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 + 5;
struct Edge {
  int to, nxt;
} edge[maxn << 1];
int head[maxn], siz[maxn], son[maxn], color[maxn], cnt[maxn];
long long sum[maxn], ans;
int n, tot, Son, maxcnt;
inline void addedge(int u, int v) {
  edge[++tot].to = v, edge[tot].nxt = head[u], head[u] = tot;
}
void dfs1(int u, int f) {
  siz[u] = 1;
  int v;
  for (int i = head[u]; i; i = edge[i].nxt) {
    v = edge[i].to;
    if (v == f) continue;
    dfs1(v, u);
    siz[u] += siz[v];
    if (siz[v] > siz[son[u]]) son[u] = v;
  }
}
inline void modify(int u, int f, int val) {
  cnt[color[u]] += val;
  if (cnt[color[u]] > maxcnt)
    maxcnt = cnt[color[u]], ans = color[u];
  else if (cnt[color[u]] == maxcnt)
    ans += color[u];
  int v;
  for (int i = head[u]; i; i = edge[i].nxt) {
    v = edge[i].to;
    if (v == f || v == Son) continue;
    modify(v, u, val);
  }
}
void dfs2(int u, int f, bool tag) {
  int v;
  for (int i = head[u]; i; i = edge[i].nxt) {
    v = edge[i].to;
    if (v == f || v == son[u]) continue;
    dfs2(v, u, 0);
  }
  if (son[u]) dfs2(son[u], u, 1), Son = son[u];
  modify(u, f, 1);
  sum[u] = ans;
  Son = 0;
  if (!tag) {
    modify(u, f, -1);
    maxcnt = ans = 0;
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &color[i]);
  int u, v;
  for (int i = 1; i < n; i++) {
    scanf("%d %d", &u, &v);
    addedge(u, v), addedge(v, u);
  }
  dfs1(1, 0);
  dfs2(1, 0, 0);
  for (int i = 1; i <= n; i++) printf("%lld ", sum[i]);
  return 0;
}
