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 javafx.util.Pair;

import java.io.*;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        __SolutionBase begin = new __SolutionBase();
        begin.Solve();
    }
}

class __SolutionBase {

    public void Solve() {
        init();
        Solution();
        out.close();
    }

    private final int INF = -1000500;

    private void Solution() {

        int n = readInt();

        int[] input = new int[n];

        for (int i = 0;i < n;i++) input[i] = readInt();

        HashSet<Integer> one = new HashSet<>();
        HashSet<Integer> two = new HashSet<>();

        for (int i = 0; i< n;i++){
            if (!one.contains(input[i]))
                one.add(input[i]);
            else if (!two.contains(input[i]))
                two.add((input[i]));
            else{
                out.println("NO");
                return;
            }
        }

        List<Integer> oness = new ArrayList<>();

        for (int elem :one)
            oness.add(elem);

        oness.sort((o1,o2) -> o1.compareTo(o2));

        List<Integer> twoss = new ArrayList<>();

        for (int elem :two)
            twoss.add(elem);

        twoss.sort((o1,o2) -> -o1.compareTo(o2));

        out.println("YES");

        out.println(oness.size());

        for ( int elem:oness)
            out.print(elem + " ");

        out.println('\n' + "" + twoss.size());

        for (int elem:twoss)
            out.print(elem + " ");

    }

    /**
     * readLong, readDouble and other are similar
     *
     * @return int type from input
     */
    private int readInt() {
        return Integer.parseInt(readString());
    }

    private long readLong() {
        return Long.parseLong(readString());
    }
    /**
     * Tokens are separated by space or endExclusive of line
     *
     * @return non-empty string token from input (or null if there is no any token)
     */
    private String readString() {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine) return null;
            tok = new StringTokenizer(nextLine);
        }

        return tok.nextToken();
    }

    /**
     * @return whole line from input
     */
    private String readLine() {
        try {
            return in.readLine();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }
    private BufferedReader in;
    private PrintWriter out;
    private StringTokenizer tok = new StringTokenizer(" ");

    /**
     * For local testing I use pair 'input.txt'/'output.txt' in the project root
     */
    private void init() {
        try {
            in = new BufferedReader(new FileReader("lepus.in"));
            out = new PrintWriter("lepus.out");
        } catch (FileNotFoundException e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
    }
}