4
$\begingroup$

Tom has written numbers 1, 2, 3, 4, 5, 6, and 7 in one sequence, but in such an order that if we cross out any three numbers, there will always remain four numbers, which do not form a descending nor an ascending sequence.

Can you possibly recreate the sequence given by Tom?

Is there but only one way of forming such a sequence?

$\endgroup$
6
$\begingroup$

There are plenty of ways, so no, we cannot recreate the sequence.

Any sequence will work, as long as it has exactly three increasing parts, and the parts are ordered so that no later part has an element greater than the parts before. Similar logic works for making the parts decreasing.

 3 2 1 4 7 6 5 (monotonous parts of length 3-1-3)
 5 6 7 4 1 2 3 (ditto)
6 7 3 4 5 1 2 (2-3-2) 2 1 5 4 3 7 6 (ditto)
3 2 1 6 5 4 7 (3-3-1) 5 6 7 2 3 4 1
2 1 4 3 7 6 5 (2-2-3) and so on, you get the point.

There are several other solutions too:

you can also intersperse the monotonous sequences:

 7 4 1 5 2 6 3 (the parts are 7, 4-5-6 and 1-2-3 (also found by Sneftel.))
 3 6 2 5 1 4 7 (its reverse)
 7 4 5 1 2 6 3 (you can also intersperse only a little. This is 7, 4-5-6 and 1-2-3, where the 6 was moved 2 places to the right)
 
When interspersing, you don't always even have to keep all the parts in order:
 6 1 7 4 2 5 3 (6-7, 1-2-3 and 4-5 creatively interspersed)
 
You must be careful with this method though, it's easy to accidentally complete the three-length part to four.

Finally, you can mix all the approaches:
 6 7 1 4 2 5 3 (1-2-3 interspersed with 4-5, preceded by 6-7)
 3 2 1 7 5 6 4 (3-2-1, followed by interspersed 7-6 and 5-4.)

There may be other solutions, but I couldn't find them.

NB. most of these methods should work even if Tom had added the numbers 8 and 9.

$\endgroup$
2
  • 1
    $\begingroup$ You forgot to include the obvious condition that each of the parts must consist of fewer than 4 digits. This is also the real reason why you can't use fewer than three parts. $\endgroup$ Dec 1 '17 at 9:25
  • $\begingroup$ @Bass After plugging this into a quick python program, out of the 5040 possible arrangements of [1,2,3,4,5,6,7] 2127 of them are possible solutions. The way i looked at this is if the longest increasing or decreasing sub-sequence is greater than 4 the arrangement will not work. $\endgroup$
    – lPlant
    Dec 1 '17 at 17:49
2
$\begingroup$

Well,

1 4 7 3 6 2 5 (cycling around in increments of 3)

seems to fit the bill.

5 2 6 3 7 4 1 (the reverse of the first sequence) does as well. Naturally, any valid sequence could not be unique, because its reverse would work. I have my doubts there are any others than these two, though.

EDIT:

Nope, there's also 7 4 1 5 2 6 3 (8-n of the first sequence) and its reverse.

$\endgroup$
1
  • $\begingroup$ +1, but Bass's is more descriptive. $\endgroup$
    – prog_SAHIL
    Dec 1 '17 at 12:37
0
$\begingroup$

Since this did not say no computers I wrote a program to get all arrangements. A permutation of [1,2,3,4,5,6,7] is valid if the longest increasing and decreasing sub sequences are at most length 3.

