.
No need to make conjectures upon conjectures.
My calculations are based on mith's public collection of
- 847,778 minimal puzzles corresponding to :
- 158,276 min-expands
- 48,071 max-expands
- 44,251 different solution grids.
This is largely enough for precise statistical estimates.
And the estimated ratio of solution grids having a "solution tridagon" according to your definition is only 26.66 %
.
tridagon??
44 posts
• Page 2 of 3 • 1, 2, 3
Re: tridagon??
by denis_berthier » Sat Feb 22, 2025 12:10 pm
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Re: tridagon??
by champagne » Sat Feb 22, 2025 3:47 pm
No conjecture, no estimate, I got 54789/67539 =81.1% solution grids with at least one such pattern
???
???
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Re: tridagon??
by denis_berthier » Sat Feb 22, 2025 5:57 pm
.
While modifying the tridagon rule to make it applicable to complete grids, I had kept a condition that no longer applies.
After correction, I find a proportion of 86.07%. So, your remark was certainly interesting.
Whatever the real proportion, this also shows that there remains numerous cases (15-20%) where the final value in more than one of the tridagon cells is not one of the 3 values of the pattern.
It also shows that searching for tridagons only in solution grids that have a "solution-tridagon" is condemned to miss many interesting cases.
There also remains to see if the ratio minimal-puzzles/solutions is the same for grids with a "solution-tridagon". I would bet that the stats are very different when done on the minimal puzzles rather than the solution grids.
.
While modifying the tridagon rule to make it applicable to complete grids, I had kept a condition that no longer applies.
After correction, I find a proportion of 86.07%. So, your remark was certainly interesting.
Whatever the real proportion, this also shows that there remains numerous cases (15-20%) where the final value in more than one of the tridagon cells is not one of the 3 values of the pattern.
It also shows that searching for tridagons only in solution grids that have a "solution-tridagon" is condemned to miss many interesting cases.
There also remains to see if the ratio minimal-puzzles/solutions is the same for grids with a "solution-tridagon". I would bet that the stats are very different when done on the minimal puzzles rather than the solution grids.
.
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Re: tridagon??
by denis_berthier » Sun Feb 23, 2025 5:37 am
.
Regarding my last question, I tried a random sample of 1000 min-expands, generating:
- 4844 minimals
- 4844 solution grids for these minimals (with repetitions)
- 879 unique solution grids
The percentage of "solution-tridagons" in the last two cases are very close.
The interpretation isn't straightforward. It can mean the presence/absence of a "solution-tridagon" has no impact on the number of minimals in T&E(3) per grid in the collection.
I also made a quick test: setting aside the case with only 1 guardian, puzzles with no "solution-tridagon" have no special solving characteristics; they don't seem to have more or fewer guardians or to be easier or harder to solve with my usual sets of rules.
That's not really surprising: once the ORk relation is deduced from the presence of the tridagon pattern, what happens later is independent of the origin of this relation.
.
Regarding my last question, I tried a random sample of 1000 min-expands, generating:
- 4844 minimals
- 4844 solution grids for these minimals (with repetitions)
- 879 unique solution grids
The percentage of "solution-tridagons" in the last two cases are very close.
The interpretation isn't straightforward. It can mean the presence/absence of a "solution-tridagon" has no impact on the number of minimals in T&E(3) per grid in the collection.
I also made a quick test: setting aside the case with only 1 guardian, puzzles with no "solution-tridagon" have no special solving characteristics; they don't seem to have more or fewer guardians or to be easier or harder to solve with my usual sets of rules.
That's not really surprising: once the ORk relation is deduced from the presence of the tridagon pattern, what happens later is independent of the origin of this relation.
.
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Re: tridagon??
by denis_berthier » Sun Feb 23, 2025 8:03 am
.
One more remark about the "solution tridagon".
It is present in 49.9 % of the solution grids of minimal puzzles in the "small" controlled-bias collection - in which there is exactly 0 tridagon.
Example: #3, solvable in BC3
Solution grid with "solution-tridagon":
Conclusion: the "solution-tridagon" pattern might have been an interesting idea as a filter of complete grids potentially having minimal puzzles with a tridagon, but elementary experiments with it show it is not worth much in practice.
Remember that the T&E(3) collection and the T&E(2) collections with high BxB ratings have never been based on the explicit search of tridagon patterns.
In particular, the T&E(3) collection has been based only on the T&E-depth criterion. It's indeed what makes all the interest of the result that all the known T&E(3) puzzles have a tridagon.
.
One more remark about the "solution tridagon".
It is present in 49.9 % of the solution grids of minimal puzzles in the "small" controlled-bias collection - in which there is exactly 0 tridagon.
Example: #3, solvable in BC3
- Code: Select all
+-------+-------+-------+
! . 2 3 ! . . 6 ! . 8 . !
! . . . ! . . 9 ! 1 . . !
! . 8 . ! 1 . . ! 4 . . !
+-------+-------+-------+
! 2 . . ! . . . ! . . 7 !
! . . . ! 8 . . ! . . . !
! 6 7 8 ! . 1 . ! . . . !
+-------+-------+-------+
! . . 7 ! . 3 . ! 2 . . !
! . 3 . ! . . 4 ! . 7 . !
! . . . ! 5 . 1 ! . 6 . !
+-------+-------+-------+
Solution grid with "solution-tridagon":
- Code: Select all
Sol-Trid for digits 3, 4 and 5 in blocks:
b6, with cells (marked #): r5c9, r4c8, r6c7
b5, with cells (marked #): r5c5, r4c6, r6c4
b9, with cells (marked #): r8c9, r7c8, r9c7
b8, with cells (marked #): r8c6, r7c5, r9c4
+----------+----------+----------+
! 1 2 3 ! 4 5 6 ! 7 8 9 !
! 4 5 6 ! 7 8 9 ! 1 2 3 !
! 7 8 9 ! 1 2 3 ! 4 5 6 !
+----------+----------+----------+
! 2 1 4 ! 6 9 5# ! 8 3# 7 !
! 3 9 5 ! 8 4# 7 ! 6 1 2# !
! 6 7 8 ! 3# 1 2 ! 5# 9 4 !
+----------+----------+----------+
! 5 6 7 ! 9 3# 8 ! 2 4# 1 !
! 8 3 1 ! 2 6 4# ! 9 7 5# !
! 9 4 2 ! 5# 7 1 ! 3# 6 8 !
+----------+----------+----------+
Note: n1r5c9 is the only non-tridagon value allowed by the "solution tridagon" pattern.
Conclusion: the "solution-tridagon" pattern might have been an interesting idea as a filter of complete grids potentially having minimal puzzles with a tridagon, but elementary experiments with it show it is not worth much in practice.
Remember that the T&E(3) collection and the T&E(2) collections with high BxB ratings have never been based on the explicit search of tridagon patterns.
In particular, the T&E(3) collection has been based only on the T&E-depth criterion. It's indeed what makes all the interest of the result that all the known T&E(3) puzzles have a tridagon.
.
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Re: tridagon??
by champagne » Sun Feb 23, 2025 8:33 am
denis_berthier wrote:.
Whatever the real proportion, this also shows that there remains numerous cases (15-20%) where the final value in more than one of the tridagon cells is not one of the 3 values of the pattern.
It also shows that searching for tridagons only in solution grids that have a "solution-tridagon" is condemned to miss many interesting cases.
.
In my sample test on a chunk of 600 000 solution grids, I had 10 expected grids matching with mith's file. For 2 of them, I had no match due to the lack of target (tridagon pattern in the solution grid).
I think that all records in mith's file are T&E(3), and I always read that all T&E(3) had this pattern. Looking at SKFR path, I understood why and I have seen that the PM had one of these tridagon pattern with guardians. This is why I open this thread as tridagon?? with one puzzle of mith's file.
In my view, it's difficult to put in the same bag both groups, but it's not a key point.
Finding puzzles of interest for the players is another story. As far as I know, all puzzles of the current T&E(3) file are derived from "Loki", the nugget, by more or less a "vicinity" search.
I have a code to search directly puzzles with the "loki" PM at start hoping to get one day another nugget.
Unhappily, till now, this gives more gold powder and thousand tons of sand to sort.
I have in mind some ideas to get a feasible process, but the result will continue to produce seeds. If one has the potential, then it will be possible to get other sets of puzzles.
This is already complex, and I see no easy way to get out of the loki vicinity that limiting the search to a typical loki pattern.
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Re: tridagon??
by denis_berthier » Sun Feb 23, 2025 8:54 am
.
If you want a grid far from the Loki solution, try the one in my previous post.
.
If you want a grid far from the Loki solution, try the one in my previous post.
.
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Re: tridagon??
by champagne » Sun Feb 23, 2025 9:15 am
denis_berthier wrote:.
If you want a grid far from the Loki solution, try the one in my previous post.
.
As I wrote, I have billions of them, but the best ones with a skfr rating in the range 10.0 to 11.1
edit: but your point can be different.
if the point is that all these impossible patterns discovered around the loki case can be used in quite different situations, it's not surprising for me.
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Re: tridagon??
by denis_berthier » Sun Feb 23, 2025 11:25 am
champagne wrote:denis_berthier wrote:.If you want a grid far from the Loki solution, try the one in my previous post.
As I wrote, I have billions of them, but the best ones with a skfr rating in the range 10.0 to 11.1
edit: but your point can be different.
if the point is that all these impossible patterns discovered around the loki case can be used in quite different situations, it's not surprising for me.
No. My point is, it is a solution grid that has nothing to do with Loki, but that has a "solution tridagon", a totally random complete grid among the 49.9 % that have this pattern.
I'm curious to see if you can find a minimal puzzle for it with a non-degenerate tridagon.
.
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Re: tridagon??
by champagne » Sun Feb 23, 2025 1:45 pm
[quote="denis_berthier"]I'm curious to see if you can find a minimal puzzle for it with a non-degenerate tridagon.[/quote]
This is the solution grid 856940 of the minlex catalog.
The code finds only one possible start for this solution grid and the morph used for the scan is
123645879456978213789312546567893421942157638831426795214569387678231954395784162;856940
with the magic square located in boxes 5689.
123 645 879
456 978 213
789 312546
567 893 421
942 157 638
831 426 795
214 569 387
678 231 954
395 784 162 ;856940
for this solution grid, the scan gives 1664 puzzles of size 26/27, most of them size 27 here the top part of the list
only 2 of them pass the T&E(1) filter with an skfr rating of 9.2
This is the solution grid 856940 of the minlex catalog.
