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 + 20;
int n;
int fist[N], idx;
struct Edge {
  int to, nxt;
} line[N << 1];
int t, Q[N], tmp;
int sz[N], son[N], cnt[N], col[N];
long long ans[N], res;
void add(int x, int y) {
  line[++idx] = (Edge){y, fist[x]};
  fist[x] = idx;
}
void dfs(int u, int fa) {
  sz[u] = 1;
  for (int i = fist[u]; i != -1; i = line[i].nxt) {
    int v = line[i].to;
    if (v == fa) continue;
    dfs(v, u);
    sz[u] += sz[v];
    if (sz[v] > sz[son[u]]) son[u] = v;
  }
}
void del() {
  while (t) cnt[Q[t--]] = 0;
  res = tmp = 0;
}
void insert(int u) {
  ++cnt[Q[++t] = col[u]];
  if (cnt[col[u]] > tmp)
    tmp = cnt[res = col[u]];
  else if (cnt[col[u]] == tmp)
    res += col[u];
}
void addson(int u, int fa) {
  insert(u);
  for (int i = fist[u]; i != -1; i = line[i].nxt) {
    int v = line[i].to;
    if (v == fa) continue;
    addson(v, u);
  }
}
void dsu(int u, int fa) {
  for (int i = fist[u]; i != -1; i = line[i].nxt) {
    int v = line[i].to;
    if (v == fa || v == son[u]) continue;
    dsu(v, u);
    del();
  }
  if (son[u]) dsu(son[u], u);
  for (int i = fist[u]; i != -1; i = line[i].nxt) {
    int v = line[i].to;
    if (v == fa || v == son[u]) continue;
    addson(v, u);
  }
  insert(u), ans[u] = res;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", &col[i]);
  memset(fist, -1, sizeof fist);
  for (int i = 1; i < n; ++i) {
    int x, y;
    scanf("%d%d", &x, &y);
    add(x, y);
    add(y, x);
  }
  dfs(1, -1);
  dsu(1, -1);
  for (int i = 1; i <= n; ++i) printf("%lld%c", ans[i], i == n ? '\n' : ' ');
  return 0;
}