There are 2127 valid solutions to this, here are a bunch of them.
(Format) List: Longest Ascending, Longest Descending
(5, 4, 2, 6, 1, 7, 3) : [2, 6, 7] [5, 4, 2]
(5, 4, 2, 6, 3, 1, 7) : [2, 3, 7] [5, 4, 2]
(5, 4, 2, 6, 3, 7, 1) : [2, 3, 7] [5, 4, 2]
(5, 4, 2, 6, 7, 1, 3) : [2, 6, 7] [5, 4, 2]
(5, 4, 2, 6, 7, 3, 1) : [2, 6, 7] [5, 4, 2]
(5, 4, 2, 7, 1, 3, 6) : [1, 3, 6] [5, 4, 2]
(5, 4, 2, 7, 1, 6, 3) : [1, 3] [5, 4, 2]
(5, 4, 2, 7, 3, 1, 6) : [2, 3, 6] [5, 4, 2]
(5, 4, 2, 7, 3, 6, 1) : [2, 3, 6] [5, 4, 2]
(5, 4, 2, 7, 6, 1, 3) : [1, 3] [5, 4, 2]
(5, 4, 3, 6, 1, 2, 7) : [1, 2, 7] [5, 4, 3]
(5, 4, 3, 6, 1, 7, 2) : [3, 6, 7] [5, 4, 3]
(5, 4, 3, 6, 2, 1, 7) : [3, 6, 7] [5, 4, 3]
(5, 4, 3, 6, 2, 7, 1) : [3, 6, 7] [5, 4, 3]
(5, 4, 3, 6, 7, 1, 2) : [3, 6, 7] [5, 4, 3]
(5, 4, 3, 6, 7, 2, 1) : [3, 6, 7] [5, 4, 3]
(5, 4, 3, 7, 1, 2, 6) : [1, 2, 6] [5, 4, 3]
(5, 4, 3, 7, 1, 6, 2) : [1, 2] [5, 4, 3]
(5, 4, 3, 7, 2, 1, 6) : [1, 6] [5, 4, 3]
(5, 4, 3, 7, 2, 6, 1) : [2, 6] [5, 4, 3]
(5, 4, 3, 7, 6, 1, 2) : [1, 2] [5, 4, 3]
(5, 4, 6, 1, 2, 7, 3) : [1, 2, 3] [5, 4]
(5, 4, 6, 1, 3, 2, 7) : [1, 2, 7] [5, 4]
(5, 4, 6, 1, 3, 7, 2) : [1, 3, 7] [5, 4]
(5, 4, 6, 1, 7, 2, 3) : [1, 2, 3] [5, 4]
(5, 4, 6, 1, 7, 3, 2) : [4, 6, 7] [7, 3, 2]
(5, 4, 6, 2, 1, 3, 7) : [1, 3, 7] [6, 2, 1]
(5, 4, 6, 2, 1, 7, 3) : [4, 6, 7] [6, 2, 1]
(5, 4, 6, 2, 3, 1, 7) : [2, 3, 7] [5, 4]
(5, 4, 6, 2, 3, 7, 1) : [2, 3, 7] [5, 4]
(5, 4, 6, 2, 7, 1, 3) : [4, 6, 7] [5, 4]
(5, 4, 6, 2, 7, 3, 1) : [4, 6, 7] [7, 3, 1]
(5, 4, 6, 3, 1, 2, 7) : [1, 2, 7] [6, 3, 1]
(5, 4, 6, 3, 1, 7, 2) : [4, 6, 7] [6, 3, 1]
(5, 4, 6, 3, 2, 7, 1) : [4, 6, 7] [6, 3, 2]
(5, 4, 6, 3, 7, 1, 2) : [4, 6, 7] [5, 4]
(5, 4, 6, 3, 7, 2, 1) : [4, 6, 7] [7, 2, 1]
(5, 4, 6, 7, 1, 2, 3) : [1, 2, 3] [5, 4]
(5, 4, 6, 7, 1, 3, 2) : [4, 6, 7] [5, 4]
(5, 4, 6, 7, 2, 1, 3) : [4, 6, 7] [7, 2, 1]
(5, 4, 6, 7, 2, 3, 1) : [4, 6, 7] [5, 4]
(5, 4, 6, 7, 3, 1, 2) : [4, 6, 7] [7, 3, 1]
(5, 4, 7, 1, 2, 6, 3) : [1, 2, 3] [5, 4]
(5, 4, 7, 1, 3, 2, 6) : [1, 2, 6] [5, 4]
(5, 4, 7, 1, 3, 6, 2) : [1, 3, 6] [5, 4]
(5, 4, 7, 1, 6, 2, 3) : [1, 2, 3] [5, 4]
(5, 4, 7, 1, 6, 3, 2) : [1, 2] [6, 3, 2]
(5, 4, 7, 2, 1, 3, 6) : [1, 3, 6] [7, 2, 1]
(5, 4, 7, 2, 1, 6, 3) : [1, 3] [7, 2, 1]
(5, 4, 7, 2, 3, 1, 6) : [2, 3, 6] [5, 4]
(5, 4, 7, 2, 3, 6, 1) : [2, 3, 6] [5, 4]
(5, 4, 7, 2, 6, 1, 3) : [1, 3] [5, 4]
(5, 4, 7, 2, 6, 3, 1) : [2, 3] [6, 3, 1]
(5, 4, 7, 3, 1, 2, 6) : [1, 2, 6] [7, 3, 1]
(5, 4, 7, 3, 1, 6, 2) : [1, 2] [7, 3, 1]
(5, 4, 7, 3, 2, 6, 1) : [2, 6] [7, 3, 2]
(5, 4, 7, 3, 6, 1, 2) : [1, 2] [5, 4]
(5, 4, 7, 3, 6, 2, 1) : [3, 6] [6, 2, 1]
(5, 4, 7, 6, 1, 2, 3) : [1, 2, 3] [7, 6, 1]
(5, 4, 7, 6, 1, 3, 2) : [1, 2] [7, 6, 1]
(5, 4, 7, 6, 2, 3, 1) : [2, 3] [7, 6, 2]
(5, 6, 1, 2, 7, 4, 3) : [1, 2, 3] [7, 4, 3]
(5, 6, 1, 3, 2, 7, 4) : [1, 2, 4] [6, 1]
(5, 6, 1, 3, 7, 2, 4) : [1, 2, 4] [6, 1]
(5, 6, 1, 3, 7, 4, 2) : [1, 3, 4] [7, 4, 2]
(5, 6, 1, 4, 2, 7, 3) : [1, 2, 3] [6, 1]
(5, 6, 1, 4, 3, 2, 7) : [1, 2, 7] [4, 3, 2]
(5, 6, 1, 4, 3, 7, 2) : [1, 3, 7] [6, 1]