The code finds only one possible start for this solution grid and the morph used for the scan is
123645879456978213789312546567893421942157638831426795214569387678231954395784162;856940
with the magic square located in boxes 5689.
123 645 879
456 978 213
789 312546
567 893 421
942 157 638
831 426 795
214 569 387
678 231 954
395 784 162 ;856940
for this solution grid, the scan gives 1664 puzzles of size 26/27, most of them size 27 here the top part of the list
- Code: Select all
..36..8..4...78.......12..6.6789..21...1.7..8....2..9.2...69..7..8............16.;27
..3...8..4...78.......12..6.6789..21...1.7..8....26.9.2...69..7..8............16.;27
..36..8..4....8.......12..6.6789..21...1.7..8....2..9.2...69..7.78............16.;27
..36..8..4....8.......12..6.6789..21...1.7..8....2..9.2...69..7..8.........7..16.;27
..3...8..4....8.......12..6.6789..21...1.7..8....26.9.2...69..7.78............16.;27
..3...8..4....8.......12..6.6789..21...1.7..8....26.9.2...69..7..8.........7..16.;27
..36..8..4....8.......12..6.67.9..21...1.7...8...2..9.2...69.87.7...........8.16.;27
..36..8..4....8.......12..6.67.9..21...1.7...8...2..9.2...69.87............78.16.;27
..3...8..4..9.8.......12....67.9..21...1.7...8...26.9.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6.67.9..21...1.7...8...26.9.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6.67.9..21...1.7...8...26.9.2...69.87............78.16.;27
..36..8..4...78.......12..6.6789..2....1.7..8..1.2..9.2...69..7..8............16.;27
..3...8..4..978.......12....6789..2....1.7..8..1.26.9.2...69..7..8............16.;27
..3...8..4...78.......12..6.6789..2....1.7..8..1.26.9.2...69..7..8............16.;27
..36..8..4....8.......12..6.6789..2....1.7..8..1.2..9.2...69..7.78............16.;27
..36..8..4....8.......12..6.6789..2....1.7..8..1.2..9.2...69..7..8.........7..16.;27
..3...8..4..9.8.......12....6789..2....1.7..8..1.26.9.2...69..7.78............16.;27
..3...8..4..9.8.......12....6789..2....1.7..8..1.26.9.2...69..7..8.........7..16.;27
..3...8..4....8.......12..6.6789..2....1.7..8..1.26.9.2...69..7.78............16.;27
..3...8..4....8.......12..6.6789..2....1.7..8..1.26.9.2...69..7..8.........7..16.;27
..36..8..4....8.......12..6.67.9..2....1.7...8.1.2..9.2...69.87.7...........8.16.;27
..36..8..4....8.......12..6.67.9..2....1.7...8.1.2..9.2...69.87............78.16.;27
..3...8..4..9.8.......12....67.9..2....1.7...8.1.26.9.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6.67.9..2....1.7...8.1.26.9.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6.67.9..2....1.7...8.1.26.9.2...69.87............78.16.;27
..36..8..4...78.......12..6.678...219..1.7..8....2..9.2...69..7..8............16.;27
..3...8..4...78.......12..6.678...219..1.7..8....26.9.2...69..7..8............16.;27
..36..8..4....8.......12..6.678...219..1.7..8....2..9.2...69..7.78............16.;27
..36..8..4....8.......12..6.678...219..1.7..8....2..9.2...69..7..8.........7..16.;27
..3...8..4....8.......12..6.678...219..1.7..8....26.9.2...69..7.78............16.;27
..3...8..4....8.......12..6.678...219..1.7..8....26.9.2...69..7..8.........7..16.;27
..36..8..4....8.......12..6.67....219..1.7...8...2..9.2...69.87.7...........8.16.;27
..36..8..4....8.......12..6.67....219..1.7...8...2..9.2...69.87............78.16.;27
..3...8..4..9.8.......12....67....219..1.7...8...26.9.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6.67....219..1.7...8...26.9.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6.67....219..1.7...8...26.9.2...69.87............78.16.;27
..36..8..4...78.......12..6.678...2.9..1.7..8..1.2..9.2...69..7..8............16.;27
..3...8..4..978.......12....678...2.9..1.7..8..1.26.9.2...69..7..8............16.;27
..3...8..4...78.......12..6.678...2.9..1.7..8..1.26.9.2...69..7..8............16.;27
..36..8..4....8.......12..6.678...2.9..1.7..8..1.2..9.2...69..7.78............16.;27
..36..8..4....8.......12..6.678...2.9..1.7..8..1.2..9.2...69..7..8.........7..16.;27
..3...8..4..9.8.......12....678...2.9..1.7..8..1.26.9.2...69..7.78............16.;27
..3...8..4....8.......12..6.678...2.9..1.7..8..1.26.9.2...69..7.78............16.;27
..3...8..4..9.8.......12....678...2.9..1.7..8..1.26.9.2...69..7..8.........7..16.;27
..3...8..4....8.......12..6.678...2.9..1.7..8..1.26.9.2...69..7..8.........7..16.;27
..36..8..4....8.......12..6.67....2.9..1.7...8.1.2..9.2...69.87.7...........8.16.;27
..36..8..4....8.......12..6.67....2.9..1.7...8.1.2..9.2...69.87............78.16.;27
..3...8..4..9.8.......12....67....2.9..1.7...8.1.26.9.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6.67....2.9..1.7...8.1.26.9.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6.67....2.9..1.7...8.1.26.9.2...69.87............78.16.;27
..36..8..4...7........12..6.6789..21...1.7..8....2..9.2...69..7..8..........8.16.;27
..3...8..4...7........12..6.6789..21...1.7..8....26.9.2...69..7..8..........8.16.;27
..36..8..4............12..6.6789..21...1.7..8....2..9.2...69.87.7...........8.16.;27
..36..8..4............12..6.6789..21...1.7..8....2..9.2...69.87............78.16.;27
..36..8..4............12..6.6789..21...1.7..8....2..9.2...69..7.78..........8.16.;27
..36..8..4............12..6.6789..21...1.7..8....2..9.2...69..7..8.........78.16.;27
..36.....45...........12..6.6789..21...1.7..8....2..9.2...69.87.7...........8.16.;27
..36.....45...........12..6.6789..21...1.7..8....2..9.2...69.87............78.16.;27
..3...8..4............12..6.6789..21...1.7..8....26.9.2...69..7.78..........8.16.;27
..3...8..4............12..6.6789..21...1.7..8....26.9.2...69..7..8.........78.16.;27
..36..8..4............12..6.6789..21...1.7...8...2..9.2...69.87.7...........8.16.;27
..36.....45...........12..6.6789..21...1.7...8...2..9.2...69.87.7...........8.16.;27
..36..8..4............12..6.6789..21...1.7...8...2..9.2...69.87............78.16.;27
..36.....45...........12..6.6789..21...1.7...8...2..9.2...69.87............78.16.;27
..3...8..4..9.........12....6789..21...1.7...8...26.9.2...69.87.7...........8.16.;27
..3...8..4............12..6.6789..21...1.7...8...26.9.2...69.87.7...........8.16.;27
..3......45...........12..6.6789..21...1.7...8...26.9.2...69.87.7...........8.16.;27
..3...8..4............12..6.6789..21...1.7...8...26.9.2...69.87............78.16.;27
..3......45...........12..6.6789..21...1.7...8...26.9.2...69.87............78.16.;27
..36..8..4...7........12..6.6789..2....1.7..8..1.2..9.2...69..7..8..........8.16.;27
...6....945..7........12..6.6789..2....1.7..8..1.2..9.2...69.87.............8.16.;27
..3...8..4..97........12....6789..2....1.7..8..1.26.9.2...69..7..8..........8.16.;27
..3...8..4...7........12..6.6789..2....1.7..8..1.26.9.2...69..7..8..........8.16.;27
........9456.7........12....6789..2....1.7..8..1.26.9.2...69.87.............8.16.;27
...6....945..7........12..6.6789..2....1.7...8.1.2..9.2...69.87.............8.16.;27
..36..8..4............12..6.6789..2....1.7..8..1.2..9.2...69.87.7...........8.16.;27
..36..8..4............12..6.6789..2....1.7..8..1.2..9.2...69.87............78.16.;27
..36..8..4............12..6.6789..2....1.7..8..1.2..9.2...69..7.78..........8.16.;27
..36..8..4............12..6.6789..2....1.7..8..1.2..9.2...69..7..8.........78.16.;27
..36.....45...........12..6.6789..2....1.7..8..1.2..9.2...69.87.7...........8.16.;27
..36.....45...........12..6.6789..2....1.7..8..1.2..9.2...69.87............78.16.;27
...6....945...........12..6.6789..2....1.7..8..1.2..9.2...69.87.7...........8.16.;27
...6....945...........12..6.6789..2....1.7..8..1.2..9.2...69.87............78.16.;27
..3...8..4..9.........12....6789..2....1.7..8..1.26.9.2...69.87.7...........8.16.;27
..3...8..4..9.........12....6789..2....1.7..8..1.26.9.2...69..7.78..........8.16.;27
..3...8..4..9.........12....6789..2....1.7..8..1.26.9.2...69..7..8.........78.16.;27
..3...8..4............12..6.6789..2....1.7..8..1.26.9.2...69.87.7...........8.16.;27
..3...8..4............12..6.6789..2....1.7..8..1.26.9.2...69.87............78.16.;27
..3...8..4............12..6.6789..2....1.7..8..1.26.9.2...69..7.78..........8.16.;27
..3...8..4............12..6.6789..2....1.7..8..1.26.9.2...69..7..8.........78.16.;27
..3......45...........12..6.6789..2....1.7..8..1.26.9.2...69.87.7...........8.16.;27
..3......45...........12..6.6789..2....1.7..8..1.26.9.2...69.87............78.16.;27
........9456..........12....6789..2....1.7..8..1.26.9.2...69.87.7...........8.16.;27
........9456..........12....6789..2....1.7..8..1.26.9.2...69.87............78.16.;27
..36..8..4............12..6.6789..2....1.7...8.1.2..9.2...69.87.7...........8.16.;27
..36.....45...........12..6.6789..2....1.7...8.1.2..9.2...69.87.7...........8.16.;27
..36..8..4............12..6.6789..2....1.7...8.1.2..9.2...69.87............78.16.;27
