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.io.*;

public class test {

    public static void main (String[] args) {
        InputReader in = new InputReader(System.in);      //creating input reader
        PrintWriter w = new PrintWriter(System.out);     //creating writer

        int n = in.nextInt();
        HashMap<Integer, Integer> hm = new HashMap<>();
        for (int i = 0; i < n; i++) {
            int temp = in.nextInt();
            if (!hm.containsKey(temp))
                hm.put(temp, 0);
            hm.put(temp, hm.get(temp) + 1);

        }
        ArrayList<Integer> inc = new ArrayList<>(), dec = new ArrayList<>();
        boolean ok = true;
        for (int x : hm.keySet()) {
            if (hm.get(x) >= 3) {
                ok = false;
                break;
            } else if (hm.get(x) == 2) {
                inc.add(x);
                dec.add(x);
            } else
                inc.add(x);
        }
        if (!ok) {
            w.println("NO");
            w.close();
            return;
        }
        Collections.sort(inc);
        Collections.sort(dec);
        w.println("YES");
        w.println(inc.size());
        for (int x : inc)
            w.print(x + " ");
        w.println();
        w.println(dec.size());
        for (int i = 0; i < dec.size(); i++)
            w.print(dec.get(dec.size() - 1 - i) + " ");


        w.close();
    }
    //definging class treeNode
    static  class TreeNode {
        int val;
        TreeNode left;
        TreeNode right;
        TreeNode(int x) { val = x; }
    }
    static TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {

        // Stack for tree traversal
        Deque<TreeNode> stack = new ArrayDeque<>();

        // HashMap for parent pointers
        Map<TreeNode, TreeNode> parent = new HashMap<>();

        parent.put(root, null);
        stack.push(root);

        // Iterate until we find both the nodes p and q
        while (!parent.containsKey(p) || !parent.containsKey(q)) {

            TreeNode node = stack.pop();

            // While traversing the tree, keep saving the parent pointers.
            if (node.left != null) {
                parent.put(node.left, node);
                stack.push(node.left);
            }
            if (node.right != null) {
                parent.put(node.right, node);
                stack.push(node.right);
            }
        }

        // Ancestors set() for node p.
        Set<TreeNode> ancestors = new HashSet<>();

        // Process all ancestors for node p using parent pointers.
        while (p != null) {
            ancestors.add(p);
            p = parent.get(p);
        }

        // The first ancestor of q which appears in
        // p's ancestor set() is their lowest common ancestor.
        while (!ancestors.contains(q))
            q = parent.get(q);
        return q;
    }
    static int calculatePro(ArrayList<Integer> al) {
        int pro = 1;
        for (int x : al)
            pro *= x;
        return pro;
    }
    static class Obj implements Comparable<Obj> {
        String key;
        int frequency;
        Obj(String key, int freq) {
            this.key = key;
            this.frequency = freq;
        }
        public int compareTo(Obj O) {
            if (this.key.equals(O.key))
                return 0;
            if (this.frequency == O.frequency)
                return this.key.compareTo(O.key);
            return O.frequency - this.frequency;
        }
        public String toString() {
            return key + ":" + frequency;
        }
    }
    static int findMin(int[] a) {
        int ans = a.length - 1;
        for (int x : a)
            if (x > -1)
                ans = Math.min(ans, x);
        return ans;
    }
    static long pow(long x, long p, long mod) {
        long ans = 1;
        x %= mod;
        while (p > 0) {
            if (p % 2 == 1)
                ans = (ans * x) % mod;
            x = (x * x) % mod;
            p /= 2;
        }
        return ans;
    }
    static boolean nextPermutation(int[] a) {
        int n = a.length;
        int ptr = n - 1;
        while (ptr > 0 && a[ptr - 1] >= a[ptr]) {
            ptr--;
        }

        for (int i = ptr, j = n - 1; i < j; i++, j--) {
            int tmp = a[i];
            a[i] = a[j];
            a[j] = tmp;
        }

        if (ptr == 0) {
            return false;
        }

        for (int i = ptr;; i++) {
            if (a[ptr - 1] < a[i]) {
                int tmp = a[ptr - 1];
                a[ptr - 1] = a[i];
                a[i] = tmp;
                return true;
            }
        }
    }
    static int fibo(int n) {
        if (n == 1 || n == 2)
            return 1;
        return fibo(n - 1) + fibo(n - 2);
    }
    /*static int fibo(int n) {
        if (n == 0)
            return 0;
        if (n == 1 || n == 2)
            return f[n] = 1;
        if (f[n] != 0)
            return f[n];
        if (n % 2 == 0) {
            int k = (n) / 2;
            return f[n] = (fibo(k - 1) * 2 + fibo(k)) * fibo(k);
        } else {
            int k = (n + 1) / 2;
            return f[n] = fibo(k - 1) * fibo(k - 1) + fibo(k) * fibo(k);
        }
    }*/
    static class Edge implements Comparable<Edge> {
        int from, to, cost;
        Edge(int from, int to, int cost) {
            this.from = from;
            this.to = to;
            this.cost = cost;
        }
        public int compareTo(Edge O) {
            return this.cost - O.cost;
        }
    }
    static String swap(String s, int i, int j) {
        char[] ca = s.toCharArray();
        char temp = ca[i];
        ca[i] = ca[j];
        ca[j] = temp;
        return new String(ca);
    }
    static void findMissExtra(int[] a) {
        HashSet<Integer> hs = new HashSet<>();
        int n = a.length, extra = 0, miss = 0;
        for (int i = 0; i < n; i++) {
            if (hs.contains(a[i]))
                extra = a[i];
            hs.add(a[i]);

        }
        for (int i = 1; i <= n; i++) {
            if (!hs.contains(i)) {
                miss = i;
                break;
            }
        }
        System.out.println(miss + ", " + extra);
    }
    static void find(int m, int s) {
        if (s == 0 || s > m * 9) {
            System.out.println("Impossible");
            return ;
        }
        s -= 1;
        int[] num = new int[m];
        for (int i = m - 1; i > 0; i--) {
            int temp = Math.min(s, 9);
            num[i] = temp;
            s -= temp;
        }
        num[0] += s + 1;
        for (int x : num)
            System.out.print(x);
    }
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

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

        public int read() {
            if (numChars == -1)
                throw new UnknownError();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int peek() {
            if (numChars == -1)
                return -1;
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar];
        }

        public void skip(int x) {
            while (x-- > 0)
                read();
        }

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

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

        public String nextString() {
            return next();
        }

        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        public String nextLine() {
            StringBuffer buf = new StringBuffer();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r')
                    buf.appendCodePoint(c);
                c = read();
            }
            return buf.toString();
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }
        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
        public boolean hasNext() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1)
                read();
            return value != -1;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}