kumi na tano 3.00 - sliding tile puzzle suboptimal solver

stannic · Sep 24, 2012

kumi na tano 3.10 beta (Update 1)

Hello all.

I wrote a program capable to solve (MxN-1) sliding tile puzzles, such as the Fifteen puzzle. The program can solve puzzles from 2x2 to 11x11.

You can download the program by the following link:

Latest version (3.10 beta update 1, 10/05/2012): http://www.mediafire.com/?1sbq081n5ecv0ab

version 3.10 beta (Update 1) (10/05/2012): http://www.mediafire.com/?1sbq081n5ecv0ab

- Batch solver reports the number of instances solved in exactly N moves
- Manual updated to the current version

version 3.10 beta (10/04/2012): http://www.mediafire.com/?x5sjnoa3necoqjg

- Batch solver improved: information window (progress, current averages etc.); Save Report function (plain ASCII format)
- Added missing feature "Stop at slackness" (set to 1 to search only optimal solutions for each phase)
- Added antipodes for puzzles 2x2, 3x2, 4x2, 5x2, 6x2, 3x3, 4x3 in metrics 2TM, 3TM, 4TM
- Single click on ANP button will show the first antipode, and two small buttons will appear. Use these buttons to navigate between antipodes.
- Indicators "Parity error" and "Symmetric" in the Edit Instance window (Solver tab).
- Fixed bug with truncated text in message dialogs.

version 3.02 beta (9/29/2012): http://www.mediafire.com/?mmdyogbo6pqkdd2

- All found solutions are shown (longer solution does not disappear after shorter one is found).
- Bug fixed: Flip Rgn button should be disabled for non-square puzzles.
- Improved Create Project dialog: selecting both puzzle width and height by single click, accepting by double-click; additional information is in program hints.
- MD5-checksumming lookup tables to minimize risk of errors.
- Interface logic: STM and MTM aliases in filters on Regions tab changed back to 1TM and 10TM.
- Added two formats of the solution (Tile Compact and Blank Compact). See Options tab.
- Pop-up menu in the instance editor.
- Copy/paste instance (text format, blank square denoted by 0). Use CPY/PTE buttons or items in the popup menu.
- You can copy instance directly from takaken's solver.
- Batch solver improved (formerly Demo button).

- Antipodes and God's numbers for the following puzzles are hard-coded into the program:
STM metric: 2x2, 3x2, 4x2, 5x2, 6x2, 7x2, 8x2, 3x3, 4x3, 5x3, 4x4
MTM metric: 2x2, 3x2, 4x2, 5x2, 6x2, 3x3, 4x3, 4x4
- God's numbers are shown in the title and in hints in the Create Project dialog.
- Use ANP button to see antipodes (when available).

version 3.01 (9/25/2012): http://www.mediafire.com/?17qnfshue7dgcpn

- added aliases STM and MTM
- fixed bug with displaying length of the solution in various metrics
- updated manual

version 3.00 (9/24/2012): http://www.mediafire.com/?99dqxi7xi8nmh8c

Here are described some things that can be done with kumi na tano. For the full reference, please see the manual included in the archive (file manual.pdf or manual.rtf)

Wizard > Project Actions > Metric = MTM means that you have to switch to the Wizard tab (if you aren't already on it), find in the Project Actions window drop-down list Metric and set its value to MTM.

Also, for instance, Solver > Edit Instance > ANP denotes the small button ANP in the Edit Instance window on the Solver tab.

The following steps allow you to solve suboptimally any legal configuration of any MxN puzzle (M,N <= 11). Note, however, that the solution will be generally far from optimal. To find better solution, you may need to create project as described in the manual (page 26).

1. Run kumi na tano.

2. Click Wizard > Project Actions > Create button.

3. Set Box Width and Box Height to the width and height of the puzzle you want to solve.

4. Set Metric as you want.
STM is single-tile metric (only one tile per move); MTM is multi-tile metric (any number of tiles per move); 2TM, for example, is the metric that allows moving only 1 or 2 tiles per move (but not 3).

5. Check "Human "row-by-row" solving algorithm" checkbox.

6. Click OK button to close project creation dialog.

7. You will see the message asking if you want to activate the project. Click Activate button.

8. Wait until the activation is done. After activation, Solver tab will become active.

9. Click Solver > Edit Instance > RND button to scramble the puzzle.

10. Click Solver > Solver > Search to start search. The current best solution will display in the Solver > Solutions window.

11. Stop the solver at any time using Solver > Solver > Stop button when you decide that the solution is good enough.

12. Click Solver > Solutions > Play to view the solution in animation.

13. If you want to solve a particular configuration (not just random), check Solver > Edit Instance > D&S Mode checkbox.

14. Edit the configuration by dragging-and-dropping the tiles one onto another.

15. After editing is done, click Solver > Solver > Search button to solve the configuration.

kumi na tano has an internal database containing God's numbers and antipodes for already solved puzzles. The following steps allow you to view all 17 STM antipodes (80-move positions) of the Fifteen Puzzle.

1. Run kumi na tano.

2. Click Wizard > Project Actions > Create button.

3. Set Box Width = 4 and Box Height = 4.

4. Set Metric = STM.

5. Uncheck "Human "row-by-row" solving algorithm" checkbox if it is checked.

6. Click OK button to close project creation dialog.

7. Manually switch to the Solver tab.

8. Click Solver > Edit Instance > ANP button. The first of 17 antipodes will be displayed in the Current Instance window.

9. Note that after clicking ANP button, two more small buttons appear on each side of the button. Use these buttons to view all antipodes one-by-one.

10. Click ANP button second time. You'll see the full list of antipode configurations.

11. Double-click on any line in the list to view the antipode.

You can copy and paste the puzzle configuration from/to kumi na tano.

1. Create the simple project (Wizard > Project Actions > Create; Box Width = Box Height = 4; Metric = STM).

2 Right-click in the Solver > Current Instance window. The pop-up menu will display.

3. Click Copy to clipboard item to copy current puzzle configuration.

4. Paste it anywhere you want (e.g., in Notepad). It's simple text format.

5. Copy the following line to the clipboard:
1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 0

6. Right-click in the Current Instance window and select Paste from clipboard menu item.

7. You can use also buttons CPY and PTE in the Solver > Edit Instance window.

There are two common goal configurations used for MxN sliding tile puzzles:

Code:

Classic goal (Blank Last)
  1  2  3  4
  5  6  7  8
  9 10 11 12
 13 14 15  x

Blank First goal
  x  1  2  3
  4  5  6  7
  8  9 10 11
 12 13 14 15

You can set your preferred goal configuration from the Options tab.

The program searches for suboptimal solutions like Kociemba's Cube Explorer. However, it can use more than two search phases. Additionally, the user can manually configure search phases.

The basic algorithm used in kumi na tano is multi-phase approach with slackness described on the Jaap's Puzzle Page. I've further generalized this algorithm to "multi-chained" version. The algorithm details are described in the manual, as well as usage of the program.

The program should run on Windows XP/Vista/7 x86/x64. There are two binaries knt32.exe and knt64.exe. Use one of them, depending on the OS installed.

For quick look at the program, click Wizard > Project Actions > Project > Open, then open project "sample" and click Activate button. When Solver tab becomes active, try scramble the puzzle using RND button and then click Search to find the solution.

I'll be glad to head any feedback about the program.

- stannic

ben1996123 · Sep 24, 2012

Nice, works well and looks pretty good.

cuBerBruce · Sep 25, 2012

Overall, this looks very nice. I think some additional documentation on how to create custom search phases should be provided. I think I pretty much understand "regions," and I'm presuming "chains" are sequences of regions that define phases of a solve. Does the program allow you to use multiple chains in a single search? If so, it would be nice to have explained how to do that. It also appears to be restricted what can be defined as a region. OK, I see that what I tried to do would leave a square that could not be solved without moving already solved piece(s), so the restriction makes sense.

When searching, I initially thought the "s" and "m" stood for single-tile metric and multi-tile metric, but clearly I was getting "m" numbers that were not correct for multi-tile metric.

For example, a simple test case with basic5x5 gave:

#1 (12s / 12m) [A,B,C,D,E,F]
3U 3L 2D 1L 3U

This, of course, is 12 moves in single-tile metric. But in multi-tile metric, it is only 5 moves. So the "m" clearly does not mean multi-tile metric, but apparently whatever metric is selected in the project (1TM, 2TM, 3TM, etc.). Perhaps you should display all three: single-tile metric, multi-tile metric, and the selected metric.

I think it is somewhat interesting that you bother to support 2TM, 3TM, etc. at all instead of just single-tile metric and multi-tile metric. I suspect not that many people are particularly interested in these "in-between" metrics. But if someone actually wants to search for solutions "optimized" for 2-tile metric (or 3-tile, 4-tile, etc.), they can with this program.

stannic · Sep 25, 2012

cuBerBruce said:
Does the program allow you to use multiple chains in a single search? If so, it would be nice to have explained how to do that.

Yes; this is the main difference from all previous (known to me) implementations, including the slackness approach proposed by Jaap. Multi-chained search allows you to use multiple chains in a single search; these chains may fork and merge in any user-defined way.
Some information about this is on the pages 9-11 of manual; also, there is a step-by-step tutorial in the end that shows how to create two-chained project.
The example on the p.10 is a four-chained project; that is, it uses four chains in a single search.
However, I see now that the manual should be elaborated. Added to the to-do list.

cuBerBruce said:
It also appears to be restricted what can be defined as a region. OK, I see that what I tried to do would leave a square that could not be solved without moving already solved piece(s), so the restriction makes sense.

Probably you're getting E001 error 'The region has cut squares'. Indeed, the error shows that some tile(s) cannot move to some location(s) without moving already "fixed" tiles (as if you're leaved unsolved the last square in the row).

cuBerBruce said:
When searching, I initially thought the "s" and "m" stood for single-tile metric and multi-tile metric, but clearly I was getting "m" numbers that were not correct for multi-tile metric.

For example, a simple test case with basic5x5 gave:

#1 (12s / 12m) [A,B,C,D,E,F]
3U 3L 2D 1L 3U

This, of course, is 12 moves in single-tile metric. But in multi-tile metric, it is only 5 moves. So the "m" clearly does not mean multi-tile metric, but apparently whatever metric is selected in the project (1TM, 2TM, 3TM, etc.). Perhaps you should display all three: single-tile metric, multi-tile metric, and the selected metric.

Thanks; this is a bug. It should display 12s / 5m in your example. Added to the to-do list.

cuBerBruce said:
I think it is somewhat interesting that you bother to support 2TM, 3TM, etc. at all instead of just single-tile metric and multi-tile metric. I suspect not that many people are particularly interested in these "in-between" metrics. But if someone actually wants to search for solutions "optimized" for 2-tile metric (or 3-tile, 4-tile, etc.), they can with this program.

I think it's a convenient way to generalize the notation, as well as the implementation of do_move routine. Instead of metric, you have the maximal allowed move amount, and it supports old STM and MTM as well.

Thanks for the replies.
- stannic

Edit: The following text under spoiler is an example 4-chained project from p.10 of the manual. Just copy in Notepad, save with extension .p in the projects\ subdirectory and open from the kumi na tano.