..36.....45...........12..6.6789..2....1.7...8.1.2..9.2...69.87............78.16.;27
...6....945...........12..6.6789..2....1.7...8.1.2..9.2...69.87.7...........8.16.;27
...6....945...........12..6.6789..2....1.7...8.1.2..9.2...69.87............78.16.;27
..3...8..4..9.........12....6789..2....1.7...8.1.26.9.2...69.87.7...........8.16.;27
..3...8..4............12..6.6789..2....1.7...8.1.26.9.2...69.87.7...........8.16.;27
..3......45...........12..6.6789..2....1.7...8.1.26.9.2...69.87.7...........8.16.;27
..3...8..4............12..6.6789..2....1.7...8.1.26.9.2...69.87............78.16.;27
..3......45...........12..6.6789..2....1.7...8.1.26.9.2...69.87............78.16.;27
..36..8..4...7........12..6.678...219..1.7..8....2..9.2...69..7..8..........8.16.;27
..3...8..4...7........12..6.678...219..1.7..8....26.9.2...69..7..8..........8.16.;27
..36.....45..7........12..6.678...219..1.7...8...2..9.2...69.87.............8.16.;27
..36......5..7....7...12..6.678...219..1.7...8...2..9.2...69.87.............8.16.;27
..3......45..7........12..6.678...219..1.7...8...26.9.2...69.87.............8.16.;27
..3.......5..7....7...12..6.678...219..1.7...8...26.9.2...69.87.............8.16.;27
..36..8..4............12..6.678...219..1.7..8....2..9.2...69.87.7...........8.16.;27
..36..8..4............12..6.678...219..1.7..8....2..9.2...69.87............78.16.;27
..36..8..4............12..6.678...219..1.7..8....2..9.2...69..7.78..........8.16.;27
..36..8..4............12..6.678...219..1.7..8....2..9.2...69..7..8.........78.16.;27
..36.....45...........12..6.678...219..1.7..8....2..9.2...69.87.7...........8.16.;27
..36.....45...........12..6.678...219..1.7..8....2..9.2...69.87............78.16.;27
..3...8..4............12..6.678...219..1.7..8....26.9.2...69..7.78..........8.16.;27
..3...8..4............12..6.678...219..1.7..8....26.9.2...69..7..8.........78.16.;27
..36...7..5...........12..6.678...219..1.7...8...2..9.2...69.87.7...........8.16.;27
..36..8..4............12..6.678...219..1.7...8...2..9.2...69.87.7...........8.16.;27
..36.....45...........12..6.678...219..1.7...8...2..9.2...69.87.7...........8.16.;27
..36..8..4............12..6.678...219..1.7...8...2..9.2...69.87............78.16.;27
..36.....45...........12..6.678...219..1.7...8...2..9.2...69.87............78.16.;27
..3...8..4..9.........12....678...219..1.7...8...26.9.2...69.87.7...........8.16.;27
..3....7..5...........12..6.678...219..1.7...8...26.9.2...69.87.7...........8.16.;27
..3...8..4............12..6.678...219..1.7...8...26.9.2...69.87.7...........8.16.;27
..3......45...........12..6.678...219..1.7...8...26.9.2...69.87.7...........8.16.;27
..3...8..4............12..6.678...219..1.7...8...26.9.2...69.87............78.16.;27
..3......45...........12..6.678...219..1.7...8...26.9.2...69.87............78.16.;27
...6....945..7........12..6.678...2.9..1.7..8..1.2..9.2...69.87.............8.16.;27
..36..8..4...7........12..6.678...2.9..1.7..8..1.2..9.2...69..7..8..........8.16.;27
........9456.7........12....678...2.9..1.7..8..1.26.9.2...69.87.............8.16.;27
..3...8..4..97........12....678...2.9..1.7..8..1.26.9.2...69..7..8..........8.16.;27
..3...8..4...7........12..6.678...2.9..1.7..8..1.26.9.2...69..7..8..........8.16.;27
...6....945..7........12..6.678...2.9..1.7...8.1.2..9.2...69.87.............8.16.;27
..36.....45..7........12..6.678...2.9..1.7...8.1.2..9.2...69.87.............8.16.;27
..36......5..7....7...12..6.678...2.9..1.7...8.1.2..9.2...69.87.............8.16.;27
..3......45..7........12..6.678...2.9..1.7...8.1.26.9.2...69.87.............8.16.;27
..3.......5..7....7...12..6.678...2.9..1.7...8.1.26.9.2...69.87.............8.16.;27
...6....945...........12..6.678...2.9..1.7..8..1.2..9.2...69.87.7...........8.16.;27
...6....945...........12..6.678...2.9..1.7..8..1.2..9.2...69.87............78.16.;27
..36..8..4............12..6.678...2.9..1.7..8..1.2..9.2...69.87.7...........8.16.;27
..36..8..4............12..6.678...2.9..1.7..8..1.2..9.2...69.87............78.16.;27
..36..8..4............12..6.678...2.9..1.7..8..1.2..9.2...69..7.78..........8.16.;27
..36..8..4............12..6.678...2.9..1.7..8..1.2..9.2...69..7..8.........78.16.;27
..36.....45...........12..6.678...2.9..1.7..8..1.2..9.2...69.87.7...........8.16.;27
..36.....45...........12..6.678...2.9..1.7..8..1.2..9.2...69.87............78.16.;27
........9456..........12....678...2.9..1.7..8..1.26.9.2...69.87.7...........8.16.;27
........9456..........12....678...2.9..1.7..8..1.26.9.2...69.87............78.16.;27
..3...8..4..9.........12....678...2.9..1.7..8..1.26.9.2...69.87.7...........8.16.;27
..3...8..4............12..6.678...2.9..1.7..8..1.26.9.2...69.87.7...........8.16.;27
..3...8..4............12..6.678...2.9..1.7..8..1.26.9.2...69.87............78.16.;27
..3...8..4..9.........12....678...2.9..1.7..8..1.26.9.2...69..7.78..........8.16.;27
..3...8..4............12..6.678...2.9..1.7..8..1.26.9.2...69..7.78..........8.16.;27
..3...8..4..9.........12....678...2.9..1.7..8..1.26.9.2...69..7..8.........78.16.;27
..3...8..4............12..6.678...2.9..1.7..8..1.26.9.2...69..7..8.........78.16.;27
..3......45...........12..6.678...2.9..1.7..8..1.26.9.2...69.87.7...........8.16.;27
..3......45...........12..6.678...2.9..1.7..8..1.26.9.2...69.87............78.16.;27
...6....945...........12..6.678...2.9..1.7...8.1.2..9.2...69.87.7...........8.16.;27
...6....945...........12..6.678...2.9..1.7...8.1.2..9.2...69.87............78.16.;27
..36..8..4............12..6.678...2.9..1.7...8.1.2..9.2...69.87.7...........8.16.;27
..36.....45...........12..6.678...2.9..1.7...8.1.2..9.2...69.87.7...........8.16.;27
..36..8..4............12..6.678...2.9..1.7...8.1.2..9.2...69.87............78.16.;27
..36.....45...........12..6.678...2.9..1.7...8.1.2..9.2...69.87............78.16.;27
..36...7..5...........12..6.678...2.9..1.7...8.1.2..9.2...69.87.7...........8.16.;27
..3...8..4..9.........12....678...2.9..1.7...8.1.26.9.2...69.87.7...........8.16.;27
..3...8..4............12..6.678...2.9..1.7...8.1.26.9.2...69.87.7...........8.16.;27
..3......45...........12..6.678...2.9..1.7...8.1.26.9.2...69.87.7...........8.16.;27
..3...8..4............12..6.678...2.9..1.7...8.1.26.9.2...69.87............78.16.;27
..3......45...........12..6.678...2.9..1.7...8.1.26.9.2...69.87............78.16.;27
..3....7..5...........12..6.678...2.9..1.7...8.1.26.9.2...69.87.7...........8.16.;27
..36...7..5...8.......12..6.6.....219..1.7..88...2.79.2...69.8...8.........7..16.;27
..3....7..5.9.8.......12....6.....219..1.7..88...2679.2...69.8...8.........7..16.;27
..3....7..5...8.......12..6.6.....219..1.7..88...2679.2...69.8...8.........7..16.;27
..3....7..5.9.8.......12....6.....219..1.7..88...2679.2...69.8.............78.16.;27
..36...7..5...8.......12..6.6.8...219..1.7...8...2.79.2...69.8...8.........7..16.;27
..3...8..4..9.8.......12....6.....219..1.7...8...2679.2...69.87.7...........8.16.;27
..3....7..5...8.......12..6.6.8...219..1.7...8...2679.2...69.8...8.........7..16.;27
..3...87.4..9.8.......12....6.....219..1.7...8...2679.2...69.8.............78.16.;27
..3...8..4..9.8.......12....6.....219..1.7...8...2679.2...69.8..7..........78.16.;27
..3...87..5.9.8.......12....6.....219..1.7...8...2679.2...69.8.............78.16.;27
..3...87..5.9.8.......1.....6.....2.9.21.7...8.1..679.2...69.8....2........78.16.;27
..36...7..5...8.......12..6.6.....2.9..1.7..88.1.2.79.2...69.8...8.........7..16.;27
..3....7..5.9.8.......12....6.....2.9..1.7..88.1.2679.2...69.8...8.........7..16.;27
..3....7..5...8.......12..6.6.....2.9..1.7..88.1.2679.2...69.8...8.........7..16.;27
..3....7..5.9.8.......12....6.....2.9..1.7..88.1.2679.2...69.8.............78.16.;27
..36..8..4....8.......12..6.6.....2.9..1.7...8.1.2.79.2...69.87.7...........8.16.;27
..36...7..5...8.......12..6.6.8...2.9..1.7...8.1.2.79.2...69.8...8.........7..16.;27
..36..87.4....8.......12..6.6.....2.9..1.7...8.1.2.79.2...69.8.............78.16.;27
..36..8..4....8.......12..6.6.....2.9..1.7...8.1.2.79.2...69.8..7..........78.16.;27
..3...8..4..9.8.......12....6.....2.9..1.7...8.1.2679.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6.6.....2.9..1.7...8.1.2679.2...69.87.7...........8.16.;27
..3....7..5...8.......12..6.6.8...2.9..1.7...8.1.2679.2...69.8...8.........7..16.;27
..3...87.4..9.8.......12....6.....2.9..1.7...8.1.2679.2...69.8.............78.16.;27
..3...87.4....8.......12..6.6.....2.9..1.7...8.1.2679.2...69.8.............78.16.;27
..3...8..4..9.8.......12....6.....2.9..1.7...8.1.2679.2...69.8..7..........78.16.;27
..3...8..4....8.......12..6.6.....2.9..1.7...8.1.2679.2...69.8..7..........78.16.;27
..3...87..5.9.8.......12....6.....2.9..1.7...8.1.2679.2...69.8.............78.16.;27
..36...7..5.........9.12....6.89..21...1.76..8...2.79.2...69.8.6...........78.1..;27
