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 java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.StringTokenizer;

public class LomsatGelral
{
	static int n, color[];
	static long res[];
	static ArrayList<Integer>[] adj;
	static boolean vis[];
	public static void main(String[] args) throws IOException
	{
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		color = new int[n];
		adj = new ArrayList[n];
		vis = new boolean[n];
		res = new long[n];
		for (int i = 0; i < adj.length; i++)
			adj[i] = new ArrayList<Integer>();
		for (int i = 0; i < n; i++)
			color[i] = sc.nextInt();
		
		for (int i = 0; i < n-1; i++)
		{
			int a = sc.nextInt()-1;
			int b=  sc.nextInt()-1;
			adj[a].add(b);
			adj[b].add(a);
		}
		
		solve(0);
		for (int i = 0; i < res.length; i++)
		{
			pw.print(res[i] + " ");
		}
		pw.println();
		pw.flush();
		pw.close();
	}
	static pair solve(int u)
	{
		vis[u] = true;
		
		HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
		
		map.put(-1, 1);
//		map.put(-2, color[u]);
		long ss = color[u];
		map.put(color[u], 1);
		
		
		for (int v : adj[u])
		{
			if(!vis[v])
			{
				pair pp = solve(v);
				HashMap<Integer, Integer> m2 = pp.map;
				if(map.size() < m2.size())
				{
					HashMap<Integer, Integer> tmp = m2;
					m2 = map;
					map = tmp;
					
					ss = pp.sum;
				}
				
				int cnt = map.get(-1);
				long sum = ss;
				
				for (int c : m2.keySet())
				{
					if(c == -1 || c == -2)
						continue;
					int r1 = map.getOrDefault(c, 0);
					r1 += m2.get(c);
					if(r1 > cnt)
					{
						cnt = r1;
						sum = c;
					}
					else if(r1 == cnt)
					{
						sum += c;
					}
					map.put(c, r1);
				}
				map.put(-1, cnt);
//				map.put(-2, sum);
				ss = sum;
			}
		}
		
		res[u] = ss;
		return new pair(ss, map);
	}
	
	static class pair
	{
		long sum;
		HashMap<Integer, Integer> map;
		public pair(long sum, HashMap<Integer, Integer> map)
		{
			this.map = map;
			this.sum = sum;
		}
	}
	static class Scanner
	{
		StringTokenizer st; BufferedReader br;
		public Scanner(InputStream s){br = new BufferedReader(new InputStreamReader(s));}
		public String next() throws IOException{while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine()); return st.nextToken();}
		public int nextInt() throws IOException{return Integer.parseInt(next());}
		public long nextLong() throws IOException{return Long.parseLong(next());}
		public String nextLine() throws IOException{return br.readLine();}
		public double nextDouble() throws IOException{return Double.parseDouble(next());}
		public boolean ready() throws IOException{return br.ready();}
	}
}