(5, 6, 1, 4, 7, 2, 3) : [1, 2, 3] [6, 1]
(5, 6, 1, 4, 7, 3, 2) : [1, 4, 7] [7, 3, 2]
(5, 6, 1, 7, 2, 4, 3) : [1, 2, 3] [6, 1]
(5, 6, 1, 7, 3, 2, 4) : [1, 2, 4] [7, 3, 2]
(5, 6, 1, 7, 3, 4, 2) : [1, 3, 4] [6, 1]
(5, 6, 1, 7, 4, 2, 3) : [1, 2, 3] [7, 4, 2]
(5, 6, 2, 1, 3, 7, 4) : [1, 3, 4] [6, 2, 1]
(5, 6, 2, 1, 4, 3, 7) : [1, 3, 7] [6, 2, 1]
(5, 6, 2, 1, 4, 7, 3) : [1, 4, 7] [6, 2, 1]
(5, 6, 2, 1, 7, 3, 4) : [1, 3, 4] [6, 2, 1]
(5, 6, 2, 1, 7, 4, 3) : [5, 6, 7] [6, 2, 1]
(5, 6, 2, 3, 1, 7, 4) : [2, 3, 4] [6, 2]
(5, 6, 2, 3, 7, 1, 4) : [2, 3, 4] [6, 2]
(5, 6, 2, 3, 7, 4, 1) : [2, 3, 4] [7, 4, 1]
(5, 6, 2, 4, 1, 3, 7) : [1, 3, 7] [6, 2]
(5, 6, 2, 4, 1, 7, 3) : [2, 4, 7] [6, 2]
(5, 6, 2, 4, 3, 1, 7) : [2, 3, 7] [4, 3, 1]
(5, 6, 2, 4, 3, 7, 1) : [2, 3, 7] [6, 2]
(5, 6, 2, 4, 7, 1, 3) : [2, 4, 7] [6, 2]
(5, 6, 2, 4, 7, 3, 1) : [2, 4, 7] [7, 3, 1]
(5, 6, 2, 7, 1, 3, 4) : [1, 3, 4] [6, 2]
(5, 6, 2, 7, 1, 4, 3) : [5, 6, 7] [6, 2]
(5, 6, 2, 7, 3, 1, 4) : [2, 3, 4] [7, 3, 1]
(5, 6, 2, 7, 3, 4, 1) : [2, 3, 4] [6, 2]
(5, 6, 2, 7, 4, 1, 3) : [5, 6, 7] [7, 4, 1]
(5, 6, 3, 1, 2, 7, 4) : [1, 2, 4] [6, 3, 1]
(5, 6, 3, 1, 4, 2, 7) : [1, 2, 7] [6, 3, 1]
(5, 6, 3, 1, 4, 7, 2) : [1, 4, 7] [6, 3, 1]
(5, 6, 3, 1, 7, 2, 4) : [1, 2, 4] [6, 3, 1]
(5, 6, 3, 1, 7, 4, 2) : [5, 6, 7] [6, 3, 1]
(5, 6, 3, 2, 4, 1, 7) : [2, 4, 7] [6, 3, 2]
(5, 6, 3, 2, 4, 7, 1) : [2, 4, 7] [6, 3, 2]
(5, 6, 3, 2, 7, 1, 4) : [5, 6, 7] [6, 3, 2]
(5, 6, 3, 2, 7, 4, 1) : [5, 6, 7] [6, 3, 2]
(5, 6, 3, 4, 1, 2, 7) : [1, 2, 7] [6, 3]
(5, 6, 3, 4, 1, 7, 2) : [3, 4, 7] [6, 3]
(5, 6, 3, 4, 2, 1, 7) : [3, 4, 7] [4, 2, 1]
(5, 6, 3, 4, 2, 7, 1) : [3, 4, 7] [6, 3]
(5, 6, 3, 4, 7, 1, 2) : [3, 4, 7] [6, 3]
(5, 6, 3, 4, 7, 2, 1) : [3, 4, 7] [7, 2, 1]
(5, 6, 3, 7, 1, 2, 4) : [1, 2, 4] [6, 3]
(5, 6, 3, 7, 1, 4, 2) : [5, 6, 7] [6, 3]
(5, 6, 3, 7, 2, 1, 4) : [5, 6, 7] [7, 2, 1]
(5, 6, 3, 7, 2, 4, 1) : [5, 6, 7] [6, 3]
(5, 6, 3, 7, 4, 1, 2) : [5, 6, 7] [7, 4, 1]
(5, 6, 4, 1, 2, 7, 3) : [1, 2, 3] [6, 4, 1]
(5, 6, 4, 1, 3, 2, 7) : [1, 2, 7] [6, 4, 1]
(5, 6, 4, 1, 3, 7, 2) : [1, 3, 7] [6, 4, 1]
(5, 6, 4, 1, 7, 2, 3) : [1, 2, 3] [6, 4, 1]
(5, 6, 4, 1, 7, 3, 2) : [5, 6, 7] [6, 4, 1]
(5, 6, 4, 2, 3, 1, 7) : [2, 3, 7] [6, 4, 2]
(5, 6, 4, 2, 3, 7, 1) : [2, 3, 7] [6, 4, 2]
(5, 6, 4, 2, 7, 1, 3) : [5, 6, 7] [6, 4, 2]
(5, 6, 4, 2, 7, 3, 1) : [5, 6, 7] [6, 4, 2]
(5, 6, 4, 3, 7, 1, 2) : [5, 6, 7] [6, 4, 3]
(5, 6, 4, 3, 7, 2, 1) : [5, 6, 7] [6, 4, 3]
(5, 6, 4, 7, 1, 2, 3) : [1, 2, 3] [6, 4]
(5, 6, 4, 7, 1, 3, 2) : [5, 6, 7] [6, 4]
(5, 6, 4, 7, 2, 1, 3) : [5, 6, 7] [7, 2, 1]
(5, 6, 4, 7, 2, 3, 1) : [5, 6, 7] [6, 4]
(5, 6, 4, 7, 3, 1, 2) : [5, 6, 7] [7, 3, 1]
(5, 6, 7, 1, 2, 4, 3) : [1, 2, 3] [7, 1]
(5, 6, 7, 1, 3, 2, 4) : [1, 2, 4] [7, 1]
(5, 6, 7, 1, 3, 4, 2) : [1, 3, 4] [7, 1]
(5, 6, 7, 1, 4, 2, 3) : [1, 2, 3] [7, 1]
(5, 6, 7, 1, 4, 3, 2) : [5, 6, 7] [4, 3, 2]
(5, 6, 7, 2, 1, 3, 4) : [1, 3, 4] [7, 2, 1]
(5, 6, 7, 2, 1, 4, 3) : [5, 6, 7] [7, 2, 1]
(5, 6, 7, 2, 3, 1, 4) : [2, 3, 4] [7, 2]
(5, 6, 7, 2, 3, 4, 1) : [2, 3, 4] [7, 2]
