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;
int n, color[maxN];
vector<int> edge[maxN];
map<int, int> vertex_color[maxN];
long long id[maxN], max_number[maxN], max_value[maxN], ans[maxN];
void merge(int cur, int child) {
  int x = id[cur], y = id[child];
  if (vertex_color[x].size() < vertex_color[y].size()) {
    id[cur] = y;
    swap(x, y);
  }
  for (map<int, int>::iterator it = vertex_color[y].begin();
       it != vertex_color[y].end(); it++) {
    vertex_color[x][it->first] += it->second;
    if (vertex_color[x][it->first] > max_number[x]) {
      max_number[x] = vertex_color[x][it->first];
      max_value[x] = it->first;
    } else if (vertex_color[x][it->first] == max_number[x]) {
      max_value[x] += it->first;
    }
  }
}
void dfs(int cur, int fa) {
  for (int i = 0; i < edge[cur].size(); i++) {
    int next = edge[cur][i];
    if (next == fa) {
      continue;
    }
    dfs(next, cur);
    merge(cur, next);
  }
  ans[cur] = max_value[id[cur]];
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &color[i]);
    id[i] = i;
    max_number[i] = 1;
    max_value[i] = color[i];
    vertex_color[i][color[i]] = 1;
  }
  int x, y;
  for (int i = 1; i <= n - 1; i++) {
    scanf("%d%d", &x, &y);
    edge[x].push_back(y);
    edge[y].push_back(x);
  }
  dfs(1, 0);
  for (int i = 1; i <= n; i++) {
    cout << ans[i] << " ";
  }
  return 0;
}
