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;
long long head[100011], nex[200011], to[200011], tot;
inline void build(long long x, long long y) {
  to[++tot] = y;
  nex[tot] = head[x];
  head[x] = tot;
}
long long n, val[100011], fa[100011], Big[100011], size[100011];
inline void dfs(long long x, long long ne) {
  fa[x] = ne;
  long long i, y;
  size[x] = 1;
  for (i = head[x]; !!i; i = nex[i]) {
    y = to[i];
    if (y == fa[x]) continue;
    dfs(y, x);
    size[x] += size[y];
    if (size[y] > size[Big[x]]) Big[x] = y;
  }
}
long long ans[100011], co[100011], Most, f[100011], s;
inline void Go(long long x, long long tp) {
  ans[val[x]] += val[x] * tp;
  co[val[x]] += tp;
  if (tp == 1 && co[val[x]] > Most)
    Most = co[val[x]], s = val[x];
  else if (tp == 1 && co[val[x]] == Most)
    s += val[x];
  long long i;
  for (i = head[x]; !!i; i = nex[i])
    if (to[i] != fa[x]) Go(to[i], tp);
}
inline void bfs(long long x, bool del) {
  long long i, y;
  for (i = head[x]; !!i; i = nex[i]) {
    y = to[i];
    if (y == fa[x] || y == Big[x]) continue;
    bfs(y, 1);
  }
  if (!!Big[x]) bfs(Big[x], 0);
  ++co[val[x]];
  ans[val[x]] += val[x];
  if (co[val[x]] > Most)
    Most = co[val[x]], s = val[x];
  else if (co[val[x]] == Most)
    s += val[x];
  for (i = head[x]; !!i; i = nex[i]) {
    y = to[i];
    if (y == fa[x] || y == Big[x]) continue;
    Go(y, 1);
  }
  f[x] = s;
  if (del) Go(x, -1), Most = 0, s = 0;
}
signed main() {
  scanf("%lld", &n);
  long long i, x, y;
  for (i = 1; i <= n; ++i) scanf("%lld", &val[i]);
  for (i = 1; i < n; ++i) {
    scanf("%lld%lld", &x, &y);
    build(x, y);
    build(y, x);
  }
  dfs(1, 0);
  bfs(1, 0);
  for (i = 1; i <= n; ++i) printf("%lld ", f[i]);
}