4 4
1
9
3 3 0 0
3 0 0 0
0 0 0 0
1 1 1 1

3 3 0 1
3 0 0 1
0 0 0 1
2 2 2 2

3 3 1 2
3 1 1 2
1 1 1 2
2 2 2 2

3 3 0 1
3 0 0 1
0 0 0 1
0 0 0 1

3 3 0 2
3 0 0 2
0 0 0 2
1 1 1 2

3 3 0 0
3 0 0 0
0 0 0 1
0 0 1 1

3 3 0 1
3 0 0 1
0 0 0 2
1 1 2 2

3 3 0 0
3 0 0 0
1 1 1 1
2 2 2 2

3 3 1 1
3 1 1 1
2 2 2 2
2 2 2 2

cuBerBruce · Sep 25, 2012

stannic said:
Some information about this is on the pages 9-11 of manual;

Duh. Sorry, for some reason I didn't notice the manual in the zip archive. My bad.

stannic said:
Probably you're getting E001 error 'The region has cut squares'.

Yes, exactly what I was seeing.

stannic said:
Thanks; this is a bug. It should display 12s / 5m in your example. Added to the to-do list.

Of course, you want to be sure to at least show the length in the metric the search is based upon. It's simply nice to know the single-tile metric (or 1TM as you refer to it) and multiple-tile metric as well. If the search metric is equivalent to one of these, then only showing two metric numbers would suffice.

stannic said:
I think it's a convenient way to generalize the notation, as well as the implementation of do_move routine. Instead of metric, you have the maximal allowed move amount, and it supports old STM and MTM as well.

Well, I agree that it is a valid generalization, and it's fine with me if you want to support them. It just seems a bit arbitrary to restrict how many tiles can be "pushed" as a single move (other than the maximum number possible for that puzzle) once you allow more than one as a single move. A person manipulating an actual mechanical version of the puzzle is not likely to restrict himself/herself to only pushing at most two tiles at a time, for instance. It appears you can just select "10TM" if you simply always want to use multi-tile metric regardless of what size of puzzle you select (in the current version of the program, at least). If you select the number that's just large enough (say 3TM for 4x4), then if you change the puzzle size to something larger (say 5x5), then you need to also change the metric selection if you still want to use MTM.

stannic · Sep 25, 2012

It's simply nice to know the single-tile metric (or 1TM as you refer to it) and multiple-tile metric as well. If the search metric is equivalent to one of these, then only showing two metric numbers would suffice.

This?

Code:

#6
2TM 8, STM 13, MTM 5
[A,B,C,D]
 3D 2R 1D 3L 4U

Code:

#12
2TM 42, STM 78, MTM 23
[A,B,C,D]
 4R 4U 4L 4D 4R 4U 3L 4D 3R 4U 4L 4D 4R 4U 4L 3D 3R 2U 2L 2D 2R 3U 3L

Code:

#20
STM 78, MTM 23
[A,B,D,C]
 4R 4U 4L 4D 4R 4U 3L 4D 3R 4U 4L 4D 4R 4U 4L 3D 3R 2U 2L 2D 2R 3U 3L

If you select the number that's just large enough (say 3TM for 4x4), then if you change the puzzle size to something larger (say 5x5), then you need to also change the metric selection if you still want to use MTM.

I've added aliases for 1TM = STM and 10TM = MTM. Everywhere in the user interface will be STM and MTM instead.

Edit: 3.01 is available.
- stannic

stannic · Sep 25, 2012

I've solved all sixteen antipodes from cubezzz discussion using kumi na tano (Box Width = Box Height = 4, Metric = MTM). They were all solved in 43 MTM. Hardest instance was the first antipode which is diagonally flipped goal; this configuration took about 10 minutes.
- stannic

stannic · Sep 29, 2012

3.02 beta is available. See features in first post. Manual is not updated yet, zip contains only binaries.

Can anyone run the program on 64-bit Windows with 5 or more GB of RAM? The 3.02b zip archive includes three huge projects: 3GB, 5GB and 6GB. It would be great if anyone can confirm that the program works with this amount of memory.

Also, any bugs or suggestions are welcome.
- stannic

ben1996123 · Sep 29, 2012

stannic said:
3.02 beta is available. See features in first post. Manual is not updated yet, zip contains only binaries.

Can anyone run the program on 64-bit Windows with 5 or more GB of RAM? The 3.02b zip archive includes three huge projects: 3GB, 5GB and 6GB. It would be great if anyone can confirm that the program works with this amount of memory.

Also, any bugs or suggestions are welcome.
- Bulat

Works fine for me, running windows 7 64 bit with 8gb ram.

stannic · Sep 29, 2012

ben1996123 said:
Works fine for me, running windows 7 64 bit with 8gb ram.

I'm surprised that the tables were compiled so fast. What project did you ran?

stannic said:
It would be great if anyone can confirm that the program works with this amount of memory.

Sorry, maybe I was not clear. I wanted to ask someone to run one of three projects included in 3.02b zip archive and see if the solver can actually handle large amount of memory. These projects are:
huge6x4_x64_3GB (6x4 puzzle three-phase solution; the total amount of memory required to run is 2,144,257,920 bytes);
huge6x6_x64_5GB (6x6 puzzle 3-chained 6-phase solution; memory required is 4,722,656,400 bytes);
huge8x8_x64_6GB (8x8 puzzle 13-phase solution; the total space is 5,411,802,480 bytes).

If anyone wants to test it, just open the largest project you can run with your RAM (Wizard > Project Actions > Open), activate (Project Actions > Activate) and let it compile all tables. This should take a few hours, I think, and does not require any additional user actions during this time.
After the project activation is complete, you can solve some random instances to test tables. Also, you can select any generated table on Regions tab and click Find Distribution button to output the number of puzzle positions as the function of depth. If you do it, please copy these distributions and post or pm it to me as shown under spoiler.

File Name: 3x3_1TM_d2bdb5.t
Distribution:
depth new total
0 1 1
1 2 3
2 4 7
3 8 15
4 16 31
5 20 51
6 39 90
7 62 152
8 116 268
9 152 420
10 286 706
11 396 1,102
12 748 1,850
13 1,024 2,874
14 1,893 4,767
15 2,512 7,279
16 4,485 11,764
17 5,638 17,402
18 9,529 26,931
19 10,878 37,809
20 16,993 54,802
21 17,110 71,912
22 23,952 95,864
23 20,224 116,088
24 24,047 140,135
25 15,578 155,713
26 14,560 170,273
27 6,274 176,547
28 3,910 180,457
29 760 181,217
30 221 181,438
31 2 181,440

Thanks for testing, anyway.
- stannic

cuBerBruce · Sep 30, 2012

stannic said:
Sorry, maybe I was not clear. I wanted to ask someone to run one of three projects included in 3.02b zip archive and see if the solver can actually handle large amount of memory. These projects are:
huge6x4_x64_3GB (6x4 puzzle three-phase solution; the total amount of memory required to run is 2,144,257,920 bytes);
huge6x6_x64_5GB (6x6 puzzle 3-chained 6-phase solution; memory required is 4,722,656,400 bytes);
huge8x8_x64_6GB (8x8 puzzle 13-phase solution; the total space is 5,411,802,480 bytes).

If anyone wants to test it, just open the largest project you can run with your RAM (Wizard > Project Actions > Open), activate (Project Actions > Activate) and let it compile all tables. This should take a few hours, I think, and does not require any additional user actions during this time.
After the project activation is complete, you can solve some random instances to test tables. Also, you can select any generated table on Regions tab and click Find Distribution button to output the number of puzzle positions as the function of depth. If you do it, please copy these distributions and post or pm it to me as shown under spoiler.

I was able to run it. Results in the spoiler

Code:

File Name: 6x4_1TM_d2a4da11b6.t
Distribution:
 depth        new         total
     0         18            18
     1          6            24
     2         10            34
     3         18            52
     4         42            94
     5        102           196
     6        186           382
     7        308           690
     8        514         1,204
     9        938         2,142
    10      1,748         3,890
    11      3,074         6,964
    12      5,174        12,138
    13      8,638        20,776
    14     14,300        35,076
    15     23,168        58,244
    16     37,234        95,478
    17     59,182       154,660
    18     93,398       248,058
    19    144,444       392,502
    20    220,392       612,894
    21    330,656       943,550
    22    492,322     1,435,872
    23    721,732     2,157,604
    24  1,045,836     3,203,440
    25  1,489,958     4,693,398
    26  2,098,134     6,791,532
    27  2,911,352     9,702,884
    28  3,986,862    13,689,746
    29  5,378,914    19,068,660
    30  7,158,850    26,227,510
    31  9,390,866    35,618,376
    32 12,139,396    47,757,772
    33 15,478,518    63,236,290
    34 19,434,006    82,670,296
    35 24,069,962   106,740,258
    36 29,342,172   136,082,430
    37 35,308,846   171,391,276
    38 41,757,016   213,148,292
    39 48,725,414   261,873,706
    40 55,868,828   317,742,534
    41 63,237,200   380,979,734
    42 70,247,258   451,226,992
    43 76,982,220   528,209,212
    44 82,736,870   610,946,082
    45 87,679,894   698,625,976
    46 91,085,300   789,711,276
    47 93,230,470   882,941,746
    48 93,488,154   976,429,900
    49 92,300,040 1,068,729,940
    50 89,237,434 1,157,967,374
    51 84,867,406 1,242,834,780
    52 79,034,358 1,321,869,138
    53 72,303,636 1,394,172,774
    54 64,763,078 1,458,935,852
    55 56,919,066 1,515,854,918
    56 48,965,720 1,564,820,638
    57 41,253,874 1,606,074,512
    58 33,990,544 1,640,065,056
    59 27,385,668 1,667,450,724
    60 21,544,634 1,688,995,358
    61 16,516,714 1,705,512,072
    62 12,335,516 1,717,847,588
    63  8,951,510 1,726,799,098
    64  6,304,416 1,733,103,514
    65  4,294,578 1,737,398,092
    66  2,822,620 1,740,220,712
    67  1,784,242 1,742,004,954
    68  1,080,612 1,743,085,566
    69    624,342 1,743,709,908
    70    340,554 1,744,050,462
    71    174,736 1,744,225,198
    72     82,590 1,744,307,788
    73     36,094 1,744,343,882
    74     13,810 1,744,357,692
    75      4,712 1,744,362,404
    76      1,340 1,744,363,744
    77        338 1,744,364,082
    78         62 1,744,364,144
    79         14 1,744,364,158
    80          2 1,744,364,160

