// output of ./demo/comb/binary-rot-demo.cc:
// Description:
//% Binary strings by rotations of prefixes.
//% This is the "cooler" order from:
//% Brett Stevens, Aaron Williams: The coolest order of binary strings,
//% 6th International Conference on Fun with Algorithms (FUN 2012),
//% San Servolo, Italy. LNCS 7288, pp.322-333, (2012).

arg 1: 6 == n  [Number of bits]  default=6
   1:    ......   0
   2:    .....1   1
   3:    ....11   2
   4:    ...111   3
   5:    ..1111   4
   6:    .11111   5
   7:    111111   6
   8:    11111.   5
   9:    1111.1   5
  10:    111.11   5
  11:    11.111   5
  12:    1.1111   5
  13:    .1111.   4
  14:    1111..   4
  15:    111.1.   4
  16:    11.11.   4
  17:    1.111.   4
  18:    .111.1   4
  19:    111..1   4
  20:    11.1.1   4
  21:    1.11.1   4
  22:    .11.11   4
  23:    11..11   4
  24:    1.1.11   4
  25:    .1.111   4
  26:    1..111   4
  27:    ..111.   3
  28:    .111..   3
  29:    111...   3
  30:    11.1..   3
  31:    1.11..   3
  32:    .11.1.   3
  33:    11..1.   3
  34:    1.1.1.   3
  35:    .1.11.   3
  36:    1..11.   3
  37:    ..11.1   3
  38:    .11..1   3
  39:    11...1   3
  40:    1.1..1   3
  41:    .1.1.1   3
  42:    1..1.1   3
  43:    ..1.11   3
  44:    .1..11   3
  45:    1...11   3
  46:    ...11.   2
  47:    ..11..   2
  48:    .11...   2
  49:    11....   2
  50:    1.1...   2
  51:    .1.1..   2
  52:    1..1..   2
  53:    ..1.1.   2
  54:    .1..1.   2
  55:    1...1.   2
  56:    ...1.1   2
  57:    ..1..1   2
  58:    .1...1   2
  59:    1....1   2
  60:    ....1.   1
  61:    ...1..   1
  62:    ..1...   1
  63:    .1....   1
  64:    1.....   1
 ct = 64