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;
int n, x, y, Son, Max;
int tot, point[100005], nxt[100005 * 2], v[100005 * 2];
int c[100005], size[100005], son[100005], cnt[100005];
long long sum, ans[100005];
void add(int x, int y) {
  ++tot;
  nxt[tot] = point[x];
  point[x] = tot;
  v[tot] = y;
}
void getson(int x, int fa) {
  size[x] = 1;
  for (int i = point[x]; i; i = nxt[i])
    if (v[i] != fa) {
      getson(v[i], x);
      size[x] += size[v[i]];
      if (size[v[i]] > size[son[x]]) son[x] = v[i];
    }
}
void calc(int x, int fa, int val) {
  cnt[c[x]] += val;
  if (cnt[c[x]] > Max)
    sum = (long long)c[x], Max = cnt[c[x]];
  else if (cnt[c[x]] == Max)
    sum += (long long)c[x];
  for (int i = point[x]; i; i = nxt[i])
    if (v[i] != fa && v[i] != Son) calc(v[i], x, val);
}
void dfs(int x, int fa, int k) {
  for (int i = point[x]; i; i = nxt[i])
    if (v[i] != fa && v[i] != son[x]) dfs(v[i], x, 0);
  if (son[x]) dfs(son[x], x, 1), Son = son[x];
  calc(x, fa, 1);
  Son = 0;
  ans[x] = sum;
  if (!k) calc(x, fa, -1), Max = sum = 0;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", &c[i]);
  for (int i = 1; i < n; ++i) {
    scanf("%d%d", &x, &y);
    add(x, y), add(y, x);
  }
  getson(1, 0);
  dfs(1, 0, 0);
  for (int i = 1; i <= n; ++i) printf("%I64d%c", ans[i], " \n"[i == n]);
}