File Name: 6x6_1TM_d2a4da16ba5ba3b3.t
Distribution:
 depth        new         total
     0         31            31
     1          6            37
     2         12            49
     3         24            73
     4         50           123
     5        102           225
     6        185           410
     7        335           745
     8        581         1,326
     9        967         2,293
    10      1,650         3,943
    11      2,821         6,764
    12      4,711        11,475
    13      7,743        19,218
    14     12,646        31,864
    15     20,423        52,287
    16     32,298        84,585
    17     50,354       134,939
    18     76,706       211,645
    19    114,599       326,244
    20    167,533       493,777
    21    240,001       733,778
    22    337,254     1,071,032
    23    465,031     1,536,063
    24    631,216     2,167,279
    25    842,355     3,009,634
    26  1,110,303     4,119,937
    27  1,443,195     5,563,132
    28  1,857,497     7,420,629
    29  2,359,802     9,780,431
    30  2,975,142    12,755,573
    31  3,706,825    16,462,398
    32  4,585,758    21,048,156
    33  5,607,444    26,655,600
    34  6,815,848    33,471,448
    35  8,191,305    41,662,753
    36  9,782,747    51,445,500
    37 11,560,522    63,006,022
    38 13,568,459    76,574,481
    39 15,762,563    92,337,044
    40 18,172,643   110,509,687
    41 20,738,179   131,247,866
    42 23,485,669   154,733,535
    43 26,336,095   181,069,630
    44 29,310,210   210,379,840
    45 32,332,022   242,711,862
    46 35,402,272   278,114,134
    47 38,413,996   316,528,130
    48 41,364,139   357,892,269
    49 44,155,078   402,047,347
    50 46,788,780   448,836,127
    51 49,149,222   497,985,349
    52 51,209,847   549,195,196
    53 52,885,440   602,080,636
    54 54,139,321   656,219,957
    55 54,906,980   711,126,937
    56 55,159,109   766,286,046
    57 54,879,010   821,165,056
    58 54,070,948   875,236,004
    59 52,764,659   928,000,663
    60 50,974,947   978,975,610
    61 48,753,839 1,027,729,449
    62 46,148,080 1,073,877,529
    63 43,201,503 1,117,079,032
    64 40,012,468 1,157,091,500
    65 36,612,038 1,193,703,538
    66 33,135,878 1,226,839,416
    67 29,583,738 1,256,423,154
    68 26,127,683 1,282,550,837
    69 22,702,994 1,305,253,831
    70 19,526,250 1,324,780,081
    71 16,484,498 1,341,264,579
    72 13,772,224 1,355,036,803
    73 11,257,822 1,366,294,625
    74  9,114,662 1,375,409,287
    75  7,193,323 1,382,602,610
    76  5,603,193 1,388,205,803
    77  4,241,092 1,392,446,895
    78  3,159,236 1,395,606,131
    79  2,279,433 1,397,885,564
    80  1,607,100 1,399,492,664
    81  1,099,855 1,400,592,519
    82    727,648 1,401,320,167
    83    467,025 1,401,787,192
    84    283,638 1,402,070,830
    85    166,930 1,402,237,760
    86     89,659 1,402,327,419
    87     47,333 1,402,374,752
    88     21,013 1,402,395,765
    89      9,754 1,402,405,519
    90      3,166 1,402,408,685
    91      1,209 1,402,409,894
    92        250 1,402,410,144
    93         80 1,402,410,224
    94         12 1,402,410,236
    95          4 1,402,410,240

File Name: 8x8_1TM_d2a6da45b2a6b2.t
Distribution:
 depth        new       total
     0         60          60
     1          4          64
     2         10          74
     3         22          96
     4         42         138
     5         81         219
     6        154         373
     7        281         654
     8        478       1,132
     9        813       1,945
    10      1,330       3,275
    11      2,126       5,401
    12      3,368       8,769
    13      5,286      14,055
    14      8,101      22,156
    15     12,340      34,496
    16     18,228      52,724
    17     26,230      78,954
    18     36,646     115,600
    19     50,312     165,912
    20     67,458     233,370
    21     89,154     322,524
    22    115,552     438,076
    23    148,347     586,423
    24    188,097     774,520
    25    236,143   1,010,663
    26    292,725   1,303,388
    27    360,379   1,663,767
    28    439,960   2,103,727
    29    533,370   2,637,097
    30    641,927   3,279,024
    31    767,450   4,046,474
    32    912,113   4,958,587
    33  1,077,237   6,035,824
    34  1,267,009   7,302,833
    35  1,481,645   8,784,478
    36  1,726,624  10,511,102
    37  2,000,121  12,511,223
    38  2,307,874  14,819,097
    39  2,649,212  17,468,309
    40  3,032,777  20,501,086
    41  3,454,364  23,955,450
    42  3,923,327  27,878,777
    43  4,432,968  32,311,745
    44  4,994,007  37,305,752
    45  5,593,190  42,898,942
    46  6,246,885  49,145,827
    47  6,943,583  56,089,410
    48  7,694,996  63,784,406
    49  8,477,746  72,262,152
    50  9,307,116  81,569,268
    51 10,163,467  91,732,735
    52 11,063,308 102,796,043
    53 11,983,455 114,779,498
    54 12,933,620 127,713,118
    55 13,886,660 141,599,778
    56 14,858,860 156,458,638
    57 15,826,762 172,285,400
    58 16,793,414 189,078,814
    59 17,745,354 206,824,168
    60 18,683,624 225,507,792
    61 19,579,027 245,086,819
    62 20,446,702 265,533,521
    63 21,264,453 286,797,974
    64 22,034,839 308,832,813
    65 22,734,940 331,567,753
    66 23,379,627 354,947,380
    67 23,936,163 378,883,543
    68 24,418,553 403,302,096
    69 24,799,239 428,101,335
    70 25,100,843 453,202,178
    71 25,283,747 478,485,925
    72 25,373,983 503,859,908
    73 25,323,459 529,183,367
    74 25,175,449 554,358,816
    75 24,890,474 579,249,290
    76 24,508,460 603,757,750
    77 23,990,356 627,748,106
    78 23,376,342 651,124,448
    79 22,633,251 673,757,699
    80 21,804,395 695,562,094
    81 20,864,091 716,426,185
    82 19,855,272 736,281,457
    83 18,764,003 755,045,460
    84 17,627,998 772,673,458
    85 16,448,681 789,122,139
    86 15,252,897 804,375,036
    87 14,038,971 818,414,007
    88 12,834,398 831,248,405
    89 11,645,790 842,894,195
    90 10,491,926 853,386,121
    91  9,379,363 862,765,484
    92  8,317,355 871,082,839
    93  7,315,027 878,397,866
    94  6,371,628 884,769,494
    95  5,501,734 890,271,228
    96  4,704,057 894,975,285
    97  3,982,440 898,957,725
    98  3,333,832 902,291,557
    99  2,763,796 905,055,353
   100  2,258,940 907,314,293
   101  1,826,067 909,140,360
   102  1,450,979 910,591,339
   103  1,143,083 911,734,422
   104    882,896 912,617,318
   105    674,292 913,291,610
   106    500,172 913,791,782
   107    368,771 914,160,553
   108    261,614 914,422,167
   109    184,818 914,606,985
   110    123,834 914,730,819
   111     83,392 914,814,211
   112     52,510 914,866,721
   113     33,566 914,900,287
   114     19,432 914,919,719
   115     11,263 914,930,982
   116      5,786 914,936,768
   117      3,032 914,939,800
   118      1,132 914,940,932
   119        424 914,941,356
   120         64 914,941,420
   121         20 914,941,440

File Name: 8x8_1TM_d2a6da43b2c2a4b2c2.t
Distribution:
 depth        new       total
     0         56          56
     1          4          60
     2         10          70
     3         22          92
     4         45         137
     5         91         228
     6        171         399
     7        303         702
     8        518       1,220
     9        882       2,102
    10      1,448       3,550
    11      2,314       5,864
    12      3,696       9,560
    13      5,817      15,377
    14      9,030      24,407
    15     13,795      38,202
    16     20,525      58,727
    17     29,662      88,389
    18     41,994     130,383
    19     58,190     188,573
    20     79,134     267,707
    21    105,749     373,456
    22    139,441     512,897
    23    181,518     694,415
    24    234,195     928,610
    25    298,755   1,227,365
    26    377,700   1,605,065
    27    472,023   2,077,088
    28    586,263   2,663,351
    29    721,340   3,384,691
    30    882,161   4,266,852
    31  1,068,710   5,335,562
    32  1,287,320   6,622,882
    33  1,536,341   8,159,223
    34  1,824,193   9,983,416
    35  2,147,449  12,130,865
    36  2,516,184  14,647,049
    37  2,924,352  17,571,401
    38  3,381,138  20,952,539
    39  3,879,671  24,832,210
    40  4,430,954  29,263,164
    41  5,026,007  34,289,171
    42  5,676,317  39,965,488
    43  6,370,095  46,335,583
    44  7,119,080  53,454,663
    45  7,904,331  61,358,994
    46  8,739,326  70,098,320
    47  9,606,000  79,704,320
    48 10,515,585  90,219,905
    49 11,440,366 101,660,271
    50 12,395,103 114,055,374
    51 13,348,522 127,403,896
    52 14,312,113 141,716,009
    53 15,253,111 156,969,120
    54 16,181,356 173,150,476
    55 17,060,745 190,211,221
    56 17,904,562 208,115,783
    57 18,672,346 226,788,129
    58 19,378,233 246,166,362
    59 19,985,650 266,152,012
    60 20,512,574 286,664,586
    61 20,908,901 307,573,487
    62 21,195,883 328,769,370
    63 21,333,866 350,103,236
    64 21,350,047 371,453,283
    65 21,213,453 392,666,736
    66 20,954,540 413,621,276
    67 20,542,498 434,163,774
    68 20,004,657 454,168,431
    69 19,321,344 473,489,775
    70 18,530,166 492,019,941
    71 17,627,519 509,647,460
    72 16,642,866 526,290,326
    73 15,569,960 541,860,286
    74 14,453,151 556,313,437
    75 13,296,437 569,609,874
    76 12,129,820 581,739,694
    77 10,960,098 592,699,792
    78  9,816,289 602,516,081
    79  8,696,089 611,212,170
    80  7,633,869 618,846,039
    81  6,633,943 625,479,982
    82  5,706,674 631,186,656
    83  4,846,484 636,033,140
    84  4,069,253 640,102,393
    85  3,375,144 643,477,537
    86  2,762,008 646,239,545
    87  2,229,959 648,469,504
    88  1,773,437 650,242,941
    89  1,388,379 651,631,320
    90  1,065,021 652,696,341
    91    803,907 653,500,248
    92    592,088 654,092,336
    93    428,334 654,520,670
    94    300,316 654,820,986
    95    207,132 655,028,118
    96    137,180 655,165,298
    97     89,252 655,254,550
    98     55,152 655,309,702
    99     33,463 655,343,165
   100     18,806 655,361,971
   101     10,300 655,372,271
   102      5,140 655,377,411
   103      2,491 655,379,902
   104        988 655,380,890
   105        364 655,381,254
   106        128 655,381,382
   107         45 655,381,427
   108         12 655,381,439
   109          1 655,381,440

5x5_1TM_d2a3da9cb3c2b3c.t
 depth        new       total
     0         15          15
     1          3          18
     2          7          25
     3         14          39
     4         28          67
     5         56         123
     6        104         227
     7        198         425
     8        346         771
     9        603       1,374
    10      1,018       2,392
    11      1,759       4,151
    12      2,996       7,147
    13      5,187      12,334
    14      8,712      21,046
    15     14,558      35,604
    16     23,377      58,981
    17     37,865      96,846
    18     59,244     156,090
    19     93,017     249,107
    20    139,900     389,007
    21    211,349     600,356
    22    305,648     906,004
    23    444,001   1,350,005
    24    619,006   1,969,011
    25    871,750   2,840,761
    26  1,180,058   4,020,819
    27  1,613,340   5,634,159
    28  2,123,744   7,757,903
    29  2,824,265  10,582,168
    30  3,611,339  14,193,507
    31  4,653,624  18,847,131
    32  5,775,260  24,622,391
    33  7,213,875  31,836,266
    34  8,678,029  40,514,295
    35 10,494,585  51,008,880
    36 12,279,611  63,288,491
    37 14,412,659  77,701,150
    38 16,411,404  94,112,554
    39 18,705,800 112,818,354
    40 20,742,014 133,560,368
    41 22,921,650 156,482,018
    42 24,721,679 181,203,697
    43 26,454,762 207,658,459
    44 27,751,513 235,409,972
    45 28,774,236 264,184,208
    46 29,378,854 293,563,062
    47 29,468,449 323,031,511
    48 29,270,711 352,302,222
    49 28,352,672 380,654,894
    50 27,361,565 408,016,459
    51 25,567,930 433,584,389
    52 23,976,400 457,560,789
    53 21,584,088 479,144,877
    54 19,642,126 498,787,003
    55 16,994,417 515,781,420
    56 14,981,408 530,762,828
    57 12,423,339 543,186,167
    58 10,564,252 553,750,419
    59  8,349,950 562,100,369
    60  6,810,090 568,910,459
    61  5,094,477 574,004,936
    62  3,958,260 577,963,196
    63  2,785,279 580,748,475
    64  2,034,050 582,782,525
    65  1,324,941 584,107,466
    66    879,088 584,986,554
    67    514,407 585,500,961
    68    298,548 585,799,509
    69    151,848 585,951,357
    70     67,118 586,018,475
    71     25,096 586,043,571
    72      6,189 586,049,760
    73      1,306 586,051,066
    74        128 586,051,194
    75          6 586,051,200

