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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}
const int mod = 1000000007, MAX = 200005;
const int INF = 1 << 30;
int main() {
  std::ifstream in("text.txt");
  std::cin.rdbuf(in.rdbuf());
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N;
  cin >> N;
  vector<int> A(N);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
  }
  vector<vector<int>> ans;
  while (1) {
    bool ok = true;
    for (int i = 0; i < N; i++)
      if (A[i] != i + 1) ok = false;
    if (ok) break;
    for (int i = 1; i + 1 <= N; i++) {
      int a, b;
      for (int j = 0; j < N; j++) {
        if (A[j] == i) a = j;
        if (A[j] == i + 1) b = j;
      }
      if (b < a) {
        int bb = b;
        while (A[bb] - A[b] == bb - b) bb++;
        vector<int> S;
        vector<vector<int>> T;
        if (b) S.push_back(b);
        S.push_back(bb - b);
        if (a - bb + 1) S.push_back(a - bb + 1);
        if (N - 1 - a) S.push_back(N - 1 - a);
        ans.push_back(S);
        int id = 0;
        for (int a : S) {
          vector<int> U;
          for (int x = id; x < id + a; x++) {
            U.push_back(A[x]);
          }
          T.push_back(U);
          id += a;
        }
        reverse((T).begin(), (T).end());
        A.clear();
        for (int i = 0; i < int(T.size()); i++) {
          for (int x : T[i]) A.push_back(x);
        }
        break;
      }
    }
  }
  cout << int(ans.size()) << "\n";
  for (int i = 0; i < int(ans.size()); i++) {
    cout << int(ans[i].size()) << " ";
    for (int a : ans[i]) cout << a << " ";
    cout << "\n";
  }
}