..36...7..5.........9.12....6.89..21...1.76..8...2679.2....9.8.6...........78.1..;27
..36...7..5.........9.12....6.89..21...1.76..8...2.79.2....9.8.6...........78.16.;27
..36...7..5.........9.12..6.6.89..21...1.7...8...2.79.2...69.8.............78.16.;27
..3....7..5.........9.12..6.6.89..21...1.7...8...2679.2...69.8.............78.16.;27
..36...7..5.........9.12....6.89..2....1.76..8.1.2.79.2...69.8.6...........78.1..;27
..36...7..5.........9.12....6.89..2....1.76..8.1.2679.2....9.8.6...........78.1..;27
..36...7..5.........9.12....6.89..2....1.76..8.1.2.79.2....9.8.6...........78.16.;27
..36...7..5.........9.12..6.6.89..2....1.7...8.1.2.79.2...69.8.............78.16.;27
..3....7..5.........9.12..6.6.89..2....1.7...8.1.2679.2...69.8.............78.16.;27
..36...7..5.........9.12....6.8...219..1.76.8....2.79.2...69.8.6...........78.1..;27
..36...7..5.........9.12....6.8...219..1.76.8....2679.2....9.8.6...........78.1..;27
..36...7..5.........9.12....6.8...219..1.76.8....2.79.2....9.8.6...........78.16.;27
..36...7..56..........12....6.8...219..1.76..8...2.79.2...69.8.6...........78.1..;27
..36...7..5.........9.12....6.8...219..1.76..8...2.79.2...69.8.6...........78.1..;27
..36...7..5...........12..6.6.8...219..1.76..8...2.79.2...69.8.6...........78.1..;27
..36...7..56..........12....6.8...219..1.76..8...2.79.2...69.8.............78.16.;27
..36...7..5.........9.12....6.8...219..1.76..8...2.79.2...69.8.............78.16.;27
..36...7..56..........12....6.8...219..1.76..8...2679.2....9.8.6...........78.1..;27
..36...7..5.........9.12....6.8...219..1.76..8...2679.2....9.8.6...........78.1..;27
..36...7..5...........12..6.6.8...219..1.76..8...2679.2....9.8.6...........78.1..;27
..36...7..56..........12....6.8...219..1.76..8...2.79.2....9.8.6...........78.16.;27
..36...7..5.........9.12....6.8...219..1.76..8...2.79.2....9.8.6...........78.16.;27
..36...7..5...........12..6.6.8...219..1.76..8...2.79.2....9.8.6...........78.16.;27
..3....7..5...........12..6.6.8...219..1.76..8...2679.2...69.8.6...........78.1..;27
..36...7..5.........9.12....6.8...219..1.7..8....2679.2....9.8.6...........78.16.;27
..36.....45..7........12..6.6.8...219..1.7...8...2.79.2...69.87.............8.16.;27
..36......5..7....7...12..6.6.8...219..1.7...8...2.79.2...69.87.............8.16.;27
..36...7..5...........12..6.6.8...219..1.7...8...2.79.2...69.87.7...........8.16.;27
..36.....45...........12..6.6.8...219..1.7...8...2.79.2...69.87.7...........8.16.;27
..36.....45...........12..6.6.8...219..1.7...8...2.79.2...69.87............78.16.;27
..36...7.45...........12..6.6.8...219..1.7...8...2.79.2...69.8.............78.16.;27
..36.....45...........12..6.6.8...219..1.7...8...2.79.2...69.8..7..........78.16.;27
..36...7.45...........12..6.6.8...219..1.7...8...2.79.2...69.8.............78.16.;27
..36...7..56..........12..6.6.8...219..1.7...8...2.79.2...69.8.............78.16.;27
..36...7..5........8..12..6.6.8...219..1.7...8...2.79.2...69.8.............78.16.;27
..36...7..5.........9.12..6.6.8...219..1.7...8...2.79.2...69.8.............78.16.;27
..36...7..5...........12..6.6.8...219..1.7...8...2.79.2...69.8.6...........78.16.;27
..36...7..5...........12..6.6.8...219..1.7...8...2.79.2...69.8..7..........78.16.;27
..36...7..5...........12..6.6.8...219..1.7...8...2.79.2...69.8...8.........78.16.;27
..36...7..5...........12..6.6.8...219..1.7...8...2.79.2...69.8..7..........78.16.;27
..36.....45...........12..6.6.8...219..1.7...8...2.79.2...69.8..7..........78.16.;27
..36...7..5...........12..6.6.8...219..1.7...8...2679.2....9.8.6...........78.16.;27
..3...8..4..9.........12....6.8...219..1.7...8...2679.2...69.87.7...........8.16.;27
..3......45..7........12..6.6.8...219..1.7...8...2679.2...69.87.............8.16.;27
..3.......5..7....7...12..6.6.8...219..1.7...8...2679.2...69.87.............8.16.;27
..3....7..5...........12..6.6.8...219..1.7...8...2679.2...69.87.7...........8.16.;27
..3......45...........12..6.6.8...219..1.7...8...2679.2...69.87.7...........8.16.;27
..3......45...........12..6.6.8...219..1.7...8...2679.2...69.87............78.16.;27
..3...87.4..9.........12....6.8...219..1.7...8...2679.2...69.8.............78.16.;27
..3....7.45...........12..6.6.8...219..1.7...8...2679.2...69.8.............78.16.;27
..3...87..5.9.........12....6.8...219..1.7...8...2679.2...69.8.............78.16.;27
..3....7.45...........12..6.6.8...219..1.7...8...2679.2...69.8.............78.16.;27
..3....7..56..........12..6.6.8...219..1.7...8...2679.2...69.8.............78.16.;27
..3....7..5........8..12..6.6.8...219..1.7...8...2679.2...69.8.............78.16.;27
..3....7..5.........9.12..6.6.8...219..1.7...8...2679.2...69.8.............78.16.;27
..3....7..5...........12..6.6.8...219..1.7...8...2679.2...69.8.6...........78.16.;27
..3....7..5...........12..6.6.8...219..1.7...8...2679.2...69.8..7..........78.16.;27
..3....7..5...........12..6.6.8...219..1.7...8...2679.2...69.8...8.........78.16.;27
..3...8..4..9.........12....6.8...219..1.7...8...2679.2...69.8..7..........78.16.;27
..3......45...........12..6.6.8...219..1.7...8...2679.2...69.8..7..........78.16.;27
...6...7945............2..6.6.8...219..1.7...8...2.79.21..69.8......1......78..6.;27
..36...7.45............2..6.6.8...219..1.7...8...2.79.21..69.8......1......78..6.;27
..36...7.45............2..6.6.8...219..1.7...8...2.79.2...69.8......1......78.16.;27
..3...87..5.9.........1.....6.8...2.9.21.7...8.1..679.2...69.8....2........78.16.;27
..36...7..5.........9.12....6.8...2.9..1.76.8..1.2.79.2...69.8.6...........78.1..;27
..36...7..5.........9.12....6.8...2.9..1.76.8..1.2.79.2...69.8.............78.16.;27
..36...7..5.........9.12....6.8...2.9..1.76.8..1.2679.2....9.8.6...........78.1..;27
..36...7..5.........9.12....6.8...2.9..1.76.8..1.2.79.2....9.8.6...........78.16.;27
..36...7..56..........12....6.8...2.9..1.76..8.1.2.79.2...69.8.6...........78.1..;27
..36...7..5.........9.12....6.8...2.9..1.76..8.1.2.79.2...69.8.6...........78.1..;27
..36...7..5...........12..6.6.8...2.9..1.76..8.1.2.79.2...69.8.6...........78.1..;27
..36...7..56..........12....6.8...2.9..1.76..8.1.2.79.2...69.8.............78.16.;27
..36...7..5.........9.12....6.8...2.9..1.76..8.1.2.79.2...69.8.............78.16.;27
..36...7..56..........12....6.8...2.9..1.76..8.1.2679.2....9.8.6...........78.1..;27
..36...7..5.........9.12....6.8...2.9..1.76..8.1.2679.2....9.8.6...........78.1..;27
..36...7..5...........12..6.6.8...2.9..1.76..8.1.2679.2....9.8.6...........78.1..;27
..36...7..56..........12....6.8...2.9..1.76..8.1.2.79.2....9.8.6...........78.16.;27
..36...7..5.........9.12....6.8...2.9..1.76..8.1.2.79.2....9.8.6...........78.16.;27
..36...7..5...........12..6.6.8...2.9..1.76..8.1.2.79.2....9.8.6...........78.16.;27
..3....7..5...........12..6.6.8...2.9..1.76..8.1.2679.2...69.8.6...........78.1..;27
..36...7..5........8..12..6.6.8...2.9..1.7..8..1.2.79.2...69.8.............78.16.;27
..36...7..5.........9.12..6.6.8...2.9..1.7..8..1.2.79.2...69.8.............78.16.;27
..36...7..5.........9.12....6.8...2.9..1.7..8..1.2679.2...69.8.............78.16.;27
..36...7..5.........9.12....6.8...2.9..1.7..8..1.2679.2....9.8.6...........78.16.;27
..3....79.5.........9.12....6.8...2.9..1.7..8..1.2679.2...69.8.............78.16.;27
..3....7..5.9.......9.12....6.8...2.9..1.7..8..1.2679.2...69.8.............78.16.;27
..3....7..5.9.........12....6.8...2.9..1.7..8..1.2679.2...69.8...........9.78.16.;27
..3....7..5........8..12..6.6.8...2.9..1.7..8..1.2679.2...69.8.............78.16.;27
..3....7..5.........9.12..6.6.8...2.9..1.7..8..1.2679.2...69.8.............78.16.;27
...6....945...........12..6.6.8...2.9..1.7...8.1.2.79.2...69.87.7...........8.16.;27
...6...7945...........12..6.6.8...2.9..1.7...8.1.2.79.2...69.8.............78.16.;27
...6....945...........12..6.6.8...2.9..1.7...8.1.2.79.2...69.8..7..........78.16.;27
..36.....45..7........12..6.6.8...2.9..1.7...8.1.2.79.2...69.87.............8.16.;27
..36..8..4............12..6.6.8...2.9..1.7...8.1.2.79.2...69.87.7...........8.16.;27
..36.....45...........12..6.6.8...2.9..1.7...8.1.2.79.2...69.87.7...........8.16.;27
..36.....45...........12..6.6.8...2.9..1.7...8.1.2.79.2...69.87............78.16.;27
..36......5..7....7...12..6.6.8...2.9..1.7...8.1.2.79.2...69.87.............8.16.;27
..36...7..5...........12..6.6.8...2.9..1.7...8.1.2.79.2...69.87.7...........8.16.;27
..36..87.4............12..6.6.8...2.9..1.7...8.1.2.79.2...69.8.............78.16.;27
..36...7.45...........12..6.6.8...2.9..1.7...8.1.2.79.2...69.8.............78.16.;27
..36..8..4............12..6.6.8...2.9..1.7...8.1.2.79.2...69.8..7..........78.16.;27
..36.....45...........12..6.6.8...2.9..1.7...8.1.2.79.2...69.8..7..........78.16.;27