File Name: 6x4_1TM_d2a3bda4ba5bc2b3c.t
Distribution:
 depth        new       total
     0         15          15
     1          6          21
     2          8          29
     3         12          41
     4         27          68
     5         67         135
     6        112         247
     7        185         432
     8        294         726
     9        511       1,237
    10        889       2,126
    11      1,540       3,666
    12      2,491       6,157
    13      4,129      10,286
    14      6,705      16,991
    15     10,967      27,958
    16     17,502      45,460
    17     27,938      73,398
    18     43,733     117,131
    19     67,997     185,128
    20    104,183     289,311
    21    158,335     447,646
    22    237,036     684,682
    23    347,600   1,032,282
    24    502,949   1,535,231
    25    710,999   2,246,230
    26    993,847   3,240,077
    27  1,349,847   4,589,924
    28  1,823,132   6,413,056
    29  2,383,565   8,796,621
    30  3,106,345  11,902,966
    31  3,914,183  15,817,149
    32  4,943,522  20,760,671
    33  6,028,169  26,788,840
    34  7,395,367  34,184,207
    35  8,750,075  42,934,282
    36 10,457,250  53,391,532
    37 12,046,256  65,437,788
    38 14,066,057  79,503,845
    39 15,826,238  95,330,083
    40 18,077,266 113,407,349
    41 19,867,918 133,275,267
    42 22,191,245 155,466,512
    43 23,801,841 179,268,353
    44 25,951,949 205,220,302
    45 27,084,508 232,304,810
    46 28,760,993 261,065,803
    47 29,087,395 290,153,198
    48 29,995,748 320,148,946
    49 29,310,536 349,459,482
    50 29,306,589 378,766,071
    51 27,568,590 406,334,661
    52 26,666,760 433,001,421
    53 24,110,573 457,111,994
    54 22,543,763 479,655,757
    55 19,578,782 499,234,539
    56 17,675,895 516,910,434
    57 14,720,424 531,630,858
    58 12,800,797 544,431,655
    59 10,194,924 554,626,579
    60  8,515,567 563,142,146
    61  6,440,578 569,582,724
    62  5,124,663 574,707,387
    63  3,633,615 578,341,002
    64  2,732,730 581,073,732
    65  1,803,709 582,877,441
    66  1,274,193 584,151,634
    67    780,084 584,931,718
    68    510,409 585,442,127
    69    285,036 585,727,163
    70    168,229 585,895,392
    71     82,936 585,978,328
    72     43,223 586,021,551
    73     18,565 586,040,116
    74      8,062 586,048,178
    75      2,405 586,050,583
    76        602 586,051,185
    77         15 586,051,200

File Name: 6x6_1TM_d2a4da11ba4cba4cb3c3.t
Distribution:
 depth        new       total
     0         26          26
     1          5          31
     2          9          40
     3         16          56
     4         34          90
     5         72         162
     6        121         283
     7        214         497
     8        359         856
     9        601       1,457
    10      1,001       2,458
    11      1,712       4,170
    12      2,745       6,915
    13      4,524      11,439
    14      7,241      18,680
    15     11,789      30,469
    16     18,247      48,716
    17     28,563      77,279
    18     42,358     119,637
    19     63,599     183,236
    20     90,318     273,554
    21    130,104     403,658
    22    177,150     580,808
    23    245,296     826,104
    24    322,384   1,148,488
    25    432,717   1,581,205
    26    551,516   2,132,721
    27    722,476   2,855,197
    28    899,207   3,754,404
    29  1,155,007   4,909,411
    30  1,408,324   6,317,735
    31  1,777,187   8,094,922
    32  2,122,263  10,217,185
    33  2,629,990  12,847,175
    34  3,075,498  15,922,673
    35  3,742,099  19,664,772
    36  4,288,833  23,953,605
    37  5,139,382  29,092,987
    38  5,775,067  34,868,054
    39  6,806,699  41,674,753
    40  7,501,854  49,176,607
    41  8,707,036  57,883,643
    42  9,409,453  67,293,096
    43 10,760,462  78,053,558
    44 11,425,671  89,479,229
    45 12,896,988 102,376,217
    46 13,463,606 115,839,823
    47 14,997,627 130,837,450
    48 15,377,577 146,215,027
    49 16,895,674 163,110,701
    50 17,011,454 180,122,155
    51 18,434,729 198,556,884
    52 18,230,555 216,787,439
    53 19,492,880 236,280,319
    54 18,936,115 255,216,434
    55 19,982,494 275,198,928
    56 19,061,825 294,260,753
    57 19,840,420 314,101,173
    58 18,578,424 332,679,597
    59 19,067,046 351,746,643
    60 17,511,748 369,258,391
    61 17,705,322 386,963,713
    62 15,952,871 402,916,584
    63 15,866,898 418,783,482
    64 13,992,143 432,775,625
    65 13,680,374 446,455,999
    66 11,802,395 458,258,394
    67 11,321,061 469,579,455
    68  9,539,415 479,118,870
    69  8,966,589 488,085,459
    70  7,369,090 495,454,549
    71  6,772,240 502,226,789
    72  5,423,592 507,650,381
    73  4,872,123 512,522,504
    74  3,790,835 516,313,339
    75  3,314,438 519,627,777
    76  2,498,305 522,126,082
    77  2,125,958 524,252,040
    78  1,548,683 525,800,723
    79  1,276,833 527,077,556
    80    891,538 527,969,094
    81    709,784 528,678,878
    82    473,530 529,152,408
    83    360,405 529,512,813
    84    225,885 529,738,698
    85    162,173 529,900,871
    86     92,682 529,993,553
    87     61,447 530,055,000
    88     30,924 530,085,924
    89     19,480 530,105,404
    90      8,640 530,114,044
    91      4,901 530,118,945
    92      1,917 530,120,862
    93      1,065 530,121,927
    94        274 530,122,201
    95        119 530,122,320

File Name: 6x6_1TM_d2a4da10ba4bca3b2ca2bc3.t
Distribution:
 depth        new       total
     0         26          26
     1          8          34
     2         12          46
     3         26          72
     4         54         126
     5        108         234
     6        178         412
     7        310         722
     8        466       1,188
     9        800       1,988
    10      1,224       3,212
    11      2,082       5,294
    12      3,088       8,382
    13      5,076      13,458
    14      7,402      20,860
    15     11,808      32,668
    16     16,412      49,080
    17     25,804      74,884
    18     35,471     110,355
    19     54,234     164,589
    20     73,060     237,649
    21    109,638     347,287
    22    144,196     491,483
    23    212,432     703,915
    24    274,428     978,343
    25    393,700   1,372,043
    26    497,377   1,869,420
    27    700,330   2,569,750
    28    866,445   3,436,195
    29  1,194,498   4,630,693
    30  1,451,301   6,081,994
    31  1,962,876   8,044,870
    32  2,339,059  10,383,929
    33  3,103,132  13,487,061
    34  3,627,033  17,114,094
    35  4,714,280  21,828,374
    36  5,396,235  27,224,609
    37  6,863,852  34,088,461
    38  7,682,102  41,770,563
    39  9,549,808  51,320,371
    40 10,452,968  61,773,339
    41 12,708,842  74,482,181
    42 13,598,589  88,080,770
    43 16,153,436 104,234,206
    44 16,873,203 121,107,409
    45 19,565,822 140,673,231
    46 19,938,177 160,611,408
    47 22,570,384 183,181,792
    48 22,427,018 205,608,810
    49 24,767,738 230,376,548
    50 23,962,258 254,338,806
    51 25,813,092 280,151,898
    52 24,262,113 304,414,011
    53 25,451,792 329,865,803
    54 23,200,074 353,065,877
    55 23,702,468 376,768,345
    56 20,916,785 397,685,130
    57 20,777,096 418,462,226
    58 17,697,215 436,159,441
    59 17,072,336 453,231,777
    60 14,003,463 467,235,240
    61 13,095,862 480,331,102
    62 10,323,628 490,654,730
    63  9,341,874 499,996,604
    64  7,055,729 507,052,333
    65  6,157,662 513,209,995
    66  4,446,708 517,656,703
    67  3,728,470 521,385,173
    68  2,562,137 523,947,310
    69  2,056,316 526,003,626
    70  1,343,422 527,347,048
    71  1,028,138 528,375,186
    72    634,536 529,009,722
    73    458,100 529,467,822
    74    265,016 529,732,838
    75    178,414 529,911,252
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    77     59,450 530,065,781
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    79     15,850 530,110,923
    80      6,673 530,117,596
    81      3,206 530,120,802
    82      1,080 530,121,882
    83        346 530,122,228
    84         76 530,122,304
    85         12 530,122,316
    86          4 530,122,320

File Name: 4x4_1TM_d2abda2ba3b5.t
Distribution:
 depth        new       total
     0          9           9
     1          6          15
     2         10          25
     3         16          41
     4         34          75
     5         80         155
     6        145         300
     7        247         547
     8        431         978
     9        798       1,776
    10      1,465       3,241
    11      2,621       5,862
    12      4,572      10,434
    13      8,047      18,481
    14     13,954      32,435
    15     23,868      56,303
    16     40,278      96,581
    17     67,543     164,124
    18    111,227     275,351
    19    180,560     455,911
    20    287,535     743,446
    21    452,045   1,195,491
    22    696,765   1,892,256
    23  1,054,877   2,947,133
    24  1,563,878   4,511,011
    25  2,277,199   6,788,210
    26  3,242,281  10,030,491
    27  4,528,109  14,558,600
    28  6,183,684  20,742,284
    29  8,272,922  29,015,206
    30 10,801,962  39,817,168
    31 13,806,194  53,623,362
    32 17,189,599  70,812,961
    33 20,944,686  91,757,647
    34 24,819,539 116,577,186
    35 28,694,784 145,271,970
    36 32,206,268 177,478,238
    37 35,202,050 212,680,288
    38 37,254,740 249,935,028
    39 38,276,999 288,212,027
    40 37,968,631 326,180,658
    41 36,417,934 362,598,592
    42 33,570,076 396,168,668
    43 29,752,613 425,921,281
    44 25,232,779 451,154,060
    45 20,462,700 471,616,760
    46 15,780,584 487,397,344
    47 11,561,793 498,959,137
    48  7,990,773 506,949,910
    49  5,211,819 512,161,729
    50  3,177,550 515,339,279
    51  1,817,094 517,156,373
    52    956,729 518,113,102
    53    470,200 518,583,302
    54    207,334 518,790,636
    55     85,174 518,875,810
    56     29,738 518,905,548
    57      9,683 518,915,231
    58      2,495 518,917,726
    59        582 518,918,308
    60         82 518,918,390
    61         10 518,918,400

