text:
Longest hypercube path
Challenge
You are given two distinct bit strings of the same length. (For example, 000 and 111.) Your goal is to find a path from one to the other such that:

At each step, you change only one bit (you can go from 000 to any of 001, 010, 100).
You cannot visit the same bit string twice.
The path is as long as possible, under these constraints.

For example, going from 000 to 111, we can take the path
000, 001, 011, 010, 110, 100, 101, 111

which visits all 8 bit strings of length 3, so it has to be the longest possible.
Rules

Standard loopholes apply.
You may take the input as two strings of zeroes and ones, or as two arrays of zeroes and ones, or as two arrays of boolean values.
You may not take the input as two integers with the right binary representation (writing 000 and 111 as 0 and 7 is not valid).
If you want, you may take the length of the bit strings as input.
Your program is allowed to output the path by printing the bit strings visited one at a time, or by returning an array of the bit strings visited (each in the same format as the input).
Your output should include the start and end of the path (which are your inputs).
This is code-golf, the shortest code in bytes wins.

Examples
0 1 -> 0, 1
10 01 -> 10, 00, 01 or 10, 11, 01
000 111 -> any of the following:

   000, 100, 110, 010, 011, 001, 101, 111

   000, 100, 101, 001, 011, 010, 110, 111

   000, 010, 110, 100, 101, 001, 011, 111

   000, 010, 011, 001, 101, 100, 110, 111

   000, 001, 101, 100, 110, 010, 011, 111

   000, 001, 011, 010, 110, 100, 101, 111

1001 1100 -> 1001, 0001, 0000, 0010, 0011, 0111, 0101, 0100, 0110, 1110, 1010, 1011, 1111, 1101, 1100 (other paths exist)

Can we also take boolean values instead of ones and zeros?

@flawr Sure, that's fine.

May we assume we will not receive two equal bit-strings (or that we may do anything if so)?

@JonathanAllan Yes, let's assume that the bit-strings are not equal.

Related

Never mind that comment, close vote retracted.

@LeakyNun The Gray code gives us the "go from 00...00 to 00...01" case of this problem. (And, of course, it can be tweaked for other cases where the start and end are adjacent.) But it would be interesting if there's a more general solution along those lines.

Can I take input as 0b input...

@StanStrum Assuming that you mean "as binary integers" then I've said in the rules that you can't.

Husk, 27 26 24 bytes
→foΛεẊδṁ≠ÖLm↓≠⁰←ġ→PΠmṠe¬

Brute force, so very slow.
Try it online!
Explanation
Husk reads naturally from right to left.
←ġ→PΠmṠe¬  Hypercube sequences ending in second input, say y=[1,1,0]
     mṠe¬  Pair each element with its negation: [[0,1],[0,1],[1,0]]
    Π      Cartesian product: [[0,0,1],[1,0,1],..,[1,1,0]]
   P       Permutations.
 ġ→        Group by last element
←          and take first group.
           The permutations are ordered so that those with last element y come first,
           so they are grouped together and returned here.

ÖLm↓≠⁰  Find first input.
  m     For each permutation,
   ↓≠⁰  drop all elements before the first input.
ÖL      Sort by length.

foΛεẊδṁ≠  Check path condition.
fo        Keep those lists that satisfy:
    Ẋ      For each adjacent pair (e.g. [0,1,0] and [1,1,0]),
      ṁ    take sum of
       ≠   absolute differences
     δ     of corresponding elements: 1+0+0 gives 1.
  Λε       Each value is at most 1.

→  Finally, return last element (which has greatest length).

Mathematica, 108 bytes
a=#~FromDigits~2+1&;Last@PadLeft[IntegerDigits[#-1,2]&/@FindPath[HypercubeGraph@Length@#,a@#,a@#2,∞,All]]&

Input:
[{0, 0, 0, 0}, {1, 1, 1, 1}]

Output:
{{0, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 1}, {0, 0, 1, 0}, {0, 1, 1, 0},
 {0, 1, 0, 0}, {0, 1, 0, 1}, {1, 1, 0, 1}, {1, 0, 0, 1}, {1, 0, 0, 0},
 {1, 1, 0, 0}, {1, 1, 1, 0}, {1, 0, 1, 0}, {1, 0, 1, 1}, {1, 1, 1, 1}}

Haskell, 141 123 bytes
c(a:b)=(1-a:b):map(a:)(c b)
c _=[]
q#z=[z]:[z:s|w<-c z,notElem w q,s<-(w:q)#w]
x!y=snd$maximum[(p*>x,p)|p<-[x]#x,last p==y]

Uses lists of integers.
Try it online!
Explanation
The main function is !, and the auxiliary functions are # and c.
Given a list of bits, c gives all possible ways of flipping one of them, e.g. [0,1,1] -> [[1,1,1],[0,0,1],[0,1,0]].
c(a:b)=        -- c on nonempty list with head a and tail b is
 (1-a:b):      -- the list with negated a tacked to b, then
 map(a:)(c b)  -- c applied recursively to b, with a tacked to each of the results.
c _=[]         -- c on empty list gives an empty list.

The function # takes a list of lists (the "memory") and a list (the "initial bitstring").
It constructs all hypercube paths that begin with the initial element, contain only distinct bitstrings, and do not step on the strings in the memory.
q#z=            -- # on memory q and initial string z is
 [z]:           -- the singleton path [z], and
 [z:s|          -- z tacked to each path s, where
  w<-c z,       -- w is obtained by flipping a bit of z,
  notElem w q,  -- w is not in the memory, and
  s<-(w:q)#w]   -- s is a path starting from w that avoids w and all elements of q.

The main function ! ties it all together.
A trick I use here is p*>x (x repeated length p times) instead of length p.
Since longer repetitions of x come later in the natural ordering of lists, maximum chooses the longest path in either case, since the first coordinates of pairs are compared before the second ones.
x!y=          -- ! on inputs x and y is
 snd$maximum  -- the second element of the maximal pair in
 [(p*>x,p)|   -- the list of pairs (p*>x,p), where
  p<-[x]#x,   -- p is a path starting from x that avoids stepping on x, and
  last p==y]  -- p ends in y.

Mathematica, 175 bytes
Nice first question!
(m=#;n=#2;Last@SortBy[(S=Select)[S[Rest@Flatten[Permutations/@Subsets[Tuples[{0,1},(L=Length)@m]],1],First@#==m&&Last@#==n&],Union[EditDistance@@@Partition[#,2,1]]=={1}&],L])&

Input

[{0, 0, 0}, {1, 1, 1}]

Haskell, 212 207 bytes
This is probably way too long, but it finally works now. (Thanks to @Lynn for the cartesian product trick!) Thansk @nimi for -5 bytes!
import Data.List
b%l=[l++[x|b/=last l,x`notElem`l,1==sum[1|(u,v)<-x`zip`last l,u/=v]]|x<-mapM id$[0>1..]<$b]
b!a|f<-nub.concat.((b%)<$>)=snd$maximum$map(length>>=(,))$filter((==b).last)$until(f>>=(==))f[[a]]

Try it online!
Explanation:
b%l -- helper function:
    -- given a path l (that should end in b) this generates all possible extensions
    -- of l (if not possible also l itself)
            x<-mapM id$[0>1..]<$b -- generate all possible vertices of the hypercube
             -- and check the criteria
           b/=last l,x`notElem`l,1==sum[1|(u,v)<-x`zip`last l,u/=v]
             -- extend if possible
    [l++[x|  ...                                                   ]| ... ]
b!a| -- actual function:
     -- first define a helper function:
    f<-nub.concat.((b%)<$>)
     -- begin with the vertex a and apply the function from above repeatedly
     -- until you cannot make the path any longer without violating the
     -- criteria
                                                                             until(f>>=(==))f[[a]]
     -- only take the paths that actually end in b
                                                          filter((==b).last)$
     -- and find the one with the maximum length
                           =snd$maximum$map(length>>=(,))$

x<-mapM id$[1>0,1<0]<$b

... do you need [True,False]? If [False,True] also works, you can use [0>1..].

Oh great, thanks, I didn't know that Bool is Enum, and I forgot that <$ is available (first tried *> which is not in Prelude)!

Mathematica 116 114 bytes
With several bytes saved thanks to Misha Lavrov.
Last@FindPath[Graph[Rule@@@Cases[Tuples[Tuples[{0,1},{l=Length@#}],{2}],x_/;Count[Plus@@x,1]==1]],##,{1,2^l},Alll]&

