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;
struct data {
  int to;
  int nextt;
} line[2 * 100005];
int tail, first[100005];
void add(int x, int y) {
  tail++;
  line[tail].to = y;
  line[tail].nextt = first[x];
  first[x] = tail;
}
int t;
int root[100005];
int ls[50 * 100005];
int rs[50 * 100005];
int maxx[50 * 100005];
long long sum[50 * 100005];
void push_up(int k) {
  if (maxx[ls[k]] > maxx[rs[k]]) {
    sum[k] = sum[ls[k]];
  }
  if (maxx[ls[k]] < maxx[rs[k]]) {
    sum[k] = sum[rs[k]];
  }
  if (maxx[ls[k]] == maxx[rs[k]]) {
    sum[k] = sum[ls[k]] + sum[rs[k]];
  }
  maxx[k] = max(maxx[ls[k]], maxx[rs[k]]);
}
void insert(int &k, int l, int r, int x) {
  if (!k) k = ++t;
  if (l == r) {
    sum[k] = l, maxx[k]++;
    return;
  }
  int mid = (l + r) >> 1;
  if (x <= mid)
    insert(ls[k], l, mid, x);
  else
    insert(rs[k], mid + 1, r, x);
  push_up(k);
}
void merge(int &v1, int v2, int l, int r) {
  if (!v1 || !v2) {
    v1 = v1 + v2;
    return;
  }
  if (l == r) {
    maxx[v1] += maxx[v2];
    return;
  }
  int mid = (l + r) >> 1;
  merge(ls[v1], ls[v2], l, mid);
  merge(rs[v1], rs[v2], mid + 1, r);
  push_up(v1);
}
int vis[100005];
long long ans[100005];
void dfs(int x) {
  vis[x] = 1;
  for (int i = first[x]; i; i = line[i].nextt) {
    int y = line[i].to;
    if (vis[y]) continue;
    dfs(y);
    ans[y] = sum[root[y]];
    merge(root[x], root[y], 1, n);
  }
}
int main() {
  scanf("%d", &n);
  int xx;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &xx);
    insert(root[i], 1, n, xx);
  }
  int a, b;
  for (int i = 1; i < n; i++) {
    scanf("%d%d", &a, &b);
    add(a, b);
    add(b, a);
  }
  dfs(1);
  ans[1] = sum[root[1]];
  for (int i = 1; i <= n; i++) {
    printf("%lld ", ans[i]);
  }
  return 0;
}