File Name: 8x8_1TM_d2a6da43c4b4c4.t
Distribution:
 depth        new       total
     0         52          52
     1          4          56
     2          6          62
     3         10          72
     4         22          94
     5         51         145
     6         92         237
     7        157         394
     8        259         653
     9        435       1,088
    10        725       1,813
    11      1,175       2,988
    12      1,845       4,833
    13      2,877       7,710
    14      4,386      12,096
    15      6,442      18,538
    16      9,311      27,849
    17     13,295      41,144
    18     18,590      59,734
    19     25,379      85,113
    20     33,820     118,933
    21     44,606     163,539
    22     57,819     221,358
    23     73,720     295,078
    24     92,300     387,378
    25    114,357     501,735
    26    140,221     641,956
    27    170,851     812,807
    28    205,673   1,018,480
    29    246,121   1,264,601
    30    292,933   1,557,534
    31    347,437   1,904,971
    32    409,632   2,314,603
    33    480,997   2,795,600
    34    559,816   3,355,416
    35    650,441   4,005,857
    36    750,958   4,756,815
    37    865,499   5,622,314
    38    993,568   6,615,882
    39  1,140,009   7,755,891
    40  1,299,915   9,055,806
    41  1,479,919  10,535,725
    42  1,675,230  12,210,955
    43  1,895,175  14,106,130
    44  2,132,569  16,238,699
    45  2,396,316  18,635,015
    46  2,677,496  21,312,511
    47  2,988,272  24,300,783
    48  3,315,453  27,616,236
    49  3,673,584  31,289,820
    50  4,045,396  35,335,216
    51  4,446,732  39,781,948
    52  4,858,627  44,640,575
    53  5,298,759  49,939,334
    54  5,743,897  55,683,231
    55  6,213,621  61,896,852
    56  6,679,370  68,576,222
    57  7,163,693  75,739,915
    58  7,640,971  83,380,886
    59  8,132,054  91,512,940
    60  8,604,792 100,117,732
    61  9,084,322 109,202,054
    62  9,539,183 118,741,237
    63  9,993,797 128,735,034
    64 10,414,339 139,149,373
    65 10,828,206 149,977,579
    66 11,194,583 161,172,162
    67 11,538,892 172,711,054
    68 11,832,976 184,544,030
    69 12,102,750 196,646,780
    70 12,311,931 208,958,711
    71 12,486,724 221,445,435
    72 12,598,836 234,044,271
    73 12,671,630 246,715,901
    74 12,674,700 259,390,601
    75 12,632,743 272,023,344
    76 12,523,172 284,546,516
    77 12,366,462 296,912,978
    78 12,142,740 309,055,718
    79 11,871,209 320,926,927
    80 11,537,456 332,464,383
    81 11,152,832 343,617,215
    82 10,711,530 354,328,745
    83 10,232,500 364,561,245
    84  9,719,245 374,280,490
    85  9,173,071 383,453,561
    86  8,603,285 392,056,846
    87  8,011,143 400,067,989
    88  7,406,590 407,474,579
    89  6,796,011 414,270,590
    90  6,191,808 420,462,398
    91  5,589,786 426,052,184
    92  5,008,235 431,060,419
    93  4,445,177 435,505,596
    94  3,914,369 439,419,965
    95  3,408,763 442,828,728
    96  2,939,825 445,768,553
    97  2,506,918 448,275,471
    98  2,111,226 450,386,697
    99  1,754,590 452,141,287
   100  1,441,285 453,582,572
   101  1,165,052 454,747,624
   102    926,456 455,674,080
   103    727,004 456,401,084
   104    559,201 456,960,285
   105    422,063 457,382,348
   106    310,534 457,692,882
   107    226,136 457,919,018
   108    158,502 458,077,520
   109    109,766 458,187,286
   110     72,694 458,259,980
   111     47,915 458,307,895
   112     29,839 458,337,734
   113     18,411 458,356,145
   114     10,246 458,366,391
   115      5,897 458,372,288
   116      3,016 458,375,304
   117      1,547 458,376,851
   118        690 458,377,541
   119        276 458,377,817
   120         88 458,377,905
   121         15 458,377,920

File Name: 8x7_1TM_d2a6da39b4c4.t
Distribution:
 depth       new       total
     0        48          48
     1         4          52
     2         6          58
     3        10          68
     4        23          91
     5        55         146
     6       100         246
     7       169         415
     8       280         695
     9       469       1,164
    10       775       1,939
    11     1,269       3,208
    12     2,032       5,240
    13     3,203       8,443
    14     4,889      13,332
    15     7,225      20,557
    16    10,564      31,121
    17    15,236      46,357
    18    21,545      67,902
    19    29,738      97,640
    20    40,234     137,874
    21    53,769     191,643
    22    70,607     262,250
    23    91,379     353,629
    24   116,283     469,912
    25   146,292     616,204
    26   181,785     797,989
    27   223,745   1,021,734
    28   271,983   1,293,717
    29   328,452   1,622,169
    30   394,386   2,016,555
    31   470,845   2,487,400
    32   557,791   3,045,191
    33   658,074   3,703,265
    34   770,957   4,474,222
    35   899,478   5,373,700
    36 1,042,349   6,416,049
    37 1,203,812   7,619,861
    38 1,382,175   9,002,036
    39 1,583,592  10,585,628
    40 1,804,212  12,389,840
    41 2,049,466  14,439,306
    42 2,312,327  16,751,633
    43 2,601,410  19,353,043
    44 2,906,206  22,259,249
    45 3,237,535  25,496,784
    46 3,582,810  29,079,594
    47 3,950,591  33,030,185
    48 4,325,127  37,355,312
    49 4,720,080  42,075,392
    50 5,111,263  47,186,655
    51 5,518,048  52,704,703
    52 5,917,212  58,621,915
    53 6,326,555  64,948,470
    54 6,718,155  71,666,625
    55 7,110,183  78,776,808
    56 7,472,773  86,249,581
    57 7,829,308  94,078,889
    58 8,152,225 102,231,114
    59 8,462,302 110,693,416
    60 8,726,449 119,419,865
    61 8,967,157 128,387,022
    62 9,161,397 137,548,419
    63 9,321,996 146,870,415
    64 9,430,796 156,301,211
    65 9,499,894 165,801,105
    66 9,508,054 175,309,159
    67 9,472,297 184,781,456
    68 9,383,559 194,165,015
    69 9,242,741 203,407,756
    70 9,044,456 212,452,212
    71 8,793,932 221,246,144
    72 8,497,481 229,743,625
    73 8,155,491 237,899,116
    74 7,777,480 245,676,596
    75 7,358,553 253,035,149
    76 6,914,600 259,949,749
    77 6,440,278 266,390,027
    78 5,956,490 272,346,517
    79 5,455,666 277,802,183
    80 4,958,237 282,760,420
    81 4,460,514 287,220,934
    82 3,980,918 291,201,852
    83 3,516,214 294,718,066
    84 3,077,623 297,795,689
    85 2,657,100 300,452,789
    86 2,273,076 302,725,865
    87 1,916,998 304,642,863
    88 1,597,416 306,240,279
    89 1,308,503 307,548,782
    90 1,059,254 308,608,036
    91   842,579 309,450,615
    92   659,182 310,109,797
    93   505,840 310,615,637
    94   380,428 310,996,065
    95   279,953 311,276,018
    96   201,291 311,477,309
    97   141,010 311,618,319
    98    96,134 311,714,453
    99    63,832 311,778,285
   100    40,779 311,819,064
   101    25,175 311,844,239
   102    14,797 311,859,036
   103     8,231 311,867,267
   104     4,325 311,871,592
   105     2,132 311,873,724
   106       960 311,874,684
   107       383 311,875,067
   108       113 311,875,180
   109        20 311,875,200

File Name: 4x3_1TM_d2b2db7.t
Distribution:
 depth        new       total
     0          1           1
     1          2           3
     2          4           7
     3          9          16
     4         20          36
     5         37          73
     6         63         136
     7        122         258
     8        232         490
     9        431         921
    10        781       1,702
    11      1,392       3,094
    12      2,494       5,588
    13      4,442      10,030
    14      7,854      17,884
    15     13,899      31,783
    16     24,215      55,998
    17     41,802      97,800
    18     71,167     168,967
    19    119,888     288,855
    20    198,363     487,218
    21    323,206     810,424
    22    515,778   1,326,202
    23    811,000   2,137,202
    24  1,248,011   3,385,213
    25  1,885,279   5,270,492
    26  2,782,396   8,052,888
    27  4,009,722  12,062,610
    28  5,621,354  17,683,964
    29  7,647,872  25,331,836
    30 10,065,800  35,397,636
    31 12,760,413  48,158,049
    32 15,570,786  63,728,835
    33 18,171,606  81,900,441
    34 20,299,876 102,200,317
    35 21,587,248 123,787,565
    36 21,841,159 145,628,724
    37 20,906,905 166,535,629
    38 18,899,357 185,434,986
    39 16,058,335 201,493,321
    40 12,772,603 214,265,924
    41  9,515,217 223,781,141
    42  6,583,181 230,364,322
    43  4,242,753 234,607,075
    44  2,503,873 237,110,948
    45  1,350,268 238,461,216
    46    643,245 239,104,461
    47    270,303 239,374,764
    48     92,311 239,467,075
    49     27,116 239,494,191
    50      5,390 239,499,581
    51      1,115 239,500,696
    52         86 239,500,782
    53         18 239,500,800

File Name: 8x6_1TM_d2a6da29b2a6b2.t
Distribution:
 depth       new       total
     0        44          44
     1         4          48
     2        10          58
     3        22          80
     4        42         122
     5        81         203
     6       153         356
     7       273         629
     8       457       1,086
     9       779       1,865
    10     1,273       3,138
    11     2,010       5,148
    12     3,160       8,308
    13     4,954      13,262
    14     7,600      20,862
    15    11,507      32,369
    16    16,861      49,230
    17    24,033      73,263
    18    33,337     106,600
    19    45,305     151,905
    20    60,059     211,964
    21    78,406     290,370
    22   100,761     391,131
    23   128,100     519,231
    24   161,132     680,363
    25   200,497     880,860
    26   246,704   1,127,564
    27   300,977   1,428,541
    28   364,491   1,793,032
    29   437,889   2,230,921
    30   522,668   2,753,589
    31   618,329   3,371,918
    32   727,326   4,099,244
    33   848,301   4,947,545
    34   984,349   5,931,894
    35 1,132,790   7,064,684
    36 1,297,730   8,362,414
    37 1,474,787   9,837,201
    38 1,666,698  11,503,899
    39 1,869,760  13,373,659
    40 2,088,694  15,462,353
    41 2,318,957  17,781,310
    42 2,563,737  20,345,047
    43 2,817,262  23,162,309
    44 3,083,728  26,246,037
    45 3,353,639  29,599,676
    46 3,634,030  33,233,706
    47 3,918,334  37,152,040
    48 4,208,185  41,360,225
    49 4,492,631  45,852,856
    50 4,778,363  50,631,219
    51 5,054,054  55,685,273
    52 5,324,352  61,009,625
    53 5,577,026  66,586,651
    54 5,815,610  72,402,261
    55 6,029,280  78,431,541
    56 6,222,615  84,654,156
    57 6,383,889  91,038,045
    58 6,514,617  97,552,662
    59 6,609,473 104,162,135
    60 6,670,329 110,832,464
    61 6,681,020 117,513,484
    62 6,651,906 124,165,390
    63 6,571,928 130,737,318
    64 6,450,879 137,188,197
    65 6,281,997 143,470,194
    66 6,076,576 149,546,770
    67 5,827,978 155,374,748
    68 5,546,634 160,921,382
    69 5,230,605 166,151,987
    70 4,892,394 171,044,381
    71 4,533,033 175,577,414
    72 4,160,978 179,738,392
    73 3,780,664 183,519,056
    74 3,404,593 186,923,649
    75 3,033,704 189,957,353
    76 2,676,688 192,634,041
    77 2,334,371 194,968,412
    78 2,013,608 196,982,020
    79 1,714,409 198,696,429
    80 1,444,011 200,140,440
    81 1,197,857 201,338,297
    82   980,658 202,318,955
    83   788,733 203,107,688
    84   624,579 203,732,267
    85   485,901 204,218,168
    86   371,289 204,589,457
    87   277,304 204,866,761
    88   201,888 205,068,649
    89   143,685 205,212,334
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    91    66,251 205,377,246
    92    42,079 205,419,325
    93    26,254 205,445,579
    94    14,930 205,460,509
    95     8,509 205,469,018
    96     4,150 205,473,168
    97     2,061 205,475,229
    98       809 205,476,038
    99       310 205,476,348
   100        98 205,476,446
   101        30 205,476,476
   102         4 205,476,480