Input (8 dimensions)
[{1,0,0,1,0,0,0,1},{1,1,0,0,0,0,1,1}]//AbsoluteTiming

Output (length = 254, after 1.82 seconds)
{1.82393, {{1, 0, 0, 1, 0, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0,0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 0,1, 1, 1,0}, {0, 0, 0, 0, 1, 0, 1, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 1}, {0, 0, 0, 0, 1, 0, 1, 1}, {0, 0, 0, 0,1, 1, 1, 1}, {0, 0, 0, 0, 1, 1, 0, 1}, {0, 0, 0, 0, 1, 1, 0, 0}, {0, 0, 0, 1, 1, 1, 0, 0}, {0, 0, 0, 1, 0, 1, 0, 0}, {0, 0, 0, 1,0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0}, {0, 0, 0, 1, 0, 0, 1, 1}, {0, 0, 0, 1, 0, 1, 1, 1}, {0, 0, 0, 1, 0, 1, 0, 1}, {0, 0, 0, 1, 1, 1, 0, 1}, {0, 0, 0, 1, 1, 0, 0, 1}, {0, 0, 0, 1, 1, 0, 0, 0}, {0, 0, 0, 1, 1, 0, 1, 0}, {0, 0, 0, 1, 1, 0, 1, 1}, {0, 0, 0, 1,1, 1, 1, 1}, {0, 0, 0, 1, 1, 1, 1, 0}, {0, 0, 0, 1, 0, 1, 1, 0}, {0, 0, 1, 1, 0, 1, 1, 0}, {0, 0, 1, 0, 0, 1, 1, 0}, {0, 0, 1, 0,0, 0, 1, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 1}, {0, 0, 1, 0, 0, 0, 1, 1}, {0, 0, 1, 0, 0, 1, 1, 1}, {0, 0, 1, 0,0, 1, 0, 1}, {0, 0, 1, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 0}, {0, 0, 1, 0, 1, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 0, 1}, {0, 0, 1, 0,1, 0, 1, 1}, {0, 0, 1, 0, 1, 0, 1, 0}, {0, 0, 1, 0, 1, 1, 1, 0}, {0, 0, 1, 0, 1, 1, 1, 1}, {0, 0, 1, 0, 1, 1, 0, 1}, {0, 0, 1, 1,1, 1, 0, 1}, {0, 0, 1, 1, 0, 1, 0, 1}, {0, 0, 1, 1, 0, 0, 0, 1}, {0, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 1, 0}, {0, 0, 1, 1,0, 0, 1, 1}, {0, 0, 1, 1, 0, 1, 1,1}, {0, 0, 1, 1, 1, 1, 1, 1}, {0, 0, 1, 1, 1, 0, 1, 1}, {0, 0, 1, 1, 1, 0, 0, 1}, {0, 0, 1, 1,1, 0, 0, 0}, {0, 0, 1, 1, 1, 0, 1, 0}, {0, 0, 1, 1, 1, 1, 1, 0}, {0, 0, 1, 1, 1, 1, 0, 0}, {0, 0, 1, 1, 0, 1, 0, 0}, {0, 1, 1, 1,0, 1, 0, 0}, {0, 1, 0, 1, 0, 1, 0, 0}, {0, 1, 0, 0, 0, 1, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0,0, 0, 1, 1}, {0, 1, 0, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 0, 1, 1, 0}, {0, 1, 0, 0, 0, 1, 1, 1}, {0, 1, 0, 0, 0, 1, 0, 1}, {0, 1, 0, 0,1, 1, 0, 1}, {0, 1, 0, 0, 1, 0, 0, 1}, {0, 1, 0, 0, 1, 0, 0, 0}, {0, 1, 0, 0, 1, 0, 1, 0}, {0, 1, 0, 0, 1, 0, 1, 1}, {0, 1, 0, 0,1, 1, 1, 1}, {0, 1, 0, 0, 1, 1, 1, 0}, {0, 1, 0, 0, 1, 1, 0,0}, {0, 1, 0, 1, 1, 1, 0, 0}, {0, 1, 0, 1, 1, 0, 0, 0}, {0, 1, 0, 1,0, 0, 0, 0}, {0, 1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 0, 1, 1}, {0, 1, 0, 1, 0, 0, 1, 0}, {0, 1, 0, 1, 0, 1, 1, 0}, {0, 1, 0, 1,0, 1, 1, 1}, {0, 1, 0, 1, 0, 1, 0, 1}, {0, 1, 0, 1, 1, 1, 0, 1}, {0, 1, 0, 1, 1, 0, 0, 1}, {0, 1, 0, 1, 1, 0, 1, 1}, {0, 1, 0, 1,1, 0, 1, 0}, {0, 1, 0, 1, 1, 1, 1, 0}, {0, 1, 0, 1, 1, 1, 1, 1}, {0, 1, 1, 1, 1, 1, 1, 1}, {0, 1, 1, 0, 1, 1, 1, 1}, {0, 1, 1, 0,0, 1, 1, 1}, {0, 1, 1, 0, 0, 0, 1, 1}, {0, 1, 1, 0, 0, 0, 0, 1}, {0, 1, 1, 0, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0, 1, 0}, {0, 1, 1, 0,0, 1, 1, 0}, {0, 1, 1, 0, 0, 1, 0, 0}, {0, 1, 1, 0, 0, 1, 0, 1}, {0, 1, 1, 0, 1, 1, 0, 1}, {0, 1, 1, 0, 1, 0, 0, 1}, {0, 1, 1, 0,1, 0, 0, 0}, {0, 1, 1, 0, 1, 0, 1, 0}, {0, 1, 1, 0, 1, 0, 1, 1}, {0, 1, 1, 1, 1, 0, 1, 1}, {0, 1, 1, 1, 0, 0, 1, 1}, {0, 1, 1, 1,0, 0, 0, 1}, {0, 1, 1, 1, 0, 0, 0, 0}, {0, 1, 1, 1, 0, 0, 1, 0}, {0, 1, 1, 1, 0, 1, 1, 0}, {0, 1, 1, 1, 0, 1, 1, 1}, {0, 1, 1, 1,0, 1, 0, 1}, {0, 1, 1, 1, 1, 1, 0, 1}, {0, 1, 1, 1, 1, 0, 0, 1}, {0, 1, 1, 1, 1, 0, 0, 0}, {0, 1, 1, 1, 1, 0, 1, 0}, {0, 1, 1, 1,1, 1, 1, 0}, {0, 1, 1, 0, 1, 1, 1, 0}, {0, 1, 1, 0, 1, 1, 0, 0}, {0, 1, 1, 1, 1, 1, 0, 0}, {1, 1, 1, 1, 1, 1, 0, 0}, {1, 0, 1, 1,1, 1, 0, 0}, {1, 0, 0, 1, 1, 1, 0, 0}, {1, 0, 0, 0, 1, 1, 0, 0}, {1, 0, 0, 0, 0, 1, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0,0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 1, 1}, {1, 0, 0, 0, 0, 0, 1, 0}, {1, 0, 0, 0, 0, 1, 1, 0}, {1, 0, 0, 0, 0, 1, 1, 1}, {1, 0, 0, 0,0, 1, 0, 1}, {1, 0, 0, 0, 1, 1, 0, 1}, {1, 0, 0, 0, 1, 0, 0, 1}, {1, 0, 0, 0, 1, 0, 0, 0}, {1, 0, 0, 0, 1, 0, 1, 0}, {1, 0, 0, 0,1, 0, 1, 1}, {1, 0, 0, 0, 1, 1, 1, 1}, {1, 0, 0, 0, 1, 1, 1, 0}, {1, 0, 0, 1, 1, 1, 1, 0}, {1, 0, 0, 1, 0, 1, 1, 0}, {1, 0, 0, 1,0, 0, 1, 0}, {1, 0, 0, 1, 0, 0, 0, 0}, {1, 0, 0, 1, 0, 1, 0, 0}, {1, 0, 0, 1, 0, 1, 0, 1}, {1, 0, 0, 1, 0, 1, 1, 1}, {1, 0, 0, 1,0, 0, 1, 1}, {1, 0, 0, 1, 1, 0, 1, 1}, {1, 0, 0, 1, 1, 0, 0, 1}, {1, 0, 0, 1, 1, 0, 0, 0}, {1, 0, 0, 1, 1, 0, 1, 0}, {1, 0, 1, 1,1, 0, 1, 0}, {1, 0, 1, 0, 1, 0, 1, 0}, {1, 0, 1, 0, 0, 0, 1, 0}, {1, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 1, 0, 0, 0, 0, 1}, {1, 0, 1, 0,0, 0, 1, 1}, {1, 0, 1, 0, 0, 1, 1, 1}, {1, 0, 1, 0, 0, 1, 0, 1}, {1, 0, 1, 0, 0, 1, 0, 0}, {1, 0, 1, 0, 0, 1, 1, 0}, {1, 0, 1, 0,1, 1, 1, 0}, {1, 0, 1, 0, 1, 1, 0, 0}, {1, 0, 1, 0, 1, 0, 0, 0}, {1, 0, 1, 0, 1, 0, 0, 1}, {1, 0, 1, 0, 1, 0, 1, 1}, {1, 0, 1, 0,1, 1, 1, 1}, {1, 0, 1, 0, 1, 1, 0, 1}, {1, 0, 1, 1, 1, 1, 0, 1}, {1, 0, 0, 1, 1, 1, 0, 1}, {1, 0, 0, 1, 1, 1, 1, 1}, {1, 0, 1, 1,1, 1, 1, 1}, {1, 0, 1, 1, 0, 1, 1, 1}, {1, 0, 1, 1, 0, 0, 1, 1}, {1, 0, 1, 1, 0, 0, 0, 1}, {1, 0, 1, 1, 0, 0, 0, 0}, {1, 0, 1, 1,0, 0, 1, 0}, {1, 0, 1, 1, 0, 1, 1, 0}, {1, 0, 1, 1, 0, 1, 0, 0}, {1, 0, 1, 1, 0, 1, 0, 1}, {1, 1, 1, 1, 0, 1, 0, 1}, {1, 1, 0, 1,0, 1, 0, 1}, {1, 1, 0, 0, 0, 1, 0,1}, {1, 1, 0, 0, 0, 0, 0, 1}, {1, 1, 0, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 0, 0, 1, 0}, {1, 1, 0, 0,0, 1, 1, 0}, {1, 1, 0, 0, 0, 1, 0, 0}, {1, 1, 0, 0, 1, 1, 0, 0}, {1, 1, 0, 0, 1, 0, 0, 0}, {1, 1, 0, 0, 1, 0, 0, 1}, {1, 1, 0, 0,1, 0, 1, 1}, {1, 1, 0, 0, 1, 0, 1, 0}, {1, 1, 0, 0, 1, 1, 1, 0}, {1, 1, 0, 0, 1, 1, 1, 1}, {1, 1, 0, 0, 0, 1, 1, 1}, {1, 1, 0, 1,0, 1, 1, 1}, {1, 1, 0, 1, 0, 0, 1, 1}, {1, 1, 0, 1, 0, 0, 0, 1}, {1, 1, 0, 1, 0, 0, 0, 0}, {1, 1, 0, 1, 0, 0, 1, 0}, {1, 1, 0, 1,0, 1, 1, 0}, {1, 1, 0, 1, 0, 1, 0, 0}, {1, 1, 0, 1, 1, 1, 0, 0}, {1, 1, 0, 1, 1, 0, 0, 0}, {1, 1, 0, 1, 1, 0, 0, 1}, {1, 1, 0, 1,1, 0, 1, 1}, {1, 1, 0, 1, 1, 0, 1, 0}, {1, 1, 0, 1, 1, 1, 1, 0}, {1, 1, 0, 1, 1, 1, 1, 1}, {1, 1, 0, 1, 1, 1, 0, 1}, {1, 1, 0, 0,1, 1, 0, 1}, {1, 1, 1, 0, 1, 1, 0, 1}, {1, 1, 1, 0, 0, 1, 0, 1}, {1, 1, 1, 0, 0, 0, 0, 1}, {1, 1, 1, 0, 0, 0, 0, 0}, {1, 1, 1, 0,0, 0, 1, 0}, {1, 1, 1, 0, 0, 1, 1, 0}, {1, 1, 1, 0, 0, 1, 0, 0}, {1, 1, 1, 0, 1, 1, 0, 0}, {1, 1, 1, 0, 1, 0, 0, 0}, {1, 1, 1, 0,1, 0, 0, 1}, {1, 1, 1, 0, 1, 0, 1, 1}, {1, 1, 1, 0, 1, 0, 1, 0}, {1, 1, 1, 0, 1, 1, 1, 0}, {1, 1, 1, 0, 1, 1, 1, 1}, {1, 1, 1, 0,0, 1, 1, 1}, {1, 1, 1, 1, 0, 1, 1, 1}, {1, 1, 1, 1, 0, 1, 1, 0}, {1, 1, 1, 1, 0, 0, 1, 0}, {1, 1, 1, 1, 0, 0, 0, 0}, {1, 1, 1, 1,0, 0, 0, 1}, {1, 1, 1, 1, 1, 0, 0, 1}, {1, 1, 1, 1, 1, 1, 0, 1}, {1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 0}, {1, 1, 1, 1,1, 0, 1, 0}, {1, 1, 1, 1, 1, 0, 0, 0}, {1, 0, 1, 1, 1, 0, 0, 0}, {1, 0, 1, 1, 1, 0, 0, 1}, {1, 0, 1, 1, 1, 0, 1, 1}, {1, 1, 1, 1,1, 0, 1, 1}, {1, 1, 1, 1, 0, 0, 1, 1}, {1, 1, 1, 0, 0, 0, 1, 1}, {1, 1, 0, 0, 0, 0, 1, 1}}}

Tuples[{0,1},{l=Length@#}],{2}]& generates the numbers 0...8 as binary lists.
The outer Tuples...{2} produces all ordered pairs of those binary numbers.
Plus@@x sums each of the pairs, generating triplets of 0, 1.
Cases....Count[Plus@@x, 1]==1 returns all of the sums that contain a single 1.  These arise when the two original binary numbers are connected by an edge.
Rules connects the vertices of the graph, each vertex being a binary number.
Graph creates a graph corresponding to said vertices and edges.
FindPath finds up to 2^n paths connecting vertex a to vertex b, the given numbers.
Last takes the longest of these paths.

