Folding a Cube

It is well known that a set of six unit squares that are attached together in a “cross” can be folded into a cube.

But what about other initial shapes? That is, given six unit squares that are attached together along some of their sides, can we form a unit cube by folding this arrangement?

Input consists of $6$
lines each containing $6$
characters, describing the initial arrangement of unit squares.
Each character is either a `.`, meaning it is empty, or
a `#` meaning it is a unit square.

There are precisely $6$
occurrences of `#` indicating the unit squares. These
form a connected component, meaning it is possible to reach any
`#` from any other `#` without touching a
`.` by making only horizontal and vertical movements.
Furthermore, there is no $2
\times 2$ subsquare consisting of only `#`. That
is, the pattern

## ##

does not appear in the input.

If you can fold the unit squares into a cube, display
`can fold`. Otherwise display `cannot fold`.

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

...... ...... ###### ...... ...... ...... |
cannot fold |

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

...... #..... ####.. #..... ...... ...... |
can fold |

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

..##.. ...#.. ..##.. ...#.. ...... ...... |
cannot fold |

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

...... ...#.. ...#.. ..###. ..#... ...... |
can fold |