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:
//package Codeforces.GlobalRound11;

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

public class D {
    public static int findPos(int[] arr, int ind)
    {
        int n = arr.length;
        for(int i=0;i<n;i++)
        {
            if(arr[i]==ind)
                return i;
        }
        return -1;
    }
    public static void swap1(int[] arr, int p)
    {
        int n = arr.length;
        int[] k = new int[n];
        int j= 0;

        for(int i=p+1;i<n;i++)
        {
            k[j] = arr[i];
            j++;
        }

        for(int i=0;i<=p;i++)
        {
            k[j] = arr[i];
            j++;
        }

        System.arraycopy(k, 0, arr, 0, n);
    }
    public static void swap2(int[] arr, int p1, int p2)
    {
        int n = arr.length;
        int[] arr1 = new int[n];
        int j = 0;
        for(int i=n-1;i>=p2;i--)
        {
            arr1[j] = arr[i];
            j++;
        }

        for(int i=p1;i<p2;i++)
        {
            arr1[j] = arr[i];
            j++;
        }

        for(int i=0;i<p1;i++)
        {
            arr1[j] = arr[i];
            j++;
        }

        System.arraycopy(arr1, 0, arr, 0, n);
    }
    public static void swap3(int[] arr, int p1, int p2)
    {
        int n = arr.length;
        int[] arr1 = new int[n];
        int j = 0;

        for(int i=p1+1;i<n;i++)
        {
            arr1[j] = arr[i];
            j++;
        }

        for(int i=p2+1;i<=p1;i++)
        {
            arr1[j] = arr[i];
            j++;
        }

        for(int i=p2;i>=0;i--)
        {
            arr1[j] = arr[i];
            j++;
        }

        System.arraycopy(arr1, 0, arr, 0, n);
    }
    public static void main(String[] args) throws IOException {
        Soumit sc = new Soumit();

        int n = sc.nextInt();
        int[] arr = sc.nextIntArray(n);

        int count = 0;
        StringBuilder sb = new StringBuilder();

        int pos1 = findPos(arr, 1);
        if(pos1!=n-1)
        {
            count++;
            sb.append("2 ");
            swap1(arr, pos1);
            sb.append(pos1+1).append(" ").append(n - pos1 - 1).append("\n");
        }

        for(int i=2;i<n;i++)
        {
            count++;
            int p = findPos(arr, i);
            int p1 = findPos(arr, i-1);
            if(i%2==0)
            {
                if(p==0)
                {
                    sb.append(i).append(" ");
                    sb.append(p1-p).append(" ");
                    for(int j=1;j<i;j++)
                        sb.append("1 ");
                }
                else
                {
                    sb.append(i+1).append(" ");
                    sb.append(p).append(" ");
                    sb.append(p1-p).append(" ");
                    for(int j=1;j<i;j++)
                        sb.append("1 ");
                }
                sb.append("\n");
                swap2(arr, p, p1);
            }
            else
            {
                if(p==n-1)
                {
                    sb.append(i).append(" ");
                    for(int j=1;j<i;j++)
                        sb.append("1 ");
                    sb.append(p-p1).append(" ");
                }
                else
                {
                    sb.append(i+1).append(" ");
                    for(int j=1;j<i;j++)
                        sb.append("1 ");
                    sb.append(p-p1).append(" ");
                    sb.append(n-p-1).append(" ");
                }
                sb.append("\n");
                swap3(arr, p, p1);
            }
        }

        if(n%2==0)
        {
            count++;
            sb.append(n).append(" ");
            for(int i=0;i<n;i++)
                sb.append("1 ");
            sb.append("\n");
        }

        System.out.println(count);
        System.out.println(sb);

        sc.close();
    }

    static class Soumit {
        final private int BUFFER_SIZE = 1 << 18;
        final private DataInputStream din;
        final private byte[] buffer;
        private PrintWriter pw;
        private int bufferPointer, bytesRead;
        StringTokenizer st;

        public Soumit() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Soumit(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public void streamOutput(String file) throws IOException {
            FileWriter fw = new FileWriter(file);
            BufferedWriter bw = new BufferedWriter(fw);
            pw = new PrintWriter(bw);
        }

        public void println(String a) {
            pw.println(a);
        }

        public void print(String a) {
            pw.print(a);
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[100064]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

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

        public int[] nextIntArray(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }

            return arr;
        }

        public long[] nextLongArray(int n) throws IOException {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }

            return arr;
        }

        public double[] nextDoubleArray(int n) throws IOException {
            double[] arr = new double[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextDouble();
            }

            return arr;
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            /*if (din == null)
                return;*/
            if (din != null) din.close();
            if (pw != null) pw.close();
        }
    }
}