For three dimensions, the graph can be represented in a plane as shown here:

For the input, {0,0,0}, {1,1,1}, the following is output:
{{{0, 0, 0}, {0, 0, 1}, {0, 1, 1}, {0, 1, 0}, {1, 1, 0}, {1, 0,
   0}, {1, 0, 1}, {1, 1, 1}}}
This path can be found in the above graph.
It can also be conceived as the following path in 3-space,
where each vertex corresponds to a point {x,y,z}.  {0,0,0} represents the origin and {1,1,1} represents the "opposite" point in a unit cube.
So the solution path corresponds to a traversal of edges along the unit cube.  In this case, the path is Hamiltonian: it visits each vertex one time (i.e. with no crossings and no vertices omitted).

Is there a simple reason why 2^n paths from a to b are enough paths for the longest one of them to be the longest overall?

@Misha, A  very good question.

Here's one way to think about it. The longest path, a Hamiltonian path, will be one less than the number of corners. (We're counting  the number of edges on the path.) The number of corners is 2 ^n.   So the max path length would be 2^n-1.

I agree that the maximum path length always visits either 2^n vertices (if it's Hamiltonian) or 2^n-1 vertices (if a Hamiltonian path is impossible due to parity). That's different from my question, which is: why does generating 2^(n+2) (I guess 2^n was the wrong number) different paths (some of which may be very short) guarantee that the longest of them will be the longest of all different paths.

In other words, why the 2^(l+2) in your code?

The 2^(l+2) was to specify the maximum number of paths returned.  I do not know what a reasonable estimate for this would  consist of.  Surely 2^l will be enough, so I will reduce it to that to save a few bytes.  Do you have a better value?

I do have one. All :)

Jelly,  25  27 bytes
+2 bytes to fix a bug with my golfing :( hopefully I'll find a shorter way though.
ṫi¥³ḣi
L2ṗŒ!ç€µạ2\S€ỊẠ×LµÞṪ

A full program taking the bit-strings using 1 and 2* as lists. The arguments are from and to. The program prints a list of lists of the same.
* 0 and 1 may be used instead at the cost of a byte (add ’ between L2ṗ and Œ!ç€... to decrement).
Try it online!
How?
updating...
ṫi¥³ḣi - Link 1, getSlice: list of lists, bitstrings; list, toBitstring
   ³   - get 3rd command line argument (fromBitstring)
  ¥    - last two links as a dyad:
 i     -   index (of fromBitstring in bitstrings)
ṫ      -   tail (bitstrings) from (that) index
     i - index (of toBitstring in that result)
    ḣ  - head to (that) index

L2ṗŒ!ç€µạ2\S€ỊẠ×LµÞṪ - Main link: list, fromBitstring; list, toBitstring
L                    - length (of fromBitstring)
 2                   - literal two
  ṗ                  - Cartesian power (of implicit range(2)=[1,2] with L(fromBitstring))
                     - ...i.e. all unique bitstrings of the required length (using [1,2])
   Œ!                - all permutations (of that list)
     ç€              - call the last link (1) as a dyad (i.e. f(that, toBitstring))
       µ         µÞ  - sort by the monadic function:
         2\          -   2-wise reduce with:
        ạ            -     absolute difference
           S€        -   sum €ach
             Ị       -   insignificant (vectorises) (abs(z)<=1 - for our purposes it's really just used for z==1 since only positive integers are possible)
              Ạ      -   all truthy? (1 if so 0 otherwise)
                L    -   length
               ×     -   multiply
                   Ṫ - tail (the last one is one of the maximal results)
                     - implicit print

How Jelly works is a mystery to me, but an input of [1,1] and [2,2] produces output of [[1, 1], [2, 1], [1, 2], [2, 2]] when I Try It Online, which isn't a valid path.

Hmm I must have done something wrong - looking...

OK fixed by reverting one of my golfs for 2 bytes.


text:
Exact Cover Puzzle
CHALLENGE
Given a set of grouped letters, arrange them onto the board so that they cover the area entirely.
Board Representation (a.k.a. the SHIP DECK)

The board is a 6x6 grid.
There will always be 36 total squares.
Columns are marked A-F.
Rows are marked 1-6.

Example:
    A   B   C   D   E   F
  +---+---+---+---+---+---+
1 :   :   :   :   :   :   :
  +---+---+---+---+---+---+
2 :   :   :   :   :   :   :
  +---+---+---+---+---+---+
3 :   :   :   :   :   :   :
  +---+---+---+---+---+---+
4 :   :   :   :   :   :   :
  +---+---+---+---+---+---+
5 :   :   :   :   :   :   :
  +---+---+---+---+---+---+
6 :   :   :   :   :   :   :
  +---+---+---+---+---+---+

INPUT (a.k.a. the CRATES)

A multiline string containing the set of grouped letters.
Crates are made from the groups of identical letters.
The crates are IMMUTABLE, meaning they can't be rotated or flipped.
The starting point for each crate is on the top left (should be taken into account when moving a crate onto the deck).
From the top left point of a crate, the following identical squares can only be to the right or below.
Any letter can be used to represent a crate. The crates always start at letter [a] and move up the alphabet.
Crates are labeled by their letter (i.e. crate A, crate B, etc.)
The number of crates can vary (it isn't always 10, despite the examples given).
There are 24 characters separating each block of crates per line. (start of [a] to start of [b] separated by 24 characters, etc.)

Example:
[a][a][a]               [b]                     [c][c]
      [a]               [b][b][b]                  [c]
      [a]               [b][b]

[d]                     [e]                     [f][f][f][f][f]
[d][d]                  [e]
[d][d]                  [e]
                        [e]
                        [e][e]

[g]                     [h]                     [i]
[g]                                             [i]
                                                [i]

OUTPUT
It is required that you print out a series of commands that place the crates in positions on the deck so that it is covered completely (no empty spaces).
The command format is like so:
HAUL <crate> TO <column> <row>
i.e. HAUL E TO A 1
For clarification, there will always be a solution for the input given.
TEST CASES <-- Click for more.
Input
[a][a][a]               [b]                     [c][c][c]
   [a][a]               [b]
   [a]                  [b][b]
                        [b][b]

[d]                     [e]                     [f]
[d]                                             [f]
[d]                                             [f]
[d]
[d]

[g][g]                  [h]                     [i]
                                                [i][i]
                                                   [i]
                                                   [i][i]

[j][j][j]

Output
HAUL I TO A 1
HAUL B TO A 3
HAUL A TO B 1
HAUL J TO D 6
HAUL D TO F 1
HAUL F TO E 1
HAUL C TO C 5
HAUL G TO D 4
HAUL E TO D 3
HAUL H TO C 6

Result:
    A   B   C   D   E   F
  +---+---+---+---+---+---+
1 : i : a : a : a : f : d :
  +---+---+---+---+---+---+
2 : i : i : a : a : f : d :
  +---+---+---+---+---+---+
3 : b : i : a : e : f : d :
  +---+---+---+---+---+---+
4 : b : i : i : g : g : d :
  +---+---+---+---+---+---+
5 : b : b : c : c : c : d :
  +---+---+---+---+---+---+
6 : b : b : h : j : j : j :
  +---+---+---+---+---+---+

SCORING
This is code-golf so the shortest answer in characters wins.

Can one assume that no crate will ever have any holes?

I assume there can be at most twenty-six crates?

The crate layout brackets are an unnecessary part of input, in the sense that the input could be clearer without them, and the layout is tedious to parse. As is, the parsing stage could be predominant in the answers respect to the real problem solving stage. But it's your challenge after all, so we need to follow your rules

Python 3.6, 435 437 385 331 bytes
Call F() with the crate string.
def R(b,d,i=0):
 if not d:return 1
 (k,x),*d=d
 while x:
  if x&b<1and R(b|x,d):print(f'HAUL {k.upper()} TO {i%7+65:c} {i//7+1}');return 1
  i+=1;x>>=1
def F(t,d={},e={}):
 r=c=0
 for a in t:
  if'`'<a<'{':e[a]=x,y=e.get(a,(r,c));d[a]=d.get(a,0)+(1<<(48-(r-x)*7-(c-y)//3))
  elif'\n'==a:r+=1;c=-1
  c+=1
 R(4432676798719,d.items())

Managed to golf it a lot more:

Parse the crate string directly instead of using the re library.
Used setdefault to save the first coordinate of a set of crates, so that the bitmask can be created when parsing the crate string.  Eliminating a for loop.

Prior version

import re
def R(b,d,i=0):
 if not d:return 1
 (k,x),*d=d
 while x:
  if not x&b and R(b|x,d):print(f'HAUL {k.upper()} TO {i%7+65:c} {i//7+1}');return 1
  i+=1;x>>=1
def F(t,d={},n=0):
 for r in t.split('\n'):
  for m in re.finditer(r'(.)]',r):d[m[1]]=d.get(m[1],[])+[(n,m.start())]
  n+=1
 R(4432676798719,[(k,sum(1<<(48-(r-v[0][0])*7-(c-v[0][1])//3)for r,c in v))for k,v in d.items()])

Restructured the code to remove redundant loops.

