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.*;
import java.math.*;
import java.util.BitSet;
public class population
{


     static int MAXN=5*1000001; static int arr[]=new int[MAXN];
    static int spf[] = new int[MAXN]; 
   
    static int power(int x, int y) 
    { 
     
    int res = 1;  
  
    while (y > 0)  
    { 
       
        if ((y & 1) == 1) 
            res = res * x; 
  
        
        y = y >> 1;
        x = x * x;
    } 
    return res; 
    } 


    static void sieveOfEratosthenes(boolean prime[],int n) 
    { 
        for(int i=0;i<n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p*p <=n; p++) 
        { 
            
            if(prime[p] == true) 
            { 
        
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 
    }
    
     
    static int gcd(int a, int b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 


     private static void union(int[] parent,int src,int dest)
    {
        int a = find(parent,src);
        int b = find(parent,dest);
        if(a!=b)
        parent[a]=b;
        return;
    }
    private static int find(int[] parent, int source) 
    {
        if(parent[source]==-1)
        return source;
        return find(parent,parent[source]);
    }
    

    public static void main(String ag[])
    {
       FastReader sc=new FastReader();
        /*ArrayList<Integer> al=new ArrayList<Integer>();*/ 
        /*String s=sc.nextLine();*/
        //hm.containsKey(); hm.get(k); hm.put(k,v); HashMap<Integer,Integer> hm=new HashMap<>();
        /*String[] arrOfStr = s.split(" "); */
        /*boolean visited[]=new boolean[arrOfStr.length];*/
        //Scanner sc=new Scanner(System.in);
        int j,i;
        int n=sc.nextInt();
        int arr[]=new int[n];
         boolean flag=true;
         int f[]=new int[200001];
        for(i=0;i<n;i++)
        {
          arr[i]=sc.nextInt();
          f[arr[i]]++;
          if(f[arr[i]]>2)
          {
              flag=false;
          }   
        }
       
        Arrays.sort(arr);
        ArrayList<Integer> al=new ArrayList<>();
        ArrayList<Integer> bl=new ArrayList<>();
        
        

        for(i=0;i<n;i++)
        {
        
        
            if(i<n-1&&arr[i]==arr[i+1])
            {
                
                al.add(arr[i]);
                
                
                
               
            }
            else
            {
                bl.add(arr[i]);
               
               
            }
        }
       
        if(flag==false)
        System.out.println("NO");
        else
        {
            System.out.println("YES");
            System.out.println(al.size());
            
            for(i=0;i<al.size();i++)
            System.out.print(al.get(i)+" ");
            System.out.println();
            System.out.println(bl.size());
           
            for(i=bl.size()-1;i>=0;i--)
            System.out.print(bl.get(i)+" ");
        }
    } 
   
   
   
   public static void sieves() 
    { 
        spf[1] = 1; 
        for (int i=2; i<MAXN; i++) 
            spf[i] = i; 
        for (int i=4; i<MAXN; i+=2) 
            spf[i] = 2; 
        for (long i=3; i*i<MAXN; i++) 
        { 
            if (spf[(int)i] == i) 
            { 
                for (long j=i*i; j<MAXN; j+=i) 
                    if (spf[(int)j]==j) 
                        spf[(int)j] = (int)i; 
            } 
        } 
    } 
    static void getFactorizations(int x) 
    { 
        int num=x;
        while (x != 1) 
        { 
            arr[num]++;
            x = x / spf[x]; 
        }
    } 
}

class Edge
{
    int v,w;
    Edge(int v,int w)
    {
        this.v=v;
        this.w=w;
    }
}

class Graph
{
    int V;
    int E;
    boolean visited[];
    ArrayList<Edge> adjLists[];
    BitSet bs;
    HashSet<Integer> hs[];
 
    Graph(int V,int E)
    {
        this.V=V;
        this.E=E;
        visited=new boolean[V+1];
        adjLists=new ArrayList[V+1];
        bs=new BitSet(V+1); 
        hs=new HashSet[V+1];      
        for (int i = 0; i <=V; i++)
        {
            adjLists[i]=new ArrayList<Edge>();
            hs[i]=new HashSet<Integer>();
        }
        
    }
 

    public void addEdge(int s,int d)
    {
        
        Edge e=new Edge(d,0);
        adjLists[s].add(e);
        Edge e1=new Edge(s,0);
        adjLists[d].add(e1);
       
    }


    public void DFS(int v) 
    { 
    Iterator<Edge> i = adjLists[v].listIterator(); 
    while (i.hasNext()) 
    { 
        Edge e=i.next();
        int n = e.v; 
       
        if (bs.get(n)==false) 
        {
          hs[v].add(n);
          bs.set(n);
          DFS(n);    
        }
       
    } 
    }
    
    public boolean isEulerCircuit()
    {
       for(int i=1;i<=V;i++)
       {
           if(bs.get(i)==false||adjLists[i].size()%2!=0)
           return false;
       } 
       return true;
    }
    public void BFS()
    {
        Queue<Edge> q=new LinkedList<>();
        int price[]=new int[V+1];
        Arrays.fill(price,Integer.MAX_VALUE);
        q.add(new Edge(1,0));
        price[1]=0;
        while(!q.isEmpty())
        {
            Edge e=q.poll();
            int cost=e.w;
            if(e.v!=V)
            {
             for(Edge s:adjLists[e.v])
            {
            if(cost+s.w<price[s.v])
            {
                price[s.v]=cost+s.w;
                q.add(new Edge(s.v,cost+s.w));
            }    
            }   
            }
            
        }
        if(price[V]==Integer.MAX_VALUE)
        System.out.println(-1);
        else
        System.out.println(price[V]);
    } 
  
}


class Tcomp implements Comparator<Node>
{
    @Override
    public int compare(Node e1, Node e2) {
        if(e1.e<e2.e)
        {
        return 1;
        }
        else if(e1.e>e2.e)
        {
            return -1;
        }
        if(e1.d<e2.d)
        {
            return 1;
        }
        else if(e1.d>e2.d)
        {
            return -1;
        }

       if(e1.b<e2.b)
        {
            return 1;
        }
        else if(e1.b>e2.b)
        {
            return -1;
        }

        if(e1.a<e2.a)
        {
            return 1;
        }
       else
       {
           return -1;
       }
    }
    
}


class Node
{
    int a;
    int b;
    int c;
    int d;
    int e;
    Node(int a,int b,int c,int d,int e)
    {
        this.a=a;
        this.b=b;
        this.c=c;
        this.d=d;
        this.e=e;
       
        
    }
}


class FastReader {

    BufferedReader bf;
    StringTokenizer st;

    public FastReader() {
        bf = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(bf.readLine());
            } catch (Exception e) {
                System.out.println(e);
            }
        }
        return st.nextToken();
    }

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

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

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        String str = "";
        try {
            str = bf.readLine();
        } catch (Exception e) {
            System.out.println(e);
        }
        return str;
    }
}