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>
const int N = 100000 + 5;
std::vector<int> edges[N];
int color[N];
long long answer[N];
int n;
struct Information {
  std::map<int, int> map;
  int cmax;
  long long sum;
  Information() {}
  Information(int x) {
    cmax = 1;
    map[x] = 1;
    sum = x;
  }
  void insert(int a, int b) {
    if (map[a] == cmax) {
      sum -= a;
    }
    b += map[a];
    if (b > cmax) {
      cmax = b;
      sum = a;
    } else if (b == cmax) {
      sum += a;
    }
    map[a] = b;
  }
};
Information pool[N], *ptr[N];
Information *merge(Information *a, Information *b) {
  if (a->map.size() < b->map.size()) {
    std::swap(a, b);
  }
  for (auto t : b->map) {
    a->insert(t.first, t.second);
  }
  return a;
}
void dfs(int u, int fa) {
  for (int v : edges[u]) {
    if (v == fa) continue;
    dfs(v, u);
    ptr[u] = merge(ptr[u], ptr[v]);
  }
  answer[u] = ptr[u]->sum;
}
void work() {
  for (int i = 0; i < n; ++i) {
    ptr[i] = new (pool + i) Information(color[i]);
  }
  dfs(0, -1);
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", color + i);
  }
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    a--;
    b--;
    edges[a].push_back(b);
    edges[b].push_back(a);
  }
  work();
  for (int i = 0; i < n; ++i) {
    if (i) putchar(' ');
    std::cout << answer[i];
  }
  puts("");
}
