// output of ./demo/comb/catalan-subset-lex-demo.cc:
// Description:
//% Catalan restricted growth strings (RGS) and parentheses strings in 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.    [ . . . . 1 ]
   3:    [ . 1 1 . . ]   2    (()())()()    11.1..1.1.    [ . . . 1 1 ]
   4:    [ . 1 2 . . ]   2    ((()))()()    111...1.1.    [ . . . 1 2 ]
   5:    [ . 1 2 1 . ]   3    ((())())()    111..1..1.    [ . . 1 1 2 ]
   6:    [ . 1 2 2 . ]   3    ((()()))()    111.1...1.    [ . . 1 2 2 ]
   7:    [ . 1 2 3 . ]   3    (((())))()    1111....1.    [ . . 1 2 3 ]
   8:    [ . 1 2 3 1 ]   4    (((()))())    1111...1..    [ . 1 1 2 3 ]
   9:    [ . 1 2 3 2 ]   4    (((())()))    1111..1...    [ . 1 2 2 3 ]
  10:    [ . 1 2 3 3 ]   4    (((()())))    1111.1....    [ . 1 2 3 3 ]
  11:    [ . 1 2 3 4 ]   4    ((((()))))    11111.....    [ . 1 2 3 4 ]
  12:    [ . 1 2 2 1 ]   4    ((()())())    111.1..1..    [ . 1 1 2 2 ]
  13:    [ . 1 2 2 2 ]   4    ((()()()))    111.1.1...    [ . 1 2 2 2 ]
  14:    [ . 1 2 2 3 ]   4    ((()(())))    111.11....    [ . 1 2 3 2 ]
  15:    [ . 1 2 1 1 ]   4    ((())()())    111..1.1..    [ . 1 1 1 2 ]
  16:    [ . 1 2 1 2 ]   4    ((())(()))    111..11...    [ . 1 2 1 2 ]
  17:    [ . 1 2 . 1 ]   4    ((()))(())    111...11..    [ . 1 . 1 2 ]
  18:    [ . 1 1 1 . ]   3    (()()())()    11.1.1..1.    [ . . 1 1 1 ]
  19:    [ . 1 1 2 . ]   3    (()(()))()    11.11...1.    [ . . 1 2 1 ]
  20:    [ . 1 1 2 1 ]   4    (()(())())    11.11..1..    [ . 1 1 2 1 ]
  21:    [ . 1 1 2 2 ]   4    (()(()()))    11.11.1...    [ . 1 2 2 1 ]
  22:    [ . 1 1 2 3 ]   4    (()((())))    11.111....    [ . 1 2 3 1 ]
  23:    [ . 1 1 1 1 ]   4    (()()()())    11.1.1.1..    [ . 1 1 1 1 ]
  24:    [ . 1 1 1 2 ]   4    (()()(()))    11.1.11...    [ . 1 2 1 1 ]
  25:    [ . 1 1 . 1 ]   4    (()())(())    11.1..11..    [ . 1 . 1 1 ]
  26:    [ . 1 . 1 . ]   3    (())(())()    11..11..1.    [ . . 1 . 1 ]
  27:    [ . 1 . 1 1 ]   4    (())(()())    11..11.1..    [ . 1 1 . 1 ]
  28:    [ . 1 . 1 2 ]   4    (())((()))    11..111...    [ . 1 2 . 1 ]
  29:    [ . 1 . . 1 ]   4    (())()(())    11..1.11..    [ . 1 . . 1 ]
  30:    [ . . 1 . . ]   2    ()(())()()    1.11..1.1.    [ . . . 1 . ]
  31:    [ . . 1 1 . ]   3    ()(()())()    1.11.1..1.    [ . . 1 1 . ]
  32:    [ . . 1 2 . ]   3    ()((()))()    1.111...1.    [ . . 1 2 . ]
  33:    [ . . 1 2 1 ]   4    ()((())())    1.111..1..    [ . 1 1 2 . ]
  34:    [ . . 1 2 2 ]   4    ()((()()))    1.111.1...    [ . 1 2 2 . ]
  35:    [ . . 1 2 3 ]   4    ()(((())))    1.1111....    [ . 1 2 3 . ]
  36:    [ . . 1 1 1 ]   4    ()(()()())    1.11.1.1..    [ . 1 1 1 . ]
  37:    [ . . 1 1 2 ]   4    ()(()(()))    1.11.11...    [ . 1 2 1 . ]
  38:    [ . . 1 . 1 ]   4    ()(())(())    1.11..11..    [ . 1 . 1 . ]
  39:    [ . . . 1 . ]   3    ()()(())()    1.1.11..1.    [ . . 1 . . ]
  40:    [ . . . 1 1 ]   4    ()()(()())    1.1.11.1..    [ . 1 1 . . ]
  41:    [ . . . 1 2 ]   4    ()()((()))    1.1.111...    [ . 1 2 . . ]
  42:    [ . . . . 1 ]   4    ()()()(())    1.1.1.11..    [ . 1 . . . ]
 ct=42
