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.*;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main {
    static ArrayList<Integer> adjList[];
    static int[] cnt, biggest, tin, tout, vert, size, color;
    static long[] ans;
    static int time, max[];

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = sc.nextInt();
        adjList = new ArrayList[n];
        for (int i = 0; i < n; i++)
            adjList[i] = new ArrayList<>();
        color = sc.nextIntArray(n);
        for (int i = 0; i < n - 1; i++) {
            int u = sc.nextInt() - 1, v = sc.nextInt() - 1;
            adjList[u].add(v);
            adjList[v].add(u);
        }
        max = new int[n];
        cnt = new int[n + 1];
        biggest = new int[n];
        tin = new int[n];
        tout = new int[n];
        vert = new int[n];
        size = new int[n];
        preDfs(0, 0);
        ans = new long[n];
        dfs(0, 0, 1);
        for (long x : ans)
            out.print(x + " ");
        out.flush();
        out.close();
    }

    static void dfs(int u, int p, int keep) {
        for (int v : adjList[u])
            if (v != p && v != biggest[u]) dfs(v, u, 0);
        if (biggest[u] != -1) {
            dfs(biggest[u], u, 1);
            ans[u] = ans[biggest[u]];
            max[u] = max[biggest[u]];
        }
        for (int v : adjList[u]) {
            if (v == p || v == biggest[u]) continue;
            for (int i = tin[v]; i <= tout[v]; i++) {
                int tmp = color[vert[i]];
                cnt[tmp]++;
                if (max[u] == cnt[tmp]) ans[u] += tmp;
                else if (cnt[tmp] > max[u]) {
                    max[u] = cnt[tmp];
                    ans[u] = tmp;
                }
            }
        }
        cnt[color[u]]++;
        if (max[u]== cnt[color[u]]) ans[u] += color[u];
        else if (cnt[color[u]] > max[u]) {
            ans[u] = color[u];
            max[u] = cnt[color[u]];
        }
        if (keep == 0)
            for (int i = tin[u]; i <= tout[u]; i++)
                cnt[color[vert[i]]]--;
    }

    static void preDfs(int u, int p) {
        biggest[u] = -1;
        vert[time] = u;
        tin[u] = time++;
        size[u] = 1;
        for (int v : adjList[u]) {
            if (v == p) continue;
            preDfs(v, u);
            size[u] += size[v];
            if (biggest[u] == -1 || size[biggest[u]] < size[v]) biggest[u] = v;
        }
        tout[u] = time - 1;
    }


    static class Scanner {

        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }


        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

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

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

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

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

        public boolean ready() throws IOException {
            return br.ready();
        }


        public int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public long[] nextLongArray(int n) throws IOException {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }


        public Integer[] nextIntegerArray(int n) throws IOException {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public double[] nextDoubleArray(int n) throws IOException {
            double[] ans = new double[n];
            for (int i = 0; i < n; i++)
                ans[i] = nextDouble();
            return ans;
        }

        public short nextShort() throws IOException {
            return Short.parseShort(next());
        }

    }
}