combinatorics.md
In nn2poly: Neural Network Weights Transformation into Polynomial Coefficients

combinations with repetition algorithm works

Code
  combinations_with_repetition(5, 3)
Output
        [,1] [,2] [,3]
   [1,]    1    1    1
   [2,]    1    1    2
   [3,]    1    1    3
   [4,]    1    1    4
   [5,]    1    1    5
   [6,]    1    2    2
   [7,]    1    2    3
   [8,]    1    2    4
   [9,]    1    2    5
  [10,]    1    3    3
  [11,]    1    3    4
  [12,]    1    3    5
  [13,]    1    4    4
  [14,]    1    4    5
  [15,]    1    5    5
  [16,]    2    2    2
  [17,]    2    2    3
  [18,]    2    2    4
  [19,]    2    2    5
  [20,]    2    3    3
  [21,]    2    3    4
  [22,]    2    3    5
  [23,]    2    4    4
  [24,]    2    4    5
  [25,]    2    5    5
  [26,]    3    3    3
  [27,]    3    3    4
  [28,]    3    3    5
  [29,]    3    4    4
  [30,]    3    4    5
  [31,]    3    5    5
  [32,]    4    4    4
  [33,]    4    4    5
  [34,]    4    5    5
  [35,]    5    5    5

Code
  combinations_with_repetition(3, 5)
Output
        [,1] [,2] [,3] [,4] [,5]
   [1,]    1    1    1    1    1
   [2,]    1    1    1    1    2
   [3,]    1    1    1    1    3
   [4,]    1    1    1    2    2
   [5,]    1    1    1    2    3
   [6,]    1    1    1    3    3
   [7,]    1    1    2    2    2
   [8,]    1    1    2    2    3
   [9,]    1    1    2    3    3
  [10,]    1    1    3    3    3
  [11,]    1    2    2    2    2
  [12,]    1    2    2    2    3
  [13,]    1    2    2    3    3
  [14,]    1    2    3    3    3
  [15,]    1    3    3    3    3
  [16,]    2    2    2    2    2
  [17,]    2    2    2    2    3
  [18,]    2    2    2    3    3
  [19,]    2    2    3    3    3
  [20,]    2    3    3    3    3
  [21,]    3    3    3    3    3

multiset partitions are correctly generated

Code
  generate_partitions(5, 3)
Output
  [[1]]
  [[1]][[1]]
  [[1]][[1]][[1]]
  [1] 1