..36...7..56..........12..6.6.8...2.9..1.7...8.1.2.79.2...69.8.............78.16.;27
..36...7..5.9.........12..6.6.8...2.9..1.7...8.1.2.79.2...69.8.............78.16.;27
..36...7..5.......7...12..6.6.8...2.9..1.7...8.1.2.79.2...69.8.............78.16.;27
..36...7..5........8..12..6.6.8...2.9..1.7...8.1.2.79.2...69.8.............78.16.;27
..36...7..5.........9.12..6.6.8...2.9..1.7...8.1.2.79.2...69.8.............78.16.;27
..36...7..5...........12..6.6.8...2.9..1.7...8.1.2.79.2...69.8.6...........78.16.;27
..36...7..5...........12..6.6.8...2.9..1.7...8.1.2.79.2...69.8..7..........78.16.;27
..36...7..5...........12..6.6.8...2.9..1.7...8.1.2.79.2...69.8...8.........78.16.;27
..36...7..5...........12..6.6.8...2.9..1.7...8.1.2679.2....9.8.6...........78.16.;27
..3...8..4..9.........12....6.8...2.9..1.7...8.1.2679.2...69.87.7...........8.16.;27
..3......45..7........12..6.6.8...2.9..1.7...8.1.2679.2...69.87.............8.16.;27
..3...8..4............12..6.6.8...2.9..1.7...8.1.2679.2...69.87.7...........8.16.;27
..3......45...........12..6.6.8...2.9..1.7...8.1.2679.2...69.87.7...........8.16.;27
..3......45...........12..6.6.8...2.9..1.7...8.1.2679.2...69.87............78.16.;27
..3.......5..7....7...12..6.6.8...2.9..1.7...8.1.2679.2...69.87.............8.16.;27
..3....7..5...........12..6.6.8...2.9..1.7...8.1.2679.2...69.87.7...........8.16.;27
..3...87.4..9.........12....6.8...2.9..1.7...8.1.2679.2...69.8.............78.16.;27
..3...87.4............12..6.6.8...2.9..1.7...8.1.2679.2...69.8.............78.16.;27
..3....7.45...........12..6.6.8...2.9..1.7...8.1.2679.2...69.8.............78.16.;27
..3...8..4..9.........12....6.8...2.9..1.7...8.1.2679.2...69.8..7..........78.16.;27
..3...8..4............12..6.6.8...2.9..1.7...8.1.2679.2...69.8..7..........78.16.;27
..3......45...........12..6.6.8...2.9..1.7...8.1.2679.2...69.8..7..........78.16.;27
..3...87..5.9.........12....6.8...2.9..1.7...8.1.2679.2...69.8.............78.16.;27
..3....7..56..........12..6.6.8...2.9..1.7...8.1.2679.2...69.8.............78.16.;27
..3....7..5.9.........12..6.6.8...2.9..1.7...8.1.2679.2...69.8.............78.16.;27
..3....7..5.......7...12..6.6.8...2.9..1.7...8.1.2679.2...69.8.............78.16.;27
..3....7..5........8..12..6.6.8...2.9..1.7...8.1.2679.2...69.8.............78.16.;27
..3....7..5.........9.12..6.6.8...2.9..1.7...8.1.2679.2...69.8.............78.16.;27
..3....7..5...........12..6.6.8...2.9..1.7...8.1.2679.2...69.8.6...........78.16.;27
..3....7..5...........12..6.6.8...2.9..1.7...8.1.2679.2...69.8..7..........78.16.;27
..3....7..5...........12..6.6.8...2.9..1.7...8.1.2679.2...69.8...8.........78.16.;27
...6...7945............2..6.6.8...2.9..1.7...8.1.2.79.2...69.8......1......78.16.;27
..36...7.45............2..6.6.8...2.9..1.7...8.1.2.79.2...69.8......1......78.16.;27
...6..8..45..78.....9.1......7.9..21..21.76..8....6.9.2....9.876..2.........8.1..;27
...6..8..45...8.....9.1......7.9..21..21.76..8....6.9.2....9.8767.2.........8.1..;27
...6..8..45...8.....9.1......7.9..21..21.76..8....6.9.2....9.876..2........78.1..;27
..3...8..4...78.......12..6..789..21...1.76.8....26.9.2...69..76.8............1..;27
..36..8..4...78.....9.12.....7.9..21...1.76..8...26.9.2....9.876............8.1..;27
..3...8..4....8.......12..6..789..21...1.76.8....26.9.2...69..7678............1..;27
..3...8..4....8.......12..6..789..21...1.76.8....26.9.2...69..76.8.........7..1..;27
..3...8..4....8.......12..6..789..21...1.76.8....26.9.2...69..7.78............16.;27
..36..8..4..9.8.......12.....7.9..21...1.76..8...26.9.2....9.8767...........8.1..;27
..36..8..4..9.8.......12.....7.9..21...1.76..8...26.9.2....9.876...........78.1..;27
..36..8..4.6..8.......12.....7.9..21...1.76..8...26.9.2....9.8767...........8.1..;27
..36..8..4....8.....9.12.....7.9..21...1.76..8...26.9.2....9.8767...........8.1..;27
..36..8..4....8.......12..6..7.9..21...1.76..8...26.9.2....9.8767...........8.1..;27
..36..8..4.6..8.......12.....7.9..21...1.76..8...26.9.2....9.876...........78.1..;27
..36..8..4....8.....9.12.....7.9..21...1.76..8...26.9.2....9.876...........78.1..;27
..36..8..4....8.......12..6..7.9..21...1.76..8...26.9.2....9.876...........78.1..;27
..3...8..4..9.8.......12.....7.9..21...1.76..8...26.9.2...69.8767...........8.1..;27
..3...8..4..9.8.......12.....7.9..21...1.76..8...26.9.2...69.876...........78.1..;27
..3...8..4..9.8.......12.....7.9..21...1.76..8...26.9.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6..7.9..21...1.76..8...26.9.2...69.8767...........8.1..;27
..3...8..4....8.......12..6..7.9..21...1.76..8...26.9.2...69.876...........78.1..;27
..3...8..4....8.......12..6..7.9..21...1.76..8...26.9.2...69.87.7...........8.16.;27
...6..8..45..78.....9.1......7.9..2...21.76..8.1..6.9.2....9.876..2.........8.1..;27
...6..8..45...8.....9.1......7.9..2...21.76..8.1..6.9.2....9.8767.2.........8.1..;27
...6..8..45...8.....9.1......7.9..2...21.76..8.1..6.9.2....9.876..2........78.1..;27
..3...8..4...78.......12..6..789..2....1.76.8..1.26.9.2...69..76.8............1..;27
..36..8..4...78.....9.12.....7.9..2....1.76..8.1.26.9.2....9.876............8.1..;27
...6..8..45..78.....9.12.....7.9..2....1.76..8.1.26.9.2....9.876............8.1..;27
...6..8..45..78.....9.1......7.9..2....1.76..8.1.26.9.2....9.876..2.........8.1..;27
..3...8..4..9.8.......12.....789..2....1.76.8..1.26.9.2...69..7678............1..;27
..3...8..4..9.8.......12.....789..2....1.76.8..1.26.9.2...69..76.8.........7..1..;27
..3...8..4..9.8.......12.....789..2....1.76.8..1.26.9.2...69..7.78............16.;27
..3...8..4....8.......12..6..789..2....1.76.8..1.26.9.2...69..7678............1..;27
..3...8..4....8.......12..6..789..2....1.76.8..1.26.9.2...69..76.8.........7..1..;27
..3...8..4....8.......12..6..789..2....1.76.8..1.26.9.2...69..7.78............16.;27
..36..8..4..9.8.......12.....7.9..2....1.76..8.1.26.9.2....9.8767...........8.1..;27
..36..8..4..9.8.......12.....7.9..2....1.76..8.1.26.9.2....9.876...........78.1..;27
..36..8..4.6..8.......12.....7.9..2....1.76..8.1.26.9.2....9.8767...........8.1..;27
..36..8..4....8.....9.12.....7.9..2....1.76..8.1.26.9.2....9.8767...........8.1..;27
..36..8..4....8.......12..6..7.9..2....1.76..8.1.26.9.2....9.8767...........8.1..;27
..36..8..4.6..8.......12.....7.9..2....1.76..8.1.26.9.2....9.876...........78.1..;27
..36..8..4....8.....9.12.....7.9..2....1.76..8.1.26.9.2....9.876...........78.1..;27
..36..8..4....8.......12..6..7.9..2....1.76..8.1.26.9.2....9.876...........78.1..;27
...6..8..45...8.....9.12.....7.9..2....1.76..8.1.26.9.2....9.8767...........8.1..;27
...6..8..45...8.....9.12.....7.9..2....1.76..8.1.26.9.2....9.876...........78.1..;27
...6..8..45...8.....9.1......7.9..2....1.76..8.1.26.9.2....9.8767.2.........8.1..;27
...6..8..45...8.....9.1......7.9..2....1.76..8.1.26.9.2....9.876..2........78.1..;27
..3...8..4..9.8.......12.....7.9..2....1.76..8.1.26.9.2...69.8767...........8.1..;27
..3...8..4..9.8.......12.....7.9..2....1.76..8.1.26.9.2...69.876...........78.1..;27
..3...8..4..9.8.......12.....7.9..2....1.76..8.1.26.9.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6..7.9..2....1.76..8.1.26.9.2...69.8767...........8.1..;27
..3...8..4....8.......12..6..7.9..2....1.76..8.1.26.9.2...69.876...........78.1..;27
..3...8..4....8.......12..6..7.9..2....1.76..8.1.26.9.2...69.87.7...........8.16.;27
...6..8..45..78.....9.1......7....219.21.76..8....6.9.2....9.876..2.........8.1..;27
...6..8..45...8.....9.1......7....219.21.76..8....6.9.2....9.8767.2.........8.1..;27
...6..8..45...8.....9.1......7....219.21.76..8....6.9.2....9.876..2........78.1..;27
..3...8..4...78.......12..6..78...219..1.76.8....26.9.2...69..76.8............1..;27
..36..8..4...78.....9.12.....7....219..1.76..8...26.9.2....9.876............8.1..;27
..3...8..4....8.......12..6..78...219..1.76.8....26.9.2...69..7678............1..;27
..3...8..4....8.......12..6..78...219..1.76.8....26.9.2...69..76.8.........7..1..;27
..3...8..4....8.......12..6..78...219..1.76.8....26.9.2...69..7.78............16.;27
..36..8..4.6..8.......12.....7....219..1.76..8...26.9.2....9.8767...........8.1..;27
..36..8..4..9.8.......12.....7....219..1.76..8...26.9.2....9.8767...........8.1..;27
..36..8..4....8.....9.12.....7....219..1.76..8...26.9.2....9.8767...........8.1..;27
..36..8..4....8.......12..6..7....219..1.76..8...26.9.2....9.8767...........8.1..;27
..36..8..4.6..8.......12.....7....219..1.76..8...26.9.2....9.876...........78.1..;27
..36..8..4..9.8.......12.....7....219..1.76..8...26.9.2....9.876...........78.1..;27
..36..8..4....8.....9.12.....7....219..1.76..8...26.9.2....9.876...........78.1..;27
..36..8..4....8.......12..6..7....219..1.76..8...26.9.2....9.876...........78.1..;27
..3...8..4..9.8.......12.....7....219..1.76..8...26.9.2...69.8767...........8.1..;27