File Name: 6x5_1TM_d2a3bda4ba5bca3bc2a3bc.t
Distribution:
 depth       new       total
     0        21          21
     1         6          27
     2         9          36
     3        16          52
     4        34          86
     5        70         156
     6       115         271
     7       195         466
     8       316         782
     9       516       1,298
    10       824       2,122
    11     1,340       3,462
    12     2,103       5,565
    13     3,336       8,901
    14     5,126      14,027
    15     7,972      21,999
    16    11,951      33,950
    17    17,950      51,900
    18    26,289      78,189
    19    38,677     116,866
    20    55,305     172,171
    21    79,100     251,271
    22   110,195     361,466
    23   152,943     514,409
    24   206,531     720,940
    25   278,422     999,362
    26   367,548   1,366,910
    27   482,545   1,849,455
    28   620,277   2,469,732
    29   793,312   3,263,044
    30   994,862   4,257,906
    31 1,236,805   5,494,711
    32 1,508,641   7,003,352
    33 1,824,206   8,827,558
    34 2,173,309  11,000,867
    35 2,568,009  13,568,876
    36 2,987,858  16,556,734
    37 3,448,813  20,005,547
    38 3,924,206  23,929,753
    39 4,433,515  28,363,268
    40 4,935,370  33,298,638
    41 5,456,032  38,754,670
    42 5,939,702  44,694,372
    43 6,426,011  51,120,383
    44 6,843,686  57,964,069
    45 7,235,176  65,199,245
    46 7,512,077  72,711,322
    47 7,745,652  80,456,974
    48 7,836,345  88,293,319
    49 7,861,811  96,155,130
    50 7,734,761 103,889,891
    51 7,541,735 111,431,626
    52 7,204,658 118,636,284
    53 6,809,680 125,445,964
    54 6,304,000 131,749,964
    55 5,760,254 137,510,218
    56 5,156,035 142,666,253
    57 4,542,395 147,208,648
    58 3,919,478 151,128,126
    59 3,320,466 154,448,592
    60 2,749,641 157,198,233
    61 2,224,624 159,422,857
    62 1,761,499 161,184,356
    63 1,355,132 162,539,488
    64 1,016,678 163,556,166
    65   740,521 164,296,687
    66   523,394 164,820,081
    67   358,678 165,178,759
    68   236,617 165,415,376
    69   150,122 165,565,498
    70    90,913 165,656,411
    71    53,082 165,709,493
    72    29,051 165,738,544
    73    14,980 165,753,524
    74     7,129 165,760,653
    75     3,085 165,763,738
    76     1,206 165,764,944
    77       450 165,765,394
    78       160 165,765,554
    79        41 165,765,595
    80         5 165,765,600

File Name: 6x6_1TM_d2a4da10ca4c2b3c3b2c4.t
Distribution:
 depth       new       total
     0        21          21
     1         3          24
     2         6          30
     3        11          41
     4        19          60
     5        39          99
     6        70         169
     7       124         293
     8       191         484
     9       319         803
    10       510       1,313
    11       833       2,146
    12     1,268       3,414
    13     2,012       5,426
    14     3,086       8,512
    15     4,761      13,273
    16     6,906      20,179
    17    10,277      30,456
    18    14,631      45,087
    19    21,189      66,276
    20    29,383      95,659
    21    41,677     137,336
    22    56,462     193,798
    23    77,737     271,535
    24   102,303     373,838
    25   136,758     510,596
    26   174,761     685,357
    27   227,483     912,840
    28   284,350   1,197,190
    29   362,459   1,559,649
    30   445,071   2,004,720
    31   553,704   2,558,424
    32   667,214   3,225,638
    33   816,204   4,041,842
    34   970,114   5,011,956
    35 1,165,145   6,177,101
    36 1,362,609   7,539,710
    37 1,604,443   9,144,153
    38 1,843,801  10,987,954
    39 2,125,987  13,113,941
    40 2,399,072  15,513,013
    41 2,709,916  18,222,929
    42 3,002,933  21,225,862
    43 3,326,499  24,552,361
    44 3,627,246  28,179,607
    45 3,944,916  32,124,523
    46 4,239,254  36,363,777
    47 4,534,070  40,897,847
    48 4,804,231  45,702,078
    49 5,053,469  50,755,547
    50 5,282,897  56,038,444
    51 5,466,221  61,504,665
    52 5,639,883  67,144,548
    53 5,740,223  72,884,771
    54 5,846,734  78,731,505
    55 5,864,017  84,595,522
    56 5,903,745  90,499,267
    57 5,830,361  96,329,628
    58 5,800,635 102,130,263
    59 5,637,721 107,767,984
    60 5,532,485 113,300,469
    61 5,285,976 118,586,445
    62 5,112,814 123,699,259
    63 4,794,789 128,494,048
    64 4,571,499 133,065,547
    65 4,196,118 137,261,665
    66 3,935,042 141,196,707
    67 3,533,179 144,729,886
    68 3,258,358 147,988,244
    69 2,854,815 150,843,059
    70 2,581,310 153,424,369
    71 2,201,601 155,625,970
    72 1,949,703 157,575,673
    73 1,617,737 159,193,410
    74 1,401,098 160,594,508
    75 1,126,946 161,721,454
    76   951,167 162,672,621
    77   741,247 163,413,868
    78   608,810 164,022,678
    79   460,931 164,483,609
    80   368,264 164,851,873
    81   268,772 165,120,645
    82   205,819 165,326,464
    83   143,637 165,470,101
    84   104,927 165,575,028
    85    69,717 165,644,745
    86    48,557 165,693,302
    87    29,825 165,723,127
    88    19,029 165,742,156
    89    10,834 165,752,990
    90     6,110 165,759,100
    91     3,187 165,762,287
    92     1,733 165,764,020
    93       892 165,764,912
    94       414 165,765,326
    95       187 165,765,513
    96        70 165,765,583
    97        16 165,765,599
    98         1 165,765,600

File Name: 6x5_1TM_d2a4da11cba3c2b4c.t
Distribution:
 depth       new       total
     0        21          21
     1         5          26
     2         9          35
     3        16          51
     4        33          84
     5        72         156
     6       136         292
     7       235         527
     8       372         899
     9       612       1,511
    10     1,058       2,569
    11     1,827       4,396
    12     3,025       7,421
    13     4,972      12,393
    14     7,945      20,338
    15    12,446      32,784
    16    19,116      51,900
    17    29,075      80,975
    18    43,362     124,337
    19    63,483     187,820
    20    90,611     278,431
    21   127,456     405,887
    22   175,978     581,865
    23   238,980     820,845
    24   318,290   1,139,135
    25   418,574   1,557,709
    26   540,555   2,098,264
    27   692,509   2,790,773
    28   874,336   3,665,109
    29 1,094,968   4,760,077
    30 1,351,780   6,111,857
    31 1,657,430   7,769,287
    32 2,004,781   9,774,068
    33 2,404,024  12,178,092
    34 2,836,842  15,014,934
    35 3,316,036  18,330,970
    36 3,812,818  22,143,788
    37 4,336,128  26,479,916
    38 4,855,333  31,335,249
    39 5,379,532  36,714,781
    40 5,873,746  42,588,527
    41 6,346,640  48,935,167
    42 6,765,944  55,701,111
    43 7,137,283  62,838,394
    44 7,420,474  70,258,868
    45 7,625,887  77,884,755
    46 7,726,614  85,611,369
    47 7,737,272  93,348,641
    48 7,630,602 100,979,243
    49 7,433,140 108,412,383
    50 7,130,288 115,542,671
    51 6,751,914 122,294,585
    52 6,293,657 128,588,242
    53 5,796,704 134,384,946
    54 5,246,150 139,631,096
    55 4,686,523 144,317,619
    56 4,108,458 148,426,077
    57 3,554,712 151,980,789
    58 3,010,606 154,991,395
    59 2,514,333 157,505,728
    60 2,050,683 159,556,411
    61 1,646,113 161,202,524
    62 1,284,119 162,486,643
    63   984,575 163,471,218
    64   733,350 164,204,568
    65   532,664 164,737,232
    66   374,848 165,112,080
    67   255,690 165,367,770
    68   165,803 165,533,573
    69   103,577 165,637,150
    70    61,283 165,698,433
    71    34,438 165,732,871
    72    18,305 165,751,176
    73     8,952 165,760,128
    74     3,686 165,763,814
    75     1,342 165,765,156
    76       377 165,765,533
    77        63 165,765,596
    78         4 165,765,600

File Name: 6x3_1TM_d2a2b2da3b2a4b2.t
Distribution:
 depth       new       total
     0        12          12
     1         3          15
     2         7          22
     3        14          36
     4        26          62
     5        48         110
     6        94         204
     7       174         378
     8       296         674
     9       511       1,185
    10       886       2,071
    11     1,479       3,550
    12     2,510       6,060
    13     4,204      10,264
    14     7,098      17,362
    15    11,487      28,849
    16    18,504      47,353
    17    29,006      76,359
    18    45,128     121,487
    19    67,658     189,145
    20   100,555     289,700
    21   144,816     434,516
    22   204,472     638,988
    23   279,214     918,202
    24   374,654   1,292,856
    25   492,081   1,784,937
    26   634,012   2,418,949
    27   804,587   3,223,536
    28 1,005,889   4,229,425
    29 1,243,476   5,472,901
    30 1,516,760   6,989,661
    31 1,831,764   8,821,425
    32 2,187,992  11,009,417
    33 2,587,357  13,596,774
    34 3,032,384  16,629,158
    35 3,516,203  20,145,361
    36 4,048,998  24,194,359
    37 4,613,419  28,807,778
    38 5,210,341  34,018,119
    39 5,798,096  39,816,215
    40 6,374,243  46,190,458
    41 6,873,902  53,064,360
    42 7,310,658  60,375,018
    43 7,618,864  67,993,882
    44 7,842,110  75,835,992
    45 7,910,363  83,746,355
    46 7,898,851  91,645,206
    47 7,731,687  99,376,893
    48 7,502,342 106,879,235
    49 7,123,713 114,002,948
    50 6,712,691 120,715,639
    51 6,171,447 126,887,086
    52 5,638,623 132,525,709
    53 5,012,408 137,538,117
    54 4,428,992 141,967,109
    55 3,796,002 145,763,111
    56 3,234,992 148,998,103
    57 2,673,863 151,671,966
    58 2,191,176 153,863,142
    59 1,741,182 155,604,324
    60 1,364,468 156,968,792
    61 1,036,305 158,005,097
    62   766,580 158,771,677
    63   554,930 159,326,607
    64   385,615 159,712,222
    65   264,219 159,976,441
    66   169,590 160,146,031
    67   109,258 160,255,289
    68    62,783 160,318,072
    69    38,087 160,356,159
    70    19,145 160,375,304
    71    10,673 160,385,977
    72     4,256 160,390,233
    73     2,045 160,392,278
    74       432 160,392,710
    75       210 160,392,920
    76        28 160,392,948
    77        12 160,392,960

