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;
long long int z[1], x[100][100], y[100], m, szu, wy[100][100];
char s[10000000];
int main() {
  long long int chu, d, e, f, i, j, q, t, k, a, n, b, c, w, p, aa, bb, cc, dd,
      nn, kk;
  t = 1;
  for (q = 1; q <= t; q++) {
    scanf("%lld", &n);
    for (i = 0; i < n; i++) {
      scanf("%lld", &x[0][i]);
    }
    a = 1;
    if (n % 2 == 0) a = n;
    w = n;
    if (x[0][0] == a) w--;
    printf("%lld\n", w);
    for (i = 0; i < n; i++) {
      b = 0;
      c = 0;
      for (j = 0; j < n; j++) {
        if (x[i][j] == a) b = j;
      }
      d = (i + 1) / 2;
      for (j = 0; j < d; j++) {
        y[c] = 1;
        c++;
      }
      if (b - d > 0) {
        y[c] = b - d;
        c++;
      }
      y[c] = n - b - i / 2;
      c++;
      for (j = 0; j < i / 2; j++) {
        y[c] = 1;
        c++;
      }
      if (c > 1) {
        printf("%lld", c);
        for (j = 0; j < c; j++) printf(" %lld", y[j]);
        printf("\n");
      }
      b = 0;
      d = n;
      for (j = c - 1; j >= 0; j--) {
        d -= y[j];
        for (k = 0; k < y[j]; k++) {
          x[i + 1][b] = x[i][d + k];
          b++;
        }
      }
      a = n - a;
      if (n % 2 == 0 && i % 2 == 0) a++;
      if (n % 2 == 1) a++;
      if (n % 2 == 1 && i % 2 == 1) a++;
    }
  }
  return (0);
}