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 + 10;
int n, u, v, col[maxn];
struct Edge {
  int to, nex;
} edge[maxn << 1];
int head[maxn], ecnt;
void add_edge(int u, int v) {
  edge[++ecnt] = {v, head[u]};
  head[u] = ecnt;
}
int hson[maxn], siz[maxn], cnt[maxn], maxx;
long long ans[maxn], sum;
void get_hson(int now, int fa) {
  siz[now] = 1;
  for (int i = head[now]; i; i = edge[i].nex) {
    int to = edge[i].to;
    if (to == fa) continue;
    get_hson(to, now);
    siz[now] += siz[to];
    if (siz[to] > siz[hson[now]]) hson[now] = to;
  }
}
int start;
void go(int now, int fa, int val) {
  cnt[col[now]] += val;
  if (cnt[col[now]] > maxx) {
    sum = col[now];
    maxx = cnt[col[now]];
  } else if (cnt[col[now]] == maxx)
    sum += 1LL * col[now];
  for (int i = head[now]; i; i = edge[i].nex) {
    int to = edge[i].to;
    if (to == fa || to == start) continue;
    go(to, now, val);
  }
}
void dfs(int now, int fa, int flag) {
  for (int i = head[now]; i; i = edge[i].nex) {
    int to = edge[i].to;
    if (to == fa || to == hson[now]) continue;
    dfs(to, now, -1);
  }
  if (hson[now]) {
    dfs(hson[now], now, 1);
    start = hson[now];
  }
  go(now, fa, 1);
  start = 0;
  ans[now] = sum;
  if (flag == -1) {
    go(now, fa, -1);
    maxx = 0;
    sum = 0LL;
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", col + i);
  for (int i = 1; i < n; i++) {
    scanf("%d %d", &u, &v);
    add_edge(u, v);
    add_edge(v, u);
  }
  get_hson(1, 0);
  dfs(1, 0, 1);
  for (int i = 1; i <= n; i++) printf("%lld ", ans[i]);
  return 0;
}
