CF1427D.Unshuffling a Deck

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 $2 \le k \le n$ 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].

你有一副包含 $n$ 张卡片的牌组，卡片编号为 $1$ 到 $n$（在牌组中不一定按此顺序排列）。你需要通过重复执行以下操作来将牌组排序。

• 选择一个满足 $2 \le k \le n$ 的整数 $k$，并将牌组划分为 $k$ 个非空、连续的部分 $D_1, D_2,\dots, D_k$（其中 $D_1$ 包含牌组最前面 $|D_1|$ 张卡片，$D_2$ 包含接下来的 $|D_2|$ 张卡片，依此类推）。然后将这些部分的顺序反转，使牌组变为 $D_k, D_{k-1}, \dots, D_2, D_1$（即新牌组最前面 $|D_k|$ 张卡片是 $D_k$，接下来的 $|D_{k-1}|$ 张卡片是 $D_{k-1}$，依此类推）。每个子段 $D_i$ 内部卡片的相对顺序在该操作中保持不变。

你需要在至多 $n$ 次操作内，将牌组变为升序排列（即第一张卡片为 $1$，第二张为 $2$，……，第 $n$ 张为 $n$）。可以证明：对任意初始排列，总存在一种策略，在至多 $n$ 次操作内完成排序。

操作示例：以下是三个在不同大小牌组上进行的有效操作示例。

• 若牌组为 [3 6 2 1 4 5 7]（即 $3$ 是第一张卡片，$7$ 是最后一张），可选取 $k=4$，并令 $D_1=$[3 6]，$D_2=$[2 1 4]，$D_3=$[5]，$D_4=$[7]。执行该操作后，牌组变为 [7 5 2 1 4 3 6]。
• 若牌组为 [3 1 2]，可选取 $k=3$，并令 $D_1=$[3]，$D_2=$[1]，$D_3=$[2]。执行该操作后，牌组变为 [2 1 3]。
• 若牌组为 [5 1 2 4 3 6]，可选取 $k=2$，并令 $D_1=$[5 1]，$D_2=$[2 4 3 6]。执行该操作后，牌组变为 [2 4 3 6 5 1]。

The 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 $c_j = i$.

输入的第一行包含一个整数 $n$（$1\le n\le 52$）—— 表示牌组中的卡片数量。

第二行包含 $n$ 个整数 $c_1, c_2, \dots, c_n$ —— 表示牌组中的卡片。第一张牌为 $c_1$，第二张牌为 $c_2$，依此类推。

保证对所有 $i=1,\dots,n$，均存在唯一一个 $j\in\{1,\dots,n\}$，使得 $c_j = i$。

On 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.

第一行输出你执行的操作次数 $q$（需满足 $0\le q\le n$）。

随后输出 $q$ 行，每行描述一次操作。

为描述一次操作，在一行中先输出你要将牌堆分割成的段数 $k$，再输出这 $k$ 段的大小：$|D_1|, |D_2|, \dots , |D_k|$。

需满足 $2\le k\le n$，对所有 $i=1,\dots,k$ 有 $|D_i|\ge 1$，且 $|D_1|+|D_2|+\cdots + |D_k| = n$。

可以证明：总存在一种方式，至多通过 $n$ 次操作即可将牌堆排序。若存在多种排序方案，输出任意一种即可。

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].

第一个测试用例的解释：初始牌组为 [3\ 1\ 2\ 4]。

• 第一次操作将牌组分割为 [(3)\ (1\ 2)\ (4)]，然后将其变换为 [4\ 1\ 2\ 3]。
• 第二次操作将牌组分割为 [(4)\ (1\ 2\ 3)]，然后将其变换为 [1\ 2\ 3\ 4]。

第二个测试用例的解释：初始牌组为 [6\ 5\ 4\ 3\ 2\ 1]。

• 第一次（也是唯一一次）操作将牌组分割为 [(6)\ (5)\ (4)\ (3)\ (2)\ (1)]，然后将其变换为 [1\ 2\ 3\ 4\ 5\ 6]。