(5, 6, 7, 2, 4, 1, 3) : [5, 6, 7] [7, 2]
(5, 6, 7, 2, 4, 3, 1) : [5, 6, 7] [4, 3, 1]
(5, 6, 7, 3, 1, 2, 4) : [1, 2, 4] [7, 3, 1]
(5, 6, 7, 3, 1, 4, 2) : [5, 6, 7] [7, 3, 1]
(5, 6, 7, 3, 2, 4, 1) : [5, 6, 7] [7, 3, 2]
(5, 6, 7, 3, 4, 1, 2) : [5, 6, 7] [7, 3]
(5, 6, 7, 3, 4, 2, 1) : [5, 6, 7] [4, 2, 1]
(5, 6, 7, 4, 1, 2, 3) : [1, 2, 3] [7, 4, 1]
(5, 6, 7, 4, 1, 3, 2) : [5, 6, 7] [7, 4, 1]
(5, 6, 7, 4, 2, 3, 1) : [5, 6, 7] [7, 4, 2]
(5, 7, 1, 2, 6, 4, 3) : [1, 2, 3] [6, 4, 3]
(5, 7, 1, 3, 2, 6, 4) : [1, 2, 4] [7, 1]
(5, 7, 1, 3, 6, 2, 4) : [1, 2, 4] [7, 1]
(5, 7, 1, 3, 6, 4, 2) : [1, 3, 4] [6, 4, 2]
(5, 7, 1, 4, 2, 6, 3) : [1, 2, 3] [7, 1]
(5, 7, 1, 4, 3, 2, 6) : [1, 2, 6] [4, 3, 2]
(5, 7, 1, 4, 3, 6, 2) : [1, 3, 6] [7, 1]
(5, 7, 1, 4, 6, 2, 3) : [1, 2, 3] [7, 1]
(5, 7, 1, 4, 6, 3, 2) : [1, 4, 6] [6, 3, 2]
(5, 7, 1, 6, 2, 4, 3) : [1, 2, 3] [7, 1]
(5, 7, 1, 6, 3, 2, 4) : [1, 2, 4] [6, 3, 2]
(5, 7, 1, 6, 3, 4, 2) : [1, 3, 4] [7, 1]
(5, 7, 1, 6, 4, 2, 3) : [1, 2, 3] [6, 4, 2]
(5, 7, 2, 1, 3, 6, 4) : [1, 3, 4] [7, 2, 1]
(5, 7, 2, 1, 4, 3, 6) : [1, 3, 6] [7, 2, 1]
(5, 7, 2, 1, 4, 6, 3) : [1, 4, 6] [7, 2, 1]
(5, 7, 2, 1, 6, 3, 4) : [1, 3, 4] [7, 2, 1]
(5, 7, 2, 1, 6, 4, 3) : [1, 3] [7, 2, 1]
(5, 7, 2, 3, 1, 6, 4) : [2, 3, 4] [7, 2]
(5, 7, 2, 3, 6, 1, 4) : [2, 3, 4] [7, 2]
(5, 7, 2, 3, 6, 4, 1) : [2, 3, 4] [6, 4, 1]
(5, 7, 2, 4, 1, 3, 6) : [1, 3, 6] [7, 2]
(5, 7, 2, 4, 1, 6, 3) : [2, 4, 6] [7, 2]
(5, 7, 2, 4, 3, 1, 6) : [2, 3, 6] [4, 3, 1]
(5, 7, 2, 4, 3, 6, 1) : [2, 3, 6] [7, 2]
(5, 7, 2, 4, 6, 1, 3) : [2, 4, 6] [7, 2]
(5, 7, 2, 4, 6, 3, 1) : [2, 4, 6] [6, 3, 1]
(5, 7, 2, 6, 1, 3, 4) : [1, 3, 4] [7, 2]
(5, 7, 2, 6, 1, 4, 3) : [1, 3] [7, 2]
(5, 7, 2, 6, 3, 1, 4) : [2, 3, 4] [6, 3, 1]
(5, 7, 2, 6, 3, 4, 1) : [2, 3, 4] [7, 2]
(5, 7, 2, 6, 4, 1, 3) : [1, 3] [6, 4, 1]
(5, 7, 3, 1, 2, 6, 4) : [1, 2, 4] [7, 3, 1]
(5, 7, 3, 1, 4, 2, 6) : [1, 2, 6] [7, 3, 1]
(5, 7, 3, 1, 4, 6, 2) : [1, 4, 6] [7, 3, 1]
(5, 7, 3, 1, 6, 2, 4) : [1, 2, 4] [7, 3, 1]
(5, 7, 3, 1, 6, 4, 2) : [1, 2] [7, 3, 1]
(5, 7, 3, 2, 4, 1, 6) : [2, 4, 6] [7, 3, 2]
(5, 7, 3, 2, 4, 6, 1) : [2, 4, 6] [7, 3, 2]
(5, 7, 3, 2, 6, 1, 4) : [1, 4] [7, 3, 2]
(5, 7, 3, 2, 6, 4, 1) : [2, 4] [7, 3, 2]
(5, 7, 3, 4, 1, 2, 6) : [1, 2, 6] [7, 3]
(5, 7, 3, 4, 1, 6, 2) : [3, 4, 6] [7, 3]
(5, 7, 3, 4, 2, 1, 6) : [3, 4, 6] [4, 2, 1]
(5, 7, 3, 4, 2, 6, 1) : [3, 4, 6] [7, 3]
(5, 7, 3, 4, 6, 1, 2) : [3, 4, 6] [7, 3]
(5, 7, 3, 4, 6, 2, 1) : [3, 4, 6] [6, 2, 1]
(5, 7, 3, 6, 1, 2, 4) : [1, 2, 4] [7, 3]
(5, 7, 3, 6, 1, 4, 2) : [1, 2] [7, 3]
(5, 7, 3, 6, 2, 1, 4) : [1, 4] [6, 2, 1]
(5, 7, 3, 6, 2, 4, 1) : [2, 4] [7, 3]
(5, 7, 3, 6, 4, 1, 2) : [1, 2] [6, 4, 1]
(5, 7, 4, 1, 2, 6, 3) : [1, 2, 3] [7, 4, 1]
(5, 7, 4, 1, 3, 2, 6) : [1, 2, 6] [7, 4, 1]
(5, 7, 4, 1, 3, 6, 2) : [1, 3, 6] [7, 4, 1]
(5, 7, 4, 1, 6, 2, 3) : [1, 2, 3] [7, 4, 1]
(5, 7, 4, 1, 6, 3, 2) : [1, 2] [7, 4, 1]
(5, 7, 4, 2, 3, 1, 6) : [2, 3, 6] [7, 4, 2]
(5, 7, 4, 2, 3, 6, 1) : [2, 3, 6] [7, 4, 2]
(5, 7, 4, 2, 6, 1, 3) : [1, 3] [7, 4, 2]