..3...8..4....8.......12..6..7....219..1.76..8...26.9.2...69.8767...........8.1..;27
..3...8..4..9.8.......12.....7....219..1.76..8...26.9.2...69.876...........78.1..;27
..3...8..4....8.......12..6..7....219..1.76..8...26.9.2...69.876...........78.1..;27
..3...8..4..9.8.......12.....7....219..1.76..8...26.9.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6..7....219..1.76..8...26.9.2...69.87.7...........8.16.;27
...6..8..45..78.....9.1......7....2.9.21.76..8.1..6.9.2....9.876..2.........8.1..;27
...6..8..45...8.....9.1......7....2.9.21.76..8.1..6.9.2....9.8767.2.........8.1..;27
...6..8..45...8.....9.1......7....2.9.21.76..8.1..6.9.2....9.876..2........78.1..;27
..3...8..4...78.......12..6..78...2.9..1.76.8..1.26.9.2...69..76.8............1..;27
..3...8..4..978.......12.....78...2.9..1.76.8..1.26.9.2...69..7..8............16.;27
..36..8..4...78.....9.12.....7....2.9..1.76..8.1.26.9.2....9.876............8.1..;27
...6..8..45..78.....9.12.....7....2.9..1.76..8.1.26.9.2....9.876............8.1..;27
...6..8..45..78.....9.1......7....2.9..1.76..8.1.26.9.2....9.876..2.........8.1..;27
..3...8..4..9.8.......12.....78...2.9..1.76.8..1.26.9.2...69..7678............1..;27
..3...8..4....8.......12..6..78...2.9..1.76.8..1.26.9.2...69..7678............1..;27
..3...8..4..9.8.......12.....78...2.9..1.76.8..1.26.9.2...69..76.8.........7..1..;27
..3...8..4....8.......12..6..78...2.9..1.76.8..1.26.9.2...69..76.8.........7..1..;27
..3...8..4..9.8.......12.....78...2.9..1.76.8..1.26.9.2...69..7.78............16.;27
..3...8..4....8.......12..6..78...2.9..1.76.8..1.26.9.2...69..7.78............16.;27
..36..8..4.6..8.......12.....7....2.9..1.76..8.1.26.9.2....9.8767...........8.1..;27
..36..8..4..9.8.......12.....7....2.9..1.76..8.1.26.9.2....9.8767...........8.1..;27
..36..8..4....8.....9.12.....7....2.9..1.76..8.1.26.9.2....9.8767...........8.1..;27
..36..8..4....8.......12..6..7....2.9..1.76..8.1.26.9.2....9.8767...........8.1..;27
..36..8..4.6..8.......12.....7....2.9..1.76..8.1.26.9.2....9.876...........78.1..;27
..36..8..4..9.8.......12.....7....2.9..1.76..8.1.26.9.2....9.876...........78.1..;27
..36..8..4....8.....9.12.....7....2.9..1.76..8.1.26.9.2....9.876...........78.1..;27
..36..8..4....8.......12..6..7....2.9..1.76..8.1.26.9.2....9.876...........78.1..;27
...6..8..45...8.....9.12.....7....2.9..1.76..8.1.26.9.2....9.8767...........8.1..;27
...6..8..45...8.....9.12.....7....2.9..1.76..8.1.26.9.2....9.876...........78.1..;27
...6..8..45...8.....9.1......7....2.9..1.76..8.1.26.9.2....9.8767.2.........8.1..;27
...6..8..45...8.....9.1......7....2.9..1.76..8.1.26.9.2....9.876..2........78.1..;27
..3...8..4..9.8.......12.....7....2.9..1.76..8.1.26.9.2...69.8767...........8.1..;27
..3...8..4....8.......12..6..7....2.9..1.76..8.1.26.9.2...69.8767...........8.1..;27
..3...8..4..9.8.......12.....7....2.9..1.76..8.1.26.9.2...69.876...........78.1..;27
..3...8..4....8.......12..6..7....2.9..1.76..8.1.26.9.2...69.876...........78.1..;27
..3...8..4..9.8.......12.....7....2.9..1.76..8.1.26.9.2...69.87.7...........8.16.;27
..3...8..4....8.......12..6..7....2.9..1.76..8.1.26.9.2...69.87.7...........8.16.;27
.2.6.....45..7.2....9.1......789...1..21.76..8...26.9......9.876..2.........8.1..;27
.2.6.....45..7.2....9.1......789..21..21.76..8....6.9......9.876..2.........8.1..;27
.2.6.....45....2....9.1......789...1..21.76..8...26.9......9.8767.2.........8.1..;27
.2.6.....45....2....9.1......789...1..21.76..8...26.9......9.876..2........78.1..;27
.2.6.....45....2....9.1......789..21..21.76..8....6.9......9.8767.2.........8.1..;27
.2.6.....45....2....9.1......789..21..21.76..8....6.9......9.876..2........78.1..;27
...6..8..45..7......9.1......789..21..21.76..8....6.9.2....9.876..2.........8.1..;27
...6.....45..7......9.12.....789..21..21.76..8....6.9.2....9.876..2.........8.1..;27
...6.....45.........9.12.....789..21..21.76..8...26.9.2....9.8767...........8.1..;27
...6.....45.........9.12.....789..21..21.76..8...26.9.2....9.876...........78.1..;27
...6..8..45.........9.1......789..21..21.76..8....6.9.2....9.8767.2.........8.1..;27
...6.....45.........9.12.....789..21..21.76..8....6.9.2....9.8767.2.........8.1..;27
...6..8..45.........9.1......789..21..21.76..8....6.9.2....9.876..2........78.1..;27
...6.....45.........9.12.....789..21..21.76..8....6.9.2....9.876..2........78.1..;27
..36..8..4...7......9.12.....789..21...1.76.8....26.9.2....9..76.8..........8.1..;27
..36..8..4...7........12..6..789..21...1.76.8....26.9.2....9..76.8..........8.1..;27
..3...8..4...7........12..6..789..21...1.76.8....26.9.2...69..76.8..........8.1..;27
..36...7..5..7......9.12.....789..21...1..6..8...2679.2....9.8.6...........78.1..;27
..36..8..4...7......9.12.....789..21...1.76..8...26.9.2....9.876............8.1..;27
..36...7..5..7......9.12.....789..21...1..6..8...26.9.2....9.876...........78.1..;27
..36..8..4.6..........12.....789..21...1.76.8....26.9.2....9.8767...........8.1..;27
..36..8..4..........9.12.....789..21...1.76.8....26.9.2....9.8767...........8.1..;27
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..36..8..4.6..........12.....789..21...1.76.8....26.9.2....9.876...........78.1..;27
..36..8..4..........9.12.....789..21...1.76.8....26.9.2....9.876...........78.1..;27
..36..8..4............12..6..789..21...1.76.8....26.9.2....9.876...........78.1..;27
..36..8..4.6..........12.....789..21...1.76.8....26.9.2....9..7678..........8.1..;27
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..36..8..4.6..........12.....789..21...1.76.8....26.9.2....9..76.8.........78.1..;27
..36..8..4..........9.12.....789..21...1.76.8....26.9.2....9..76.8.........78.1..;27
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..36.....45.........9.12.....789..21...1.76.8....26.9.2....9.876...........78.1..;27
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...6.....45.........9.12.....789..2...21.76.8..1..6.9.2....9.8767.2.........8.1..;27
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...6..8..45.........9.1......789..2...21.76..8.1..6.9.2....9.8767.2.........8.1..;27
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..36..8..4...7........12..6..789..2....1.76.8..1.26.9.2....9..76.8..........8.1..;27
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..36..8..4..9.........12.....789..2....1.76.8..1.26.9.2....9..76.8.........78.1..;27
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..36..8..4.6..........12.....789..2....1.76.8..1.26.9.2....9.8767...........8.1..;27
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..36..8..4.6..........12.....789..2....1.76.8..1.26.9.2....9.876...........78.1..;27
..36..8..4..........9.12.....789..2....1.76.8..1.26.9.2....9.876...........78.1..;27
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..3...8..4............12..6..789..2....1.76.8..1.26.9.2...69.8767...........8.1..;27
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..36......5..7....7.9.12.....78...219..1.76.8....26.9.2....9.876............8.1..;27
..36......5..7....7...12..6..78...219..1.76.8....26.9.2....9.876............8.1..;27
..36...7..56.7........12.....78...219..1..6.8....26.9.2....9.876...........78.1..;27
..36...7..5..7......9.12.....78...219..1..6.8....26.9.2....9.876...........78.1..;27
..36...7..5..7........12..6..78...219..1..6.8....26.9.2....9.876...........78.1..;27
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..36...7..56.7........12.....78...219..1..6..8...2679.2....9.8.6...........78.1..;27
..36...7..5..7......9.12.....78...219..1..6..8...2679.2....9.8.6...........78.1..;27
..36...7..5..7........12..6..78...219..1..6..8...2679.2....9.8.6...........78.1..;27
..3....7..5..7........12..6..78...219..1..6..8...2679.2...69.8.6...........78.1..;27
..36..8..4...7......9.12.....78...219..1.76..8...26.9.2....9.876............8.1..;27
1.36......5..7......9.12.....78...219..1.76..8...26.9.2....9.876............8.1..;27
..36...7..5..7......9.12.....78...219..1.76..8...26.9.2....9.876............8.1..;27
..36.....45..7......9.12.....78...219..1.76..8...26.9.2....9.876............8.1..;27
..36......5..7..1...9.12.....78...219..1.76..8...26.9.2....9.876............8.1..;27
..36......5..7....7.9.12.....78...219..1.76..8...26.9.2....9.876............8.1..;27
1.36......5..7........12..6..78...219..1.76..8...26.9.2....9.876............8.1..;27
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..36.....45..7........12..6..78...219..1.76..8...26.9.2....9.876............8.1..;27
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..36......5..7....7...12..6..78...219..1.76..8...26.9.2....9.876............8.1..;27
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..36...7..5..7......9.12.....78...219..1..6..8...26.9.2....9.876...........78.1..;27
