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.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;

public class Codeforces {


    static long MOD = 1_000_000_007L;
    static int MAX = -1 >>> 1;

    static void main2() throws Exception {
        int n = ni();
        int[] a = nia(n);
        Arrays.sort(a);
        for(int i = 0; i < n - 2; i++) {
            if(a[i] == a[i + 1] && a[i] == a[i + 2]) {
                println("NO");
                return;
            }
        }
        List<Integer> inc = new ArrayList<>();
        List<Integer> dec = new ArrayList<>();

        int prev = -1 >>> 1;
        for(int i = n - 1; i >= 0; i--) {
            if(a[i] != prev) {
                dec.add(a[i]);
            } else {
                inc.add(a[i]);
            }
            prev = a[i];
        }
        println("YES");
        println(inc.size());
        for(int i = inc.size() - 1; i >= 0; i--) {
            print(inc.get(i) + " ");
        }
        println();
        println(dec.size());
        for(int i = 0; i < dec.size(); i++) {
            print(dec.get(i) + " ");
        }
        println();
    }

    // ____________________________________________________________________________
    //|                                                                            |
    //|  /$$$$$$  /$$$$$$         /$$$$$$   /$$                /$$$$$$   /$$$$$$   |
    //| |_  $$_/ /$$__  $$       /$$__  $$ | $$               /$$__  $$ /$$__  $$  |
    //|   | $$  | $$  \ $$      | $$  \__//$$$$$$   /$$   /$$| $$  \__/| $$  \__/  |
    //|   | $$  | $$  | $$      |  $$$$$$|_  $$_/  | $$  | $$| $$$$    | $$$$      |
    //|   | $$  | $$  | $$       \____  $$ | $$    | $$  | $$| $$_/    | $$_/      |
    //|   | $$  | $$  | $$       /$$  \ $$ | $$ /$$| $$  | $$| $$      | $$        |
    //|  /$$$$$$|  $$$$$$/      |  $$$$$$/ |  $$$$/|  $$$$$$/| $$      | $$        |
    //| |______/ \______/        \______/   \___/   \______/ |__/      |__/        |
    //|____________________________________________________________________________|



    private static byte[] scannerByteBuffer = new byte[1024]; // Buffer of Bytes
    private static int scannerIndex;
    private static InputStream scannerIn;
    private static int scannerTotal;
    private static BufferedWriter printerBW;
    private static boolean DEBUG = false;

    private static int next() throws IOException { // Scan method used to scan buf
        if (scannerTotal < 0)
            throw new InputMismatchException();
        if (scannerIndex >= scannerTotal) {
            scannerIndex = 0;
            scannerTotal = scannerIn.read(scannerByteBuffer);
            if (scannerTotal <= 0)
                return -1;
        }
        return scannerByteBuffer[scannerIndex++];
    }

    static int ni() throws IOException {
        int integer = 0;
        int n = next();
        while (isWhiteSpace(n)) // Removing startPointing whitespaces
            n = next();
        int neg = 1;
        if (n == '-') { // If Negative Sign encounters
            neg = -1;
            n = next();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = next();
            } else
                throw new InputMismatchException();
        }
        return neg * integer;
    }

    static long nl() throws IOException {
        long integer = 0;
        int n = next();
        while (isWhiteSpace(n)) // Removing startPointing whitespaces
            n = next();
        int neg = 1;
        if (n == '-') { // If Negative Sign encounters
            neg = -1;
            n = next();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = next();
            } else
                throw new InputMismatchException();
        }
        return neg * integer;
    }

    static String line() throws IOException {
        StringBuilder sb = new StringBuilder();
        int n = next();
        while (isWhiteSpace(n))
            n = next();
        while (!isNewLine(n)) {
            sb.append((char) n);
            n = next();
        }
        return sb.toString();
    }

    private static boolean isNewLine(int n) {
        return n == '\n' || n == '\r' || n == -1;
    }

    private static boolean isWhiteSpace(int n) {
        return n == ' ' || isNewLine(n) || n == '\t';
    }

