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.HashMap;
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
 */
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);
        ELomsatGelral solver = new ELomsatGelral();
        solver.solve(1, in, out);
        out.close();
    }

    static class ELomsatGelral {
        int[] col;
        ArrayList<Integer>[] g;
        HashMap<Integer, Integer>[] cnt;
        long[] sum;
        int[] max;
        int[] sz;
        int[] big;
        long[] ans;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int N = in.nextInt();
            g = new ArrayList[N];
            cnt = new HashMap[N];
            sum = new long[N];
            max = new int[N];
            sz = new int[N];
            big = new int[N];
            ans = new long[N];
            col = in.nextIntArray(N);
            for (int i = 0; i < N; i++) {
                g[i] = new ArrayList<>();
                cnt[i] = new HashMap<>();
            }
            for (int i = 0; i < N - 1; i++) {
                int u = in.nextInt() - 1;
                int v = in.nextInt() - 1;
                g[u].add(v);
                g[v].add(u);
            }
            dfs(0, -1);
            for (int i = 0; i < N; i++) {
                out.print(ans[i] + " ");
            }
        }

        void add(int u, int color, int occur) {
            if (cnt[u].containsKey(color)) {
                cnt[u].put(color, cnt[u].get(color) + occur);
            } else {
                cnt[u].put(color, occur);
            }
            if (cnt[u].get(color) > max[u]) {
                max[u] = cnt[u].get(color);
                sum[u] = color;
            } else if (cnt[u].get(color) == max[u]) {
                sum[u] += color;
            }
        }

        void dfs(int u, int p) {
            int m = -1;
            int bigC = -1;
            sz[u] = 1;
            for (int ele : g[u]) {
                if (ele == p) continue;
                dfs(ele, u);
                sz[u] += sz[ele];
                if (sz[ele] > m) {
                    bigC = ele;
                    m = sz[ele];
                }
            }

            if (bigC == -1) {
                big[u] = u;
                add(u, col[u], 1);
            } else {
                int B = bigC;
                bigC = big[bigC];
                big[u] = bigC;
                add(bigC, col[u], 1);
                for (int ele : g[u]) {
                    if (ele != p && ele != B) {
                        for (int colors : cnt[big[ele]].keySet()) {
                            add(bigC, colors, cnt[big[ele]].get(colors));
                        }
                    }
                }
            }
            ans[u] = sum[big[u]];
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

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

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

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

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int[] nextIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++)
                array[i] = nextInt();
            return array;
        }

    }
}

