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.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class edRound2E {
	public static void main(String[] args) throws IOException {
		FS inn = new FS();
		int n = inn.nextInt();
		color = new int[n];
		sz = new int[n];
		rev = new int[n];
		out = new int[n];
		in = new int[n];
		for (int i = 0; i < n; i++)
			color[i] = inn.nextInt() - 1;
		adj = new ArrayList[n];
		for (int i = 0; i < n; i++)
			adj[i] = new ArrayList<>();

		for (int i = 0; i < n - 1; i++) {
			int u = inn.nextInt() - 1;
			int v = inn.nextInt() - 1;
			adj[u].add(v);
			adj[v].add(u);
		}
		dfs(0, -1);
		ans = new long[n];
		cnt = new int[n];
		ts = new TreeMap<>();
		long sum = 0;
		for (int i = 0; i < n; i++) {
			sum += color[i];
		}
		ts.put(0, sum);
		
		solve(0, -1, false);
		PrintWriter out = new PrintWriter(System.out);
		for (int i = 0; i < n; i++) {
			out.print(ans[i] + " ");
		}
		out.close();
	}

	static void solve(int u, int p, boolean undo) {
		int bigChild = -1, bigSize = 0;
		for (int v : adj[u]) {
			if (v != p)
				if (sz[v] > bigSize) {
					bigChild = v;
					bigSize = sz[v];
				}
		}

		for (int v : adj[u]) {
			if (v != p && v != bigChild) {
				solve(v, u, true);
			}
		}
		if (bigChild != -1)
			solve(bigChild, u, false);
		
		
		increment(color[u]);
		for (int v : adj[u]) {
			if (v != p && v != bigChild) {
				for (int pointer = in[v]; pointer < out[v]; pointer++) {
					int w = rev[pointer];
					increment(color[w]);
				}
			}
		}
		ans[u] = ts.lastEntry().getValue();
		if (undo) {
			for (int pointer = in[u]; pointer < out[u]; pointer++) {
				int w = rev[pointer];
				decrement(color[w]);
			}
		}
	}

	static void increment(int c) {
		long count = ts.getOrDefault(cnt[c], 0l);
		ts.put(cnt[c], count - 1 - c);
		if(count - 1 - c == 0)
			ts.remove(cnt[c]);
		count = ts.getOrDefault(cnt[c] + 1, 0l);
		ts.put(cnt[c] + 1, count + 1 + c);
		cnt[c]++;
	}

	static void decrement(int c) {
		long count = ts.get(cnt[c]);
		ts.put(cnt[c], count - 1 - c);
		if(count - 1 - c == 0)
			ts.remove(cnt[c]);
		count = ts.getOrDefault(cnt[c] - 1, 0l);
		ts.put(cnt[c] - 1, count + 1 + c);
		cnt[c]--;
	}

	static ArrayList<Integer> adj[];

	static int idx = 0;

	static int dfs(int u, int p) {
		sz[u] = 1;
		rev[idx] = u;
		in[u] = idx++;
		for (int v : adj[u])
			if (v != p)
				sz[u] += dfs(v, u);
		out[u] = idx;
		return sz[u];
	}

	static int[] color, sz, in, out, cnt, rev;
	static long[] ans;
	static TreeMap<Integer, Long> ts;

	static class FS {
		BufferedReader br;
		StringTokenizer st;

		FS() {
			br = new BufferedReader(new InputStreamReader(System.in));
			st = new StringTokenizer("");
		}

		String next() throws IOException {
			if (!st.hasMoreElements())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
	}
}