..36...7..5..7........12..6..78...219..1..6..8...26.9.2....9.876...........78.1..;27
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..3......45..7........12..6..78...219..1.76..8...26.9.2...69.87.............8.16.;27
..3.......5..7....7...12..6..78...219..1.76..8...26.9.2...69.87.............8.16.;27
..36...7..56..........12.....78...219..1.76.8....2679.2....9.8.6...........78.1..;27
..36...7..5.........9.12.....78...219..1.76.8....2679.2....9.8.6...........78.1..;27
..36...7..5...........12..6..78...219..1.76.8....2679.2....9.8.6...........78.1..;27
..3....7..5...........12..6..78...219..1.76.8....2679.2...69.8.6...........78.1..;27
..36..8..4.6..........12.....78...219..1.76.8....26.9.2....9.8767...........8.1..;27
..36..8..4..........9.12.....78...219..1.76.8....26.9.2....9.8767...........8.1..;27
..36..8..4............12..6..78...219..1.76.8....26.9.2....9.8767...........8.1..;27
..36..8..4.6..........12.....78...219..1.76.8....26.9.2....9.876...........78.1..;27
..36..8..4..........9.12.....78...219..1.76.8....26.9.2....9.876...........78.1..;27
..36..8..4............12..6..78...219..1.76.8....26.9.2....9.876...........78.1..;27
..36..8..4.6..........12.....78...219..1.76.8....26.9.2....9..7678..........8.1..;27
..36..8..4..........9.12.....78...219..1.76.8....26.9.2....9..7678..........8.1..;27
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..36..8..4.6..........12.....78...219..1.76.8....26.9.2....9..76.8.........78.1..;27
..36..8..4..........9.12.....78...219..1.76.8....26.9.2....9..76.8.........78.1..;27
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..36...7..56..........12.....78...219..1.76.8....26.9.2....9.8767...........8.1..;27
..36...7..5.........9.12.....78...219..1.76.8....26.9.2....9.8767...........8.1..;27
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..36.....456..........12.....78...219..1.76.8....26.9.2....9.8767...........8.1..;27
..36.....45.........9.12.....78...219..1.76.8....26.9.2....9.8767...........8.1..;27
..36.....45...........12..6..78...219..1.76.8....26.9.2....9.8767...........8.1..;27
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..36...7..5.........9.12.....78...219..1.76.8....26.9.2....9.876...........78.1..;27
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..36.....45.........9.12.....78...219..1.76.8....26.9.2....9.876...........78.1..;27
..36.....45...........12..6..78...219..1.76.8....26.9.2....9.876...........78.1..;27
..3...8..4............12..6..78...219..1.76.8....26.9.2...69.8767...........8.1..;27
..3...8..4............12..6..78...219..1.76.8....26.9.2...69.876...........78.1..;27
..3...8..4............12..6..78...219..1.76.8....26.9.2...69..7678..........8.1..;27
..3...8..4............12..6..78...219..1.76.8....26.9.2...69..76.8.........78.1..;27
..3...8..4............12..6..78...219..1.76.8....26.9.2...69..7.78..........8.16.;27
..3....7..5...........12..6..78...219..1.76.8....26.9.2...69.8767...........8.1..;27
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..3....7..5...........12..6..78...219..1.76..8...26.9.2...69.87.7...........8.16.;27
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...6.....45.........9.12.....78...2.9.21.76.8..1..6.9.2....9.8767.2.........8.1..;27
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...6.....45.........9.12.....78...2.9.21.76..8.1.26.9.2....9.8767...........8.1..;27
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...6..8..45.........9.1......78...2.9.21.76..8.1..6.9.2....9.8767.2.........8.1..;27
...6.....45.........9.12.....78...2.9.21.76..8.1..6.9.2....9.8767.2.........8.1..;27
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..36...7..56.7........12.....78...2.9..1..6.8..1.2679.2....9.8.6...........78.1..;27
..36...7..5..7......9.12.....78...2.9..1..6.8..1.2679.2....9.8.6...........78.1..;27
..36...7..5..7........12..6..78...2.9..1..6.8..1.2679.2....9.8.6...........78.1..;27
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..36...7..5..7......9.12.....78...2.9..1..6.8..1.26.9.2....9.876...........78.1..;27
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..36...7..5..7......9.12.....78...2.9..1..6..8.1.2679.2....9.8.6...........78.1..;27
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..36...7..5..7......9.12.....78...2.9..1..6..8.1.26.9.2....9.876...........78.1..;27
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..36...7..5.........9.12.....78...2.9..1.76.8..1.2679.2....9.8.6...........78.1..;27
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...6....945.........9.12.....78...2.9..1.76.8..1.26.9.2....9.8767...........8.1..;27
...6....945...........12..6..78...2.9..1.76.8..1.26.9.2....9.8767...........8.1..;27
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...6....945.9.........12.....78...2.9..1.76.8..1.26.9.2....9.876...........78.1..;27
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...6....945...........12..6..78...2.9..1.76.8..1.26.9.2....9.876...........78.1..;27
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..36..8..4.6..........12.....78...2.9..1.76.8..1.26.9.2....9.8767...........8.1..;27
..36..8..4..9.........12.....78...2.9..1.76.8..1.26.9.2....9.8767...........8.1..;27
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..36..8..4.6..........12.....78...2.9..1.76.8..1.26.9.2....9.876...........78.1..;27
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..36..8..4..........9.12.....78...2.9..1.76.8..1.26.9.2....9.876...........78.1..;27
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..36..8..4..9.........12.....78...2.9..1.76.8..1.26.9.2....9..76.8.........78.1..;27
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..36..8..4.6..........12.....78...2.9..1.76..8.1.26.9.2....9.8767...........8.1..;27
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..3....7..5...........12..6..78...2.9..1.76..8.1.26.9.2...69.876...........78.1..;27
..3...8..4..9.........12.....78...2.9..1.76..8.1.26.9.2...69.87.7...........8.16.;27
..3...8..4............12..6..78...2.9..1.76..8.1.26.9.2...69.87.7...........8.16.;27
..3......45...........12..6..78...2.9..1.76..8.1.26.9.2...69.87.7...........8.16.;27
..3......45...........12..6..78...2.9..1.76..8.1.26.9.2...69.87............78.16.;27
..3....7..5...........12..6..78...2.9..1.76..8.1.26.9.2...69.87.7...........8.16.;27
1.36......5..7......9..2.....78...2.9..1.76..8.1.26.9.2....9.876....1.......8.1..;27
1.36......5..7.........2..6..78...2.9..1.76..8.1.26.9.2....9.876....1.......8.1..;27
1.3.......5..7.........2..6..78...2.9..1.76..8.1.26.9.2...69.876....1.......8.1..;27
...6..87.45...82....9..........9...1..21.76..8...2679..1...9.8.6..2.1......78....;27
...6..87.45...82....9..........9..21..21.76..8....679..1...9.8.6..2.1......78....;27
...6..87.45...82....9..........9..21...1.76..8...2679..1...9.8.6..2.1......78....;27
..36..87..5...8.....9.1........9..21..21.76..8....679.2....9.8.6..2........78.1..;27
...6..87.45...8.....9.1........9..21..21.76..8....679.2....9.8.6..2........78.1..;27
..36...7..5...8.....9.12......89..21...1.76.8....2679.2....9.8.6.8.........7..1..;27
..36...7..5...8.....9.12......89..21...1.76.8....2679.2....9.8.6...........78.1..;27
..36...7..5...8.....9.12.......9..21...1.76.88...2679.2....9.8.6.8.........7..1..;27
..36...7..5...8.....9.12.......9..21...1.76.88...2679.2....9.8.6...........78.1..;27
..36...7..5...8.....9.12......89..21...1.76..8...2679.2....9.8.6.8.........7..1..;27
..36..87.4....8.....9.12.......9..21...1.76..8...2679.2....9.8.6...........78.1..;27
..36..87..5...8.....9.12.......9..21...1.76..8...2679.2....9.8.6...........78.1..;27
..36...7..5...8.....9.12......89..21...1.76..8...2679.2....9.8.6...........78.1..;27
..36..87..5...8.....9.1........9..21...1.76..8...2679.2....9.8.6..2........78.1..;27
...6..87.45...8.....9..........9..21..21.76..8....679.2....9.8.6..2.1......78.1..;27
..36..87..5...8.....9.1........9..2...21.76..8.1..679.2....9.8.6..2........78.1..;27
...6..87.45...8.....9.1........9..2...21.76..8.1..679.2....9.8.6..2........78.1..;27
..36...7..5...8.....9.12......89..2....1.76.8..1.2679.2....9.8.6.8.........7..1..;27
..36...7..5...8.....9.12......89..2....1.76.8..1.2679.2....9.8.6...........78.1..;27
..36...7..5...8.....9.12.......9..2....1.76.88.1.2679.2....9.8.6.8.........7..1..;27
..36...7..5...8.....9.12.......9..2....1.76.88.1.2679.2....9.8.6...........78.1..;27
..36...7..5...8.....9.12......89..2....1.76..8.1.2679.2....9.8.6.8.........7..1..;27
..36..87.4....8.....9.12.......9..2....1.76..8.1.2679.2....9.8.6...........78.1..;27
..36..87..5...8.....9.12.......9..2....1.76..8.1.2679.2....9.8.6...........78.1..;27
..36...7..5...8.....9.12......89..2....1.76..8.1.2679.2....9.8.6...........78.1..;27
..36..87..5...8.....9.1........9..2....1.76..8.1.2679.2....9.8.6..2........78.1..;27
