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 oo = 1000000000000000000;
long long sum, ans = 0, mx = 0, mn = 1000000000, num, pos;
vector<int> v[100001];
long long int a[100001], mxx[100001];
map<int, int> mp[100001];
void unin(int x, int y) {
  if (mp[x].size() < mp[y].size()) {
    mp[x].swap(mp[y]);
    mxx[x] = mxx[y];
    a[x] = a[y];
  }
  for (map<int, int>::iterator it = mp[y].begin(); it != mp[y].end(); it++) {
    mp[x][(it)->first] += (it)->second;
    if (mp[x][it->first] == mxx[x]) {
      a[x] += it->first;
    } else if (mp[x][it->first] > mxx[x]) {
      mxx[x] = mp[x][it->first];
      a[x] = it->first;
    }
  }
}
void dfs(int u, int pr = -1) {
  for (int i = 0; i < v[u].size(); i++) {
    int to = v[u][i];
    if (to == pr) continue;
    dfs(to, u);
    unin(u, to);
  }
}
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> num;
    mp[i][num]++;
    mxx[i] = 1;
    a[i] = num;
  }
  int x, y;
  for (int i = 1; i < n; i++) {
    cin >> x >> y;
    v[x].push_back(y);
    v[y].push_back(x);
  }
  dfs(1);
  for (int i = 1; i <= n; i++) {
    num = 0;
    cout << a[i] << " ";
    sum = 0;
  }
}
