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 PYTHON3):

Solution:
import math
import sys

from collections import deque
from typing import Deque, Dict, List, Optional, Set, Tuple

def data(): 
    return sys.stdin.buffer.readline().strip()

def mdata(): 
    return list(map(int, data().split()))

def outl(res): 
    sys.stdout.write(' '.join(map(str, res)) + '\n')

def out(var): 
    sys.stdout.write(str(var)+'\n')


def input_lst():
    return mdata()

def print_out(res):
    outl(res)


def main():
    n = int(data())
    a = mdata()
    a_pos = [0] * n
    for i in range(n):
        a[i] -= 1
        a_pos[a[i]] = i
    
    #print(a_pos)

    res = []
    d = True
    for i in range(n-1):
        # if (a_pos[i] == i): 
        #     continue
        
        res_str = []
        for j in range(i):
            res_str.append(1)

        a_i = a_pos[i]
        
        if a_i - i + 1 > 0:
            res_str.append(a_i - i + 1)        
        if (n - a_i - 1 > 0):
            res_str.append(n - a_i - 1)
        
        if not d:
            res_str.reverse()

        d = not d
        if len(res_str) > 1:
            res.append(res_str)
        
        for j in range(i, n):
            pos = a_pos[j]
           
            pos -= (i)
            pos = (n - i - pos)
            pos += ((a_i - i) + (n - i))
            pos %= (n-i)               
            pos += (i)        
            a_pos[j] = pos
        #print(a_pos)
    
    if not d:
        res.append([1]*n)

        
    print(len(res))
    for res_str in res:
        print(str(len(res_str)) + " " + " ".join(map(str, res_str)))

    
        

    #3 1 2 4
    #2 4 3 1
    #1 2 4 3

if __name__ == '__main__':
    main()