movement rule: right-else-left-else-straight-else-stop
               =======================================

permutation      no indoor walls           indoor walls allowed
-----------      ---------------           --------------------
                    _ _ _                   _ _ _
(1)              1_|  _  |                 |  _  |
                 |_  |_| |                 |_   _|
                   |_ _ _|                   |_|
                                               1
                 1_ _2
(12)             |_ _|                     same

                  _ _ _                         _ _ _
(1)(2)           |  _  |  _2                 1_|  _  |
                 | |_| |_| |_               _| |    _|
                 |_   _   _  |             |  _  |_|
                   |_| | |_| |             |_ _ _| 2
                   1   |_ _ _|

                     3_                      3_ _2
                    _| |_                   _| | |_
(123)             _|  _  |_2               |  _   _|
                 |_  |_|  _|               |_ _ _| 1
                 1 |_ _ _|

                    _ _ _                       _2
                 1_|  _  |                   1_| |_
(1)(23)          |_  |_| |_ _3              _| |  _|
                   |_ _ _   _|             |  _  | 3
                         |_|               |_ _ _|
                         2
                            _ _ _
(1)(2)(3)         _ _ _  3_|  _  |              _ _ _   _3
                 |  _  | |_  |_| |           1_|  _  |_| |_
                 | |_| |_ _|  _ _|          _| |    _   _  |
                 |_   _   _  |_            |  _  |_| |_ _ _|
                   |_| | |_|  _|           |_ _ _| 2
                   1   |_ _ _| 2

                    _4
(1234)           1_| |_                    same
                 |_   _|
                   |_| 3
                   2

                    _2                           4_ _3
(1)(234)          _| |_                         _| | |_
               3_|  _  |  _1                 1_|  _   _|
               |_  |_| |_| |_               _| |  _ _| 2
                 |_   _   _  |             |  _  |
                   |_| | |_| |             |_ _ _|
                   4   |_ _ _|

                    _1
(12)(34)         2_| |_ _4                 same
                 |_ _   _|
                     |_|
                     3
                  _ _ _    4_                   _ _ _
(1)(2)(34)       |  _  |   | |_3             1_|  _  |_ _4
                 | |_| |_ _|  _|            _| |    _   _|
                 |_   _   _  |_            |  _  |_| |_|
                   |_| | |_|  _|           |_ _ _| 2   3
                   1   |_ _ _| 2

                            _ _ _                         _ _ _
(1)(2)(3)(4)      _ _ _  3_|  _  |  _1          _ _ _  3_|  _  |
                 |  _  | |_  |_| |_| |_      1_|  _  |_| |    _|
                 | |_| |_ _|  _ _   _  |    _| |    _   _  |_|
                 |_   _   _  |_  | |_| |   |  _  |_| |_ _ _| 4
                   |_| | |_|  _| |_ _ _|   |_ _ _| 2
                   1   |_ _ _| 2

                      _5
(12345)            1_| |_4                      3
                   |_   _|                   4_ _ _2
                    _| |_                   _| | | |_
                  _|  _  |_3               |_   _   _|
                 |_  |_|  _|               5 |_ _ _| 1
                 2 |_ _ _|

                    _ _ _                   _ _
(1)(2345)        1_|  _  |    _5           |   |_1_5
                 |_  |_| |_ _| |_          | |  _| |_
                   |_ _ _   _   _|         |_ _     _|
                         |_| |_| 4             |_|_| 4
                         2   3                 2   3

                    _6  _5                   6_ _5
(123456)         1_| |_| |_                 _| | |_
                 |_   _   _|               |_     _|
                   |_| |_| 4               1 |_|_| 4
                   2   3                     2   3