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 = 1e5 + 10;
vector<int> vec[maxn];
int son[maxn], sz[maxn];
int col[maxn];
int cnt[maxn];
long long ans[maxn];
int maxc;
long long sum;
int n;
void dfs1(int u, int fa) {
  sz[u] = 1;
  for (auto& v : vec[u]) {
    if (v == fa) continue;
    dfs1(v, u);
    sz[u] += sz[v];
    if (sz[v] > sz[son[u]]) son[u] = v;
  }
  return;
}
void calc(int u, int fa, int tp, int val) {
  cnt[col[u]] += val;
  if (cnt[col[u]] > maxc) {
    maxc = cnt[col[u]];
    sum = col[u];
  } else if (cnt[col[u]] == maxc) {
    sum += col[u];
  }
  for (auto& v : vec[u]) {
    if (v == fa || v == tp) continue;
    calc(v, u, tp, val);
  }
  return;
}
void dfs2(int u, int fa, int del) {
  for (auto& v : vec[u]) {
    if (v == fa || v == son[u]) continue;
    dfs2(v, u, 1);
  }
  if (son[u]) dfs2(son[u], u, 0);
  calc(u, fa, son[u], 1);
  ans[u] = sum;
  if (del) {
    calc(u, fa, 0, -1);
    sum = maxc = 0;
  }
  return;
}
int main() {
  ios::sync_with_stdio(false);
  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;
    vec[u].emplace_back(v);
    vec[v].emplace_back(u);
  }
  dfs1(1, 0);
  dfs2(1, 0, 1);
  for (int i = 1; i <= n; i++) {
    cout << ans[i];
    if (i == n)
      cout << endl;
    else
      cout << ' ';
  }
  return 0;
}
