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.util.*;

public class CF600E {

    private static class Result {
        HashMap<Integer, Integer> counts;
        long dominateSum;
        int dominateCount;

        public Result(HashMap<Integer, Integer> counts, long dominateSum, int dominateCount) {
            this.counts = counts;
            this.dominateSum = dominateSum;
            this.dominateCount = dominateCount;
        }
    }

    private static Map<Integer, Integer> colors = new HashMap<>();
    private static Map<Integer, List<Integer>> tree = new HashMap<>();
    private static List<String> result = new ArrayList<>();

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int n = scanner.nextInt();
        for (int i = 0; i < n; i++) {
            colors.put(i + 1, scanner.nextInt());
            result.add(null);
        }

        for (int i = 0; i < n - 1; i++) {
            int from = scanner.nextInt();
            int to = scanner.nextInt();
            tree.computeIfAbsent(from, k -> new ArrayList<>());
            tree.computeIfAbsent(to, k -> new ArrayList<>());
            tree.get(from).add(to);
            tree.get(to).add(from);
        }

        traverse(1, 0);

        System.out.println(String.join(" ", result));
    }

    private static Result traverse(int root, int parent) {
        List<Integer> children = tree.get(root);
        if (children == null || children.size() == 1 && children.get(0) == parent) {
            HashMap<Integer, Integer> localCounts = new HashMap<>();
            localCounts.put(colors.get(root), 1);
            result.set(root - 1, "" + colors.get(root));

            return new Result(localCounts, (long)colors.get(root), 1);
        }

        List<Result> subResults = new ArrayList<>();
        Result largestResult = null;
        for (Integer child : children) {
            if (child == parent) continue;
            Result subResult = traverse(child, root);
            if (largestResult == null || largestResult.counts.size() < subResult.counts.size()) {
                if (largestResult != null) {
                    subResults.add(largestResult);
                }
                largestResult = subResult;
            } else {
                subResults.add(subResult);
            }
        }

        Integer newCount = largestResult.counts.compute(colors.get(root), (k, v) -> (v == null ? 0 : v) + 1);
        if (newCount > largestResult.dominateCount) {
            largestResult.dominateSum = colors.get(root);
            largestResult.dominateCount = newCount;
        } else if (newCount == largestResult.dominateCount) {
            largestResult.dominateSum += colors.get(root);
        }

        for (Result subResult : subResults) {
            for (Map.Entry<Integer, Integer> entry : subResult.counts.entrySet()) {
                newCount = largestResult.counts.compute(entry.getKey(), (k, v) -> (v == null ? 0 : v) + entry.getValue());
                if (newCount > largestResult.dominateCount) {
                    largestResult.dominateSum = entry.getKey();
                    largestResult.dominateCount = newCount;
                } else if (newCount == largestResult.dominateCount) {
                    largestResult.dominateSum += entry.getKey();
                }
            }
        }

        result.set(root - 1, "" + largestResult.dominateSum);
        return largestResult;
    }
}