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;
struct comparer {
  bool openator(const pair<int, int> &a, const pair<int, int> &b) {
    return a.first > b.first;
  }
};
vector<int> edg[100009];
map<int, int> amountForColor[100009];
int color[100009];
struct state {
  long long sum;
  int mi;
  int dominateValue;
  state() : sum(0), mi(0), dominateValue(0) {}
  void add(state &a) {
    if (amountForColor[a.mi].size() > amountForColor[mi].size()) {
      swap(a.mi, mi);
      dominateValue = a.dominateValue;
      sum = a.sum;
    }
    for (auto it = amountForColor[a.mi].begin();
         it != amountForColor[a.mi].end(); it++) {
      int amount = it->second;
      int clr = it->first;
      if (amount == 0) continue;
      int value = amountForColor[mi][clr] + amount;
      if (value > dominateValue) {
        sum = clr;
        dominateValue = value;
      } else if (value == dominateValue) {
        sum += clr;
      }
      amountForColor[mi][clr] = value;
    }
  }
};
bool was[100009];
state nodes[100009];
void printState(state &a) {
  cout << a.sum << endl;
  cout << a.dominateValue << endl;
  for (auto it = amountForColor[a.mi].begin(); it != amountForColor[a.mi].end();
       it++) {
    cout << it->first << " " << it->second << endl;
  }
}
void dfs(int u) {
  was[u] = true;
  nodes[u].mi = u;
  nodes[u].dominateValue = 1;
  nodes[u].sum = color[u];
  amountForColor[u][color[u]] = 1;
  for (int i = 0; i < edg[u].size(); i++) {
    int v = edg[u][i];
    if (was[v]) continue;
    dfs(v);
    nodes[u].add(nodes[v]);
  }
}
int main() {
  int n;
  scanf("%d", &n);
  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);
    edg[u].push_back(v);
    edg[v].push_back(u);
  }
  dfs(1);
  for (int i = 1; i <= n; i++) {
    printf("%I64d ", nodes[i].sum);
  }
  for (int i = 1; i <= 1; i++) {
    for (auto it = amountForColor[i].begin(); it != amountForColor[i].end();
         it++) {
      int clr = it->first;
      int amount = it->second;
      int x = clr + amount;
    }
  }
  return 0;
}
