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

//package misc;

import java.io.*;
import java.util.*;
import java.util.Map.Entry;

public class Lomsat {

	public static void main(String[] args) throws IOException {

		Lomsat obj = new Lomsat();

		obj.doStuff();

	}
	
	HashMap<Integer, Integer>[] hm;
	int[] base;
	ArrayList<Integer>[] graph;
	int[] order, parent; int count = 0;
	int[] max; long[] sum;
	@SuppressWarnings("unchecked")
	private void doStuff() throws IOException {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		hm = new HashMap[Integer.parseInt(br.readLine())];
		base = new int[hm.length];
		graph = new ArrayList[hm.length];
		StringTokenizer st = new StringTokenizer(br.readLine());
		for (int i = 0; i < base.length; i++) {
			base[i] = Integer.parseInt(st.nextToken());
			graph[i] = new ArrayList<>();
		}
		for (int i = 0; i < base.length-1; i++) {
			st = new StringTokenizer(br.readLine());
			int a = Integer.parseInt(st.nextToken())-1;
			int b = Integer.parseInt(st.nextToken())-1;
			graph[a].add(b);
			graph[b].add(a);
		}
		br.close();
		
		ArrayDeque<Integer> q = new ArrayDeque<>();
		parent = new int[graph.length];
		order = new int[graph.length];
		q.add(0);
		while (!q.isEmpty()) {
			int n = q.poll();
			if (parent[n] != 0) continue;
			parent[n] = -1;
			order[count] = n; count++;
			for (int i : graph[n]) {
				if (parent[i] != 0) parent[n] = i+1; 
				else q.add(i);
			}
		}
		
		max = new int[graph.length];
		sum = new long[graph.length]; 
		for (int i = order.length-1; i >= 0; i--) {
			int p = order[i];
			hm[p] = new HashMap<>();
			add(p, base[p], 1, p);
			for (int j : graph[p]) {
				if (j == parent[p]-1) continue;
				merge(p, j);
			}
		}

		for (int i = 0; i < sum.length; i++) {
			System.out.print((i==0?"":" ")+sum[i]);
		}
		System.out.println();

	}
	
	private void add(int n, int k, int v, int n2) {
		HashMap<Integer, Integer> hm = this.hm[n];
		if (!hm.containsKey(k)) hm.put(k, v);
		else hm.put(k, hm.get(k)+v);
		int freq = hm.get(k);
		if (freq > max[n2]) {
			max[n2] = freq;
			sum[n2] = k;
		} else if (freq == max[n2]) sum[n2] += k;
	}
	private void merge(int p, int j) {
		if (hm[j].size() > hm[p].size()) {
			max[p] = max[j];
			sum[p] = sum[j];
			for (Entry<Integer, Integer> e : hm[p].entrySet()) {
				add(j, e.getKey(), e.getValue(), p);
			}
			hm[p] = hm[j];
		} else {
			for (Entry<Integer, Integer> e : hm[j].entrySet()) {
				add(p, e.getKey(), e.getValue(), p);
			}
		}
	}

}