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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.TreeMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Ronak Vaghela
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        public static int n;
        public static ArrayList<Integer>[] adj;
        public static int[] big;
        public static int[] subtree;
        public static int[] depth;
        public static int[] parent;
        public static long[] cnt;
        public static TreeMap<Integer, Integer> tm;
        public static int[] freq;
        public static int[] col;
        static int max = 0;
        static long[] val;

        public void solve(int testNumber, InputReader in, PrintWriter out) {

            n = in.nextInt();
            // m = in.nextInt();

            adj = new ArrayList[n];
            cnt = new long[n];
            col = new int[n];
            freq = new int[n + 1];
            tm = new TreeMap<>();
            big = new int[n];
            for (int i = 0; i < n; i++)
                adj[i] = new ArrayList<Integer>();

            for (int i = 0; i < n; i++) {
                col[i] = in.nextInt();
            }
            val = new long[n];
            for (int i = 1; i < n; i++) {
                int u = in.nextInt() - 1;
                int v = in.nextInt() - 1;
                // long c = in.nextLong();
                adj[u].add(v);
                adj[v].add(u);
                // idx[u].add(i);
                // idx[v].add(i);
            }
            depth = new int[n];
            parent = new int[n];
            subtree = new int[n];
            dfs0(0, -1);

            // LOGMAXN = (int) (Math.log(n) / Math.log(2) + 3);
            // P = new int[LOGMAXN][n];
            // preprocessForLCA();

            dfs(0, -1, 0);

            for (int i = 0; i < n; i++) {
                out.print(cnt[i] + " ");
            }

            out.close();
        }

        public static void dfs0(int curr, int prev) {
            int s = adj[curr].size();
            subtree[curr] = 1;
            for (int i = 0; i < s; i++) {
                int nxt = adj[curr].get(i);
                if (nxt != prev) {
                    depth[nxt] = depth[curr] + 1;
                    parent[nxt] = curr;
                    dfs0(nxt, curr);
                    subtree[curr] += subtree[nxt];
                }
            }
        }

        public static void add(int v, int p, int x) {


            val[freq[col[v]]] = val[freq[col[v]]] - col[v];


            if (val[freq[col[v]]] == 0 && max == freq[col[v]]) {
                max--;
            }

            freq[col[v]] += x;

            val[freq[col[v]]] = val[freq[col[v]]] + col[v];

            if (freq[col[v]] > max) {
                max = freq[col[v]];
            }

            for (int u : adj[v])
                if (u != p && big[u] == 0)
                    add(u, v, x);

        }

        public static void dfs(int v, int p, int keep) {
            int mx = -1, bigChild = -1;
            for (int u : adj[v])
                if (u != p && subtree[u] > mx) {
                    mx = subtree[u];
                    bigChild = u;
                }
            for (int u : adj[v])
                if (u != p && u != bigChild)
                    dfs(u, v, 0); // run a dfs on small childs and clear them from
            // cnt
            if (bigChild != -1) {
                big[bigChild] = 1;
                dfs(bigChild, v, 1);
            } // bigChild marked as big and not cleared from cnt

            add(v, p, 1);

            cnt[v] = val[max];

            if (bigChild != -1)
                big[bigChild] = 0;

            if (keep == 0)
                add(v, p, -1);

        }

    }

    static class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar;
        private int snumChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

