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;
inline int gi() {
  int x;
  scanf("%d", &x);
  return x;
}
struct _Edge {
  int to, next;
};
_Edge Edge[200005 << 1];
bool vis[200005];
int sz[200005], son[200005], n, col[200005], cnt[200005], num[200005],
    head[200005], CNT, MAX;
long long ans[200005], sum[200005];
inline void AddEdge(int u, int v) {
  Edge[++CNT] = (_Edge){v, head[u]};
  head[u] = CNT;
  return;
}
void dfs1(int u, int From) {
  sz[u] = 1;
  son[u] = 0;
  for (int e = head[u]; e; e = Edge[e].next) {
    int v = Edge[e].to;
    if (v == From) continue;
    dfs1(v, u);
    sz[u] += sz[v];
    if (sz[v] > sz[son[u]]) son[u] = v;
  }
  return;
}
void calc(int u, int From, int vl) {
  int &c = cnt[col[u]];
  sum[c] -= col[u];
  num[c]--;
  c += vl;
  sum[c] += col[u];
  num[c]++;
  if (vl > 0)
    MAX = max(MAX, c);
  else if (!num[MAX])
    --MAX;
  for (int e = head[u]; e; e = Edge[e].next) {
    int v = Edge[e].to;
    if (v != From && !vis[v]) calc(v, u, vl);
  }
  return;
}
void dsu(int u, int From, int keep_tag) {
  for (int e = head[u]; e; e = Edge[e].next) {
    int v = Edge[e].to;
    if (v != From && v != son[u]) dsu(v, u, 0);
  }
  if (son[u]) dsu(son[u], u, 1), vis[son[u]] = 1;
  calc(u, From, 1);
  ans[u] = sum[MAX];
  if (son[u]) vis[son[u]] = 0;
  if (!keep_tag) calc(u, From, -1);
  return;
}
int main() {
  n = gi();
  for (int i = 1; i <= n; i++) col[i] = gi();
  for (int i = 1, u, v; i < n; i++)
    u = gi(), v = gi(), AddEdge(u, v), AddEdge(v, u);
  dfs1(1, 0);
  dsu(1, 0, 1);
  for (int i = 1; i <= n; i++) printf("%I64d ", ans[i]);
  return 0;
}
