Problem: Two integer sequences existed initially — one of them was strictly increasing, and the other one — strictly decreasing.

Strictly increasing sequence is a sequence of integers [x_1 < x_2 < ... < x_k]. And strictly decreasing sequence is a sequence of integers [y_1 > y_2 > ... > y_l]. Note that the empty sequence and the sequence consisting of one element can be considered as increasing or decreasing.

They were merged into one sequence a. After that sequence a got shuffled. For example, some of the possible resulting sequences a for an increasing sequence [1, 3, 4] and a decreasing sequence [10, 4, 2] are sequences [1, 2, 3, 4, 4, 10] or [4, 2, 1, 10, 4, 3].

This shuffled sequence a is given in the input.

Your task is to find any two suitable initial sequences. One of them should be strictly increasing and the other one — strictly decreasing. Note that the empty sequence and the sequence consisting of one element can be considered as increasing or decreasing.

If there is a contradiction in the input and it is impossible to split the given sequence a to increasing and decreasing sequences, print "NO".

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a.

The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 2 ⋅ 10^5), where a_i is the i-th element of a.

Output

If there is a contradiction in the input and it is impossible to split the given sequence a to increasing and decreasing sequences, print "NO" in the first line.

Otherwise print "YES" in the first line and any two suitable sequences. Note that the empty sequence and the sequence consisting of one element can be considered as increasing or decreasing.

In the second line print n_i — the number of elements in the strictly increasing sequence. n_i can be zero, in this case the increasing sequence is empty.

In the third line print n_i integers inc_1, inc_2, ..., inc_{n_i} in the increasing order of its values (inc_1 < inc_2 < ... < inc_{n_i}) — the strictly increasing sequence itself. You can keep this line empty if n_i = 0 (or just print the empty line).

In the fourth line print n_d — the number of elements in the strictly decreasing sequence. n_d can be zero, in this case the decreasing sequence is empty.

In the fifth line print n_d integers dec_1, dec_2, ..., dec_{n_d} in the decreasing order of its values (dec_1 > dec_2 > ... > dec_{n_d}) — the strictly decreasing sequence itself. You can keep this line empty if n_d = 0 (or just print the empty line).

n_i + n_d should be equal to n and the union of printed sequences should be a permutation of the given sequence (in case of "YES" answer).

Examples

Input


7
7 2 7 3 3 1 4


Output


YES
2
3 7 
5
7 4 3 2 1 


Input


5
4 3 1 5 3


Output


YES
1
3 
4
5 4 3 1 


Input


5
1 1 2 1 2


Output


NO


Input


5
0 1 2 3 4


Output


YES
0

5
4 3 2 1 0 

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.Reader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Ruins He
 */
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);
    TaskG solver = new TaskG();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskG {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
      int n = in.nextInt();
      int[] arr = in.nextInts(n);

      List<Integer> increasing = new ArrayList<>();
      List<Integer> decreasing = new ArrayList<>();

      for (int i = 0; i < n; i++) {
        boolean b1 = increasing.size() == 0 || arr[increasing.get(increasing.size() - 1)] < arr[i];
        boolean b2 = decreasing.size() == 0 || arr[decreasing.get(decreasing.size() - 1)] > arr[i];
        if (b1 && b2) {
          if (i == n - 1 || arr[i] < arr[i + 1]) {
            increasing.add(i);
          } else {
            decreasing.add(i);
          }
        } else if (b1) {
          increasing.add(i);
        } else if (b2) {
          decreasing.add(i);
        } else {
          out.println("NO");
          return;
        }
      }

      int[] answers = new int[n];
      Arrays.fill(answers, 1);
      for (int a : increasing) {
        answers[a] = 0;
      }
      out.println("YES");
      out.printInts(answers);
    }

  }

  static class OutputWriter {
    private final PrintWriter writer;

    private OutputWriter(Writer writer, boolean autoFlush) {
      this.writer = new PrintWriter(new BufferedWriter(writer, 32767), autoFlush);
    }

    public OutputWriter(Writer writer) {
      this(writer, true);
    }

    public OutputWriter(OutputStream outputStream) {
      this(new OutputStreamWriter(outputStream), false);
    }

    public OutputWriter println() {
      writer.println();
      return this;
    }

    public OutputWriter println(String string) {
      writer.println(string);
      return this;
    }

    public OutputWriter print(int value) {
      writer.print(value);
      return this;
    }

    public OutputWriter print(Object object) {
      writer.print(object);
      return this;
    }

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

    public void printInts(int[] values) {
      for (int i = 0; i < values.length; i++) {
        if (i > 0) print(" ");
        print(values[i]);
      }
      println();
    }

  }

  static class InputReader {
    public final BufferedReader reader;
    public StringTokenizer tokenizer = null;

    public InputReader(Reader reader) {
      this.reader = new BufferedReader(reader, 32767);
    }

    public InputReader(InputStream inputStream) {
      this(new InputStreamReader(inputStream));
    }

    public String next() {
      if (hasNext()) return tokenizer.nextToken();
      else throw new NoSuchElementException();
    }

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

    public int[] nextInts(int n) {
      int[] res = new int[n];
      for (int i = 0; i < n; i++) res[i] = nextInt();
      return res;
    }

    public boolean hasNext() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          String nextLine = reader.readLine();
          if (nextLine == null) return false;
          tokenizer = new StringTokenizer(nextLine);
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.hasMoreTokens();
    }

  }
}