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 N = 1e5 + 5;
int color[N];
vector<int> e[N];
;
int n;
int size[N];
int w_son[N];
long long ans[N], sum;
int num[N], mx, flag;
void dfs(int u, int f) {
  size[u] = 1;
  int mx = 0;
  for (auto v : e[u]) {
    if (v == f) continue;
    dfs(v, u);
    size[u] += size[v];
    if (size[v] > mx) mx = size[v], w_son[u] = v;
  }
}
void cal(int u, int f) {
  num[color[u]]++;
  if (num[color[u]] > mx)
    mx = num[color[u]], sum = color[u];
  else if (num[color[u]] == mx)
    sum += (long long)color[u];
  for (auto v : e[u]) {
    if (v == f || v == flag) continue;
    cal(v, u);
  }
}
void del(int u, int f) {
  num[color[u]]--;
  for (auto v : e[u]) {
    if (v == f) continue;
    del(v, u);
  }
}
void dfs(int u, int f, bool keep) {
  for (auto v : e[u]) {
    if (v == f || v == w_son[u]) continue;
    dfs(v, u, 0);
  }
  if (w_son[u]) dfs(w_son[u], u, 1);
  flag = w_son[u];
  cal(u, f);
  ans[u] = sum;
  if (!keep) {
    del(u, f);
    sum = mx = 0;
  }
}
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> color[i];
  for (int i = 1; i < n; i++) {
    int u, v;
    cin >> u >> v;
    e[u].push_back(v);
    e[v].push_back(u);
  }
  dfs(1, 1);
  dfs(1, 1, 0);
  for (int i = 1; i <= n; i++) cout << ans[i] << " ";
}
