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>
const int MAXN = 1e5 + 19;
struct Edge {
  int to, next;
} edge[MAXN << 1];
int head[MAXN], cnt;
inline void add(int from, int to) {
  edge[++cnt].to = to;
  edge[cnt].next = head[from];
  head[from] = cnt;
}
struct Node {
  int ls, rs;
  int max;
  long long sum;
} tr[MAXN << 5];
inline void push_up(int node) {
  tr[node].max = std::max(tr[tr[node].ls].max, tr[tr[node].rs].max);
  tr[node].sum = 0ll;
  if (tr[tr[node].ls].max == tr[node].max) tr[node].sum += tr[tr[node].ls].sum;
  if (tr[tr[node].rs].max == tr[node].max) tr[node].sum += tr[tr[node].rs].sum;
}
int root[MAXN], ind;
void add(int &node, int L, int R, int x) {
  if (!node) node = ++ind;
  if (L == R) {
    tr[node].max = 1;
    tr[node].sum = x;
    return;
  }
  int mid = (L + R) / 2;
  if (x <= mid)
    add(tr[node].ls, L, mid, x);
  else
    add(tr[node].rs, mid + 1, R, x);
  push_up(node);
}
int merge(int x, int y, int L, int R) {
  if (!x || !y) return x + y;
  if (L == R) {
    tr[x].max += tr[y].max;
    return x;
  }
  int mid = (L + R) / 2;
  tr[x].ls = merge(tr[x].ls, tr[y].ls, L, mid);
  tr[x].rs = merge(tr[x].rs, tr[y].rs, mid + 1, R);
  push_up(x);
  return x;
}
int n, c[MAXN];
long long ans[MAXN];
void dfs(int node, int f) {
  add(root[node], 1, n, c[node]);
  for (int i = head[node]; i; i = edge[i].next)
    if (edge[i].to != f) {
      dfs(edge[i].to, node);
      root[node] = merge(root[node], root[edge[i].to], 1, n);
    }
  ans[node] = tr[root[node]].sum;
}
int main() {
  std::scanf("%d", &n);
  for (int i = 1; i <= n; ++i) std::scanf("%d", c + i);
  for (int i = 2; i <= n; ++i) {
    int x, y;
    std::scanf("%d%d", &x, &y);
    add(x, y), add(y, x);
  }
  dfs(1, 0);
  for (int i = 1; i <= n; ++i) std::printf("%lld ", ans[i]);
  return 0;
}