Previous code built a list of all positions of a crate in F() and then iterated over the list in R(). New code creates one position of a crate in F() and R() tries all possible positions.
In previous code, R() collected a possible solution in a and F() then iterated over the returned solution.  In new code, R() prints the HAUL commands directly

Previous version

import re
def R(b,d,a=[]):
 if not d:yield a
 for x in d[0]:
  if not x&b:yield from R(b|x,d[1:],a+[x])
def F(t,d={},n=0):
 for r in t.split('\n'):
  for m in re.finditer(r'(.)]',r):d[m[1]]=d.get(m[1],[])+[(n,m.start())]
  n+=1
 for k,j in enumerate(next(R(4432676798719,[[sum(1<<(48-(r-v[0][0])*7-(c-v[0][1])//3)for r,c in v)>>i for i in range(48)]for k,v in d.items()]))):x=51-len(bin(j));print(f'HAUL {k+65:c} TO {x%7+65:c} {x//7+1}')

Explanation
The basic idea is to represent the ship's deck and the crates as bit maps. By using bitmaps, moving a crate becomes a shift of its bitmap and checking for overlap between crates becomes a bit-wise AND and test for zero.
Ungolfed code:
import re

def F(crate_string):                                                                 #  3
  coords = {}
  row_no = 0

  for row in crate_string.split('\n'):                                               #  7

    for match_obj in re.finditer('(.)]', row):                                       #  9

      crate_name = match_obj[1]                                                      # 11
      col_no = match_obj.start()                                                     # 12
      coords[crate_name] = coords.get(crate_name, []) + [(row_no, col_no)]           # 13

    row_no += 1

  normed = {k:[(r-v[0][0], (c-v[0][1])//3) for r,c in v] for k,v in coords.items()}  # 17
  bitmaps = [(k,sum(1<<(48 - r*7 - c) for r,c in v)) for k,v in normed.items()]      # 18

  R(4432676798719, bitmaps)                                                          # 20

def R(used, bitmaps):                                                                # 22
  if not bitmaps:                                                                    # 23
    return True                                                                      # 24
  shift = 0                                                                          # 25
  (crate_name, crate_bitmap),*bitmaps = bitmaps                                      # 26

  while crate_bitmap:                                                                # 28
    if not used & crate_bitmap:                                                      # 29
      if R(used | crate_bitmap, bitmaps):                                            # 30
        print(f'HAUL {crate_name.upper()} TO {shift%7 + 65:c} {shift//7 + 1}')       # 31
        return True                                                                  # 32

    shift += 1                                                                       # 34
    crate_bitmap >>= 1                                                               # 35

  return False                                                                       # 37

F() parses the crate definition string and builds the bit maps.  A regex searches (line 9) each line of the crate definition string for crates (a letter followed by a ']').  When a match is found, the corresponding (row,col) is added to a dictionary keyed by the letter (lines 11-13).  For the example crate definition string given in the problem:
coords = {'a': [(0, 5), (0, 8), (0, 11), (1, 5), (1, 8), (1, 11)],
          'b': [(0, 29), (1, 29), (2, 29)],
               ... }

The coordinates of each crate are normalized (line 17), so that each crate starts at (0,0) and each block is one unit wide (instead of 3 a la '[a]').
normed = {'a': [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2)],
          'b': [(0, 0), (1, 0), (2, 0)],
               ... }

A bitmap is then created for each crate based on the normalized coordinates (line 18).
The deck is treated as a 7 x 7 grid.  Column 'G' and row 7 are used to detect when a shape extends off the board.  A bitmap has a 1 if the crates would occupy the corresponding square on the deck.  Bits 48 to bit to 42 correspond to squares A1 to A7, bits 41 to 35 correspond to squares B1 to B7, and so on.
bitmaps = [('a', 0b1110000_1110000_0000000_0000000_0000000_0000000_0000000),
           ('b', 0b1000000_1000000_1000000_0000000_0000000_0000000_0000000),
           ...
           ]

R(used, bitmaps) then uses the bitmaps to recursively search for crate placements that don't try to put two crates in the same square.  used is a bitmask indicating which squares can't be used because they are already occupied by a crate or because they are off the board (i.e., column G and row 7).  bitmaps is a list of crates that still need to be placed.
The base case for the recursion is when there are no more crates left to place, i.e., bitmaps is empty (line 23).  In this case True is returned to indicate a solution has been found.
Otherwise, a crate name and its bitmap are popped off the list of bitmaps (line 26).  While the crate bitmap is not empty (line 28), check if the current crate placement, represented by the crate bitmap, conflicts with any previously placed crates. At line 29, not used & crate_bitmap is False if used and crate_bitmap both have a 1 in the same bit position, indicating a conflict.  If there is not a conflict, R() is called recursively (line 30) to try and place the remaining crates.
If the recursive call to R() returns True, it means that a solution has been found and that the current placement of the crates is part of that solution.  So the corresponding command to move the crates is printed and True is propagated up the recursive calls (lines 31-32).
When created in F(), each crate bitmap represents the deck squares that would be occupied by the crates if they are placed at position A1.  Shifting a bitmap one bit to the right corresponds to moving the crates to position A2.  A seven bit right shift corresponds to moving the crates to B1, etc.  For example, the following bitmaps represent crates 'a' at various positions:
0b1110000_1110000_0000000_0000000_0000000_0000000_0000000  represent crates 'a' at A1
0b0111000_0111000_0000000_0000000_0000000_0000000_0000000  represent crates 'a' at A2
0b0011100_0011100_0000000_0000000_0000000_0000000_0000000  represent crates 'a' at A3
                                 ...
0b0000000_1110000_1110000_0000000_0000000_0000000_0000000  represent crates 'a' at B1
                                 ...

If a possible placement of crates doesn't work because it conflicts with a previously placed crate (line 30) or because there is not a valid placement of the remaining crates (line 31).  The crates are moved to a different position by shifting the bitmask right one bit (line 35).  Shift keeps track of how many places the bit map has been shifted, which corresponds to the current position of the crates.
If the bitmap is empty (zero), it indicates that all possible placement have been tried.  False is returned (line 37) to indicate failure so that a call to R() earlier in the recursion will try another placement for its crates.
To ensure that the crates don't extend off the side of the deck, bits corresponding to column G and row 7 are set in used for the initial call to R() (line 20).
4432676798719 is the empty deck corresponding to 0b0000001000000100000010000001000000100000011111111

Nice work! I just tried this on one of the test cases though and it tried to haul a crate to a 0 row, but that isn't a valid row. There are only rows 1-6. Think it just needs a +1 to the division. :)

@JMPicazo - fixed it.

Python 2, 864 bytes

Thanks to Stephen for finding a bug.
The string parsing could be golfed significantly, as the input format is stricter than what it can handle.

def V(C,S=0,D=-1,J=0,H=[],E=enumerate,R=range,r=str.replace,s=str.split,e="!"):
 if[]<C*0:
	J=0;N=[J]*26;K=[]
	for c in s(r(r(r(C,"[",""),"]",""),"   ","*"),2*"\n"):
	 c=[list(_)for _ in s(c,"\n")]
	 for x,_ in E(c[0]):
		if all(c[y][x]<">"for y,_ in E(c)):
		 for y,_ in E(c):c[y][x]=e
	 for j,y in E(c):
		y="".join(y)
		while"!!"in y:y=r(y,2*e,e)
		c[j]=s(y,e)
	 K+=[],[],[],[];J+=4
	 for y in c:
		while""in y:y.remove("")
		for j,x in E(y):K[j+J-4]+=x,
	for k in K:
	 if all(k)and k:N[ord(k[0][0])-97]=[[x>"*"for x in y]for y in k]
	while 0in N:N.remove(0)
	C=N
 if[]>S:S=[0]*36
 if-~D>0:
	Y=J/6;j=0
	for y in C[D]:
	 X=J%6
	 for x in y:
		if x:
		 if X>5or Y>5or S[X+Y*6]:return
		 S[X+Y*6]=x
		X+=1
	 Y+=1
 if~-len(C)==D:
	if 0in S:return
	for h in H[1:]+[J]:print"HAUL %c TO %c %d"%(65+j,65+h%6,h/6+1);j+=1
	j/0
 for j in R(36):V(C,S[:],-~D,j,H*(D>=0)+[J])

Try it online!
Explanation
A lot of bytes are used to parse the two-dimensional crates inputted through a single string. Crates are represented as a nested list of boolean values.
After the crates are parsed, the function considers all possible positions of all crates. To do so, it iteratively calls itself. When it finds an impossible position (if the crate would be placed outside the deck or on top of another crate), it kills the current recursion tree branch to improve performance.
When it sees that a certain combination of placements resulted in a completely covered deck, it prints the recorded crate placement history and globally exits by attempting a hopeless division. The printed haul instructions are even sorted alphabetically.

Python 2, 812 bytes
def f(C,M=[],d=0,R=range,E=enumerate,L=len):
 if C*0=="":
	N=[0]*26;K=[];J=0
	r=str.replace
	for c in r(r(r(C,"[",""),"]",""),"   ","*").split("\n\n"):
	 c=[list(_)for _ in c.split("\n")]
	 for x in R(L(c[0])):
		if all(c[y][x]=="*"for y in R(L(c))):
		 for y in R(L(c)):c[y][x]="!"
	 for j,y in E(c):
		y="".join(y)
		while"!!"in y:y=r(y,"!!","!")
		c[j]=y.split("!")
	 for _ in"_"*L(c):K+=[],
	 for y in c:
		for j,x in E(y):K[j+J]+=x,
	 J+=L(c)
	for k in K:
	 if all(k)and k:N[ord(k[0][0])-97]=[[x!="*"for x in y]for y in k]
	while 0in N:N.remove(0)
	C=N
 if d==L(C):
	j=0;S=[j]*36
	for c,k in E(C):
	 Y=M[c]/6
	 for y in k:
		X=M[c]%6
		for x in y:
		 if X<6>Y:S[X+Y*6]|=x
		 X+=1
		Y+=1
	if 0in S:return
	for m in M:print"HAUL %c TO %c %d"%(65+j,65+m%6,1+m/6);j+=1
	j/0
 for j in R(36):f(C,M*(d>=0)+[j],d+1)

Try it online!
Explanation
The crate string is parsed and transformed into a listed nest of booleans representing each crate.
An iterative function generates all possible lists of length equal to the amount of crates given containing the integers 0 <= x < 36 (all possible ship deck positions). Every list is interpreted as an instruction to position all crates and tested. If the tested instruction list results in a deck with no empty spaces, the instruction list has to be valid and gets printed.
Being extremely inefficient, I did not test it on the provided test case, though on scenarios with fewer crates (see the TIO link). Because the algorithm searches through every possible arrangement, it tries to look at 36**10 = 3.656e15 of them. Yet in theory it should still work.

If you can make it work with the provided input cases, then that would make this answer-worthy. :) Otherwise good work and this is useful information!

@JonathanMicaelPicazo people in code-golf like writing answers that are a couple bytes shorter but might terminate after the heat death of the universe...

(Sadly) you will probably need to move the default values for H/M out of the function declaration, since having them in the declaration makes the functions not reusable. Good ol' Python.

@Stephen Thanks for noticing. Python and its mutability... Fixed the problem by setting the list's lengths to zero on the first function call.

@JonathanFrech Hmm. I think you took my earlier comment quite literally - it seems to only work with the given test inputs. I should have specified: "if you can make it work with inputs similar to the format provided by the test cases". I've tried experimenting with 11 different use cases, but each of them come back empty.