(5, 7, 4, 2, 6, 3, 1) : [2, 3] [7, 4, 2]
(5, 7, 4, 3, 6, 1, 2) : [1, 2] [7, 4, 3]
(5, 7, 4, 3, 6, 2, 1) : [3, 6] [7, 4, 3]
(5, 7, 4, 6, 1, 2, 3) : [1, 2, 3] [7, 4]
(5, 7, 4, 6, 1, 3, 2) : [1, 2] [7, 4]
(5, 7, 4, 6, 2, 1, 3) : [1, 3] [6, 2, 1]
(5, 7, 4, 6, 2, 3, 1) : [2, 3] [7, 4]
(5, 7, 4, 6, 3, 1, 2) : [1, 2] [6, 3, 1]
(5, 7, 6, 1, 2, 4, 3) : [1, 2, 3] [7, 6, 1]
(5, 7, 6, 1, 3, 2, 4) : [1, 2, 4] [7, 6, 1]
(5, 7, 6, 1, 3, 4, 2) : [1, 3, 4] [7, 6, 1]
(5, 7, 6, 1, 4, 2, 3) : [1, 2, 3] [7, 6, 1]
(5, 7, 6, 1, 4, 3, 2) : [1, 2] [7, 6, 1]
(5, 7, 6, 2, 3, 1, 4) : [2, 3, 4] [7, 6, 2]
(5, 7, 6, 2, 3, 4, 1) : [2, 3, 4] [7, 6, 2]
(5, 7, 6, 2, 4, 1, 3) : [1, 3] [7, 6, 2]
(5, 7, 6, 2, 4, 3, 1) : [2, 3] [7, 6, 2]
(5, 7, 6, 3, 4, 1, 2) : [1, 2] [7, 6, 3]
(5, 7, 6, 3, 4, 2, 1) : [3, 4] [7, 6, 3]
(6, 1, 3, 2, 7, 5, 4) : [1, 2, 4] [7, 5, 4]
(6, 1, 3, 7, 2, 5, 4) : [1, 2, 4] [6, 1]
(6, 1, 3, 7, 5, 2, 4) : [1, 2, 4] [7, 5, 2]
(6, 1, 4, 2, 7, 5, 3) : [1, 2, 3] [7, 5, 3]
(6, 1, 4, 3, 2, 7, 5) : [1, 2, 5] [4, 3, 2]
(6, 1, 4, 3, 7, 2, 5) : [1, 2, 5] [6, 1]
(6, 1, 4, 3, 7, 5, 2) : [1, 3, 5] [7, 5, 2]
(6, 1, 4, 7, 2, 5, 3) : [1, 2, 3] [6, 1]
(6, 1, 4, 7, 3, 2, 5) : [1, 2, 5] [7, 3, 2]
(6, 1, 4, 7, 3, 5, 2) : [1, 3, 5] [6, 1]
(6, 1, 4, 7, 5, 2, 3) : [1, 2, 3] [7, 5, 2]
(6, 1, 5, 2, 7, 4, 3) : [1, 2, 3] [7, 4, 3]
(6, 1, 5, 3, 2, 7, 4) : [1, 2, 4] [5, 3, 2]
(6, 1, 5, 3, 7, 2, 4) : [1, 2, 4] [6, 1]
(6, 1, 5, 3, 7, 4, 2) : [1, 3, 4] [7, 4, 2]
(6, 1, 5, 4, 2, 7, 3) : [1, 2, 3] [5, 4, 2]
(6, 1, 5, 4, 3, 7, 2) : [1, 3, 7] [5, 4, 3]
(6, 1, 5, 4, 7, 2, 3) : [1, 2, 3] [6, 1]
(6, 1, 5, 4, 7, 3, 2) : [1, 4, 7] [7, 3, 2]
(6, 1, 5, 7, 2, 4, 3) : [1, 2, 3] [6, 1]
(6, 1, 5, 7, 3, 2, 4) : [1, 2, 4] [7, 3, 2]
(6, 1, 5, 7, 3, 4, 2) : [1, 3, 4] [6, 1]
(6, 1, 5, 7, 4, 2, 3) : [1, 2, 3] [7, 4, 2]
(6, 1, 7, 2, 5, 4, 3) : [1, 2, 3] [5, 4, 3]
(6, 1, 7, 3, 2, 5, 4) : [1, 2, 4] [7, 3, 2]
(6, 1, 7, 3, 5, 2, 4) : [1, 2, 4] [6, 1]
(6, 1, 7, 3, 5, 4, 2) : [1, 3, 4] [5, 4, 2]
(6, 1, 7, 4, 2, 5, 3) : [1, 2, 3] [7, 4, 2]
(6, 1, 7, 4, 3, 5, 2) : [1, 3, 5] [7, 4, 3]
(6, 1, 7, 4, 5, 2, 3) : [1, 2, 3] [6, 1]
(6, 1, 7, 4, 5, 3, 2) : [1, 4, 5] [5, 3, 2]
(6, 1, 7, 5, 2, 4, 3) : [1, 2, 3] [7, 5, 2]
(6, 1, 7, 5, 3, 4, 2) : [1, 3, 4] [7, 5, 3]
(6, 2, 1, 3, 7, 5, 4) : [1, 3, 4] [6, 2, 1]
(6, 2, 1, 4, 3, 7, 5) : [1, 3, 5] [6, 2, 1]
(6, 2, 1, 4, 7, 3, 5) : [1, 3, 5] [6, 2, 1]
(6, 2, 1, 4, 7, 5, 3) : [1, 4, 5] [6, 2, 1]
(6, 2, 1, 5, 3, 7, 4) : [1, 3, 4] [6, 2, 1]
(6, 2, 1, 5, 4, 3, 7) : [1, 3, 7] [6, 2, 1]
(6, 2, 1, 5, 4, 7, 3) : [1, 4, 7] [6, 2, 1]
(6, 2, 1, 5, 7, 3, 4) : [1, 3, 4] [6, 2, 1]
(6, 2, 1, 5, 7, 4, 3) : [1, 5, 7] [6, 2, 1]
(6, 2, 1, 7, 3, 5, 4) : [1, 3, 4] [6, 2, 1]
(6, 2, 1, 7, 4, 3, 5) : [1, 3, 5] [6, 2, 1]
(6, 2, 1, 7, 4, 5, 3) : [1, 4, 5] [6, 2, 1]
(6, 2, 1, 7, 5, 3, 4) : [1, 3, 4] [6, 2, 1]
(6, 2, 3, 1, 7, 5, 4) : [2, 3, 4] [7, 5, 4]
(6, 2, 3, 7, 1, 5, 4) : [2, 3, 4] [6, 2]
(6, 2, 3, 7, 5, 1, 4) : [2, 3, 4] [7, 5, 1]
(6, 2, 4, 1, 3, 7, 5) : [1, 3, 5] [6, 2]
(6, 2, 4, 1, 7, 3, 5) : [1, 3, 5] [6, 2]