    static int[] nia(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        int[] array = new int[n];
        for (int i = 0; i < n; i++)
            array[i] = ni();
        return array;
    }

    static int[][] n2dia(int r, int c) throws Exception {
        if (r < 0 || c < 0)
            throw new Exception("Array size should be non negative");
        int[][] array = new int[r][c];
        for (int i = 0; i < r; i++)
            array[i] = nia(c);
        return array;
    }

    static long[] nla(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        long[] array = new long[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static float[] nfa(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        float[] array = new float[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static double[] nda(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        double[] array = new double[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static <T> void print(T ... str) {
        try {
            for (T ele : str)
                printerBW.append(ele.toString());
            if (DEBUG)
                flush();
        } catch (IOException e) {
            System.out.println(e.toString());
        }
    }

    static <T> void println(T ... str) {
        if (str.length == 0) {
            print('\n');
            return;
        }
        for (T ele : str)
            print(ele, '\n');
    }

    static void flush() throws IOException {
        printerBW.flush();
    }

    static void close() {
        try {
            printerBW.close();
        } catch (IOException e) {
            System.out.println(e.toString());
        }
    }

    public static void main(String[] args) throws Exception {
        long startPointTime = System.currentTimeMillis();
        scannerIn = System.in;
        printerBW = new BufferedWriter(new OutputStreamWriter(System.out));
        if (args.length > 0 && args[0].equalsIgnoreCase("debug")
                || args.length > 1 && args[1].equalsIgnoreCase("debug"))
            DEBUG = true;

        main2();
        long endTime = System.currentTimeMillis();
        float totalProgramTime = endTime - startPointTime;
        if (args.length > 0 && args[0].equalsIgnoreCase("time") || args.length > 1 && args[1].equalsIgnoreCase("time"))
            print("Execution time is " + totalProgramTime + " (" + (totalProgramTime / 1000) + "s)");
        close();
    }

    static class Pair <L, R> {
        L first;
        R second;

        Pair(L first, R second) {
            this.first = first;
            this.second = second;
        }

        public boolean equals(Object p2) {
            if (p2 instanceof Pair) {
                return ((Pair) p2).first.equals(first) && ((Pair) p2).second.equals(second);
            }
            return false;
        }

        public String toString() {
            return "(first=" + first.toString() + ",second=" + second.toString() + ")";
        }
    }

    static class DisjointSet {
        int[] arr;
        int[] size;

        DisjointSet(int n) {
            arr = new int[n + 1];
            size = new int[n + 1];
            makeSet();
        }

        void makeSet() {
            for (int i = 1; i < arr.length; i++) {
                arr[i] = i;
                size[i] = 1;
            }
        }

        void union(int i, int j) {
            if (i == j)
                return;
            if (i > j) {
                i ^= j;
                j ^= i;
                i ^= j;
            }

            i = find(i);
            j = find(j);

            if (i == j)
                return;
            arr[j] = arr[i];
            size[i] += size[j];
            size[j] = size[i];
        }

        int find(int i) {
            if (arr[i] != i) {
                arr[i] = find(arr[i]);
                size[i] = size[arr[i]];
            }
            return arr[i];
        }

        int getSize(int i) {
            i = find(i);
            return size[i];
        }

        public String toString() {
            return Arrays.toString(arr);
        }
    }

    static boolean isSqrt(double a) {
        double sr = Math.sqrt(a);
        return ((sr - Math.floor(sr)) == 0);
    }

    static long abs(long a) {
        return Math.abs(a);
    }

    static int min(int ... arr) {
        int min = Integer.MAX_VALUE;
        for (int var : arr)
            min = Math.min(min, var);
        return min;
    }

    static long min(long ... arr) {
        long min = Long.MAX_VALUE;
        for (long var : arr)
            min = Math.min(min, var);
        return min;
    }

    static int max(int... arr) {
        int max = Integer.MIN_VALUE;
        for (int var : arr)
            max = Math.max(max, var);
        return max;
    }

    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
}