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 long long inf = 0x3f3f3f3f;
map<int, int> cnt;
int maxi = 0;
int x[100005];
int head[100005], ne[200005], to[200005];
int idx = 0;
int son[100005];
int sz[100005];
long long sum = 0;
long long s[100005];
void Insert(int a, int b) {
  to[++idx] = b;
  ne[idx] = head[a];
  head[a] = idx;
}
void Add(int root, int fa) {
  cnt[x[root]]++;
  if (cnt[x[root]] == maxi) {
    sum += x[root];
  } else if (cnt[x[root]] > maxi) {
    maxi = cnt[x[root]];
    sum = x[root];
  }
  for (int i = head[root]; i != -1; i = ne[i]) {
    int a = to[i];
    if (a == fa) continue;
    Add(a, root);
  }
}
void dfs1(int root, int fa) {
  sz[root] = 1;
  for (int i = head[root]; i != -1; i = ne[i]) {
    int a = to[i];
    if (a == fa) continue;
    dfs1(a, root);
    sz[root] += sz[a];
    if (sz[a] > sz[son[root]]) {
      son[root] = a;
    }
  }
}
void dfs2(int root, int fa) {
  for (int i = head[root]; i != -1; i = ne[i]) {
    int a = to[i];
    if (a == fa || a == son[root]) continue;
    dfs2(a, root);
    maxi = 0;
    sum = 0;
    cnt.clear();
  }
  if (son[root]) dfs2(son[root], root);
  for (int i = head[root]; i != -1; i = ne[i]) {
    int a = to[i];
    if (a == fa || a == son[root]) continue;
    Add(a, root);
  }
  cnt[x[root]]++;
  if (cnt[x[root]] == maxi) {
    sum += x[root];
  } else if (cnt[x[root]] > maxi) {
    maxi = cnt[x[root]];
    sum = x[root];
  }
  s[root] = sum;
}
int main() {
  int n;
  memset(head, -1, sizeof(head));
  cin >> n;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &x[i]);
  }
  for (int i = 1; i < n; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    Insert(a, b);
    Insert(b, a);
  }
  dfs1(1, 0);
  dfs2(1, 0);
  for (int i = 1; i <= n; i++) {
    printf("%lld%c", s[i], i == n ? '\n' : ' ');
  }
  return 0;
}