  [[2]]
  [[2]][[1]]
  [[2]][[1]][[1]]
  [1] 1 1


  [[2]][[2]]
  [[2]][[2]][[1]]
  [1] 1

  [[2]][[2]][[2]]
  [1] 1



  [[3]]
  [[3]][[1]]
  [[3]][[1]][[1]]
  [1] 1 2


  [[3]][[2]]
  [[3]][[2]][[1]]
  [1] 1

  [[3]][[2]][[2]]
  [1] 2



  [[4]]
  [[4]][[1]]
  [[4]][[1]][[1]]
  [1] 1 1 1


  [[4]][[2]]
  [[4]][[2]][[1]]
  [1] 1 1

  [[4]][[2]][[2]]
  [1] 1


  [[4]][[3]]
  [[4]][[3]][[1]]
  [1] 1

  [[4]][[3]][[2]]
  [1] 1

  [[4]][[3]][[3]]
  [1] 1



  [[5]]
  [[5]][[1]]
  [[5]][[1]][[1]]
  [1] 1 1 2


  [[5]][[2]]
  [[5]][[2]][[1]]
  [1] 1 1

  [[5]][[2]][[2]]
  [1] 2


  [[5]][[3]]
  [[5]][[3]][[1]]
  [1] 1 2

  [[5]][[3]][[2]]
  [1] 1


  [[5]][[4]]
  [[5]][[4]][[1]]
  [1] 1

  [[5]][[4]][[2]]
  [1] 1

  [[5]][[4]][[3]]
  [1] 2



  [[6]]
  [[6]][[1]]
  [[6]][[1]][[1]]
  [1] 1 2 3


  [[6]][[2]]
  [[6]][[2]][[1]]
  [1] 1 2

  [[6]][[2]][[2]]
  [1] 3


  [[6]][[3]]
  [[6]][[3]][[1]]
  [1] 1 3

  [[6]][[3]][[2]]
  [1] 2


  [[6]][[4]]
  [[6]][[4]][[1]]
  [1] 1

  [[6]][[4]][[2]]
  [1] 2 3


  [[6]][[5]]
  [[6]][[5]][[1]]
  [1] 1

  [[6]][[5]][[2]]
  [1] 2

  [[6]][[5]][[3]]
  [1] 3

Code
  generate_partitions(3, 5)
Output
  [[1]]
  [[1]][[1]]
  [[1]][[1]][[1]]
  [1] 1



