There is a tree with N vertices, numbered 1 through N. The i-th of the N-1 edges connects vertices a_i and b_i.

Currently, there are A_i stones placed on vertex i. Takahashi and Aoki will play a game using this tree.

First, Takahashi will select a vertex and place a piece on it. Then, starting from Takahashi, they will alternately perform the following operation:

* Remove one stone from the vertex currently occupied by the piece.
* Then, move the piece to a vertex that is adjacent to the currently occupied vertex.



The player who is left with no stone on the vertex occupied by the piece and thus cannot perform the operation, loses the game. Find all the vertices v such that Takahashi can place the piece on v at the beginning and win the game.

Constraints

* 2 ≦ N ≦ 3000
* 1 ≦ a_i,b_i ≦ N
* 0 ≦ A_i ≦ 10^9
* The given graph is a tree.

Input

The input is given from Standard Input in the following format:


N
A_1 A_2 … A_N
a_1 b_1
:
a_{N-1} b_{N-1}


Output

Print the indices of the vertices v such that Takahashi can place the piece on v at the beginning and win the game, in a line, in ascending order.

Examples

Input

3
1 2 3
1 2
2 3


Output

2


Input

5
5 4 1 2 3
1 2
1 3
2 4
2 5


Output

1 2


Input

3
1 1 1
1 2
2 3


Output
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.Collection;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Queue;
import java.util.ArrayDeque;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author ilyakor
 */
public class Main {

  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    OutputWriter out = new OutputWriter(outputStream);
    TaskF solver = new TaskF();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskF {

    int n;
    int[] w;
    ArrayList<Integer>[] g;
    ArrayList<Integer>[] gr;

    public void solve(int testNumber, InputReader in, OutputWriter out) {
      n = in.nextInt();
      w = new int[n];
      for (int i = 0; i < n; ++i) {
        w[i] = in.nextInt();
      }
      g = new ArrayList[n];
      gr = new ArrayList[n];
      for (int i = 0; i < n; ++i) {
        g[i] = new ArrayList<>();
        gr[i] = new ArrayList<>();
      }
      for (int i = 0; i < n - 1; ++i) {
        int x = in.nextInt() - 1;
        int y = in.nextInt() - 1;
        if (w[x] < w[y]) {
          g[y].add(x);
          gr[x].add(y);
        }
        if (w[x] > w[y]) {
          g[x].add(y);
          gr[y].add(x);
        }
      }

      int[] d = new int[n];
      int[] deg = new int[n];
      for (int i = 0; i < n; ++i) {
        deg[i] = g[i].size();
      }
      Queue<Integer> q = new ArrayDeque<>();
      for (int i = 0; i < n; ++i) {
        if (g[i].size() == 0) {
          d[i] = -1;
          q.add(i);
        }
      }
      while (!q.isEmpty()) {
        int x = q.poll();
        if (d[x] == -1) {
          for (int y : gr[x]) {
            if (d[y] != 0) {
              continue;
            }
            d[y] = 1;
            q.add(y);
          }
        } else {
          for (int y : gr[x]) {
            if (d[y] != 0) {
              continue;
            }
            --deg[y];
            if (deg[y] == 0) {
              d[y] = -1;
              q.add(y);
            }
          }
        }
      }
      for (int i = 0; i < n; ++i) {
        if (d[i] == 1) {
          out.print((i + 1) + " ");
        }
      }
      out.printLine();
    }

  }

  static class InputReader {

    private InputStream stream;
    private byte[] buffer = new byte[10000];
    private int cur;
    private int count;

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

    public static boolean isSpace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

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

    public int readSkipSpace() {
      int c;
      do {
        c = read();
      } while (isSpace(c));
      return c;
    }

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

  }

  static class OutputWriter {

    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
      writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void printLine(Object... objects) {
      print(objects);
      writer.println();
    }

    public void close() {
      writer.close();
    }

  }
}