@JonathanMicaelPicazo The program expects two new lines to seperate crates vertically.

@JonathanMicaelPicazo I hopefully fixed my string parser and linked to your new test cases. Crate number three takes too long on TIO, though if you swap crate [i] with [b], it works. The algorithm could be improved by first sorting the crates so that bulkier ones get tested before small ones.

@JonathanFrech Do you by chance have an ungolfed version of that script? I'm trying to understand the way you've coded it but the single-lettered short variables are making it difficult...

@JonathanMicaelPicazo No, I do not. The program started as a golf and ended as a golf.

@JonathanFrech I see... well, would you be willing to go the extra mile and improve it so it sorts the crates from bulkiest to least bulky? I've been giving it a lot of different test cases, and some of them are solved very quickly whilst others more often than not timed out or even left unsolved... I'd understand if you don't have the time, but I figure it's at least worth asking!

I see a different brute force algorithm with order <num of crates>!, which is manageable for 10 crates or so.  But is there any actually efficient algorithm?

@JonathanMicaelPicazo if you have more test cases, put a reference to them in your question

JavaScript, 366
k=>(x=y=0,C={},B=[...k].map((c,p)=>(c<' '?(x=0,++y):c<'a'?++x:(c=C[c=parseInt(c,36)]||(C[c]=[[],x,y]))[0].push((y-c[2])*7+(x++-c[1])/3),p<8|p>48|p%7<1)),S=[],R=i=>!C[i]||B.some((v,p)=>v?0:C[i][0].every(q=>B[q+=p]?0:B[q]=i)&&R(i+1,S[i-10]=p)||!C[i][0].map(q=>B[q+=p]==i?B[q]=0:0)),R(10),S.map((v,c)=>`HAUL ${(c+10).toString(36)} TO ${(v%7+9).toString(36)} ${v/7|0}`))

Note: this function can parse a more compact input, as it does not care about spacing by 24 chars, and holes in crates are allowed.
I think it could be golfed a little more, but now it's short and not too much slow, so I like it as is
Less golfed
k=>(
  // input parsing
  var x = 0, y = 0, // current position
      C = []; // crates
  [...k].forEach( c =>
  c < ' '
  ? (x = 0, ++y) // found a newline, increment y, reset x
  : c < 'a'
    ? ++x // not a letter, increment x
    : (  // found a letter, update the crate
        c = parseInt(c,36), // letter to number (10..35)
        c = C[c], // current crate in c
        c || (C[c]=[[], x, y]), // if new crate, initialize it setting base position
        c[0].push((y - c[2])*7 + (x-c[1])/3) // add current position
        ++x // increment x also
      )
  );
  var B = [...Array(7*8)] // empty board. in golfed code I reuse k to build B. k is big enough
  B = B.map( (_, p) => // set borders
     p < 8 | p > 48 | p%7<1
  )
  var S = [] // output steps

  // recursive function to fill board
  var R = i =>
    ! C[i] // if crate at position i exists (else, we have found a solution and return true)
    ||
    B.some( (v,p) => // try to put crate at each position in B
      v // current cell is used already ?
      ? 0 // used, return false
      : C[i][0].every( q => // try this position, must place every part
          B[q+=p] // current position in B is used ?
          ? 0 // used, stop, return false
          : B[q]=i // mark as used
        )
        && R(i+1,S[i-10]=p) // ok for current crate, try next, mark step
        || // else, fail for current crate, clear position marked
        !C[i][0].map(q =>
          B[q+=p]==i ? B[q]=0:0 // clear if it was set to 'i'
        )
    ),
  R(10) // start recursive fill at position 10 (that is 'a')
  // it returns true if ok, but we don't care as we are assured a solution exists
  // now just format output
  return S.map((v,c)=>`HAUL ${(c+10).toString(36)} TO ${(v%7+9).toString(36)} ${v/7|0}`)
)

Test cases lots of them

var F=
k=>(x=y=0,C={},B=[...k].map((c,p)=>(c<' '?(x=0,++y):c<'a'?++x:(c=C[c=parseInt(c,36)]||(C[c]=[[],x,y]))[0].push((y-c[2])*7+(x++-c[1])/3),p<8|p>48|p%7<1)),S=[],R=i=>!C[i]||B.some((v,p)=>v?0:C[i][0].every(q=>B[q+=p]?0:B[q]=i)&&R(i+1,S[i-10]=p)||!C[i][0].map(q=>B[q+=p]==i?B[q]=0:0)),R(10),
// Just for debug: return the fill in addition to the steps
[B.slice(7,50).map((c,i)=>i%7?c.toString(36):'\n'),
S.map((v,c)=>`HAUL ${(c+10).toString(36)} TO ${(v%7+9).toString(36)} ${v/7|0}`)])

