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 + 9;
vector<int> G[N];
int col[N], hson[N], siz[N], num[N];
long long sum[N];
int id, mx;
void dfs1(int u, int fa) {
  siz[u] = 1;
  hson[u] = 0;
  for (int i = 0; i < G[u].size(); ++i) {
    int v = G[u][i];
    if (v == fa) continue;
    dfs1(v, u);
    hson[u] = siz[hson[u]] > siz[v] ? hson[u] : v;
    siz[u] += siz[v];
  }
}
void clear(int u, int fa) {
  --num[col[u]];
  for (int i = 0; i < G[u].size(); ++i) {
    int v = G[u][i];
    if (v == fa) continue;
    clear(v, u);
  }
}
void insert(int u, int fa, int p) {
  ++num[col[u]];
  if (num[col[u]] >= mx) {
    if (num[col[u]] > mx) sum[p] = 0, id = col[u], mx = num[col[u]];
    sum[p] += col[u];
  }
  for (int i = 0; i < G[u].size(); ++i) {
    int v = G[u][i];
    if (v == fa) continue;
    insert(v, u, p);
  }
}
void dfs2(int u, int fa) {
  for (int i = 0; i < G[u].size(); ++i) {
    int v = G[u][i];
    if (v == fa || v == hson[u]) continue;
    dfs2(v, u);
    clear(v, u);
    id = 0;
    mx = 0;
  }
  if (hson[u]) {
    dfs2(hson[u], u), sum[u] = sum[hson[u]];
  }
  for (int i = 0; i < G[u].size(); ++i) {
    int v = G[u][i];
    if (v == fa || v == hson[u]) continue;
    insert(v, u, u);
  }
  ++num[col[u]];
  if (num[col[u]] >= mx) {
    if (num[col[u]] > mx) sum[u] = 0, id = col[u], mx = num[col[u]];
    sum[u] += col[u];
  }
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", col + i);
  for (int i = 1; i < n; ++i) {
    int u, v;
    scanf("%d %d", &u, &v);
    G[u].push_back(v);
    G[v].push_back(u);
  }
  dfs1(1, 0);
  dfs2(1, 0);
  for (int i = 1; i < n; ++i) printf("%lld ", sum[i]);
  printf("%lld", sum[n]);
  return 0;
}