  [[2]]
  [[2]][[1]]
  [[2]][[1]][[1]]
  [1] 1 1


  [[2]][[2]]
  [[2]][[2]][[1]]
  [1] 1

  [[2]][[2]][[2]]
  [1] 1



  [[3]]
  [[3]][[1]]
  [[3]][[1]][[1]]
  [1] 1 2


  [[3]][[2]]
  [[3]][[2]][[1]]
  [1] 1

  [[3]][[2]][[2]]
  [1] 2



  [[4]]
  [[4]][[1]]
  [[4]][[1]][[1]]
  [1] 1 1 1


  [[4]][[2]]
  [[4]][[2]][[1]]
  [1] 1 1

  [[4]][[2]][[2]]
  [1] 1


  [[4]][[3]]
  [[4]][[3]][[1]]
  [1] 1

  [[4]][[3]][[2]]
  [1] 1

  [[4]][[3]][[3]]
  [1] 1



  [[5]]
  [[5]][[1]]
  [[5]][[1]][[1]]
  [1] 1 1 2


  [[5]][[2]]
  [[5]][[2]][[1]]
  [1] 1 1

  [[5]][[2]][[2]]
  [1] 2


  [[5]][[3]]
  [[5]][[3]][[1]]
  [1] 1 2

  [[5]][[3]][[2]]
  [1] 1


  [[5]][[4]]
  [[5]][[4]][[1]]
  [1] 1

  [[5]][[4]][[2]]
  [1] 1

  [[5]][[4]][[3]]
  [1] 2



  [[6]]
  [[6]][[1]]
  [[6]][[1]][[1]]
  [1] 1 2 3


  [[6]][[2]]
  [[6]][[2]][[1]]
  [1] 1 2

  [[6]][[2]][[2]]
  [1] 3


  [[6]][[3]]
  [[6]][[3]][[1]]
  [1] 1 3

  [[6]][[3]][[2]]
  [1] 2


  [[6]][[4]]
  [[6]][[4]][[1]]
  [1] 1

  [[6]][[4]][[2]]
  [1] 2 3


  [[6]][[5]]
  [[6]][[5]][[1]]
  [1] 1

  [[6]][[5]][[2]]
  [1] 2

  [[6]][[5]][[3]]
  [1] 3



  [[7]]
  [[7]][[1]]
  [[7]][[1]][[1]]
  [1] 1 1 1 1


  [[7]][[2]]
  [[7]][[2]][[1]]
  [1] 1 1 1

  [[7]][[2]][[2]]
  [1] 1


  [[7]][[3]]
  [[7]][[3]][[1]]
  [1] 1 1

  [[7]][[3]][[2]]
  [1] 1 1


  [[7]][[4]]
  [[7]][[4]][[1]]
  [1] 1 1

  [[7]][[4]][[2]]
  [1] 1

  [[7]][[4]][[3]]
  [1] 1


  [[7]][[5]]
  [[7]][[5]][[1]]
  [1] 1

  [[7]][[5]][[2]]
  [1] 1

  [[7]][[5]][[3]]
  [1] 1

  [[7]][[5]][[4]]
  [1] 1



  [[8]]
  [[8]][[1]]
  [[8]][[1]][[1]]
  [1] 1 1 1 2


  [[8]][[2]]
  [[8]][[2]][[1]]
  [1] 1 1 1

  [[8]][[2]][[2]]
  [1] 2


  [[8]][[3]]
  [[8]][[3]][[1]]
  [1] 1 1 2

  [[8]][[3]][[2]]
  [1] 1


  [[8]][[4]]
  [[8]][[4]][[1]]
  [1] 1 1

  [[8]][[4]][[2]]
  [1] 1 2


  [[8]][[5]]
  [[8]][[5]][[1]]
  [1] 1 1

  [[8]][[5]][[2]]
  [1] 1

  [[8]][[5]][[3]]
  [1] 2


  [[8]][[6]]
  [[8]][[6]][[1]]
  [1] 1 2

  [[8]][[6]][[2]]
  [1] 1

  [[8]][[6]][[3]]
  [1] 1


  [[8]][[7]]
  [[8]][[7]][[1]]
  [1] 1

  [[8]][[7]][[2]]
  [1] 1

  [[8]][[7]][[3]]
  [1] 1

  [[8]][[7]][[4]]
  [1] 2



  [[9]]
  [[9]][[1]]
  [[9]][[1]][[1]]
  [1] 1 1 2 2


  [[9]][[2]]
  [[9]][[2]][[1]]
  [1] 1 1 2

  [[9]][[2]][[2]]
  [1] 2


  [[9]][[3]]
  [[9]][[3]][[1]]
  [1] 1 1

  [[9]][[3]][[2]]
  [1] 2 2


  [[9]][[4]]
  [[9]][[4]][[1]]
  [1] 1 1

  [[9]][[4]][[2]]
  [1] 2

  [[9]][[4]][[3]]
  [1] 2


  [[9]][[5]]
  [[9]][[5]][[1]]