var Test = [
 "[a][a][a]               [b]                     [c][c]\n      [a]               [b][b][b]                  [c]\n      [a]               [b][b]\n\n[d]                     [e]                     [f][f][f][f][f]\n[d][d]                  [e]\n[d][d]                  [e]\n                        [e]\n                        [e][e]\n\n[g]                     [h]                     [i]\n[g]                                             [i]\n                                                [i]"
,"[a][a][a]               [b]                     [c][c][c]\n   [a][a]               [b]\n   [a]                  [b][b]\n                        [b][b]\n\n[d]                     [e]                     [f]\n[d]                                             [f]\n[d]                                             [f]\n[d]\n[d]\n\n[g][g]                  [h]                     [i]\n                                                [i][i]\n                                                   [i]\n                                                   [i][i]\n\n[j][j][j]"
,"[a]                     [b][b][b]               [c]\n[a]                           [b]\n[d]                     [e]                     [f][f]\n[d]                     [e]\n[d][d][d]\n[g]                     [h]                     [i]\n[g]                     [h][h][h]               [i]\n                              [h]               [i][i]\n                              [h]                  [i]\n                                                   [i]\n[j]                     [k][k][k]\n[j]\n[j]"
,"[a][a][a][a]            [b][b][b]               [c]\n                              [b]               [c]\n                              [b]               [c][c]\n                                                   [c][c]\n[d]                     [e]                     [f]\n[d]                                             [f][f][f]\n[g]                     [h]                     [i][i]\n                        [h][h][h]               [i][i]\n                           [h][h]\n[j]\n[j]\n[j]"
,"[a]                     [b]                     [c][c]\n[a]                     [b]\n[a]\n[d][d]                  [e]                     [f][f][f]\n[d][d][d]\n[g]                     [h]                     [i]\n                        [h]\n                        [h]\n                        [h][h]\n                           [h]\n[j]                     [k][k][k]\n[j][j]                     [k][k]\n[j][j][j]                     [k]"
,"[a]                     [b][b][b]               [c]\n[a]                                             [c]\n                                                [c]\n[d][d]                  [e]                     [f]\n[d][d][d][d]            [e]                     [f]\n                        [e][e][e][e]            [f]\n[g]                     [h][h][h]               [i][i][i]\n                              [h]               [i][i][i]\n[j][j]"
,"[a]                     [b]                     [c][c][c]\n                        [b]\n[d]                     [e][e]                  [f][f]\n[d][d][d]                                       [f][f]\n[d][d]\n[g]                     [h][h][h]               [i]\n[g]                           [h]               [i][i]\n[g]                           [h]               [i][i]\n[g]\n[g]\n[j]\n[j]\n[j]"
,"[a][a]                  [b]                     [c]\n   [a][a]               [b][b]                  [c]\n                        [b][b][b]               [c]\n[d]                     [e][e][e]               [f][f][f]\n[d]                     [e][e][e]\n[g][g]                  [h]                     [i]\n                                                [i]\n                                                [i][i]\n[j][j]\n   [j]\n   [j]\n   [j]"
,"[a][a]                  [b]                     [c]\n[a][a]                  [b][b]                  [c]\n                        [b][b][b]\n[d][d]                  [e]                     [f][f][f]\n[g]                     [h]                     [i][i]\n[g]                     [h]                        [i]\n[g]                     [h]\n[g]\n[g][g]\n[j]\n[j]\n[j]\n[j][j]\n   [j]"
,"[a]                     [b]                     [c][c][c][c][c]\n                        [b]\n                        [b][b][b]\n                              [b]\n[d]                     [e]                     [f][f][f]\n                        [e]\n                        [e]\n                        [e][e][e]\n[g]                     [h]                     [i]\n[g]                     [h]\n[g]                     [h]\n                        [h]\n[j][j]                  [k]\n[j][j]                  [k]"
,"[a]                     [b]                     [c]\n                                                [c]\n                                                [c]\n[d][d][d]               [e]                     [f]\n                        [e][e][e]               [f]\n                                                [f][f][f]\n                                                   [f]\n[g][g][g]               [h][h]                  [i]\n[g][g][g]                                       [i][i]\n                                                [i][i]\n[j]                     [k]\n[j]                     [k]\n[j]"
,"[a][a]                  [b]                     [c]\n                        [b]                     [c][c][c]\n                        [b]                           [c]\n                        [b][b]                        [c]\n                           [b]\n[d]                     [e]                     [f]\n[d]\n[g]                     [h]                     [i]\n[g][g][g]               [h]                     [i]\n                        [h][h][h]               [i]\n                              [h]\n[j][j][j]               [k][k]"
,"[a][a]                  [b][b][b]               [c]\n                        [b][b][b]\n[d]                     [e]                     [f]\n[d]                     [e]                     [f]\n                        [e]                     [f]\n                        [e][e]\n                           [e]\n[g][g][g]               [h][h]                  [i]\n                        [h][h]                  [i]\n                        [h][h]                  [i][i]\n                                                   [i]\n                                                   [i]\n[j]"
,"[a][a][a]               [b][b]                  [c][c]\n                        [b][b]                  [c][c]\n                        [b][b]                  [c][c]\n[d][d]                  [e]                     [f][f]\n   [d]                  [e]\n                        [e]\n                        [e]\n                        [e]\n[g]                     [h]                     [i][i]\n[g]                                             [i][i]\n[g]\n[g]\n[g][g]"
,"[a][a][a]               [b]                     [c]\n      [a]                                       [c]\n      [a]\n[d]                     [e][e][e]               [f][f]\n[d]\n[g]                     [h][h]                  [i]\n[g][g][g]               [h][h]                  [i]\n   [g][g]                                       [i]\n[j]                     [k]\n[j]                     [k]\n[j][j]\n   [j]\n   [j]"
,"[a][a]                  [b]                     [c][c]\n                        [b][b]\n                        [b][b][b]\n[d]                     [e][e][e]               [f][f]\n                        [e][e][e]                  [f][f][f]\n[g]                     [h]                     [i][i]\n[g]                     [h]                     [i][i]\n[g]                                             [i][i]\n[j][j][j]"
,"[a][a]                  [b][b][b]               [c]\n   [a]                     [b][b]\n   [a][a][a]\n[d][d]                  [e]                     [f]\n[d][d]                  [e][e]                  [f][f][f]\n                        [e][e]\n                           [e]\n[g][g][g]               [h]                     [i]\n                                                [i]\n                                                [i]\n                                                [i]\n[j][j]"
,"[a]                     [b][b]                  [c]\n[a]                                             [c]\n[a]\n[a][a][a]\n[d]                     [e][e][e][e]            [f]\n[d]                                             [f]\n                                                [f]\n[g]                     [h]                     [i]\n[g]                     [h][h]\n[g]                     [h][h][h]\n[g]\n[g][g]\n[j]                     [k][k]\n                           [k]"
,"[a]                     [b][b]                  [c]\n[a]                     [b][b][b]               [c]\n[a][a][a][a]                                    [c]\n[d][d][d]               [e]                     [f]\n   [d][d]               [e]\n[g]                     [h]                     [i]\n                        [h]                     [i]\n                        [h]\n                        [h]\n                        [h][h]\n[j][j][j][j][j]"
,"[a][a]                  [b][b]                  [c]\n   [a][a][a]\n   [a]\n[d]                     [e][e][e]               [f][f]\n[d]\n[g]                     [h][h]                  [i]\n[g]                     [h][h]\n[g]                     [h][h]\n[g]\n[j]                     [k]\n[j][j]                  [k][k]\n                        [k][k]\n                           [k]"
,"[a][a][a]               [b]                     [c]\n                                                [c]\n                                                [c][c][c][c]\n[d]                     [e][e][e]               [f][f][f]\n[d]                     [e][e][e]               [f][f][f]\n[d]\n[g]                     [h][h]                  [i][i]\n[g]                                             [i][i]\n[j]\n[j]\n[j]"
,"[a]                     [b]                     [c][c]\n                        [b]                     [c][c]\n                        [b]\n[d][d][d]               [e]                     [f]\n      [d]                                       [f]\n                                                [f]\n[g]                     [h]                     [i]\n[g]                     [h][h][h]               [i][i]\n                        [h][h]                  [i][i][i]\n[j]                     [k]                     [l][l][l][l]"
,"[a]                     [b]                     [c]\n[a][a]                  [b]\n[a][a]\n[d]                     [e]                     [f]\n[d]                     [e]\n[d]                     [e][e][e]\n[d]                        [e]\n[g]                     [h][h][h]               [i][i]\n[g][g]\n[j][j][j]               [k]\n[j][j][j]               [k]\n                        [k]"
,"[a]                     [b]                     [c][c]\n[a][a][a]               [b]                     [c][c]\n   [a][a]               [b]\n                        [b]\n                        [b][b]\n[d]                     [e]                     [f]\n[d]                     [e]\n[d]\n[g]                     [h][h][h][h]            [i]\n[j][j]                  [k]\n                        [k]\n                        [k][k]\n                           [k]\n                           [k]"
,"[a]                     [b][b][b]               [c]\n[a]                     [b][b][b]               [c][c][c]\n[a]\n[d]                     [e]                     [f][f][f][f]\n                        [e]\n                        [e]\n                        [e]\n                        [e]\n[g]                     [h]                     [i]\n                        [h][h]                  [i]\n                        [h][h]                  [i][i][i]\n                                                   [i]\n[j]"
,"[a][a][a]               [b]                     [c]\n                        [b]                     [c]\n                        [b][b][b]\n                              [b]\n[d][d][d]               [e][e]                  [f]\n                        [e][e]                  [f]\n                                                [f]\n                                                [f][f][f]\n[g]                     [h]                     [i]\n[g]                                             [i]\n[g]                                             [i]\n                                                [i]\n                                                [i][i]\n[j][j]"
,"[a]                     [b]                     [c]\n[a]                     [b]\n[a][a]                  [b]\n[d]                     [e][e][e]               [f]\n[d]                           [e]               [f]\n                              [e]               [f]\n                              [e]               [f][f]\n                                                   [f]\n[g][g]                  [h]                     [i]\n                                                [i]\n[j][j][j]               [k]\n                        [k][k][k]\n                        [k][k]"
,"[a][a][a]               [b][b]                  [c]\n                           [b]                  [c]\n[d]                     [e][e]                  [f]\n[d]                                             [f]\n[d][d]\n   [d][d]\n[g]                     [h]                     [i]\n                        [h]\n                        [h]\n[j][j]                  [k]                     [l]\n[j][j][j]               [k]                     [l][l][l]\n      [j]               [k]"
,"[a][a]                  [b]                     [c][c][c]\n[d]                     [e][e]                  [f][f]\n[d]                     [e][e]                  [f][f]\n[d]\n[d]\n[g]                     [h][h][h]               [i]\n[g]                                             [i]\n[g]\n[g][g][g]\n[j]                     [k]\n[j]\n[j][j][j][j]"
,"[a][a][a]               [b][b]                  [c]\n[d]                     [e]                     [f]\n[d][d][d]                                       [f][f][f][f]\n[d][d]                                                   [f]\n[g][g]                  [h][h][h]               [i]\n                                                [i]\n                                                [i]\n[j]                     [k]                     [l]\n[j]                                             [l]\n                                                [l][l]\n                                                [l][l]"
,"[a][a][a]               [b]                     [c]\n                        [b]                     [c]\n                                                [c]\n[d][d]                  [e][e]                  [f]\n   [d]\n   [d]\n   [d]\n[g]                     [h]                     [i][i]\n[g][g]                  [h]                     [i][i][i]\n                        [h][h][h]                     [i]\n                              [h]\n[j][j]                  [k]\n[j][j]"
,"[a]                     [b][b][b]               [c]\n[a]                           [b]               [c]\n[a][a]                        [b]               [c]\n   [a][a]\n[d]                     [e][e][e]               [f][f]\n[d][d][d]                                       [f][f]\n   [d][d]\n[g]                     [h]                     [i][i]\n[j]                     [k]\n[j]                     [k][k]"
,"[a]                     [b]                     [c]\n                                                [c]\n                                                [c][c]\n                                                   [c][c]\n[d][d][d][d][d]         [e]                     [f][f]\n                                                [f][f]\n[g]                     [h]                     [i][i]\n[g]                     [h][h]                  [i][i]\n[g]                                             [i][i]\n[g]\n[g]\n[j][j]\n[j][j]"
,"[a]                     [b][b]                  [c][c]\n                           [b]                  [c][c]\n                           [b]\n[d][d]                  [e][e]                  [f]\n[d][d][d]               [e][e][e]\n[g]                     [h]                     [i]\n[g]                     [h]\n[g][g][g][g]            [h]\n                        [h]\n                        [h]\n[j][j][j][j]"
,"[a]                     [b][b][b]               [c][c][c]\n[a]                        [b][b]\n[a]\n[a][a]\n   [a]\n[d]                     [e]                     [f]\n[d]                                             [f]\n[d]                                             [f]\n[g]                     [h]                     [i][i]\n[g][g]                  [h]                     [i][i]\n[g][g][g]\n[j]                     [k][k]"
