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;
vector<long long> G[100005];
long long n, cnt, ans;
long long c[100005], son[100005], siz[100005], num[100005], result[100005];
void dfs1(long long u, long long fa) {
  siz[u] = 1;
  for (long long i = 0; i < G[u].size(); i++) {
    long long v = G[u][i];
    if (v == fa) continue;
    dfs1(v, u);
    siz[u] += siz[v];
    if (!son[u] || siz[v] > siz[son[u]]) son[u] = v;
  }
}
void modify(long long u, long long fa, bool flag) {
  if (flag) {
    num[c[u]]++;
    if (num[c[u]] > cnt)
      cnt = num[c[u]], ans = c[u];
    else if (num[c[u]] == cnt)
      ans += c[u];
  } else
    num[c[u]]--;
  for (long long i = 0; i < G[u].size(); i++)
    if (G[u][i] != fa) modify(G[u][i], u, flag);
}
void dfs2(long long u, long long fa) {
  for (long long i = 0; i < G[u].size(); i++) {
    long long v = G[u][i];
    if (v == fa || v == son[u]) continue;
    dfs2(v, u);
    modify(v, u, 0);
    cnt = ans = 0;
  }
  if (son[u]) dfs2(son[u], u);
  for (long long i = 0; i < G[u].size(); i++) {
    long long v = G[u][i];
    if (v == fa || v == son[u])
      continue;
    else
      modify(v, u, 1);
  }
  num[c[u]]++;
  if (num[c[u]] > cnt)
    ans = c[u], cnt = num[c[u]];
  else if (num[c[u]] == cnt)
    ans += c[u];
  result[u] = ans;
}
signed main() {
  scanf("%lld", &n);
  for (long long i = 1; i <= n; i++) scanf("%lld", &c[i]);
  for (long long i = 1, u, v; i < n; i++) {
    scanf("%lld %lld", &u, &v);
    G[u].push_back(v);
    G[v].push_back(u);
  }
  dfs1(1, 0);
  dfs2(1, 0);
  for (long long i = 1; i <= n; i++) printf("%lld ", result[i]);
  return 0;
}