  [1] 1 2 2

  [[9]][[5]][[2]]
  [1] 1


  [[9]][[6]]
  [[9]][[6]][[1]]
  [1] 1 2

  [[9]][[6]][[2]]
  [1] 1 2


  [[9]][[7]]
  [[9]][[7]][[1]]
  [1] 1 2

  [[9]][[7]][[2]]
  [1] 1

  [[9]][[7]][[3]]
  [1] 2


  [[9]][[8]]
  [[9]][[8]][[1]]
  [1] 1

  [[9]][[8]][[2]]
  [1] 1

  [[9]][[8]][[3]]
  [1] 2 2


  [[9]][[9]]
  [[9]][[9]][[1]]
  [1] 1

  [[9]][[9]][[2]]
  [1] 1

  [[9]][[9]][[3]]
  [1] 2

  [[9]][[9]][[4]]
  [1] 2



  [[10]]
  [[10]][[1]]
  [[10]][[1]][[1]]
  [1] 1 1 2 3


  [[10]][[2]]
  [[10]][[2]][[1]]
  [1] 1 1 2

  [[10]][[2]][[2]]
  [1] 3


  [[10]][[3]]
  [[10]][[3]][[1]]
  [1] 1 1 3

  [[10]][[3]][[2]]
  [1] 2


  [[10]][[4]]
  [[10]][[4]][[1]]
  [1] 1 1

  [[10]][[4]][[2]]
  [1] 2 3


  [[10]][[5]]
  [[10]][[5]][[1]]
  [1] 1 1

  [[10]][[5]][[2]]
  [1] 2

  [[10]][[5]][[3]]
  [1] 3


  [[10]][[6]]
  [[10]][[6]][[1]]
  [1] 1 2 3

  [[10]][[6]][[2]]
  [1] 1


  [[10]][[7]]
  [[10]][[7]][[1]]
  [1] 1 2

  [[10]][[7]][[2]]
  [1] 1 3


  [[10]][[8]]
  [[10]][[8]][[1]]
  [1] 1 2

  [[10]][[8]][[2]]
  [1] 1

  [[10]][[8]][[3]]
  [1] 3


  [[10]][[9]]
  [[10]][[9]][[1]]
  [1] 1 3

  [[10]][[9]][[2]]
  [1] 1

  [[10]][[9]][[3]]
  [1] 2


  [[10]][[10]]
  [[10]][[10]][[1]]
  [1] 1

  [[10]][[10]][[2]]
  [1] 1

  [[10]][[10]][[3]]
  [1] 2 3


  [[10]][[11]]
  [[10]][[11]][[1]]
  [1] 1

  [[10]][[11]][[2]]
  [1] 1

  [[10]][[11]][[3]]
  [1] 2

  [[10]][[11]][[4]]
  [1] 3



  [[11]]
  [[11]][[1]]
  [[11]][[1]][[1]]
  [1] 1 1 1 1 1


  [[11]][[2]]
  [[11]][[2]][[1]]
  [1] 1 1 1 1

  [[11]][[2]][[2]]
  [1] 1


  [[11]][[3]]
  [[11]][[3]][[1]]
  [1] 1 1 1

  [[11]][[3]][[2]]
  [1] 1 1


  [[11]][[4]]
  [[11]][[4]][[1]]
  [1] 1 1 1

  [[11]][[4]][[2]]
  [1] 1

  [[11]][[4]][[3]]
  [1] 1


  [[11]][[5]]
  [[11]][[5]][[1]]
  [1] 1 1

  [[11]][[5]][[2]]
  [1] 1 1

  [[11]][[5]][[3]]
  [1] 1


  [[11]][[6]]
  [[11]][[6]][[1]]
  [1] 1 1

  [[11]][[6]][[2]]
  [1] 1

  [[11]][[6]][[3]]
  [1] 1

  [[11]][[6]][[4]]
  [1] 1


  [[11]][[7]]
  [[11]][[7]][[1]]
  [1] 1

  [[11]][[7]][[2]]
  [1] 1

  [[11]][[7]][[3]]
  [1] 1

  [[11]][[7]][[4]]
  [1] 1

  [[11]][[7]][[5]]
  [1] 1



  [[12]]
  [[12]][[1]]
  [[12]][[1]][[1]]
  [1] 1 1 1 1 2


  [[12]][[2]]
  [[12]][[2]][[1]]
  [1] 1 1 1 1

  [[12]][[2]][[2]]
  [1] 2


  [[12]][[3]]
  [[12]][[3]][[1]]
  [1] 1 1 1 2

  [[12]][[3]][[2]]
  [1] 1


  [[12]][[4]]
  [[12]][[4]][[1]]
  [1] 1 1 1

  [[12]][[4]][[2]]
  [1] 1 2


  [[12]][[5]]
  [[12]][[5]][[1]]
  [1] 1 1 1

