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.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * 
 * @author pttrung
 */
public class E_Edu_Round_2 {

	public static long MOD = 1000000007;
	static int cur = 0;
	static int[] first, second, index;

	public static void main(String[] args) throws FileNotFoundException {
		// PrintWriter out = new PrintWriter(new FileOutputStream(new File(
		// "output.txt")));
		PrintWriter out = new PrintWriter(System.out);
		Scanner in = new Scanner();
		int n = in.nextInt();
		long[] color = new long[n];
		for (int i = 0; i < n; i++) {
			color[i] = in.nextInt();
		}
		ArrayList<Integer>[] map = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			map[i] = new ArrayList();
		}
		for (int i = 0; i < n - 1; i++) {
			int a = in.nextInt() - 1;
			int b = in.nextInt() - 1;
			map[a].add(b);
			map[b].add(a);
		}
		first = new int[n];
		second = new int[n];
		index = new int[n];
		Arrays.fill(first, -1);
		dfs(0, map);
		long[] result = new long[n];
		int max = (int) Math.max(1, Math.ceil(Math.sqrt(n)));
		Point[] data = new Point[n];
		for (int i = 0; i < n; i++) {
			data[i] = new Point(first[i], second[i]);
		}
		Arrays.sort(data);
		ArrayList<Point>[] list = new ArrayList[(int) Math.ceil((double) n
				/ max)];
		int tmp = 0;
		int count = 0;
		list[tmp] = new ArrayList();
		for (int i = 0; i < n; i++) {
			if (count == max) {
				tmp++;
				list[tmp] = new ArrayList();
				count = 0;
			}
			list[tmp].add(data[i]);
			count++;
		}
		for (ArrayList<Point> a : list) {
			Collections.sort(a, new Comparator<Point>() {

				@Override
				public int compare(Point o1, Point o2) {
					return Integer.compare(o1.y, o2.y);
				}
			});
		}
		int[] total = new int[n + 1];

		TreeSet<Integer> q = new TreeSet<>();
		long[] set = new long[n + 1];
		int x = 0, y = -1;
		for (ArrayList<Point> a : list) {
			for (Point p : a) {
				while (y < p.y) {
					y++;
					total[(int) color[index[y]]]++;
					int v = total[(int) color[index[y]]];
					if (set[v - 1] > 0) {

						set[v - 1] -= color[index[y]];

					}

					set[v] += color[index[y]];
					q.add(v);

				}
				while (y > p.y) {
					total[(int) color[index[y]]]--;
					int v = total[(int) color[index[y]]];
					if (set[v + 1] > 0) {

						set[v + 1] -= color[index[y]];

					}

					set[v] += color[index[y]];
					q.add(v);
					y--;
				}
				while (x < p.x) {
					total[(int) color[index[x]]]--;
					int v = total[(int) color[index[x]]];
					if (set[v + 1] > 0) {

						set[v + 1] -= color[index[x]];

					}

					set[v] += color[index[x]];
					q.add(v);
					x++;
				}
				while (x > p.x) {
					x--;
					total[(int) color[index[x]]]++;
					int v = total[(int) color[index[x]]];
					if (set[v - 1] > 0) {

						set[v - 1] -= color[index[x]];

					}

					set[v] += color[index[x]];
					q.add(v);
				}
				//System.out.println(set.lastEntry().getKey() + " " + index[p.x]);
				while (set[q.last()] == 0) {
					q.pollLast();
				}
				result[index[p.x]] = set[q.last()];
			}
		}
		for (long i : result) {
			out.print(i + " ");
		}
		out.close();
	}

	static void dfs(int node, ArrayList<Integer>[] map) {
		first[node] = cur;
		index[cur++] = node;
		for (int i : map[node]) {
			if (first[i] == -1) {
				dfs(i, map);
			}
		}
		second[node] = cur - 1;
	}

	public static int[] KMP(String val) {
		int i = 0;
		int j = -1;
		int[] result = new int[val.length() + 1];
		result[0] = -1;
		while (i < val.length()) {
			while (j >= 0 && val.charAt(j) != val.charAt(i)) {
				j = result[j];
			}
			j++;
			i++;
			result[i] = j;
		}
		return result;

	}

	public static boolean nextPer(int[] data) {
		int i = data.length - 1;
		while (i > 0 && data[i] < data[i - 1]) {
			i--;
		}
		if (i == 0) {
			return false;
		}
		int j = data.length - 1;
		while (data[j] < data[i - 1]) {
			j--;
		}
		int temp = data[i - 1];
		data[i - 1] = data[j];
		data[j] = temp;
		Arrays.sort(data, i, data.length);
		return true;
	}

	public static int digit(long n) {
		int result = 0;
		while (n > 0) {
			n /= 10;
			result++;
		}
		return result;
	}

	public static double dist(long a, long b, long x, long y) {
		double val = (b - a) * (b - a) + (x - y) * (x - y);
		val = Math.sqrt(val);
		double other = x * x + a * a;
		other = Math.sqrt(other);
		return val + other;

	}

	public static class Point implements Comparable<Point> {

		int x, y;

		public Point(int start, int end) {
			this.x = start;
			this.y = end;
		}

		@Override
		public int hashCode() {
			int hash = 5;
			hash = 47 * hash + this.x;
			hash = 47 * hash + this.y;
			return hash;
		}

		@Override
		public boolean equals(Object obj) {
			if (obj == null) {
				return false;
			}
			if (getClass() != obj.getClass()) {
				return false;
			}
			final Point other = (Point) obj;
			if (this.x != other.x) {
				return false;
			}
			if (this.y != other.y) {
				return false;
			}
			return true;
		}

		@Override
		public int compareTo(Point o) {
			return x - o.x;
		}
	}

	public static class FT {

		long[] data;

		FT(int n) {
			data = new long[n];
		}

		public void update(int index, long value) {
			while (index < data.length) {
				data[index] += value;
				index += (index & (-index));
			}
		}

		public long get(int index) {
			long result = 0;
			while (index > 0) {
				result += data[index];
				index -= (index & (-index));
			}
			return result;

		}
	}

	public static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public static long pow(long a, long b) {
		if (b == 0) {
			return 1;
		}
		if (b == 1) {
			return a;
		}
		long val = pow(a, b / 2);
		if (b % 2 == 0) {
			return val * val % MOD;
		} else {
			return val * (val * a % MOD) % MOD;

		}
	}

	static class Scanner {

		BufferedReader br;
		StringTokenizer st;

		public Scanner() throws FileNotFoundException {
			// System.setOut(new PrintStream(new
			// BufferedOutputStream(System.out), true));
			br = new BufferedReader(new InputStreamReader(System.in));
			// br = new BufferedReader(new InputStreamReader(new
			// FileInputStream(new File("input.txt"))));
		}

		public String next() {

			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					throw new RuntimeException();
				}
			}
			return st.nextToken();
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

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

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String nextLine() {
			st = null;
			try {
				return br.readLine();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}

		public boolean endLine() {
			try {
				String next = br.readLine();
				while (next != null && next.trim().isEmpty()) {
					next = br.readLine();
				}
				if (next == null) {
					return true;
				}
				st = new StringTokenizer(next);
				return st.hasMoreTokens();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}
	}
}
