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:
from sys import stdin, stdout

# ( A )(9 10 11)(      8)( B )
# ( B )(      8)(9 10 11)( A )
def unshuffling_a_deck(n, c_a):

    res_a = []
    while True:
        dic = {}
        a = b = c = -1
        for i in range(n):
            if c_a[i] in dic:
                a = dic[c_a[i]]
                c = i
                break

            dic[c_a[i]-1] = i

        if a == -1:
            break

        b = a + 1
        while b < c and c_a[b] - 1 == c_a[b-1]:
            b += 1

        q = []
        res = []
        if a-1 >= 0:
            q.append(c_a[0:a])
            res.append(len(q[-1]))
        if b-1 >= a:
            q.append(c_a[a:b])
            res.append(len(q[-1]))
        if c >= b:
            q.append(c_a[b:c+1])
            res.append(len(q[-1]))
        if n-1 >= c+1:
            q.append(c_a[c+1:n])
            res.append(len(q[-1]))

        #stdout.write(str(len(res)))
        #for v in res:
        #    stdout.write(' ' + str(v))
        #stdout.write('\n')
        s = str(len(res))
        for v in res:
            s += ' ' + str(v)
        res_a.append(s)

        # block reverse
        q.reverse()
        idx = 0
        for bl in q:
            for v in bl:
                c_a[idx] = v
                idx += 1

        #print(q)
        #print(c_a)

    return res_a

n = int(stdin.readline())
c_a = list(map(int, stdin.readline().split()))

res_a = unshuffling_a_deck(n, c_a)
stdout.write(str(len(res_a)) + '\n')
stdout.write('\n'.join(res_a))