Cowboy Checkers

Theta likes to play a board game called Cowboy Checkers, also known under the name “Nine Men’s Morris.” This strategy board game, which dates at least to the Roman Empire, is played by two players on a grid with $24$ intersections, or points, as shown on the left in Figure 1. Each player has nine pieces represented by white and black colors. During the initial phase of the game, players take turns placing pieces on the board at unoccupied intersections. Once all pieces have been placed, players take turns moving pieces. Pieces can be moved along the lines of the board from one intersection (or corner) to any connected open intersection (or corner).

The goal of the game is to take one’s opponent’s pieces,
which is accomplished by forming “mills,” which consist of
three pieces that are either horizontally or vertically
adjacent. For instance, Figure 1 shows two mills: white
has a mill consisting of the pieces on `e3`, `e4`, and
`e5`, and black has a mill consisting
of the pieces on `f2`, `f4`, and `f6`.

Each time a player forms a mill they can take one piece from
their opponent. Thus, a desirable position, which almost always
results in a win, is a “double mill”: in this position, the
player whose turn it is can move one piece from one mill such
that it closes (completes) another mill. In the next move, the
player can move back, closing the first mill again and
reopening the second. For instance, in Figure 1, White has
created a double mill: the move `e3` to
`d3` would close a mill consisting of
`d1`, `d2`, and
`d3` while simultaneously creating an
open mill `e4`, `e5`.

Theta is pretty good at spotting double mills - can you write a program that does the same?

The input consists of a single test case. This test case
consists of $7$ lines with
$7$ characters each. The
letters `B` and `W` denote black and white pieces, respectively.
The character `.` denotes an open
corner or intersection, except in the center of the board,
where it has no significance. The characters `|` and `-` are used to
denote connector lines that may not contain any pieces. All
inputs represents valid positions as far as which points may
contain pieces, as displayed on the left in Figure 1.
There may be up to nine black and up to nine white pieces on
the board.

If White has at least one double mill, output `double mill`, else output `no double mill`!

Sample Input 1 | Sample Output 1 |
---|---|

.--.--. |.-.-B| ||..W|| .BB.WB. ||..W|| |B-W-B| .--W--. |
double mill |

Sample Input 2 | Sample Output 2 |
---|---|

.--.--. |.-.-.| ||...|| ....... ||...|| |.-.-.| .--.--. |
no double mill |

Sample Input 3 | Sample Output 3 |
---|---|

B--.--. |W-.-.| ||BBB|| ......B ||WWW|| |W-.-W| .--B--B |
double mill |

Sample Input 4 | Sample Output 4 |
---|---|

B--B--. |W-.-B| ||BBB|| .W....B ||WWW|| |W-W-W| .--B--B |
no double mill |