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.StringTokenizer;


public class LomsatGelral_CF600E {
	
	static int n;
	static int [] cnt, sz;
	
	static int col [];
	static ArrayList<Integer> [] g;
	static int big,occ;
	static long max,sol [];
	
	static void add(int v, int p, int x){
	    cnt[ col[v] ] += x;
	    if(cnt[col[v]] == occ)
	    	max += col[v]+1;
	    else if(cnt[col[v]] > occ){
	    	occ = cnt[col[v]];
	    	max = col[v]+1;
	    }
	    for(int u: g[v])
	        if(u != p && u != big)
	            add(u, v, x);
	}
	static void dfs(int v, int p, boolean keep){
	    
		int mx = -1, bigChild = -1;
	    
	    for(int u : g[v])
	       if(u != p && sz[u] > mx){
	          mx = sz[u];
	          bigChild = u;
	       }
	    for(int u : g[v])
	        if(u != p && u != bigChild)
	            dfs(u, v, false);  
	    if(bigChild != -1){
	        dfs(bigChild, v, true);
	        big = bigChild;  
	    }
	    add(v, p, 1);
	    sol[v] = max;
	    
	    big = -1;
	    
	    if(!keep){
	        add(v, p, -1);
	        max = occ = 0;
	    }
	}
	
	static int updateSZ(int v, int p){
		int count = 1;
		for(int i: g[v]){
			if(i != p)
			count += updateSZ(i,v);
		}
		 return sz[v] = count;
		
	}
	
	public static void main(String[] args) throws IOException {

		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		n = sc.nextInt();
		cnt = new int [n];
		col = new int [n];
		sz = new int [n];
		sol = new long [n];
		g = new ArrayList [n];
		for(int i = 0; i < n; i++)
			col[i] = sc.nextInt() - 1;
		for(int i =0 ; i < n; i++)
			g[i] = new ArrayList<Integer>();
		for(int i = 0 ; i < n -1; i++){
			int x = sc.nextInt() - 1;
			int y = sc.nextInt() - 1;
			g[x].add(y);
			g[y].add(x);
		}
		updateSZ(0,-1);
		dfs(0,-1,true);
		
		for(int i = 0;  i < n - 1; i++)
			out.print(sol[i]+" ");
		
		out.println(sol[n - 1]);
		out.flush();
		out.close();
	}
	
	
	
	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 {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}

}