  [[12]][[5]][[2]]
  [1] 1

  [[12]][[5]][[3]]
  [1] 2


  [[12]][[6]]
  [[12]][[6]][[1]]
  [1] 1 1 2

  [[12]][[6]][[2]]
  [1] 1 1


  [[12]][[7]]
  [[12]][[7]][[1]]
  [1] 1 1 2

  [[12]][[7]][[2]]
  [1] 1

  [[12]][[7]][[3]]
  [1] 1


  [[12]][[8]]
  [[12]][[8]][[1]]
  [1] 1 1

  [[12]][[8]][[2]]
  [1] 1 1

  [[12]][[8]][[3]]
  [1] 2


  [[12]][[9]]
  [[12]][[9]][[1]]
  [1] 1 1

  [[12]][[9]][[2]]
  [1] 1 2

  [[12]][[9]][[3]]
  [1] 1


  [[12]][[10]]
  [[12]][[10]][[1]]
  [1] 1 1

  [[12]][[10]][[2]]
  [1] 1

  [[12]][[10]][[3]]
  [1] 1

  [[12]][[10]][[4]]
  [1] 2


  [[12]][[11]]
  [[12]][[11]][[1]]
  [1] 1 2

  [[12]][[11]][[2]]
  [1] 1

  [[12]][[11]][[3]]
  [1] 1

  [[12]][[11]][[4]]
  [1] 1


  [[12]][[12]]
  [[12]][[12]][[1]]
  [1] 1

  [[12]][[12]][[2]]
  [1] 1

  [[12]][[12]][[3]]
  [1] 1

  [[12]][[12]][[4]]
  [1] 1

  [[12]][[12]][[5]]
  [1] 2



  [[13]]
  [[13]][[1]]
  [[13]][[1]][[1]]
  [1] 1 1 1 2 2


  [[13]][[2]]
  [[13]][[2]][[1]]
  [1] 1 1 1 2

  [[13]][[2]][[2]]
  [1] 2


  [[13]][[3]]
  [[13]][[3]][[1]]
  [1] 1 1 1

  [[13]][[3]][[2]]
  [1] 2 2


  [[13]][[4]]
  [[13]][[4]][[1]]
  [1] 1 1 1

  [[13]][[4]][[2]]
  [1] 2

  [[13]][[4]][[3]]
  [1] 2


  [[13]][[5]]
  [[13]][[5]][[1]]
  [1] 1 1 2 2

  [[13]][[5]][[2]]
  [1] 1


  [[13]][[6]]
  [[13]][[6]][[1]]
  [1] 1 1 2

  [[13]][[6]][[2]]
  [1] 1 2


  [[13]][[7]]
  [[13]][[7]][[1]]
  [1] 1 1 2

  [[13]][[7]][[2]]
  [1] 1

  [[13]][[7]][[3]]
  [1] 2


  [[13]][[8]]
  [[13]][[8]][[1]]
  [1] 1 1

  [[13]][[8]][[2]]
  [1] 1 2 2


  [[13]][[9]]
  [[13]][[9]][[1]]
  [1] 1 1

  [[13]][[9]][[2]]
  [1] 1 2

  [[13]][[9]][[3]]
  [1] 2


  [[13]][[10]]
  [[13]][[10]][[1]]
  [1] 1 1

  [[13]][[10]][[2]]
  [1] 1

  [[13]][[10]][[3]]
  [1] 2 2


  [[13]][[11]]
  [[13]][[11]][[1]]
  [1] 1 1

  [[13]][[11]][[2]]
  [1] 1

  [[13]][[11]][[3]]
  [1] 2

  [[13]][[11]][[4]]
  [1] 2


  [[13]][[12]]
  [[13]][[12]][[1]]
  [1] 1 2 2

  [[13]][[12]][[2]]
  [1] 1

  [[13]][[12]][[3]]
  [1] 1


  [[13]][[13]]
  [[13]][[13]][[1]]
  [1] 1 2

  [[13]][[13]][[2]]
  [1] 1 2

  [[13]][[13]][[3]]
  [1] 1


  [[13]][[14]]
  [[13]][[14]][[1]]
  [1] 1 2

  [[13]][[14]][[2]]
  [1] 1

  [[13]][[14]][[3]]
  [1] 1

  [[13]][[14]][[4]]
  [1] 2


  [[13]][[15]]
  [[13]][[15]][[1]]
  [1] 1

  [[13]][[15]][[2]]
  [1] 1

  [[13]][[15]][[3]]
  [1] 1

  [[13]][[15]][[4]]
  [1] 2 2


  [[13]][[16]]
  [[13]][[16]][[1]]
  [1] 1

  [[13]][[16]][[2]]
  [1] 1

  [[13]][[16]][[3]]
  [1] 1

