#D12434. Unshuffling a Deck
Unshuffling a Deck
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 ≤ 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].
inputFormat
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.
outputFormat
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].
样例
1
1
0