A king moves on a N*N truncated chessboard: only the cells below or on the main diagonal are accessible.
The king starts on the upper left square (1,1), visits all the accessible squares exactly once and returns to his starting position.

On a 4*4 chessboard, he can make 10 different tours:

  + - -  - - +   + - -  - - +   + - -  - - +   + - -  - - +   + - -  - - +
  | 1 .  . . |   | 1 .  . . |   | 1 .  . . |   | 1 .  . . |   | 1 .  . . |
  | 2 10 . . |   | 2 10 . . |   | 2 10 . . |   | 2 10 . . |   | 2 10 . . |
  | 3 4  9 . |   | 3 5  9 . |   | 3 6  9 . |   | 3 9  6 . |   | 3 9  8 . |
  | 5 6  7 8 |   | 4 6  7 8 |   | 4 5  7 8 |   | 4 5  8 7 |   | 4 5  6 7 |
  + - -  - - +   + - -  - - +   + - -  - - +   + - -  - - +   + - -  - - +
  + - -  - - +   + - -  - - +   + - -  - - +   + - -  - - +   + - -  - - +
  | 1 .  . . |   | 1 .  . . |   | 1 .  . . |   | 1 .  . . |   | 1 .  . . |
  | 2 10 . . |   | 2 10 . . |   | 2 10 . . |   | 2 10 . . |   | 2 10 . . |
  | 3 6  9 . |   | 4 3  9 . |   | 9 3  4 . |   | 5 3  9 . |   | 9 3  6 . |
  | 5 4  7 8 |   | 5 6  7 8 |   | 8 7  6 5 |   | 4 6  7 8 |   | 8 7  4 5 |
  + - -  - - +   + - -  - - +   + - -  - - +   + - -  - - +   + - -  - - +

Two tours are considered identical if one is the mirror of the other, like:

  + - -  - - +   + -  - - - +
  | 1 .  . . |   | 1  . . . |
  | 2 10 . . |   | 10 2 . . |
  | 3 4  9 . |   | 9  8 3 . |
  | 5 6  7 8 |   | 7  6 5 4 |
  + - -  - - +   + -  - - - +

In how many ways can he visit a 6*6 truncated chessboard?

Answer format: the count

[My timing : 17 sec]

P.S:
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