  [[13]][[16]][[4]]
  [1] 2

  [[13]][[16]][[5]]
  [1] 2



  [[14]]
  [[14]][[1]]
  [[14]][[1]][[1]]
  [1] 1 1 1 2 3


  [[14]][[2]]
  [[14]][[2]][[1]]
  [1] 1 1 1 2

  [[14]][[2]][[2]]
  [1] 3


  [[14]][[3]]
  [[14]][[3]][[1]]
  [1] 1 1 1 3

  [[14]][[3]][[2]]
  [1] 2


  [[14]][[4]]
  [[14]][[4]][[1]]
  [1] 1 1 1

  [[14]][[4]][[2]]
  [1] 2 3


  [[14]][[5]]
  [[14]][[5]][[1]]
  [1] 1 1 1

  [[14]][[5]][[2]]
  [1] 2

  [[14]][[5]][[3]]
  [1] 3


  [[14]][[6]]
  [[14]][[6]][[1]]
  [1] 1 1 2 3

  [[14]][[6]][[2]]
  [1] 1


  [[14]][[7]]
  [[14]][[7]][[1]]
  [1] 1 1 2

  [[14]][[7]][[2]]
  [1] 1 3


  [[14]][[8]]
  [[14]][[8]][[1]]
  [1] 1 1 2

  [[14]][[8]][[2]]
  [1] 1

  [[14]][[8]][[3]]
  [1] 3


  [[14]][[9]]
  [[14]][[9]][[1]]
  [1] 1 1 3

  [[14]][[9]][[2]]
  [1] 1 2


  [[14]][[10]]
  [[14]][[10]][[1]]
  [1] 1 1 3

  [[14]][[10]][[2]]
  [1] 1

  [[14]][[10]][[3]]
  [1] 2


  [[14]][[11]]
  [[14]][[11]][[1]]
  [1] 1 1

  [[14]][[11]][[2]]
  [1] 1 2 3


  [[14]][[12]]
  [[14]][[12]][[1]]
  [1] 1 1

  [[14]][[12]][[2]]
  [1] 1 2

  [[14]][[12]][[3]]
  [1] 3


  [[14]][[13]]
  [[14]][[13]][[1]]
  [1] 1 1

  [[14]][[13]][[2]]
  [1] 1 3

  [[14]][[13]][[3]]
  [1] 2


  [[14]][[14]]
  [[14]][[14]][[1]]
  [1] 1 1

  [[14]][[14]][[2]]
  [1] 1

  [[14]][[14]][[3]]
  [1] 2 3


  [[14]][[15]]
  [[14]][[15]][[1]]
  [1] 1 1

  [[14]][[15]][[2]]
  [1] 1

  [[14]][[15]][[3]]
  [1] 2

  [[14]][[15]][[4]]
  [1] 3


  [[14]][[16]]
  [[14]][[16]][[1]]
  [1] 1 2 3

  [[14]][[16]][[2]]
  [1] 1

  [[14]][[16]][[3]]
  [1] 1


  [[14]][[17]]
  [[14]][[17]][[1]]
  [1] 1 2

  [[14]][[17]][[2]]
  [1] 1 3

  [[14]][[17]][[3]]
  [1] 1


  [[14]][[18]]
  [[14]][[18]][[1]]
  [1] 1 2

  [[14]][[18]][[2]]
  [1] 1

  [[14]][[18]][[3]]
  [1] 1

  [[14]][[18]][[4]]
  [1] 3


  [[14]][[19]]
  [[14]][[19]][[1]]
  [1] 1 3

  [[14]][[19]][[2]]
  [1] 1

  [[14]][[19]][[3]]
  [1] 1

  [[14]][[19]][[4]]
  [1] 2


  [[14]][[20]]
  [[14]][[20]][[1]]
  [1] 1

  [[14]][[20]][[2]]
  [1] 1

  [[14]][[20]][[3]]
  [1] 1

  [[14]][[20]][[4]]
  [1] 2 3


  [[14]][[21]]
  [[14]][[21]][[1]]
  [1] 1

  [[14]][[21]][[2]]
  [1] 1

  [[14]][[21]][[3]]
  [1] 1

  [[14]][[21]][[4]]
  [1] 2

  [[14]][[21]][[5]]
  [1] 3



  [[15]]
  [[15]][[1]]
  [[15]][[1]][[1]]
  [1] 1 1 2 2 3


  [[15]][[2]]
  [[15]][[2]][[1]]
  [1] 1 1 2 2

  [[15]][[2]][[2]]
  [1] 3


  [[15]][[3]]
  [[15]][[3]][[1]]
  [1] 1 1 2 3

  [[15]][[3]][[2]]
  [1] 2


  [[15]][[4]]
