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 = 2e5 + 100;
long long ans[maxn];
vector<int> g[maxn];
int siz[maxn], son[maxn];
inline void dfs1(int u, int f) {
  siz[u] = 1;
  int maxson = -1;
  for (int v : g[u]) {
    if (v == f) continue;
    dfs1(v, u);
    siz[u] += siz[v];
    if (siz[v] > maxson) son[u] = v, maxson = siz[v];
  }
}
int flag;
long long sum, maxc;
long long col[maxn], cnt[maxn];
void Count(int x, int f, int val) {
  cnt[col[x]] += val;
  if (cnt[col[x]] > maxc) {
    maxc = cnt[col[x]];
    sum = col[x];
  } else if (cnt[col[x]] == maxc)
    sum += col[x];
  for (int v : g[x]) {
    if (v == f || v == flag) continue;
    Count(v, x, val);
  }
}
void DFS(int x, int f, bool keep) {
  for (int v : g[x]) {
    if (v == f || v == son[x]) continue;
    DFS(v, x, 0);
  }
  if (son[x]) {
    DFS(son[x], x, 1);
    flag = son[x];
  }
  Count(x, f, 1);
  flag = 0;
  ans[x] = sum;
  if (!keep) {
    Count(x, f, -1);
    sum = maxc = 0;
  }
}
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> col[i];
  for (int i = 1; i < n; i++) {
    int u, v;
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
  }
  dfs1(1, 0);
  DFS(1, 0, 0);
  for (int i = 1; i <= n; i++) cout << ans[i] << " ";
  cout << endl;
  return 0;
}
