// output of ./demo/comb/catalan-rgs-subset-lex-demo.cc:
// Description:
//% Catalan restricted growth strings (RGS):
//% strings a[0,1,...,n-1] where a[0]=0 and a[k] <= a[k-1] + 1.
//% Subset-lex order.

arg 1: 5 == n  [Number of paren pairs]  default=5
arg 2: 0 == bw  [Whether to generate backward order]  default=0
   1:    [ . . . . . ]   1    1.1.1.1.1.    ()()()()()
   2:    [ . 1 . . . ]   1    11..1.1.1.    (())()()()
   3:    [ . 1 1 . . ]   2    11.1..1.1.    (()())()()
   4:    [ . 1 2 . . ]   2    111...1.1.    ((()))()()
   5:    [ . 1 2 1 . ]   3    111..1..1.    ((())())()
   6:    [ . 1 2 2 . ]   3    111.1...1.    ((()()))()
   7:    [ . 1 2 3 . ]   3    1111....1.    (((())))()
   8:    [ . 1 2 3 1 ]   4    1111...1..    (((()))())
   9:    [ . 1 2 3 2 ]   4    1111..1...    (((())()))
  10:    [ . 1 2 3 3 ]   4    1111.1....    (((()())))
  11:    [ . 1 2 3 4 ]   4    11111.....    ((((()))))
  12:    [ . 1 2 2 1 ]   4    111.1..1..    ((()())())
  13:    [ . 1 2 2 2 ]   4    111.1.1...    ((()()()))
  14:    [ . 1 2 2 3 ]   4    111.11....    ((()(())))
  15:    [ . 1 2 1 1 ]   4    111..1.1..    ((())()())
  16:    [ . 1 2 1 2 ]   4    111..11...    ((())(()))
  17:    [ . 1 2 . 1 ]   4    111...11..    ((()))(())
  18:    [ . 1 1 1 . ]   3    11.1.1..1.    (()()())()
  19:    [ . 1 1 2 . ]   3    11.11...1.    (()(()))()
  20:    [ . 1 1 2 1 ]   4    11.11..1..    (()(())())
  21:    [ . 1 1 2 2 ]   4    11.11.1...    (()(()()))
  22:    [ . 1 1 2 3 ]   4    11.111....    (()((())))
  23:    [ . 1 1 1 1 ]   4    11.1.1.1..    (()()()())
  24:    [ . 1 1 1 2 ]   4    11.1.11...    (()()(()))
  25:    [ . 1 1 . 1 ]   4    11.1..11..    (()())(())
  26:    [ . 1 . 1 . ]   3    11..11..1.    (())(())()
  27:    [ . 1 . 1 1 ]   4    11..11.1..    (())(()())
  28:    [ . 1 . 1 2 ]   4    11..111...    (())((()))
  29:    [ . 1 . . 1 ]   4    11..1.11..    (())()(())
  30:    [ . . 1 . . ]   2    1.11..1.1.    ()(())()()
  31:    [ . . 1 1 . ]   3    1.11.1..1.    ()(()())()
  32:    [ . . 1 2 . ]   3    1.111...1.    ()((()))()
  33:    [ . . 1 2 1 ]   4    1.111..1..    ()((())())
  34:    [ . . 1 2 2 ]   4    1.111.1...    ()((()()))
  35:    [ . . 1 2 3 ]   4    1.1111....    ()(((())))
  36:    [ . . 1 1 1 ]   4    1.11.1.1..    ()(()()())
  37:    [ . . 1 1 2 ]   4    1.11.11...    ()(()(()))
  38:    [ . . 1 . 1 ]   4    1.11..11..    ()(())(())
  39:    [ . . . 1 . ]   3    1.1.11..1.    ()()(())()
  40:    [ . . . 1 1 ]   4    1.1.11.1..    ()()(()())
  41:    [ . . . 1 2 ]   4    1.1.111...    ()()((()))
  42:    [ . . . . 1 ]   4    1.1.1.11..    ()()()(())
 ct=42
