] = domSum[HCH[cur]];
  } else {
    countMap[cur] = new map<int, int>();
    domCount[cur] = domSum[cur] = 0;
  }
  (*countMap[cur])[C[cur]]++;
  if ((*countMap[cur])[C[cur]] > domCount[cur]) {
    domCount[cur] = (*countMap[cur])[C[cur]];
    domSum[cur] = C[cur];
  } else if ((*countMap[cur])[C[cur]] == domCount[cur]) {
    domSum[cur] += (0ll + C[cur]);
  }
  for (int u : G[cur]) {
    if (u != prev && u != HCH[cur]) {
      for (pair<const int, int>& kv : *countMap[u]) {
        (*countMap[cur])[kv.first] += kv.second;
        int curCount = (*countMap[cur])[kv.first];
        if (curCount > domCount[cur]) {
          domCount[cur] = curCount;
          domSum[cur] = kv.first;
        } else if (curCount == domCount[cur]) {
          domSum[cur] += (0ll + kv.first);
        }
      }
    }
  }
}
int main() {
  scanf("%d", &N);
  for (int i = 1; i <= N; ++i) scanf("%d", &C[i]);
  for (int i = 1; i <= N - 1; ++i) {
    int x, y;
    scanf("%d%d", &x, &y);
    G[x].push_back(y);
    G[y].push_back(x);
  }
  find_subtree_size(1, 0);
  find_dominating_color_sum(1, 0);
  for (int i = 1; i <= N; ++i) printf("%lld ", domSum[i]);
  printf("\n");
  return 0;
}
