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 sys
import random
from typing import NamedTuple

# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')

input = sys.stdin.readline


class Segment(NamedTuple):
	start: int
	end: int

	@property
	def size(self):
		return self.end - self.start + 1


def shuffle(a, sizes):
	n = len(a)
	assert len(sizes) > 1, len(sizes)
	assert sum(sizes) == len(a), (sum(sizes), n)
	result = [None for i in range(n)]
	offset = 0
	for size in sizes:
		assert size > 0, size
		segment = A[offset: offset + size]
		result[n - offset - size: n - offset] = segment
		offset += size
	return result

def split_into_segments(a):
	n = len(a)
	result = []
	size = 1
	for i in range(1, n):
		if a[i] == a[i-1] + 1:
			size += 1
		else:
			segment = Segment(start=a[i-size], end=a[i-1])
			result.append(segment)
			size = 1
	result.append(Segment(start=a[n-size], end=a[n-1]))

	assert sum(segment.size for segment in result) == n
	return result


N = int(input())
A = list(map(int, input().split()))

ans = []
segments = split_into_segments(A)

while len(segments) > 1:
	# print(A)
	# for segment in segments:
	# 	print(segment)
	K = len(segments)
	split = None
	for i in range(K-1):
		for j in range(i+1, K):
			if segments[i].start == segments[j].end + 1:
				split = list(filter(None, [
					sum(segments[k].size for k in range(i)) if i else 0,
					sum(segments[k].size for k in range(i, j)),
					segments[j].size,
					sum(segments[k].size for k in range(j+1, K)) if j != K - 1 else 0,
				]))
				break
		if split is not None:
			break
	# print("Fucking split is ", split)
	ans.append(split)
	A = shuffle(A, split)
	segments = split_into_segments(A)
	# print('============')

print(len(ans))
for operation in ans:
	print(len(operation), end=' ')
	print(' '.join(map(str, operation)))