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:
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#       ||      //      \\      ||     || //   ||
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#  code

def solve():
    n = int(input())
    a = list(map(int, input().split()))
    ans = []

    if n % 2 == 0:
        k = a.index(1)
        ans.append([k + 1, n - k - 1])
        done = 1
        rv = 1
        a = a[k + 1:] + a[:k + 1]

        for i in range(1, n):
            # print(a)
            if rv:
                k = a.index(done + 1)
                l = a.index(done)
                ans.append([k, l - k] + [1] * done)
                a = a[l:][::-1] + a[k:l] + a[:k]
                done += 1
                rv = 0
            else:
                k = a.index(done + 1)
                l = a.index(done)
                ans.append([1] * done + [k - l, n - k - 1])
                a = a[k + 1:] + a[l + 1:k + 1] + a[:l + 1][::-1]
                done += 1
                rv = 1
        # print(a)
    else:
        k = a.index(1)
        ans.append([k, n - k])
        done = 1
        rv = 0
        a = a[k:] + a[:k]

        for i in range(1, n):
            # print(a)
            if rv:
                k = a.index(done + 1)
                l = a.index(done)
                ans.append([k, l - k] + [1] * done)
                a = a[l:][::-1] + a[k:l] + a[:k]
                done += 1
                rv = 0
            else:
                k = a.index(done + 1)
                l = a.index(done)
                ans.append([1] * done + [k - l, n - k - 1])
                a = a[k + 1:] + a[l + 1:k + 1] + a[:l + 1][::-1]
                done += 1
                rv = 1
        # print(a)

    for i in ans:
        while 0 in i:
            i.remove(0)
        if len(i) <= 1:
            ans.remove(i)
    
    print(len(ans))
    for i in ans:
        while 0 in i:
            i.remove(0)
        print(len(i), *i)

def main():
    t = 1
    # t = int(input())
    for _ in range(t):
        solve()

if __name__ == "__main__":
    main()