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 CF;

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


public class Main {

	static int[] cnt, col, sz;
	static ArrayList<Integer>[] adj;
	static int max; static long sum, ans[];

	static void add(int v, int p, int x) {
		cnt[col[v]] += x;
		if(x > 0)
			if (cnt[col[v]] > max) {
				max = cnt[col[v]];
				sum = col[v];
			}
			else if(cnt[col[v]] == max){
				sum += col[v];
			}
		for (int u : adj[v])
			if (u != p && u != hv)
				add(u, v, x);
	}

	static int hv = -1;

	static void dfs(int v, int p, boolean keep) {
		int mx = -1, bigChild = -1;
		for (int u : adj[v])
			if (u != p && sz[u] > mx) {
				mx = sz[u];
				bigChild = u;
			}
		for (int u : adj[v])
			if (u != p && u != bigChild)
				dfs(u, v, false); 
		if (bigChild != -1) {
			dfs(bigChild, v, true);
			hv = bigChild; 
		}
		add(v, p, 1);
		ans[v] = sum;
		if (bigChild != -1)
			hv = -1;
		if (!keep){
			add(v, p, -1);
			max = 0; sum = 0;
		}
	}
	static void getsz(int v, int p){
	    sz[v] = 1;  
	    for(int u : adj[v])
	        if(u != p){
	            getsz(u, v);
	            sz[v] += sz[u]; 
	        }
	}
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt();
		col = new int[n];
		cnt = new int[n+1];
		sz = new int[n];
		ans = new long[n];
		max = 0;
		sum = 0;
		for (int i = 0; i < col.length; i++) {
			col[i] = sc.nextInt();
		}
		adj = new ArrayList[n];
		for (int i = 0; i < adj.length; i++) {
			adj[i] = new ArrayList<>();
		}
		for (int i = 0; i < n - 1; i++) {
			int u = sc.nextInt() - 1, v = sc.nextInt() - 1;
			adj[u].add(v);
			adj[v].add(u);
		}
		getsz(0, -1);
		dfs(0, -1, false);
//		System.out.println(Arrays.toString(cnt));
		for(long i:ans)
			out.print(i + " ");
		out.flush();
		out.close();
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader fileReader) {
			br = new BufferedReader(fileReader);
		}

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