2019 Rocky Mountain Regional Contest

#### Start

2019-10-26 08:00 AKDT

## 2019 Rocky Mountain Regional Contest

#### End

2019-10-26 13:00 AKDT
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# Problem CFolding 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

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.

## Output

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
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