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 = 100000;
const int MAXM = 1000000;
int scnt;
int head[maxn + 5];
struct Edge {
  int next, v;
} side[MAXM + 5];
void add(int x, int y) {
  side[++scnt] = (Edge){head[x], y};
  head[x] = scnt;
}
bool vis[maxn + 5];
long long ans[maxn + 5];
int color[maxn + 5];
void dfs(int p, map<int, long long>& appSum, map<int, int>& has) {
  vis[p] = true;
  has[color[p]] = 1;
  appSum[1] = color[p];
  for (int i = head[p]; i; i = side[i].next) {
    int v = side[i].v;
    if (vis[v]) continue;
    map<int, long long> sons;
    map<int, int> sonHas;
    dfs(v, sons, sonHas);
    if (has.size() < sonHas.size()) {
      appSum = sons;
      swap(has, sonHas);
    }
    for (map<int, int>::iterator it = sonHas.begin(); it != sonHas.end();
         it++) {
      int colr = it->first, times = it->second;
      appSum[has[colr]] -= colr;
      has[colr] += times;
      appSum[has[colr]] += colr;
    }
  }
  map<int, long long>::iterator it = appSum.end();
  ans[p] = (--it)->second;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &color[i]);
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    scanf("%d%d", &u, &v);
    add(u, v);
    add(v, u);
  }
  map<int, long long> drop;
  map<int, int> drop2;
  dfs(1, drop, drop2);
  for (int i = 1; i <= n; i++) {
    printf("%I64d ", ans[i]);
  }
  return 0;
}
