Problem: You are given a deck of n cards numbered from 1 to n (not necessarily in this order in the deck). You have to sort the deck by repeating the following operation. 

  * Choose 2 ≤ k ≤ n and split the deck in k nonempty contiguous parts D_1, D_2,..., D_k (D_1 contains the first |D_1| cards of the deck, D_2 contains the following |D_2| cards and so on). Then reverse the order of the parts, transforming the deck into D_k, D_{k-1}, ..., D_2, D_1 (so, the first |D_k| cards of the new deck are D_k, the following |D_{k-1}| cards are D_{k-1} and so on). The internal order of each packet of cards D_i is unchanged by the operation. 



You have to obtain a sorted deck (i.e., a deck where the first card is 1, the second is 2 and so on) performing at most n operations. It can be proven that it is always possible to sort the deck performing at most n operations.

Examples of operation: The following are three examples of valid operations (on three decks with different sizes). 

  * If the deck is [3 6 2 1 4 5 7] (so 3 is the first card and 7 is the last card), we may apply the operation with k=4 and D_1=[3 6], D_2=[2 1 4], D_3=[5], D_4=[7]. Doing so, the deck becomes [7 5 2 1 4 3 6]. 
  * If the deck is [3 1 2], we may apply the operation with k=3 and D_1=[3], D_2=[1], D_3=[2]. Doing so, the deck becomes [2 1 3]. 
  * If the deck is [5 1 2 4 3 6], we may apply the operation with k=2 and D_1=[5 1], D_2=[2 4 3 6]. Doing so, the deck becomes [2 4 3 6 5 1]. 

Input

The first line of the input contains one integer n (1≤ n≤ 52) — the number of cards in the deck.

The second line contains n integers c_1, c_2, ..., c_n — the cards in the deck. The first card is c_1, the second is c_2 and so on.

It is guaranteed that for all i=1,...,n there is exactly one j∈\{1,...,n\} such that c_j = i.

Output

On the first line, print the number q of operations you perform (it must hold 0≤ q≤ n).

Then, print q lines, each describing one operation.

To describe an operation, print on a single line the number k of parts you are going to split the deck in, followed by the size of the k parts: |D_1|, |D_2|, ... , |D_k|. 

It must hold 2≤ k≤ n, and |D_i|≥ 1 for all i=1,...,k, and |D_1|+|D_2|+⋅⋅⋅ + |D_k| = n.

It can be proven that it is always possible to sort the deck performing at most n operations. If there are several ways to sort the deck you can output any of them.

Examples

Input


4
3 1 2 4


Output


2
3 1 2 1
2 1 3


Input


6
6 5 4 3 2 1


Output


1
6 1 1 1 1 1 1


Input


1
1


Output


0

Note

Explanation of the first testcase: Initially the deck is [3 1 2 4]. 

  * The first operation splits the deck as [(3) (1 2) (4)] and then transforms it into [4 1 2 3]. 
  * The second operation splits the deck as [(4) (1 2 3)] and then transforms it into [1 2 3 4]. 

Explanation of the second testcase: Initially the deck is [6 5 4 3 2 1]. 

  * The first (and only) operation splits the deck as [(6) (5) (4) (3) (2) (1)] and then transforms it into [1 2 3 4 5 6]. 

Solution (in JAVA):

Solution:
import java.io.*;
import java.lang.reflect.Array;
import java.util.*;

public class D {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

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

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            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 = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    static FastReader s = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    private static int[] rai(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
        }
        return arr;
    }

    private static int[][] rai(int n, int m) {
        int[][] arr = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextInt();
            }
        }
        return arr;
    }

    private static long[] ral(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextLong();
        }
        return arr;
    }

    private static long[][] ral(int n, int m) {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextLong();
            }
        }
        return arr;
    }

    private static int ri() {
        return s.nextInt();
    }

    private static long rl() {
        return s.nextLong();
    }

    private static String rs() {
        return s.next();
    }

//    static int MOD=1000000007;




    public static void main(String[] args) {
        StringBuilder ans = new StringBuilder();
//        int t = ri();
        int t=1;
        while(t-- >0) {
            int n=ri();
            int[] arr=rai(n);
            if(n==1)
            {
                ans.append("0\n");
                continue;
            }

            int valFind=n-1;
            int count=0;
            HashSet<Integer> set=new HashSet<>();
            for(int i=1;i<n-1;i++)
            {
                set.add(i);
            }

            List<List<Integer>> list=new ArrayList<>();
            while(true)
            {
//                System.out.println(Arrays.toString(arr));
                boolean flag=true;
                for(int i=1;i<n;i++)
                {
                    if(arr[i]<arr[i-1])
                    {
                        flag=false;
                    }
                }
                if(flag)
                {
                    break;
                }

                int val=arr[n-1];
                int ind=n-1;
                for(int i=n-1;i>=0;i--){
                    if(arr[i]!=i+1)
                    {
                        val=arr[i];
                        ind=i;
                        break;
                    }
                }


                int pos=-1;
                for(int i=0;i<n;i++)
                {
                    if(arr[i]==val+1)
                    {
                        pos=i;
                        break;
                    }
                }
                List<Integer> mid=new ArrayList<>();
                int[] next=new int[n];
                int curr=-1;
                if(pos!=0) {
                    mid.add(pos);
                }
                int index=ind-1;
                while(true)
                {
                    if(arr[index]==arr[index+1]-1)
                    {
                        index--;
                    }
                    else
                    {
                        break;
                    }
                }
                mid.add(index+1-pos);

                mid.add(ind-index);
                if(n-ind-1>0) {
                    mid.add(n-ind-1);
                }



//                System.out.println("mid="+mid);
                list.add(new ArrayList<>(mid));

                int x=0;
                int posi=n;
                for(int j=mid.size()-1;j>=0;j--)
                {
                    int len=mid.get(j);
                    for(int i=posi-len;i<posi;i++)
                    {
//                        System.out.print(i+" ");
                        next[x]=arr[i];
                        x++;

                    }
//                    System.out.println();

                    posi=posi-len;
//                    last=
                }
                
                arr=next;
                count++;
//                System.out.println("next="+Arrays.toString(next));




            }
            ans.append(count).append("\n");
//            System.out.println(list);
            for(List<Integer> l:list)
            {
                ans.append(l.size()).append(" ");
                for(int i:l)
                {
                    ans.append(i).append(" ");
                }
                ans.append("\n");
            }

        }
        out.print(ans.toString());
        out.flush();

    }




}