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
import sys
from collections import Counter

n = int(input())
color = list(map(int, input().split()))
adj = [[] for _ in range(n)]

for _ in range(n-1):
    u, v = map(int, sys.stdin.readline().split())
    u -= 1
    v -= 1
    adj[u].append(v)
    adj[v].append(u)

count = [Counter() for _ in range(n)]
max_cnt = [0]*n
dp = [0]*n

stack = [0]
par = [-1]*n
order = []
while stack:
    v = stack.pop()
    order.append(v)
    for d in adj[v]:
        if d != par[v]:
            stack.append(d)
            par[d] = v

for v in reversed(order):
    child = [i for i in adj[v] if i != par[v]]
    child.sort(key=lambda v: -len(count[v]))

    if child:
        dp[v] = dp[child[0]]
        max_cnt[v] = max_cnt[child[0]]
        count[v] = count[child[0]]
        for d in child[1:]:
            for k, val in count[d].items():
                count[v][k] += val
                if count[v][k] > max_cnt[v]:
                    dp[v] = k
                    max_cnt[v] = count[v][k]
                elif count[v][k] == max_cnt[v]:
                    dp[v] += k

    count[v][color[v]] += 1
    if count[v][color[v]] > max_cnt[v]:
        dp[v] = color[v]
        max_cnt[v] = count[v][color[v]]
    elif count[v][color[v]] == max_cnt[v]:
        dp[v] += color[v]

    if par[v] != -1:
        stack.append(par[v])

print(*dp)