(6, 2, 4, 1, 7, 5, 3) : [2, 4, 5] [7, 5, 3]
(6, 2, 4, 3, 1, 7, 5) : [2, 3, 5] [4, 3, 1]
(6, 2, 4, 3, 7, 1, 5) : [2, 3, 5] [6, 2]
(6, 2, 4, 3, 7, 5, 1) : [2, 3, 5] [7, 5, 1]
(6, 2, 4, 7, 1, 3, 5) : [1, 3, 5] [6, 2]
(6, 2, 4, 7, 1, 5, 3) : [2, 4, 5] [6, 2]
(6, 2, 4, 7, 3, 1, 5) : [2, 3, 5] [7, 3, 1]
(6, 2, 4, 7, 3, 5, 1) : [2, 3, 5] [6, 2]
(6, 2, 4, 7, 5, 1, 3) : [2, 4, 5] [7, 5, 1]
(6, 2, 5, 1, 3, 7, 4) : [1, 3, 4] [6, 2]
(6, 2, 5, 1, 4, 3, 7) : [1, 3, 7] [6, 2]
(6, 2, 5, 1, 4, 7, 3) : [1, 4, 7] [6, 2]
(6, 2, 5, 1, 7, 3, 4) : [1, 3, 4] [6, 2]
(6, 2, 5, 1, 7, 4, 3) : [2, 5, 7] [7, 4, 3]
(6, 2, 5, 3, 1, 7, 4) : [2, 3, 4] [5, 3, 1]
(6, 2, 5, 3, 7, 1, 4) : [2, 3, 4] [6, 2]
(6, 2, 5, 3, 7, 4, 1) : [2, 3, 4] [7, 4, 1]
(6, 2, 5, 4, 1, 3, 7) : [1, 3, 7] [5, 4, 1]
(6, 2, 5, 4, 1, 7, 3) : [2, 4, 7] [5, 4, 1]
(6, 2, 5, 4, 3, 7, 1) : [2, 3, 7] [5, 4, 3]
(6, 2, 5, 4, 7, 1, 3) : [2, 4, 7] [6, 2]
(6, 2, 5, 4, 7, 3, 1) : [2, 4, 7] [7, 3, 1]
(6, 2, 5, 7, 1, 3, 4) : [1, 3, 4] [6, 2]
(6, 2, 5, 7, 1, 4, 3) : [2, 5, 7] [6, 2]
(6, 2, 5, 7, 3, 1, 4) : [2, 3, 4] [7, 3, 1]
(6, 2, 5, 7, 3, 4, 1) : [2, 3, 4] [6, 2]
(6, 2, 5, 7, 4, 1, 3) : [2, 5, 7] [7, 4, 1]
(6, 2, 7, 1, 3, 5, 4) : [1, 3, 4] [6, 2]
(6, 2, 7, 1, 4, 3, 5) : [1, 3, 5] [6, 2]
(6, 2, 7, 1, 4, 5, 3) : [1, 4, 5] [6, 2]
(6, 2, 7, 1, 5, 3, 4) : [1, 3, 4] [6, 2]
(6, 2, 7, 1, 5, 4, 3) : [1, 3] [5, 4, 3]
(6, 2, 7, 3, 1, 5, 4) : [2, 3, 4] [7, 3, 1]
(6, 2, 7, 3, 5, 1, 4) : [2, 3, 4] [6, 2]
(6, 2, 7, 3, 5, 4, 1) : [2, 3, 4] [5, 4, 1]
(6, 2, 7, 4, 1, 3, 5) : [1, 3, 5] [7, 4, 1]
(6, 2, 7, 4, 1, 5, 3) : [2, 4, 5] [7, 4, 1]
(6, 2, 7, 4, 3, 5, 1) : [2, 3, 5] [7, 4, 3]
(6, 2, 7, 4, 5, 1, 3) : [2, 4, 5] [6, 2]
(6, 2, 7, 4, 5, 3, 1) : [2, 4, 5] [5, 3, 1]
(6, 2, 7, 5, 1, 3, 4) : [1, 3, 4] [7, 5, 1]
(6, 2, 7, 5, 1, 4, 3) : [1, 3] [7, 5, 1]
(6, 2, 7, 5, 3, 4, 1) : [2, 3, 4] [7, 5, 3]
(6, 3, 1, 2, 7, 5, 4) : [1, 2, 4] [6, 3, 1]
(6, 3, 1, 4, 2, 7, 5) : [1, 2, 5] [6, 3, 1]
(6, 3, 1, 4, 7, 2, 5) : [1, 2, 5] [6, 3, 1]
(6, 3, 1, 4, 7, 5, 2) : [1, 4, 5] [6, 3, 1]
(6, 3, 1, 5, 2, 7, 4) : [1, 2, 4] [6, 3, 1]
(6, 3, 1, 5, 4, 2, 7) : [1, 2, 7] [6, 3, 1]
(6, 3, 1, 5, 4, 7, 2) : [1, 4, 7] [6, 3, 1]
(6, 3, 1, 5, 7, 2, 4) : [1, 2, 4] [6, 3, 1]
(6, 3, 1, 5, 7, 4, 2) : [1, 5, 7] [6, 3, 1]
(6, 3, 1, 7, 2, 5, 4) : [1, 2, 4] [6, 3, 1]
(6, 3, 1, 7, 4, 2, 5) : [1, 2, 5] [6, 3, 1]
(6, 3, 1, 7, 4, 5, 2) : [1, 4, 5] [6, 3, 1]
(6, 3, 1, 7, 5, 2, 4) : [1, 2, 4] [6, 3, 1]
(6, 3, 2, 4, 1, 7, 5) : [2, 4, 5] [6, 3, 2]
(6, 3, 2, 4, 7, 1, 5) : [2, 4, 5] [6, 3, 2]
(6, 3, 2, 4, 7, 5, 1) : [2, 4, 5] [6, 3, 2]
(6, 3, 2, 5, 1, 4, 7) : [1, 4, 7] [6, 3, 2]
(6, 3, 2, 5, 1, 7, 4) : [2, 5, 7] [6, 3, 2]
(6, 3, 2, 5, 4, 1, 7) : [2, 4, 7] [6, 3, 2]
(6, 3, 2, 5, 4, 7, 1) : [2, 4, 7] [6, 3, 2]
(6, 3, 2, 5, 7, 1, 4) : [2, 5, 7] [6, 3, 2]
(6, 3, 2, 5, 7, 4, 1) : [2, 5, 7] [6, 3, 2]
(6, 3, 2, 7, 1, 4, 5) : [1, 4, 5] [6, 3, 2]
(6, 3, 2, 7, 1, 5, 4) : [1, 4] [6, 3, 2]
(6, 3, 2, 7, 4, 1, 5) : [2, 4, 5] [6, 3, 2]
(6, 3, 2, 7, 4, 5, 1) : [2, 4, 5] [6, 3, 2]