,"[a]                     [b][b]                  [c]\n[a]                     [b][b]\n                        [b][b]\n[d]                     [e]                     [f][f][f]\n[d][d][d]\n[d][d]\n[g]                     [h]                     [i][i]\n[g]                     [h]\n[g]\n[j][j][j]               [k]\n      [j]               [k]\n                        [k]\n                        [k][k]\n                           [k]"
,"[a][a][a]               [b]                     [c]\n   [a][a]\n[d][d][d]               [e]                     [f][f]\n                        [e]\n[g]                     [h]                     [i]\n[g][g]                  [h]                     [i]\n[g][g][g]               [h]                     [i]\n[j]                     [k][k]\n[j][j]                  [k][k][k]\n[j][j]"
,"[a][a][a]               [b]                     [c][c][c][c][c]\n   [a][a]               [b]\n      [a]               [b]\n                        [b]\n[d]                     [e]                     [f]\n[d][d]                                          [f]\n[d][d][d]                                       [f]\n[g]                     [h][h]                  [i][i][i]\n                        [h][h]                  [i][i][i]"
,"[a][a]                  [b]                     [c]\n                        [b]\n                        [b]\n[d][d][d]               [e]                     [f]\n                                                [f]\n                                                [f]\n                                                [f]\n[g][g][g]               [h][h]                  [i]\n[g][g][g]               [h][h]                  [i][i]\n                                                [i][i][i]\n[j][j][j]\n   [j][j]\n      [j]"
,"[a]                     [b]                     [c]\n[a]                                             [c]\n[a]                                             [c]\n[a]                                             [c][c][c]\n[a][a]\n[d]                     [e]                     [f]\n                        [e]\n                        [e]\n[g][g]                  [h][h]                  [i][i][i]\n[g][g]\n[g][g]\n[j]                     [k][k][k]\n[j]\n[j]\n[j]"
,"[a][a][a]               [b]                     [c]\n      [a][a]            [b][b]                  [c]\n      [a]               [b][b][b]               [c]\n                                                [c]\n[d]                     [e][e][e]               [f]\n[d][d][d]\n[d][d]\n[g]                     [h]                     [i][i]\n                                                [i][i]\n[j]                     [k][k]\n[j]"
,"[a]                     [b][b]                  [c]\n                                                [c]\n                                                [c][c]\n                                                [c][c]\n[d]                     [e][e][e]               [f][f]\n[d][d][d]                                          [f][f]\n                                                      [f]\n[g]                     [h]                     [i]\n                                                [i][i]\n                                                   [i][i]\n                                                      [i]\n[j]                     [k]                     [l][l]\n[j]\n[j]\n[j]"
,"[a]                     [b]                     [c][c][c]\n[a]                     [b]                        [c][c]\n[a]                     [b]\n[a]\n[a][a]\n[d]                     [e]                     [f][f]\n                        [e][e]\n                        [e][e]\n                           [e]\n[g]                     [h]                     [i][i]\n                                                [i][i]\n                                                [i][i]\n[j]                     [k][k][k]\n[j]"
,"[a][a][a]               [b]                     [c]\n                                                [c]\n                                                [c]\n                                                [c][c]\n                                                   [c]\n[d][d][d]               [e]                     [f]\n      [d]                                       [f]\n                                                [f]\n[g][g]                  [h]                     [i]\n                        [h]                     [i][i][i]\n                                                [i][i]\n[j][j]                  [k]\n[j][j]                  [k]\n[j][j]"
,"[a][a]                  [b][b]                  [c][c]\n                           [b][b]\n                              [b]\n[d]                     [e][e][e]               [f]\n[d]                     [e][e][e]               [f]\n[d][d]\n   [d][d]\n[g][g][g]               [h]                     [i]\n                        [h]                     [i][i]\n                        [h]\n[j]                     [k]\n                        [k]\n                        [k]"
,"[a][a][a]               [b][b]                  [c]\n      [a]                                       [c][c][c]\n                                                [c][c]\n[d]                     [e]                     [f]\n                                                [f]\n                                                [f]\n                                                [f]\n[g]                     [h][h]                  [i][i][i]\n[g]                     [h][h]\n[g]                     [h][h]\n[g][g][g]\n[j][j][j]"
,"[a][a]                  [b][b]                  [c][c][c][c][c]\n[a][a][a]                  [b]\n[d]                     [e][e][e]               [f]\n[d]                     [e][e][e]               [f]\n[d][d][d][d]                                    [f]\n                                                [f]\n                                                [f]\n[g]                     [h]\n                        [h]\n                        [h]\n                        [h]\n                        [h]"
,"[a]                     [b][b]                  [c]\n[a]                                             [c]\n[a]                                             [c]\n[a]                                             [c]\n[a]\n[d]                     [e]                     [f]\n[g]                     [h][h][h][h]            [i][i][i]\n[g]                                             [i][i][i]\n[g][g][g][g]\n[j][j]\n[j][j][j][j]"
,"[a]                     [b]                     [c]\n                        [b][b]\n                        [b][b][b]\n[d][d][d]               [e]                     [f][f]\n   [d][d]               [e]                     [f][f]\n      [d]               [e]\n                        [e]\n[g][g]                  [h]                     [i][i][i]\n                        [h]                     [i][i][i]\n                        [h]\n[j][j][j]"
,"[a][a]                  [b][b]                  [c]\n                                                [c]\n                                                [c]\n                                                [c]\n                                                [c][c]\n[d]                     [e]                     [f][f][f]\n                        [e]\n                        [e]\n                        [e][e][e]\n[g][g]                  [h]                     [i]\n                        [h][h][h]               [i]\n                        [h][h]                  [i]\n[j]                     [k]\n                        [k]\n                        [k]\n                        [k]"
,"[a]                     [b]                     [c][c][c][c][c]\n[a]\n[a][a][a][a]\n[d][d]                  [e]                     [f]\n[d][d]\n[g]                     [h][h]                  [i]\n[g]                     [h][h][h]               [i]\n[j]                     [k]\n[j]                     [k]\n[j]                     [k]\n                        [k][k]\n                           [k]"
,"[a]                     [b]                     [c]\n[a][a]                  [b]\n                        [b]\n                        [b][b]\n                           [b]\n[d]                     [e]                     [f][f][f]\n[d]                     [e]                     [f][f][f]\n                        [e]\n[g]                     [h]                     [i]\n                        [h]                     [i]\n                        [h]                     [i][i][i]\n                                                      [i]\n[j][j][j][j][j]"
,"[a]                     [b]                     [c][c]\n                        [b]                     [c][c]\n                        [b]\n                        [b]\n[d][d]                  [e][e][e]               [f][f]\n[d][d]\n[g]                     [h][h]                  [i][i]\n                        [h][h]                  [i][i]\n                        [h][h]\n[j]                     [k]\n                        [k]\n                        [k][k][k]\n                              [k]"
,"[a][a]                  [b][b]                  [c]\n   [a][a]                  [b]                  [c]\n      [a]                  [b]                  [c]\n                           [b]                  [c]\n[d]                     [e]                     [f]\n                                                [f][f]\n                                                [f][f][f]\n[g][g]                  [h][h][h]               [i]\n[j][j]                  [k][k]\n                        [k][k][k][k]"
,"[a]                     [b]                     [c]\n                                                [c]\n                                                [c]\n                                                [c][c]\n                                                   [c]\n[d]                     [e][e]                  [f][f]\n                        [e][e][e]\n                              [e]\n[g]                     [h]                     [i][i][i]\n                        [h]\n                        [h]\n                        [h]\n                        [h]\n[j][j]                  [k]                     [l]\n                        [k]                     [l]\n                                                [l][l]\n                                                   [l][l]"
,"[a][a]                  [b]                     [c]\n   [a]                                          [c][c]\n   [a]                                             [c]\n   [a]                                             [c]\n   [a]                                             [c]\n[d]                     [e]                     [f]\n[d]                                             [f]\n[d][d]                                          [f]\n   [d]                                          [f]\n   [d]\n[g][g][g]               [h][h]                  [i]\n                                                [i]\n                                                [i]\n                                                [i]\n                                                [i][i]\n[j]"
,"[a]                     [b]                     [c][c]\n                        [b]\n                        [b]\n[d]                     [e][e]                  [f]\n[d][d][d]                  [e]                  [f][f]\n[d][d]                                          [f][f][f]\n[g][g][g]               [h][h][h]               [i][i]\n                              [h][h]            [i][i]\n[j]                     [k]\n[j]"
,"[a][a][a]               [b][b]                  [c]\n                           [b]                  [c][c][c]\n                                                [c][c]\n[d]                     [e][e]                  [f][f]\n[d]                                             [f][f]\n[g]                     [h]                     [i][i][i][i]\n[g][g]                  [h]                           [i][i]\n[g][g][g]               [h]\n[j]"
,"[a][a][a]               [b]                     [c]\n                                                [c]\n                                                [c][c]\n                                                [c][c]\n[d]                     [e]                     [f]\n[d][d][d]               [e]                     [f]\n                                                [f][f]\n                                                   [f][f]\n[g]                     [h]                     [i][i]\n[g]                     [h]\n[g]                     [h]\n[j][j][j]\n[j][j]\n   [j]"
,"[a]                     [b]                     [c]\n                        [b]                     [c][c][c][c]\n                        [b]                           [c]\n[d][d]                  [e][e][e]               [f]\n[d][d][d][d]\n[g]                     [h]                     [i][i][i]\n[g]                     [h]\n[g]\n[j][j]                  [k]\n                        [k]\n                        [k][k][k]\n                              [k]"
,"[a]                     [b]                     [c]\n[a]                                             [c]\n[a]                                             [c]\n[a][a]\n   [a]\n[d]                     [e][e]                  [f][f]\n[g][g]                  [h][h][h]               [i]\n[g][g]                                          [i]\n   [g]\n[j]                     [k]                     [l]\n[j]                     [k]                     [l]\n[j][j]                  [k]\n   [j][j]"
,"[a]                     [b]                     [c][c]\n                        [b]                        [c][c]\n                        [b]                        [c][c]\n                        [b]\n                        [b][b]\n[d][d][d][d]            [e]                     [f]\n                        [e][e]\n                        [e][e]\n                           [e]\n[g]                     [h]                     [i]\n                        [h]\n                        [h]\n                        [h]\n[j]                     [k]                     [l][l]\n                                                [l][l]"
,"[a]                     [b][b][b]               [c]\n[a][a]                        [b]               [c]\n[a][a]                        [b]               [c]\n                                                [c][c][c]\n[d][d]                  [e]                     [f]\n                        [e]                     [f][f][f]\n                                                [f][f]\n[g]                     [h][h][h]               [i]\n[g]\n[g]\n[j][j][j]"
,"[a][a]                  [b][b][b]               [c]\n                              [b]               [c]\n[d]                     [e]                     [f][f][f][f]\n[d][d][d][d][d]\n[g]                     [h]                     [i]\n[g]                     [h][h][h]               [i]\n[g][g][g]                     [h][h]            [i]\n      [g]\n[j]                     [k]"
,"[a]                     [b][b][b][b]            [c]\n[a][a][a]                                       [c]\n   [a][a]                                       [c]\n[d]                     [e]                     [f]\n[d]                                             [f]\n[g][g][g]               [h]                     [i][i]\n      [g]                                       [i][i]\n[j]                     [k]\n[j]                     [k]\n[j][j]                  [k]\n   [j]\n   [j]"
,"[a][a][a]               [b]                     [c][c][c]\n   [a][a]               [b]                     [c][c][c]\n      [a]               [b]\n[d]                     [e][e][e][e]            [f]\n[d]\n[d]\n[d][d]\n   [d]\n[g]                     [h]                     [i]\n[g]\n[j]\n[j][j]\n[j][j][j]"
,"[a][a][a]               [b]                     [c]\n                        [b]\n                        [b]\n[d]                     [e]                     [f]\n[d]                     [e]                     [f][f]\n[d]\n[d][d][d]\n[g]                     [h]                     [i][i][i][i]\n[j]                     [k][k]\n[j][j]                     [k][k]\n[j][j][j]                     [k]\n                              [k]"
,"[a][a]                  [b][b][b]               [c]\n[a][a]                                          [c][c]\n                                                [c][c][c]\n[d]                     [e][e]                  [f]\n                                                [f]\n                                                [f]\n                                                [f]\n[g]                     [h]                     [i][i]\n[g][g]                  [h]                        [i]\n                        [h]\n[j][j]                  [k]\n   [j][j]\n      [j]\n      [j]"