  [[15]][[4]][[1]]
  [1] 1 1 2

  [[15]][[4]][[2]]
  [1] 2 3


  [[15]][[5]]
  [[15]][[5]][[1]]
  [1] 1 1 2

  [[15]][[5]][[2]]
  [1] 2

  [[15]][[5]][[3]]
  [1] 3


  [[15]][[6]]
  [[15]][[6]][[1]]
  [1] 1 1 3

  [[15]][[6]][[2]]
  [1] 2 2


  [[15]][[7]]
  [[15]][[7]][[1]]
  [1] 1 1 3

  [[15]][[7]][[2]]
  [1] 2

  [[15]][[7]][[3]]
  [1] 2


  [[15]][[8]]
  [[15]][[8]][[1]]
  [1] 1 1

  [[15]][[8]][[2]]
  [1] 2 2 3


  [[15]][[9]]
  [[15]][[9]][[1]]
  [1] 1 1

  [[15]][[9]][[2]]
  [1] 2 2

  [[15]][[9]][[3]]
  [1] 3


  [[15]][[10]]
  [[15]][[10]][[1]]
  [1] 1 1

  [[15]][[10]][[2]]
  [1] 2 3

  [[15]][[10]][[3]]
  [1] 2


  [[15]][[11]]
  [[15]][[11]][[1]]
  [1] 1 1

  [[15]][[11]][[2]]
  [1] 2

  [[15]][[11]][[3]]
  [1] 2

  [[15]][[11]][[4]]
  [1] 3


  [[15]][[12]]
  [[15]][[12]][[1]]
  [1] 1 2 2 3

  [[15]][[12]][[2]]
  [1] 1


  [[15]][[13]]
  [[15]][[13]][[1]]
  [1] 1 2 2

  [[15]][[13]][[2]]
  [1] 1 3


  [[15]][[14]]
  [[15]][[14]][[1]]
  [1] 1 2 2

  [[15]][[14]][[2]]
  [1] 1

  [[15]][[14]][[3]]
  [1] 3


  [[15]][[15]]
  [[15]][[15]][[1]]
  [1] 1 2 3

  [[15]][[15]][[2]]
  [1] 1 2


  [[15]][[16]]
  [[15]][[16]][[1]]
  [1] 1 2 3

  [[15]][[16]][[2]]
  [1] 1

  [[15]][[16]][[3]]
  [1] 2


  [[15]][[17]]
  [[15]][[17]][[1]]
  [1] 1 2

  [[15]][[17]][[2]]
  [1] 1 2

  [[15]][[17]][[3]]
  [1] 3


  [[15]][[18]]
  [[15]][[18]][[1]]
  [1] 1 2

  [[15]][[18]][[2]]
  [1] 1 3

  [[15]][[18]][[3]]
  [1] 2


  [[15]][[19]]
  [[15]][[19]][[1]]
  [1] 1 2

  [[15]][[19]][[2]]
  [1] 1

  [[15]][[19]][[3]]
  [1] 2 3


  [[15]][[20]]
  [[15]][[20]][[1]]
  [1] 1 2

  [[15]][[20]][[2]]
  [1] 1

  [[15]][[20]][[3]]
  [1] 2

  [[15]][[20]][[4]]
  [1] 3


  [[15]][[21]]
  [[15]][[21]][[1]]
  [1] 1 3

  [[15]][[21]][[2]]
  [1] 1

  [[15]][[21]][[3]]
  [1] 2 2


  [[15]][[22]]
  [[15]][[22]][[1]]
  [1] 1 3

  [[15]][[22]][[2]]
  [1] 1

  [[15]][[22]][[3]]
  [1] 2

  [[15]][[22]][[4]]
  [1] 2


  [[15]][[23]]
  [[15]][[23]][[1]]
  [1] 1

  [[15]][[23]][[2]]
  [1] 1

  [[15]][[23]][[3]]
  [1] 2 2 3


  [[15]][[24]]
  [[15]][[24]][[1]]
  [1] 1

  [[15]][[24]][[2]]
  [1] 1

  [[15]][[24]][[3]]
  [1] 2 2

  [[15]][[24]][[4]]
  [1] 3


  [[15]][[25]]
  [[15]][[25]][[1]]
  [1] 1

  [[15]][[25]][[2]]
  [1] 1

  [[15]][[25]][[3]]
  [1] 2 3

  [[15]][[25]][[4]]
  [1] 2


  [[15]][[26]]
  [[15]][[26]][[1]]
  [1] 1

  [[15]][[26]][[2]]
  [1] 1

  [[15]][[26]][[3]]
  [1] 2

  [[15]][[26]][[4]]
  [1] 2

  [[15]][[26]][[5]]
  [1] 3