File Name: 8x6_1TM_d2a5bda6ba7ba7ba6c2a6c2.t
Distribution:
 depth       new       total
     0        40          40
     1         4          44
     2         6          50
     3        10          60
     4        22          82
     5        51         133
     6        92         225
     7       156         381
     8       253         634
     9       419       1,053
    10       698       1,751
    11     1,136       2,887
    12     1,783       4,670
    13     2,765       7,435
    14     4,191      11,626
    15     6,122      17,748
    16     8,792      26,540
    17    12,472      39,012
    18    17,341      56,353
    19    23,524      79,877
    20    31,093     110,970
    21    40,676     151,646
    22    52,328     203,974
    23    66,254     270,228
    24    82,186     352,414
    25   100,801     453,215
    26   122,548     575,763
    27   148,212     723,975
    28   177,039     901,014
    29   210,313   1,111,327
    30   248,502   1,359,829
    31   292,691   1,652,520
    32   342,739   1,995,259
    33   399,671   2,394,930
    34   461,011   2,855,941
    35   530,672   3,386,613
    36   606,324   3,992,937
    37   691,173   4,684,110
    38   783,807   5,467,917
    39   887,937   6,355,854
    40   997,298   7,353,152
    41 1,117,426   8,470,578
    42 1,242,669   9,713,247
    43 1,381,112  11,094,359
    44 1,523,862  12,618,221
    45 1,678,562  14,296,783
    46 1,835,406  16,132,189
    47 2,005,552  18,137,741
    48 2,174,734  20,312,475
    49 2,354,034  22,666,509
    50 2,527,625  25,194,134
    51 2,710,414  27,904,548
    52 2,884,460  30,789,008
    53 3,064,583  33,853,591
    54 3,230,278  37,083,869
    55 3,396,870  40,480,739
    56 3,543,826  44,024,565
    57 3,687,098  47,711,663
    58 3,804,864  51,516,527
    59 3,916,104  55,432,631
    60 3,997,001  59,429,632
    61 4,066,557  63,496,189
    62 4,104,686  67,600,875
    63 4,128,857  71,729,732
    64 4,117,510  75,847,242
    65 4,091,579  79,938,821
    66 4,028,737  83,967,558
    67 3,949,491  87,917,049
    68 3,837,805  91,754,854
    69 3,710,965  95,465,819
    70 3,552,624  99,018,443
    71 3,382,731 102,401,174
    72 3,191,213 105,592,387
    73 2,995,156 108,587,543
    74 2,780,397 111,367,940
    75 2,562,234 113,930,174
    76 2,336,994 116,267,168
    77 2,115,211 118,382,379
    78 1,893,596 120,275,975
    79 1,680,113 121,956,088
    80 1,474,549 123,430,637
    81 1,280,070 124,710,707
    82 1,097,822 125,808,529
    83   930,572 126,739,101
    84   779,175 127,518,276
    85   643,019 128,161,295
    86   522,721 128,684,016
    87   418,160 129,102,176
    88   329,467 129,431,643
    89   254,227 129,685,870
    90   192,277 129,878,147
    91   142,843 130,020,990
    92   102,761 130,123,751
    93    71,967 130,195,718
    94    48,543 130,244,261
    95    31,766 130,276,027
    96    19,705 130,295,732
    97    11,928 130,307,660
    98     6,571 130,314,231
    99     3,627 130,317,858
   100     1,781 130,319,639
   101       814 130,320,453
   102       324 130,320,777
   103       134 130,320,911
   104        40 130,320,951
   105         9 130,320,960

File Name: 7x6_1TM_d2a4bda5ba6ba6ba6ca6c.t
Distribution:
 depth       new      total
     0        36         36
     1         4         40
     2         6         46
     3        10         56
     4        23         79
     5        55        134
     6        99        233
     7       164        397
     8       267        664
     9       445      1,109
    10       735      1,844
    11     1,203      3,047
    12     1,926      4,973
    13     3,025      7,998
    14     4,577     12,575
    15     6,700     19,275
    16     9,737     29,012
    17    13,964     42,976
    18    19,619     62,595
    19    26,868     89,463
    20    36,033    125,496
    21    47,756    173,252
    22    62,186    235,438
    23    79,796    315,234
    24   100,655    415,889
    25   125,370    541,259
    26   154,088    695,347
    27   187,699    883,046
    28   225,968  1,109,014
    29   270,331  1,379,345
    30   321,155  1,700,500
    31   378,747  2,079,247
    32   443,030  2,522,277
    33   515,866  3,038,143
    34   595,182  3,633,325
    35   682,583  4,315,908
    36   775,450  5,091,358
    37   877,534  5,968,892
    38   986,069  6,954,961
    39 1,104,191  8,059,152
    40 1,226,828  9,285,980
    41 1,357,963 10,643,943
    42 1,490,484 12,134,427
    43 1,630,226 13,764,653
    44 1,767,021 15,531,674
    45 1,908,063 17,439,737
    46 2,044,679 19,484,416
    47 2,182,326 21,666,742
    48 2,308,511 23,975,253
    49 2,430,153 26,405,406
    50 2,534,509 28,939,915
    51 2,631,045 31,570,960
    52 2,707,504 34,278,464
    53 2,772,815 37,051,279
    54 2,813,023 39,864,302
    55 2,835,433 42,699,735
    56 2,831,191 45,530,926
    57 2,809,029 48,339,955
    58 2,759,980 51,099,935
    59 2,691,573 53,791,508
    60 2,598,550 56,390,058
    61 2,488,590 58,878,648
    62 2,363,251 61,241,899
    63 2,221,042 63,462,941
    64 2,066,054 65,528,995
    65 1,902,985 67,431,980
    66 1,733,652 69,165,632
    67 1,561,689 70,727,321
    68 1,392,097 72,119,418
    69 1,225,173 73,344,591
    70 1,064,323 74,408,914
    71   912,693 75,321,607
    72   772,205 76,093,812
    73   644,300 76,738,112
    74   528,442 77,266,554
    75   426,906 77,693,460
    76   338,334 78,031,794
    77   263,425 78,295,219
    78   199,860 78,495,079
    79   149,280 78,644,359
    80   107,892 78,752,251
    81    75,984 78,828,235
    82    51,427 78,879,662
    83    33,966 78,913,628
    84    20,990 78,934,618
    85    12,570 78,947,188
    86     6,966 78,954,154
    87     3,709 78,957,863
    88     1,793 78,959,656
    89       837 78,960,493
    90       314 78,960,807
    91       114 78,960,921
    92        34 78,960,955
    93         5 78,960,960

File Name: 6x4_1TM_d2a2b2da3b2a4bca4c2.t
Distribution:
 depth       new      total
     0        16         16
     1         3         19
     2         6         25
     3        11         36
     4        19         55
     5        39         94
     6        69        163
     7       119        282
     8       182        464
     9       301        765
    10       484      1,249
    11       785      2,034
    12     1,196      3,230
    13     1,880      5,110
    14     2,894      8,004
    15     4,419     12,423
    16     6,395     18,818
    17     9,396     28,214
    18    13,388     41,602
    19    19,186     60,788
    20    26,603     87,391
    21    37,274    124,665
    22    50,526    175,191
    23    68,641    243,832
    24    89,951    333,783
    25   118,228    452,011
    26   150,357    602,368
    27   192,358    794,726
    28   238,977  1,033,703
    29   298,846  1,332,549
    30   364,161  1,696,710
    31   443,303  2,140,013
    32   528,160  2,668,173
    33   630,367  3,298,540
    34   738,215  4,036,755
    35   861,413  4,898,168
    36   988,024  5,886,192
    37 1,125,016  7,011,208
    38 1,260,348  8,271,556
    39 1,397,713  9,669,269
    40 1,526,550 11,195,819
    41 1,644,640 12,840,459
    42 1,749,159 14,589,618
    43 1,831,317 16,420,935
    44 1,896,043 18,316,978
    45 1,927,172 20,244,150
    46 1,943,026 22,187,176
    47 1,914,247 24,101,423
    48 1,874,986 25,976,409
    49 1,784,521 27,760,930
    50 1,693,331 29,454,261
    51 1,552,824 31,007,085
    52 1,424,902 32,431,987
    53 1,253,469 33,685,456
    54 1,109,235 34,794,691
    55   934,907 35,729,598
    56   799,316 36,528,914
    57   643,454 37,172,368
    58   527,669 37,700,037
    59   400,992 38,101,029
    60   312,115 38,413,144
    61   221,455 38,634,599
    62   162,209 38,796,808
    63   106,576 38,903,384
    64    72,819 38,976,203
    65    42,902 39,019,105
    66    26,489 39,045,594
    67    13,456 39,059,050
    68     6,863 39,065,913
    69     2,725 39,068,638
    70     1,054 39,069,692
    71       353 39,070,045
    72        30 39,070,075
    73         5 39,070,080

File Name: 5x3_1TM_d2ab2da2b2a3b2.t
Distribution:
 depth       new      total
     0         9          9
     1         3         12
     2         7         19
     3        14         33
     4        26         59
     5        48        107
     6        90        197
     7       162        359
     8       282        641
     9       481      1,122
    10       832      1,954
    11     1,375      3,329
    12     2,374      5,703
    13     3,959      9,662
    14     6,662     16,324
    15    10,614     26,938
    16    17,211     44,149
    17    26,715     70,864
    18    41,596    112,460
    19    61,591    174,051
    20    91,882    265,933
    21   129,936    395,869
    22   183,047    578,916
    23   244,837    823,753
    24   328,559  1,152,312
    25   421,029  1,573,341
    26   539,862  2,113,203
    27   666,840  2,780,043
    28   824,991  3,605,034
    29   986,034  4,591,068
    30 1,173,702  5,764,770
    31 1,353,532  7,118,302
    32 1,542,794  8,661,096
    33 1,702,701 10,363,797
    34 1,843,881 12,207,678
    35 1,940,358 14,148,036
    36 1,994,960 16,142,996
    37 2,012,618 18,155,614
    38 1,971,353 20,126,967
    39 1,909,364 22,036,331
    40 1,776,843 23,813,174
    41 1,643,711 25,456,885
    42 1,445,572 26,902,457
    43 1,272,160 28,174,617
    44 1,050,516 29,225,133
    45   872,736 30,097,869
    46   672,695 30,770,564
    47   525,853 31,296,417
    48   378,243 31,674,660
    49   277,746 31,952,406
    50   185,145 32,137,551
    51   126,948 32,264,499
    52    75,793 32,340,292
    53    46,705 32,386,997
    54    24,027 32,411,024
    55    12,985 32,424,009
    56     5,312 32,429,321
    57     2,303 32,431,624
    58       541 32,432,165
    59       198 32,432,363
    60        24 32,432,387
    61        13 32,432,400

ben1996123 · Sep 30, 2012

stannic said:
I'm surprised that the tables were compiled so fast. What project did you ran?

Sorry, maybe I was not clear. I wanted to ask someone to run one of three projects included in 3.02b zip archive and see if the solver can actually handle large amount of memory. These projects are:
huge6x4_x64_3GB (6x4 puzzle three-phase solution; the total amount of memory required to run is 2,144,257,920 bytes);
huge6x6_x64_5GB (6x6 puzzle 3-chained 6-phase solution; memory required is 4,722,656,400 bytes);
huge8x8_x64_6GB (8x8 puzzle 13-phase solution; the total space is 5,411,802,480 bytes).