,"[a]                     [b]                     [c][c][c][c][c]\n[a]                     [b]\n[a]\n[d][d][d]               [e]                     [f]\n[d][d][d]               [e]                     [f]\n                        [e][e]                  [f]\n                        [e][e]                  [f]\n                                                [f][f]\n[g]                     [h]                     [i][i]\n                                                [i][i]\n                                                [i][i]"
,"[a]                     [b]                     [c]\n[a]                     [b]\n[a]                     [b][b]\n[a]                        [b][b]\n[d][d][d][d]            [e]                     [f][f]\n                                                [f][f]\n[g][g]                  [h]                     [i][i]\n[g][g]                  [h][h][h]               [i][i]\n   [g][g]                                          [i]\n[j]"
,"[a]                     [b][b][b]               [c]\n[a][a][a]                     [b]\n[a][a]                        [b]\n[d][d][d]               [e]                     [f]\n                        [e][e][e]\n                        [e][e]\n[g][g]                  [h]                     [i]\n                        [h]                     [i]\n                        [h]\n[j]                     [k][k]\n[j]                     [k][k]\n[j]"
,"[a][a]                  [b][b][b][b]            [c]\n   [a][a]                                       [c]\n   [a][a]\n[d]                     [e]                     [f]\n[d]\n[d][d]\n   [d]\n   [d]\n[g][g]                  [h]                     [i]\n[g][g]                                          [i]\n[j]                     [k]\n[j]                     [k][k]\n[j]                        [k]\n                           [k]\n                           [k]"
,"[a][a]                  [b]                     [c]\n                        [b]                     [c]\n                        [b]\n[d][d][d]               [e]                     [f]\n[d][d][d]               [e]                     [f][f]\n                        [e]                     [f][f][f]\n[g]                     [h]                     [i]\n                        [h]                     [i]\n                                                [i][i]\n                                                   [i]\n                                                   [i]\n[j]                     [k]                     [l][l][l]"
,"[a]                     [b]                     [c]\n                                                [c]\n                                                [c]\n[d]                     [e][e][e]               [f]\n                                                [f]\n                                                [f]\n                                                [f][f][f]\n[g]                     [h][h][h][h]            [i]\n[g]                                             [i][i]\n                                                [i][i][i]\n[j][j]                  [k][k]\n[j][j]                     [k][k]\n                              [k]"
,"[a][a][a]               [b]                     [c]\n                        [b][b][b][b]            [c]\n                                 [b]            [c]\n[d]                     [e][e][e]               [f][f]\n[d]                     [e][e][e]\n[d][d][d][d]\n[g][g]                  [h]                     [i]\n[g][g]                  [h]\n[j][j][j]"
,"[a]                     [b][b][b]               [c]\n[a]                           [b]               [c]\n[a]                                             [c][c][c]\n                                                      [c]\n[d][d]                  [e][e][e][e]            [f]\n[d][d]\n[g]                     [h]                     [i]\n                        [h][h][h]               [i]\n                              [h][h]\n[j]                     [k][k]\n                        [k][k]"
,"[a][a][a]               [b]                     [c][c][c]\n                                                      [c]\n[d]                     [e]                     [f]\n[d]                                             [f][f][f]\n[d]                                             [f][f]\n[g]                     [h][h]                  [i]\n                        [h][h]                  [i]\n                                                [i]\n[j]                     [k]                     [l][l]\n[j]                     [k][k][k]\n                        [k][k]"
,"[a]                     [b]                     [c]\n[a]                     [b][b]\n[a]                     [b][b][b]\n[a]\n[d]                     [e]                     [f][f][f]\n[d][d]                  [e]                        [f][f]\n[d][d]                  [e]\n   [d]                  [e]\n[g][g]                  [h]                     [i]\n[j]                     [k][k][k]\n[j][j]"
,"[a][a][a][a][a]         [b]                     [c][c]\n                                                [c][c]\n[d][d][d]               [e]                     [f][f]\n[d][d][d]                                          [f]\n                                                   [f]\n[g]                     [h][h]                  [i]\n[g]                     [h][h][h]               [i]\n[g][g][g][g]                                    [i]\n                                                [i]"
,"[a][a]                  [b]                     [c][c][c]\n                        [b]\n                        [b]\n                        [b][b]\n                           [b]\n[d]                     [e][e]                  [f]\n[d]\n[d]\n[d]\n[g][g]                  [h]                     [i]\n   [g]                                          [i]\n   [g]                                          [i][i]\n                                                   [i]\n                                                   [i]\n[j]                     [k]\n                        [k][k]\n                           [k]\n                           [k][k]"
,"[a][a]                  [b]                     [c][c]\n[a][a][a]               [b][b]\n      [a]\n[d]                     [e]                     [f]\n[d]                     [e]                     [f]\n[d][d][d]               [e]\n   [d]\n[g]                     [h][h][h]               [i][i][i]\n                                                [i][i][i]\n[j][j]\n   [j]\n   [j]"
,"[a][a][a][a]            [b]                     [c]\n                                                [c][c]\n                                                [c][c][c]\n[d][d][d]               [e][e][e]               [f]\n                           [e][e]               [f]\n                                                [f]\n[g]                     [h]                     [i]\n[g]                     [h]                     [i]\n                        [h]                     [i]\n                        [h]                     [i][i][i]\n                        [h]\n[j]"
,"[a]                     [b]                     [c][c][c]\n[a]                     [b]\n[a][a]                  [b][b]\n                        [b][b]\n[d][d]                  [e]                     [f]\n   [d][d]               [e][e]\n      [d]                  [e]\n      [d]                  [e]\n                           [e]\n[g][g]                  [h]                     [i]\n                        [h]\n                        [h]\n                        [h]\n                        [h]\n[j][j]"
,"[a]                     [b][b][b][b]            [c]\n[a]\n[a][a][a][a]\n[d]                     [e]                     [f]\n[d]                     [e]                     [f]\n                        [e]                     [f]\n[g][g][g]               [h][h][h]               [i][i]\n[g][g][g]               [h][h][h]               [i][i]\n[j]"
,"[a]                     [b][b][b][b]            [c]\n[a][a]                        [b][b]\n[a][a][a]\n[d]                     [e][e]                  [f][f]\n[d]                     [e][e]                     [f]\n[d]\n[d]\n[g][g][g]               [h]                     [i]\n                        [h][h][h]\n                        [h][h]\n[j][j]"
,"[a][a]                  [b]                     [c][c][c][c][c]\n[a][a][a]\n[d][d][d]               [e]                     [f][f]\n      [d]\n      [d]\n[g]                     [h]                     [i]\n[g][g][g]               [h]                     [i]\n   [g][g]                                       [i]\n[j]\n[j]\n[j][j]\n[j][j]"
,"[a][a][a]               [b]                     [c]\n                        [b][b][b]               [c]\n                        [b][b]                  [c]\n                                                [c]\n                                                [c]\n[d][d]                  [e]                     [f][f]\n                                                [f][f]\n[g][g][g]               [h]                     [i]\n      [g]                                       [i][i]\n      [g][g]                                    [i][i][i]\n[j]\n[j]"
,"[a]                     [b][b]                  [c]\n[d]                     [e]                     [f]\n[d]\n[g][g]                  [h][h]                  [i]\n[g][g][g]                                       [i]\n      [g]                                       [i][i]\n                                                   [i][i]\n[j][j][j]               [k]                     [l]\n                        [k]                     [l]\n                        [k]                     [l]\n                                                [l][l]\n                                                   [l]\n[m]\n[m]"
,"[a]                     [b]                     [c]\n                        [b]                     [c]\n                        [b][b]\n                           [b][b]\n[d][d][d][d][d]         [e]                     [f][f][f]\n                                                [f][f][f]\n[g]                     [h]                     [i][i]\n[g]                     [h][h]                     [i][i]\n[g]                                                [i][i]\n[j]\n[j]\n[j]"
,"[a]                     [b][b][b]               [c]\n[a][a]                        [b]               [c]\n[a][a][a]                     [b][b]            [c]\n[d][d]                  [e]                     [f]\n                                                [f][f][f]\n                                                [f][f]\n[g][g][g]               [h]                     [i]\n                        [h]                     [i]\n[j][j]                  [k]\n[j][j]"
,"[a][a][a]               [b][b][b]               [c]\n      [a]               [b][b][b]               [c]\n      [a]\n[d]                     [e]                     [f]\n[d]                     [e][e][e]               [f]\n[d]                        [e][e]\n[g]                     [h]                     [i][i][i]\n[g]\n[g][g]\n   [g]\n   [g]\n[j][j]"
,"[a]                     [b]                     [c][c][c][c]\n[a][a]                  [b]\n   [a]                  [b]\n   [a][a]\n[d]                     [e]                     [f]\n                        [e]\n                        [e][e]\n                           [e]\n                           [e]\n[g][g]                  [h]                     [i]\n                        [h]                     [i]\n[j]                     [k]                     [l][l]\n                        [k]                        [l][l]\n                                                   [l][l]"
,"[a]                     [b]                     [c]\n[d]                     [e]                     [f]\n[d][d]                  [e]                     [f]\n   [d][d]               [e][e]                  [f]\n      [d]                  [e][e]\n[g]                     [h]                     [i][i][i][i]\n[g]                     [h]\n[j][j][j]               [k]\n   [j][j]               [k][k][k]\n      [j]"
,"[a]                     [b]                     [c]\n[a]\n[a]\n[a]\n[d]                     [e][e][e][e]            [f][f]\n                                                [f][f]\n[g][g][g]               [h]                     [i][i][i]\n                        [h]                     [i][i][i]\n                        [h][h][h][h]\n[j]\n[j]\n[j]\n[j][j][j]"
,"[a][a]                  [b]                     [c]\n[a][a]\n[d][d][d][d][d]         [e]                     [f]\n                        [e][e][e]               [f]\n                              [e][e]            [f]\n                                                [f]\n                                                [f]\n[g]                     [h]                     [i]\n[g]                     [h][h]\n[g][g]\n   [g][g]\n[j][j][j]\n      [j]"
,"[a]                     [b][b][b]               [c]\n[a]                           [b]               [c]\n[a][a][a]                     [b]               [c]\n                              [b]\n[d]                     [e][e]                  [f][f]\n                                                [f][f]\n[g]                     [h]                     [i]\n[g]                     [h][h][h]               [i]\n                        [h][h]                  [i]\n[j]                     [k][k][k]"
,"[a]                     [b]                     [c]\n                        [b]                     [c]\n                        [b][b]\n                        [b][b]\n[d]                     [e]                     [f]\n[d]                     [e]\n[d]                     [e]\n[d]\n[d][d]\n[g]                     [h]                     [i][i]\n[g][g]                  [h][h]                     [i]\n                           [h][h]\n                              [h]\n[j]                     [k][k][k][k]"
,"[a][a]                  [b]                     [c][c][c][c][c]\n                        [b]\n                        [b]\n[d]                     [e]                     [f][f][f]\n                        [e]                     [f][f][f]\n[g]                     [h][h]                  [i]\n                           [h]                  [i]\n                           [h]                  [i][i]\n                                                   [i][i]\n[j]\n[j]\n[j]\n[j]\n[j][j]"
,"[a][a][a]               [b][b]                  [c][c]\n                        [b][b]\n[d]                     [e]                     [f][f]\n[d]                     [e]                     [f][f]\n[d]\n[g]                     [h]                     [i]\n                        [h]                     [i][i]\n                        [h]                     [i][i][i]\n                        [h]\n                        [h]\n[j][j][j]\n   [j][j]\n      [j]"
,"[a][a]                  [b][b]                  [c]\n[a][a]                                          [c][c]\n[a][a]                                             [c]\n                                                   [c]\n                                                   [c]\n[d]                     [e][e][e]               [f]\n                                                [f]\n                                                [f]\n[g]                     [h][h][h]               [i]\n[g]                        [h][h]               [i]\n[j]\n[j]\n[j][j]\n   [j]\n   [j]"
,"[a][a]                  [b]                     [c]\n[a][a]                  [b]                     [c]\n                        [b][b][b]               [c]\n                              [b]               [c][c][c]\n[d]                     [e]                     [f][f]\n[d]\n[g][g][g]               [h][h][h]               [i]\n                                                [i]\n                                                [i]\n[j]\n[j]\n[j]\n[j]\n[j][j]"
]

to=0
function update() {
  var nt=+I.value
  var test = Test[nt-1]
  if (test) {
    O.textContent = test
    clearTimeout(to)
    to = setTimeout(_=>{
      I.disabled = true
      var t = + new Date()
      var [d,r]=F(test)
      O.textContent = 'Time '+(new Date-t)/1000+' sec'+d+r.join`\n`+'\n'+test
      I.disabled = false
    }, 800)
  }
}

update()
Test # <input id=I value=1 type=number oninput='update()' max=101 min=1> (1 to 101, be patient: some testcase is slow to solve)
<pre id=O></pre>

There are other test cases linked to the TEST CASES text.

@JonathanMicaelPicazo added

source: Stack Exchange

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/

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