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 = 100100;
const int MAXM = 2 * MAXN;
int n;
int c[MAXN];
int to[MAXM], nxt[MAXM], head[MAXN], E;
long long ans[MAXN];
int mxColor[MAXN];
void addEdge(int a, int b) {
  to[E] = b;
  nxt[E] = head[a];
  head[a] = E++;
  to[E] = a;
  nxt[E] = head[b];
  head[b] = E++;
}
void merge(map<int, int> *&a, map<int, int> *&b, int v, int to) {
  if (a->size() > b->size()) {
    swap(a, b);
    ans[v] = ans[to];
    mxColor[v] = mxColor[to];
  }
  for (auto it : *a) {
    int tmp = ((*b)[it.first] += it.second);
    if (tmp > mxColor[v]) {
      mxColor[v] = tmp;
      ans[v] = it.first;
    } else if (tmp == mxColor[v]) {
      ans[v] += it.first;
    }
  }
}
map<int, int> *dfs(int v, int p = -1) {
  map<int, int> *res = new map<int, int>;
  ++(*res)[c[v]];
  mxColor[v] = 1;
  ans[v] = c[v];
  for (int id = head[v]; ~id; id = nxt[id]) {
    if (to[id] != p) {
      map<int, int> *tmp = dfs(to[id], v);
      merge(tmp, res, v, to[id]);
    }
  }
  return res;
}
int main() {
  memset(head, 0xff, sizeof head);
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", c + i);
  for (int i = 1, a, b; i < n; ++i) {
    scanf("%d%d", &a, &b);
    addEdge(a, b);
  }
  dfs(1);
  for (int i = 1; i <= n; ++i) cout << ans[i] << ' ';
  cout << '\n';
  return 0;
}