(6, 3, 2, 7, 5, 1, 4) : [1, 4] [6, 3, 2]
(6, 3, 4, 1, 2, 7, 5) : [1, 2, 5] [6, 3]
(6, 3, 4, 1, 7, 2, 5) : [1, 2, 5] [6, 3]
(6, 3, 4, 1, 7, 5, 2) : [3, 4, 5] [7, 5, 2]
(6, 3, 4, 2, 1, 7, 5) : [3, 4, 5] [4, 2, 1]
(6, 3, 4, 2, 7, 1, 5) : [3, 4, 5] [6, 3]
(6, 3, 4, 2, 7, 5, 1) : [3, 4, 5] [7, 5, 1]
(6, 3, 4, 7, 1, 2, 5) : [1, 2, 5] [6, 3]
(6, 3, 4, 7, 1, 5, 2) : [3, 4, 5] [6, 3]
(6, 3, 4, 7, 2, 1, 5) : [3, 4, 5] [7, 2, 1]
(6, 3, 4, 7, 2, 5, 1) : [3, 4, 5] [6, 3]
(6, 3, 4, 7, 5, 1, 2) : [3, 4, 5] [7, 5, 1]
(6, 3, 5, 1, 2, 7, 4) : [1, 2, 4] [6, 3]
(6, 3, 5, 1, 4, 2, 7) : [1, 2, 7] [6, 3]
(6, 3, 5, 1, 4, 7, 2) : [1, 4, 7] [6, 3]
(6, 3, 5, 1, 7, 2, 4) : [1, 2, 4] [6, 3]
(6, 3, 5, 1, 7, 4, 2) : [3, 5, 7] [7, 4, 2]
(6, 3, 5, 2, 1, 4, 7) : [1, 4, 7] [5, 2, 1]
(6, 3, 5, 2, 1, 7, 4) : [3, 5, 7] [5, 2, 1]
(6, 3, 5, 2, 4, 1, 7) : [2, 4, 7] [6, 3]
(6, 3, 5, 2, 4, 7, 1) : [2, 4, 7] [6, 3]
(6, 3, 5, 2, 7, 1, 4) : [3, 5, 7] [6, 3]
(6, 3, 5, 2, 7, 4, 1) : [3, 5, 7] [7, 4, 1]
(6, 3, 5, 4, 1, 2, 7) : [1, 2, 7] [5, 4, 1]
(6, 3, 5, 4, 1, 7, 2) : [3, 4, 7] [5, 4, 1]
(6, 3, 5, 4, 2, 7, 1) : [3, 4, 7] [5, 4, 2]
(6, 3, 5, 4, 7, 1, 2) : [3, 4, 7] [6, 3]
(6, 3, 5, 4, 7, 2, 1) : [3, 4, 7] [7, 2, 1]
(6, 3, 5, 7, 1, 2, 4) : [1, 2, 4] [6, 3]
(6, 3, 5, 7, 1, 4, 2) : [3, 5, 7] [6, 3]
(6, 3, 5, 7, 2, 1, 4) : [3, 5, 7] [7, 2, 1]
(6, 3, 5, 7, 2, 4, 1) : [3, 5, 7] [6, 3]
(6, 3, 5, 7, 4, 1, 2) : [3, 5, 7] [7, 4, 1]
(6, 3, 7, 1, 2, 5, 4) : [1, 2, 4] [6, 3]
(6, 3, 7, 1, 4, 2, 5) : [1, 2, 5] [6, 3]
(6, 3, 7, 1, 4, 5, 2) : [1, 4, 5] [6, 3]
(6, 3, 7, 1, 5, 2, 4) : [1, 2, 4] [6, 3]
(6, 3, 7, 1, 5, 4, 2) : [1, 2] [5, 4, 2]
(6, 3, 7, 2, 1, 4, 5) : [1, 4, 5] [7, 2, 1]
(6, 3, 7, 2, 1, 5, 4) : [1, 4] [7, 2, 1]
(6, 3, 7, 2, 4, 1, 5) : [2, 4, 5] [6, 3]
(6, 3, 7, 2, 4, 5, 1) : [2, 4, 5] [6, 3]
(6, 3, 7, 2, 5, 1, 4) : [1, 4] [6, 3]
(6, 3, 7, 2, 5, 4, 1) : [2, 4] [5, 4, 1]
(6, 3, 7, 4, 1, 2, 5) : [1, 2, 5] [7, 4, 1]
(6, 3, 7, 4, 1, 5, 2) : [3, 4, 5] [7, 4, 1]
(6, 3, 7, 4, 2, 5, 1) : [3, 4, 5] [7, 4, 2]
(6, 3, 7, 4, 5, 1, 2) : [3, 4, 5] [6, 3]
(6, 3, 7, 4, 5, 2, 1) : [3, 4, 5] [5, 2, 1]
(6, 3, 7, 5, 1, 2, 4) : [1, 2, 4] [7, 5, 1]
(6, 3, 7, 5, 1, 4, 2) : [1, 2] [7, 5, 1]
(6, 3, 7, 5, 2, 4, 1) : [2, 4] [7, 5, 2]
(6, 4, 1, 2, 7, 5, 3) : [1, 2, 3] [6, 4, 1]
(6, 4, 1, 3, 2, 7, 5) : [1, 2, 5] [6, 4, 1]
(6, 4, 1, 3, 7, 2, 5) : [1, 2, 5] [6, 4, 1]
(6, 4, 1, 3, 7, 5, 2) : [1, 3, 5] [6, 4, 1]
(6, 4, 1, 5, 2, 7, 3) : [1, 2, 3] [6, 4, 1]
(6, 4, 1, 5, 3, 2, 7) : [1, 2, 7] [6, 4, 1]
(6, 4, 1, 5, 3, 7, 2) : [1, 3, 7] [6, 4, 1]
(6, 4, 1, 5, 7, 2, 3) : [1, 2, 3] [6, 4, 1]
(6, 4, 1, 5, 7, 3, 2) : [1, 5, 7] [6, 4, 1]
(6, 4, 1, 7, 2, 5, 3) : [1, 2, 3] [6, 4, 1]
(6, 4, 1, 7, 3, 2, 5) : [1, 2, 5] [6, 4, 1]
(6, 4, 1, 7, 3, 5, 2) : [1, 3, 5] [6, 4, 1]
(6, 4, 1, 7, 5, 2, 3) : [1, 2, 3] [6, 4, 1]
(6, 4, 2, 3, 1, 7, 5) : [2, 3, 5] [6, 4, 2]
(6, 4, 2, 3, 7, 1, 5) : [2, 3, 5] [6, 4, 2]
(6, 4, 2, 3, 7, 5, 1) : [2, 3, 5] [6, 4, 2]
(6, 4, 2, 5, 1, 3, 7) : [1, 3, 7] [6, 4, 2]
(6, 4, 2, 5, 1, 7, 3) : [2, 5, 7] [6, 4, 2]
