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 = 1e5 + 10;
int n, tot;
int mx[maxn * 30], a[maxn], lc[maxn * 30], rc[maxn * 30], rt[maxn];
long long ans[maxn], sum[maxn * 30];
vector<int> G[maxn];
void update(int x) {
  mx[x] = max(mx[lc[x]], mx[rc[x]]);
  sum[x] = 0;
  if (mx[x] == mx[lc[x]]) sum[x] += sum[lc[x]];
  if (mx[x] == mx[rc[x]]) sum[x] += sum[rc[x]];
}
void modify(int p, int v, int l, int r, int &x) {
  if (!x) x = ++tot;
  if (l == r) {
    mx[x] = 1;
    sum[x] = v;
    return;
  }
  int mid = l + r >> 1;
  if (p <= mid)
    modify(p, v, l, mid, lc[x]);
  else
    modify(p, v, mid + 1, r, rc[x]);
  update(x);
}
void merge(int &x, int y, int l, int r) {
  if (!y) return;
  if (!x) {
    x = y;
    return;
  }
  if (l == r) {
    mx[x] += mx[y];
    return;
  }
  int mid = l + r >> 1;
  merge(lc[x], lc[y], l, mid);
  merge(rc[x], rc[y], mid + 1, r);
  update(x);
}
void dfs(int u, int fa) {
  modify(a[u], a[u], 1, n, rt[u]);
  for (auto &v : G[u]) {
    if (v == fa) continue;
    dfs(v, u);
    merge(rt[u], rt[v], 1, n);
  }
  ans[u] = sum[rt[u]];
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  int u, v;
  for (int i = 1; i < n; i++) {
    scanf("%d%d", &u, &v);
    G[u].push_back(v);
    G[v].push_back(u);
  }
  dfs(1, -1);
  for (int i = 1; i <= n; i++) printf("%lld%c", ans[i], i == n ? '\n' : ' ');
  return 0;
}