...6..87.45...8.....9.12.......9..2....1.76..8.1.2679.2....9.8.6...........78.1..;27
...6..87.45...8.....9.1........9..2....1.76..8.1.2679.2....9.8.6..2........78.1..;27
...6..87.45...8.....9..........9..2...21.76..8.1..679.2....9.8.6..2.1......78.1..;27
...6..87.45...8.....9..2.......9..2....1.76..8.1.2679.2....9.8.6....1......78.1..;27
...6..87.45...8.....9..........9..2....1.76..8.1.2679.2....9.8.6..2.1......78.1..;27
...6..87.45...82....9..............19.21.76..8...2679..1...9.8.6..2.1......78....;27
...6..87.45...82....9.............219.21.76..8....679..1...9.8.6..2.1......78....;27
...6..87.45...82....9.............219..1.76..8...2679..1...9.8.6..2.1......78....;27
...6..8..45..78.....9.1...........219.21.76..8....679.2....9.876..2.........8.1..;27
...6..8..45...8.....9.1...........219.21.76..8....679.2....9.8767.2.........8.1..;27
...6..8..45...8.....9.1...........219.21.76..8....679.2....9.876..2........78.1..;27
..36..87..5.9.8.......1...........219.21.76..8....679.2....9.8.6..2........78.1..;27
..36..87..5...8.....9.1...........219.21.76..8....679.2....9.8.6..2........78.1..;27
...6..87.45...8.....9.1...........219.21.76..8....679.2....9.8.6..2........78.1..;27
...6..8..45...8.....9.1...........219.21.76..8....679.2....9.8.67.2........78.1..;27
..3...87..5.9.8.......1...........219.21.76..8....679.2...69.8.6..2........78.1..;27
..36...7..5...8.....9.12......8...219..1.76.8....2679.2....9.8.6.8.........7..1..;27
..36...7..5...8.....9.12......8...219..1.76.8....2679.2....9.8.6...........78.1..;27
..36...7..56..8.......12..........219..1.76.88...2679.2....9.8.6.8.........7..1..;27
..36...7..5.9.8.......12..........219..1.76.88...2679.2....9.8.6.8.........7..1..;27
..36...7..5...8.....9.12..........219..1.76.88...2679.2....9.8.6.8.........7..1..;27
..36...7..5...8.......12..6.......219..1.76.88...2679.2....9.8.6.8.........7..1..;27
..36...7..56..8.......12..........219..1.76.88...2679.2....9.8.6...........78.1..;27
..36...7..5.9.8.......12..........219..1.76.88...2679.2....9.8.6...........78.1..;27
..36...7..5...8.....9.12..........219..1.76.88...2679.2....9.8.6...........78.1..;27
..36...7..5...8.......12..6.......219..1.76.88...2679.2....9.8.6...........78.1..;27
..3....7..5.9.8.......12..........219..1.76.88...2679.2...69.8.6.8.........7..1..;27
..3....7..5...8.......12..6.......219..1.76.88...2679.2...69.8.6.8.........7..1..;27
..3....7..5.9.8.......12..........219..1.76.88...2679.2...69.8.6...........78.1..;27
..3....7..5...8.......12..6.......219..1.76.88...2679.2...69.8.6...........78.1..;27
..36...7..56..8.......12......8...219..1.76..8...2679.2....9.8.6.8.........7..1..;27
..36...7..5.9.8.......12......8...219..1.76..8...2679.2....9.8.6.8.........7..1..;27
..36...7..5...8.....9.12......8...219..1.76..8...2679.2....9.8.6.8.........7..1..;27
..36...7..5...8.......12..6...8...219..1.76..8...2679.2....9.8.6.8.........7..1..;27
..36..87.4....8.....9.12..........219..1.76..8...2679.2....9.8.6...........78.1..;27
..36..87..56..8.......12..........219..1.76..8...2679.2....9.8.6...........78.1..;27
..36..87..5.9.8.......12..........219..1.76..8...2679.2....9.8.6...........78.1..;27
..36..87..5...8.....9.12..........219..1.76..8...2679.2....9.8.6...........78.1..;27
..36..87..5...8.......12..6.......219..1.76..8...2679.2....9.8.6...........78.1..;27
..36...7..56..8.......12......8...219..1.76..8...2679.2....9.8.6...........78.1..;27
..36...7..5.9.8.......12......8...219..1.76..8...2679.2....9.8.6...........78.1..;27
..36...7..5...8.....9.12......8...219..1.76..8...2679.2....9.8.6...........78.1..;27
..36...7..5...8.......12..6...8...219..1.76..8...2679.2....9.8.6...........78.1..;27
..36..87..5...8.....9.1...........219..1.76..8...2679.2....9.8.6..2........78.1..;27
..3....7..5.9.8.......12......8...219..1.76..8...2679.2...69.8.6.8.........7..1..;27
..3....7..5...8.......12..6...8...219..1.76..8...2679.2...69.8.6.8.........7..1..;27
..3...87..5.9.8.......12..........219..1.76..8...2679.2...69.8.6...........78.1..;27
only 2 of them pass the T&E(1) filter with an skfr rating of 9.2
- Code: Select all
...6...7945.9..........2......8...2.9..1.76..8.1.2679.2....9.8.6....1......78.1..;27
...6...7945.9..........2......8...2.9..1.76..8.1.267..2....9.8.6....19.....78.1..;27
- champagne
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Re: tridagon??
by denis_berthier » Sun Feb 23, 2025 4:34 pm
.
So, in summary, having a complete grid with a "solution tridagon" is of no help in finding a minimal puzzle with a tridagon.
(Which is not surprising, as about 1 complete grid in 2 has a "solution tridagon".)
.
So, in summary, having a complete grid with a "solution tridagon" is of no help in finding a minimal puzzle with a tridagon.
(Which is not surprising, as about 1 complete grid in 2 has a "solution tridagon".)
.
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Re: tridagon??
by champagne » Sun Feb 23, 2025 5:49 pm
denis_berthier wrote:.
So, in summary, having a complete grid with a "solution tridagon" is of no help in finding a minimal puzzle with a tridagon.
(Which is not surprising, as about 1 complete grid in 2 has a "solution tridagon".)
.
???????
Edit
Some misunderstanding somewhere.
1164 puzzles fitting with the request on my side; none in your post
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Re: tridagon??
by denis_berthier » Sun Feb 23, 2025 6:53 pm
.
Oh, I see.
So, OK, there are tridagons in puzzles at almost any level of difficulty - which we already knew. And starting with a complete gird that has a "solution tridagon" can help find some of them.
But this doesn't help in finding hard puzzles with a tridagon.
.
Oh, I see.
So, OK, there are tridagons in puzzles at almost any level of difficulty - which we already knew. And starting with a complete gird that has a "solution tridagon" can help find some of them.
But this doesn't help in finding hard puzzles with a tridagon.
.
- denis_berthier
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Re: tridagon??
by champagne » Sun Feb 23, 2025 7:57 pm
denis_berthier wrote:.
Oh, I see.
So, OK, there are tridagons in puzzles at almost any level of difficulty - which we already knew. And starting with a complete gird that has a "solution tridagon" can help find some of them.
But this doesn't help in finding hard puzzles with a tridagon.
.
from here, 2 points :
As I wrote above, we don't have a nugget in any solution grid. This one is very bad (the scan is exhaustive for all solutions <=27 in this run) Up to now, my best result has been a 11.5 skfr
This is a list of pure tridagon puzzles. To find other puzzles, the best results have to be used as seeds as "loki" long ago.
I did not made to many tests. I am trying to improve my process to scan easily large areas
This run lasted less than 3 seconds
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Re: tridagon??
by denis_berthier » Mon Feb 24, 2025 3:06 am
.
When there's a "nugget" in ~50% of the complete grids, it is to be expected that the nuggets are not gold but pyrite.
Continuing with the same idea as in a previous post (49.9 % of randomly selected complete grids have a "solution tridagon"), I've tried with (this time non-random) complete grids from another collection: the hardest ones in ph2010, namely the 208 ones with SER ≥ 11.7.
Result: 59.62 % of the ph2010 complete grids with SER≥11.7 have a "solution-tridagon".
Question: take any of these complete grids among the 59.62%. Does this help finding a SER-hard tridagon?
Here's the list of those that have a solution-tridagon:
.
When there's a "nugget" in ~50% of the complete grids, it is to be expected that the nuggets are not gold but pyrite.
Continuing with the same idea as in a previous post (49.9 % of randomly selected complete grids have a "solution tridagon"), I've tried with (this time non-random) complete grids from another collection: the hardest ones in ph2010, namely the 208 ones with SER ≥ 11.7.
Result: 59.62 % of the ph2010 complete grids with SER≥11.7 have a "solution-tridagon".
Question: take any of these complete grids among the 59.62%. Does this help finding a SER-hard tridagon?
Here's the list of those that have a solution-tridagon:
- Code: Select all
1 2 3 4 5 6 8 9 10 12 13 16 18 19 20 21 22 23 24 25 28 29 30 31 32 33 34 35 37 41 46 47 48 53 55 56 58 63 66 68 69 70 71 72 73 74 76 77 78 79 82 83 84 85 89 90 91 93 94 95 96 97 98 105 106 107 109 111 112 113 114 115 116 118 120 122 123 124 126 128 129 132 133 135 136 137 138 141 142 144 148 151 152 153 157 158 160 161 163 164 165 171 172 174 175 177 180 182 188 189 191 192 194 196 197 199 201 202 203 204 205 206 207 208
.
- denis_berthier
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