(6, 4, 2, 5, 3, 1, 7) : [2, 3, 7] [6, 4, 2]
(6, 4, 2, 5, 3, 7, 1) : [2, 3, 7] [6, 4, 2]
(6, 4, 2, 5, 7, 1, 3) : [2, 5, 7] [6, 4, 2]
(6, 4, 2, 5, 7, 3, 1) : [2, 5, 7] [6, 4, 2]
(6, 4, 2, 7, 1, 3, 5) : [1, 3, 5] [6, 4, 2]
(6, 4, 2, 7, 1, 5, 3) : [1, 3] [6, 4, 2]
(6, 4, 2, 7, 3, 1, 5) : [2, 3, 5] [6, 4, 2]
(6, 4, 2, 7, 3, 5, 1) : [2, 3, 5] [6, 4, 2]
(6, 4, 2, 7, 5, 1, 3) : [1, 3] [6, 4, 2]
(6, 4, 3, 5, 1, 2, 7) : [1, 2, 7] [6, 4, 3]
(6, 4, 3, 5, 1, 7, 2) : [3, 5, 7] [6, 4, 3]
(6, 4, 3, 5, 2, 1, 7) : [3, 5, 7] [6, 4, 3]
(6, 4, 3, 5, 2, 7, 1) : [3, 5, 7] [6, 4, 3]
(6, 4, 3, 5, 7, 1, 2) : [3, 5, 7] [6, 4, 3]
(6, 4, 3, 5, 7, 2, 1) : [3, 5, 7] [6, 4, 3]
(6, 4, 3, 7, 1, 2, 5) : [1, 2, 5] [6, 4, 3]
(6, 4, 3, 7, 1, 5, 2) : [1, 2] [6, 4, 3]
(6, 4, 3, 7, 2, 1, 5) : [1, 5] [6, 4, 3]
(6, 4, 3, 7, 2, 5, 1) : [2, 5] [6, 4, 3]
(6, 4, 3, 7, 5, 1, 2) : [1, 2] [6, 4, 3]
(6, 4, 5, 1, 2, 7, 3) : [1, 2, 3] [6, 4]
(6, 4, 5, 1, 3, 2, 7) : [1, 2, 7] [6, 4]
(6, 4, 5, 1, 3, 7, 2) : [1, 3, 7] [6, 4]
(6, 4, 5, 1, 7, 2, 3) : [1, 2, 3] [6, 4]
(6, 4, 5, 1, 7, 3, 2) : [4, 5, 7] [7, 3, 2]
(6, 4, 5, 2, 1, 3, 7) : [1, 3, 7] [5, 2, 1]
(6, 4, 5, 2, 1, 7, 3) : [4, 5, 7] [5, 2, 1]
(6, 4, 5, 2, 3, 1, 7) : [2, 3, 7] [6, 4]
(6, 4, 5, 2, 3, 7, 1) : [2, 3, 7] [6, 4]
(6, 4, 5, 2, 7, 1, 3) : [4, 5, 7] [6, 4]
(6, 4, 5, 2, 7, 3, 1) : [4, 5, 7] [7, 3, 1]
(6, 4, 5, 3, 1, 2, 7) : [1, 2, 7] [5, 3, 1]
(6, 4, 5, 3, 1, 7, 2) : [4, 5, 7] [5, 3, 1]
(6, 4, 5, 3, 2, 7, 1) : [4, 5, 7] [5, 3, 2]
(6, 4, 5, 3, 7, 1, 2) : [4, 5, 7] [6, 4]
(6, 4, 5, 3, 7, 2, 1) : [4, 5, 7] [7, 2, 1]
(6, 4, 5, 7, 1, 2, 3) : [1, 2, 3] [6, 4]
(6, 4, 5, 7, 1, 3, 2) : [4, 5, 7] [6, 4]
(6, 4, 5, 7, 2, 1, 3) : [4, 5, 7] [7, 2, 1]
(6, 4, 5, 7, 2, 3, 1) : [4, 5, 7] [6, 4]
(6, 4, 5, 7, 3, 1, 2) : [4, 5, 7] [7, 3, 1]
(6, 4, 7, 1, 2, 5, 3) : [1, 2, 3] [6, 4]
(6, 4, 7, 1, 3, 2, 5) : [1, 2, 5] [6, 4]
(6, 4, 7, 1, 3, 5, 2) : [1, 3, 5] [6, 4]
(6, 4, 7, 1, 5, 2, 3) : [1, 2, 3] [6, 4]
(6, 4, 7, 1, 5, 3, 2) : [1, 2] [5, 3, 2]
(6, 4, 7, 2, 1, 3, 5) : [1, 3, 5] [7, 2, 1]
(6, 4, 7, 2, 1, 5, 3) : [1, 3] [7, 2, 1]
(6, 4, 7, 2, 3, 1, 5) : [2, 3, 5] [6, 4]
(6, 4, 7, 2, 3, 5, 1) : [2, 3, 5] [6, 4]
(6, 4, 7, 2, 5, 1, 3) : [1, 3] [6, 4]
(6, 4, 7, 2, 5, 3, 1) : [2, 3] [5, 3, 1]
(6, 4, 7, 3, 1, 2, 5) : [1, 2, 5] [7, 3, 1]
(6, 4, 7, 3, 1, 5, 2) : [1, 2] [7, 3, 1]
(6, 4, 7, 3, 2, 5, 1) : [2, 5] [7, 3, 2]
(6, 4, 7, 3, 5, 1, 2) : [1, 2] [6, 4]
(6, 4, 7, 3, 5, 2, 1) : [3, 5] [5, 2, 1]
(6, 4, 7, 5, 1, 2, 3) : [1, 2, 3] [7, 5, 1]
(6, 4, 7, 5, 1, 3, 2) : [1, 2] [7, 5, 1]
(6, 4, 7, 5, 2, 3, 1) : [2, 3] [7, 5, 2]
(6, 5, 1, 2, 7, 4, 3) : [1, 2, 3] [6, 5, 1]
(6, 5, 1, 3, 2, 7, 4) : [1, 2, 4] [6, 5, 1]
(6, 5, 1, 3, 7, 2, 4) : [1, 2, 4] [6, 5, 1]
(6, 5, 1, 3, 7, 4, 2) : [1, 3, 4] [6, 5, 1]
(6, 5, 1, 4, 2, 7, 3) : [1, 2, 3] [6, 5, 1]
(6, 5, 1, 4, 3, 2, 7) : [1, 2, 7] [6, 5, 1]
(6, 5, 1, 4, 3, 7, 2) : [1, 3, 7] [6, 5, 1]
(6, 5, 1, 4, 7, 2, 3) : [1, 2, 3] [6, 5, 1]
(6, 5, 1, 4, 7, 3, 2) : [1, 4, 7] [6, 5, 1]

$\endgroup$

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