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>
struct SegmentTree {
  int l, r, maxx;
  long long ans;
} t[2000001];
int n, tot, cnt;
int a[100001], ver[200001], head[100001], next[200001], root[200001];
long long ans[100001];
void add(int u, int v) {
  ver[++tot] = v;
  next[tot] = head[u];
  head[u] = tot;
}
void spread(int a) {
  if (t[t[a].l].maxx > t[t[a].r].maxx) {
    t[a].maxx = t[t[a].l].maxx;
    t[a].ans = t[t[a].l].ans;
  } else if (t[t[a].l].maxx < t[t[a].r].maxx) {
    t[a].maxx = t[t[a].r].maxx;
    t[a].ans = t[t[a].r].ans;
  } else {
    t[a].maxx = t[t[a].l].maxx;
    t[a].ans = t[t[a].l].ans + t[t[a].r].ans;
  }
}
int merge(int r1, int r2, int l, int r) {
  if (!r1 || !r2) return r1 + r2;
  if (l == r) {
    t[r1].maxx += t[r2].maxx;
    return r1;
  }
  int mid = l + r >> 1;
  t[r1].l = merge(t[r1].l, t[r2].l, l, mid);
  t[r1].r = merge(t[r1].r, t[r2].r, mid + 1, r);
  spread(r1);
  return r1;
}
void update(int p, int l, int r, int pos) {
  if (l == r) {
    t[p].maxx++;
    t[p].ans = l;
    return;
  }
  int mid = l + r >> 1;
  if (pos <= mid) {
    if (!t[p].l) t[p].l = ++cnt;
    update(t[p].l, l, mid, pos);
  } else {
    if (!t[p].r) t[p].r = ++cnt;
    update(t[p].r, mid + 1, r, pos);
  }
  spread(p);
}
void dfs(int p, int fa) {
  for (int i = head[p]; i; i = next[i]) {
    if (fa == ver[i]) continue;
    dfs(ver[i], p);
    root[p] = merge(root[p], root[ver[i]], 1, n);
  }
  if (!root[p]) root[p] = ++cnt;
  update(root[p], 1, n, a[p]);
  ans[p] = t[root[p]].ans;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", a + i);
  for (int i = 1, u, v; i < n; i++)
    scanf("%d %d", &u, &v), add(u, v), add(v, u);
  dfs(1, 0);
  for (int i = 1; i <= n; i++) printf("%lld ", ans[i]);
}