If anyone wants to test it, just open the largest project you can run with your RAM (Wizard > Project Actions > Open), activate (Project Actions > Activate) and let it compile all tables. This should take a few hours, I think, and does not require any additional user actions during this time.
After the project activation is complete, you can solve some random instances to test tables. Also, you can select any generated table on Regions tab and click Find Distribution button to output the number of puzzle positions as the function of depth. If you do it, please copy these distributions and post or pm it to me as shown under spoiler.

File Name: 3x3_1TM_d2bdb5.t
Distribution:
depth new total
0 1 1
1 2 3
2 4 7
3 8 15
4 16 31
5 20 51
6 39 90
7 62 152
8 116 268
9 152 420
10 286 706
11 396 1,102
12 748 1,850
13 1,024 2,874
14 1,893 4,767
15 2,512 7,279
16 4,485 11,764
17 5,638 17,402
18 9,529 26,931
19 10,878 37,809
20 16,993 54,802
21 17,110 71,912
22 23,952 95,864
23 20,224 116,088
24 24,047 140,135
25 15,578 155,713
26 14,560 170,273
27 6,274 176,547
28 3,910 180,457
29 760 181,217
30 221 181,438
31 2 181,440

Thanks for testing, anyway.
- Bulat

oh ok, I just tried the basic 4x4 one before. I'm letting it compile the huge 8x8 project now.

stannic · Sep 30, 2012

cuBerBruce said:
I was able to run it. Results in the spoiler

Great!
So I made some results using these distributions.
tl,dr:
- 6x4 puzzle always can be solved in 210 STM
- 6x6 puzzle can be solved in 429 STM
- 8x8 puzzle can be solved in 1192 STM

Code:

==================================================
1. huge6x4_x64_3GB
==================================================
- 1 chain
- 3 regions
- 2,144,257,920 bytes
==================================================
region  file name                        max.value

A       6x4_1TM_d2a4da11b6.t                    80
B       6x3_1TM_d2a2b2da3b2a4b2.t               77
C       4x3_1TM_d2b2db7.t                       53
==================================================
Chains:
ABC = 80 + 77 + 53 = 210 STM
- 6x4 puzzle always can be solved in 210 STM.

==================================================
2. huge6x6_x64_5GB
==================================================
- 3 chains
- 12 regions
- 4,722,656,400 bytes
==================================================
region  file name                        max.value

A       6x6_1TM_d2a4da16ba5ba3b3.t              95
B       6x6_1TM_d2a4da11ba4cba4cb3c3.t          95
C       6x5_1TM_d2a3bda4ba5bca3bc2a3bc.t        80
D       5x5_1TM_d2a3da9cb3c2b3c.t               75
E       5x3_1TM_d2ab2da2b2a3b2.t                61
F*      3x3_1TM_d2ada5.t                        31
G       6x5_1TM_d2a4da11cba3c2b4c.t             78
H       6x4_1TM_d2a3bda4ba5bc2b3c.t             77
I       6x6_1TM_d2a4da10ba4bca3b2ca2bc3.t       86
J       6x6_1TM_d2a4da10ca4c2b3c3b2c4.t         98
K       6x4_1TM_d2a2b2da3b2a4bca4c2.t           73
L       4x4_1TM_d2abda2ba3b5.t                  61
==================================================
* Not saved to disk because of small size.

Chains:

ABCDEF = 95 + 95 + 80 + 75 + 61 + 31 = 437
(actually E=61 and F=31 can be combined into 5x3 puzzle which can be solved in 84 STM, so 429)

ABGHEF = 95 + 95 + 78 + 77 + 61 + 31 = 437 (the same remark lead to 429 STM)

AIJKLF = 95 + 86 + 98 + 73 + 61 + 31 = 444
(L and F combine to 4x4 puzzle which can be solved in 80 STM, so 432 STM)

min(429, 429, 432) = 429
- 6x6 puzzle can be solved in 429 STM.

===================================================
3. huge8x8_x64_6GB
===================================================
- 1 chain
- 13 regions
- 5,411,802,480 bytes
===================================================
A       8x8_1TM_d2a6da45b2a6b2.t                121
B       8x8_1TM_d2a6da43b2c2a4b2c2.t            109
C       8x8_1TM_d2a6da43c4b4c4.t                121
D       8x7_1TM_d2a6da39b4c4.t                  109
E       8x6_1TM_d2a6da29b2a6b2.t                102
F       8x6_1TM_d2a5bda6ba7ba7ba6c2a6c2.t       105
G       7x6_1TM_d2a4bda5ba6ba6ba6ca6c.t          93
H       6x6_1TM_d2a4da16ba5ba3b3.t               95
I       6x6_1TM_d2a4da10ba4bca3b2ca2bc3.t        86
J       6x6_1TM_d2a4da10ca4c2b3c3b2c4.t          98
K       6x4_1TM_d2a2b2da3b2a4bca4c2.t            73
L       4x4_1TM_d2abda2ba3b5.t                   61
M*       3x3_1TM_d2ada5.t                        31
===================================================
Chains:
ABCDEFGHIJKLM = 121 + 109 + ... + 61 + 31 = 1204 STM (last two phases combine to 4x4, so 1192 STM)
- 8x8 puzzle can be solved in 1192 STM.

Of course, these results are still much more than God's numbers of these puzzles; yet they are probably best known upper bounds.
Moreover, I think you now can solve random instances of 8x8 in 500 single tile moves or so using the tables. What is averaged solution length with some small time limit (say, 1 sec)?

cuBerBruce · Sep 30, 2012

stannic said:
What is averaged solution length with some small time limit (say, 1 sec)?

For 8x8, I tried 10 random positions. For 1 second (or perhaps a little longer if it was changing quickly), the average was about 700 STM. Range 611..738. For 15 seconds, the average was about 690. Range 593..738. The low was significantly lower (about 50 moves) than the other results in the sample.

stannic · Sep 30, 2012

I've just solved 100 instances with single-chained 15-phase consuming 1.2 GB View attachment 8x8_15phase_1203M.zip. With time limit of 1 second, the average was 706.46 moves (range 585...829). For 5 seconds, the average was about 690 moves.
It seems like it is too little time to improve solution, especially with long chains of 10-15 regions. And difference between single-chained 8x8 1.2GB project and single-chained 8x8 5GB project is only two phases.

edit: Oh well, attachments work in test style, thanks.

ben1996123 · Sep 30, 2012

when it generates the lookup tables, where does it save them?

stannic · Sep 30, 2012

ben1996123 said:
when it generates the lookup tables, where does it save them?

In the "tables\" subdirectory. There are *.t files (tables) and *.md5 files (hashsums used to verify tables).

ben1996123 · Sep 30, 2012

stannic said:
In the "tables\" subdirectory. There are *.t files (tables) and *.md5 files (hashsums used to verify tables).

oh ok, didn't notice the folder on my desktop.

stannic · Sep 30, 2012

ben1996123 said:
oh ok, didn't notice the folder on my desktop.

It is better to place all files in separate folder. There is also subdirectory "projects\" and one or two ini files (one for x32, one for x64 binary). The program does not create any files outside exe's directory and does not change system registry.

stannic · Oct 1, 2012

cuBerBruce said:
For 8x8, I tried 10 random positions. For 1 second (or perhaps a little longer if it was changing quickly), the average was about 700 STM. Range 611..738. For 15 seconds, the average was about 690. Range 593..738. The low was significantly lower (about 50 moves) than the other results in the sample.

I am working currently on new version. In particular, what is the most required/useful information in the statistics that need to be collected during batch solve? In what form it is better to represent it? Maybe some other options?
- stannic

Edit: two reports from the current version (have not uploaded yet). The puzzle is 5x5. rNodes column represents the number of visited regions.

Code:

10 instances solved
Total time: 602 s
Average time: 60.215 s
Min. solution length: 94
Max. solution length: 121
Average solution length: 109.6

 ID                                                          Instance Status   Time Moves  rNodes
  1  24 2 4 10 14 8 23 3 5 16 11 22 19 21 9 1 15 7 6 0 18 12 17 13 20 solved 60.203    97 1413258
  2  14 4 22 7 0 2 8 24 3 5 6 10 23 17 12 19 16 9 1 21 13 18 11 15 20 solved 60.234   100 4187846
  3  19 13 2 22 20 9 17 16 5 18 10 21 8 4 7 15 23 1 3 6 11 14 0 12 24 solved 60.219   112 3223878
  4  11 3 8 0 6 23 5 9 18 12 21 13 20 22 1 2 10 7 15 24 4 16 17 14 19 solved 60.234   109 1673128
  5  8 13 17 16 7 9 12 21 2 1 20 14 10 5 4 11 19 18 24 23 0 6 22 15 3 solved 60.219   114 3193760
  6  22 20 12 21 24 16 6 7 10 18 5 2 3 15 1 17 23 13 9 11 14 8 0 4 19 solved  60.25   118 2010781
  7  12 18 11 9 6 4 3 23 15 22 10 0 24 21 1 16 2 8 17 7 19 20 14 5 13 solved 60.297   121 2717717
  8  22 2 9 10 15 1 12 8 3 5 7 11 24 17 23 20 14 6 16 21 19 4 0 18 13 solved 60.047    94 2476623
  9  16 3 4 20 6 0 8 15 1 23 18 21 17 11 14 24 5 12 19 22 13 2 9 10 7 solved 60.219   115 2554456
 10  23 17 14 21 5 3 4 20 1 8 15 18 13 12 22 2 6 9 11 7 10 19 16 24 0 solved 60.235   116 3728189

10 instances solved
Total time: 601 s
Average time: 60.162 s
Min. solution length: 53
Max. solution length: 67
Average solution length: 62.1

 ID                                                          Instance Status   Time Moves   rNodes
  1  24 2 4 10 14 8 23 3 5 16 11 22 19 21 9 1 15 7 6 0 18 12 17 13 20 solved 60.266    53 26402827
  2  14 4 22 7 0 2 8 24 3 5 6 10 23 17 12 19 16 9 1 21 13 18 11 15 20 solved 60.297    60 16550464
  3  19 13 2 22 20 9 17 16 5 18 10 21 8 4 7 15 23 1 3 6 11 14 0 12 24 solved 60.328    66 17910719
  4  11 3 8 0 6 23 5 9 18 12 21 13 20 22 1 2 10 7 15 24 4 16 17 14 19 solved  60.11    63 23485529
  5  8 13 17 16 7 9 12 21 2 1 20 14 10 5 4 11 19 18 24 23 0 6 22 15 3 solved 60.094    61 16819467
  6  22 20 12 21 24 16 6 7 10 18 5 2 3 15 1 17 23 13 9 11 14 8 0 4 19 solved 60.125    64 24587201
  7  12 18 11 9 6 4 3 23 15 22 10 0 24 21 1 16 2 8 17 7 19 20 14 5 13 solved 60.156    67 23334389
  8  22 2 9 10 15 1 12 8 3 5 7 11 24 17 23 20 14 6 16 21 19 4 0 18 13 solved 60.031    58 22910307
  9  16 3 4 20 6 0 8 15 1 23 18 21 17 11 14 24 5 12 19 22 13 2 9 10 7 solved 60.062    66 21881110
 10  23 17 14 21 5 3 4 20 1 8 15 18 13 12 22 2 6 9 11 7 10 19 16 24 0 solved 60.156    63 15152176

kumi na tano 3.00 - sliding tile puzzle suboptimal solver

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