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>
const int S = 222222, T = 10000005;
int n, fir[S], l[S], to[S], ec, a[S], rt[S], lc[T], rc[T], mx[T], sz[S], pc;
long long w[T], ans[S];
void link(int a, int b) {
  l[++ec] = fir[a];
  fir[a] = ec;
  to[ec] = b;
}
void ins(int& p, int x, int L = 1, int R = n) {
  if (!p) p = ++pc;
  if (L == R) {
    w[p] = L;
    mx[p]++;
    return;
  }
  if (x <= (L + R >> 1))
    ins(lc[p], x, L, (L + R >> 1));
  else
    ins(rc[p], x, (L + R >> 1) + 1, R);
  if (mx[lc[p]] > mx[rc[p]])
    mx[p] = mx[lc[p]], w[p] = w[lc[p]];
  else if (mx[rc[p]] > mx[lc[p]])
    mx[p] = mx[rc[p]], w[p] = w[rc[p]];
  else
    mx[p] = mx[lc[p]], w[p] = w[lc[p]] + w[rc[p]];
}
void DFS(int& r, int p, int fa) {
  for (int i = fir[p]; i; i = l[i])
    if (to[i] != fa) DFS(r, to[i], p);
  ins(r, a[p]);
}
void dfs(int p, int fa) {
  sz[p] = 1;
  int son = 0;
  for (int i = fir[p]; i; i = l[i])
    if (to[i] != fa) {
      dfs(to[i], p);
      sz[p] += sz[to[i]];
      if (sz[to[i]] > sz[son]) son = to[i];
    }
  ins(rt[p] = rt[son], a[p]);
  for (int i = fir[p]; i; i = l[i])
    if (to[i] != fa && to[i] != son) DFS(rt[p], to[i], p);
  ans[p] = w[rt[p]];
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
  for (int i = 1, a, b; i < n; ++i)
    scanf("%d%d", &a, &b), link(a, b), link(b, a);
  dfs(1, 0);
  for (int i = 1; i <= n; ++i) printf("%lld ", ans[i]);
}
