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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Reader;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

// Educational Codeforces Round 2
// Lomsat gelral
public class Problem_600_E {
    
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        Problem_600_E solver = new Problem_600_E();
        solver.solve(1, new InputStreamReader(inputStream), out);
        out.close();
    }
    
    static class Node {
      HashMap<Integer, Integer> counts = new HashMap<>();
      long sum;
      int max;
      
      void add(Integer color, Integer count)
      {
        Integer now = counts.get(color);
        if(now == null)
          now = 0;
        Integer newCount = now + count;
        counts.put(color, newCount);
        
        if(newCount.intValue() > max) {
          sum = 0;
          max = newCount;
        }
        if(newCount.intValue() == max) {
          sum += color;
        }
      }
      
      void merge(Node other)
      {
        for(Map.Entry<Integer, Integer> entry : other.counts.entrySet())
          add(entry.getKey(), entry.getValue());
      }
    }
    
    private ArrayList<Integer>[] adj;
    long[] result;
    int[] c;
    
    Node dfs(int v, int p)
    {
      Node res = new Node();
      
      for(int child : adj[v]) {
        if(child == p) continue;
        
        Node cres = dfs(child, v);

        if(res.counts.size() < cres.counts.size()) {
          Node tmp = res;
          res = cres;
          cres = tmp;
        }
        res.merge(cres);
      }
      res.add(c[v], 1);
      
      result[v] = res.sum;
      
      return res;
    }

    @SuppressWarnings("unchecked")
    public void solve(int test, Reader input, PrintWriter out)
    {
        MyScanner in = new MyScanner(input);
        
        int n = in.nextInt();
        
        c = in.nextIntArray(n);
        
        adj = new ArrayList[n];
        
        result = new long[n];

        for(int i = 0; i < n; i++)
          adj[i] = new ArrayList<>();
        for(int i = 0; i < n - 1; i++) {
          int f = in.nextInt() - 1;
          int t = in.nextInt() - 1;
          adj[f].add(t);
          adj[t].add(f);
        }
        dfs(0, 0);
        
        for(int i = 0; i < n; i++) {
          if(i > 0) out.print(" ");
          out.print(result[i]);
        }
        out.println();
    }

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner(Reader reader) {
            br = new BufferedReader(reader);
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        
        int[] nextIntArray(int n)
        {
            int[] r = new int[n];
            for(int i = 0; i < n; i++)
                r[i] = nextInt();
            return r;
        }

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

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

        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    //--------------------------------------------------------

}
