D. Unshuffling a Decktime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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 \le k \le n and split the deck in k nonempty contiguous parts D_1, D_2,\dots, 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}, \dots, 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]. InputThe first line of the input contains one integer n (1\le n\le 52)  — the number of cards in the deck.The second line contains n integers c_1, c_2, \dots, 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,\dots,n there is exactly one j\in\{1,\dots,n\} such that c_j = i.OutputOn the first line, print the number q of operations you perform (it must hold 0\le q\le 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|, \dots , |D_k|. It must hold 2\le k\le n, and |D_i|\ge 1 for all i=1,\dots,k, and |D_1|+|D_2|+\cdots + |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.ExamplesInput
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
NoteExplanation 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]. 
4
3 1 2 4

2 3 1 2 1 2 1 3 
['constructive algorithms', 'implementation', '*2000']