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;
int c[maxn + 5], l[maxn + 5], r[maxn + 5], dfn[maxn + 5], son[maxn + 5],
    sz[maxn + 5];
long long cnt[maxn + 5], sum[maxn + 5];
long long mx;
long long ans[maxn + 5];
int n, dfstime;
vector<int> g[maxn + 5];
void pre(int k, int fa) {
  sz[k] = 1;
  l[k] = ++dfstime;
  dfn[dfstime] = k;
  for (auto u : g[k]) {
    if (u == fa) continue;
    pre(u, k);
    if (sz[u] > sz[son[k]]) son[k] = u;
    sz[k] += sz[u];
  }
  r[k] = dfstime;
}
void del(int k) {
  for (int i = l[k]; i <= r[k]; ++i) {
    int u = c[dfn[i]];
    sum[cnt[u]] -= u;
    --cnt[u];
    sum[cnt[u]] += u;
    if (sum[mx] == 0) --mx;
  }
}
void ins(int k) {
  for (int i = l[k]; i <= r[k]; ++i) {
    int u = c[dfn[i]];
    sum[cnt[u]] -= u;
    ++cnt[u];
    sum[cnt[u]] += u;
    mx = max(mx, cnt[u]);
  }
}
void dfs(int k, int fa) {
  mx = 0;
  for (auto u : g[k]) {
    if (u == fa || u == son[k]) continue;
    dfs(u, k);
    del(u);
  }
  if (son[k]) dfs(son[k], k);
  for (auto u : g[k]) {
    if (u == fa || u == son[k]) continue;
    ins(u);
  }
  int color = c[k];
  sum[cnt[color]] -= color;
  ++cnt[color];
  sum[cnt[color]] += color;
  mx = max(mx, cnt[color]);
  ans[k] = sum[mx];
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", &c[i]);
  for (int i = 1; i < n; ++i) {
    int x, y;
    scanf("%d%d", &x, &y);
    g[x].push_back(y), g[y].push_back(x);
  }
  pre(1, 0);
  dfs(1, 0);
  for (int i = 1; i <= n; ++i) printf("%lld ", ans[i]);
  printf("\n");
  return 0;
}
