kumi na tano 3.00 - sliding tile puzzle suboptimal solver

Discussion in 'Software Area' started by stannic, Sep 24, 2012.

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  1. stannic

    stannic Member

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    Jun 16, 2010
    The country of riddles
    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
     
    Last edited: Apr 13, 2017
  2. ben1996123

    ben1996123 Banned

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    Nice, works well and looks pretty good.
     
  3. cuBerBruce

    cuBerBruce Member

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    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.
     
  4. stannic

    stannic Member

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    Jun 16, 2010
    The country of riddles
    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.

    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).

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

    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
     
    Last edited: Apr 13, 2017
  5. cuBerBruce

    cuBerBruce Member

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    Duh. Sorry, for some reason I didn't notice the manual in the zip archive. My bad.
    Yes, exactly what I was seeing.
    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.
    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.
     
  6. stannic

    stannic Member

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    Jun 16, 2010
    The country of riddles
    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
    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
     
    Last edited: Apr 13, 2017
  7. stannic

    stannic Member

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    Jun 16, 2010
    The country of riddles
    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
     
    Last edited: Apr 13, 2017
  8. stannic

    stannic Member

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    Jun 16, 2010
    The country of riddles
    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
     
    Last edited: Apr 13, 2017
  9. ben1996123

    ben1996123 Banned

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

    stannic Member

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    Jun 16, 2010
    The country of riddles
    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.
    - stannic
     
    Last edited: Apr 13, 2017
  11. cuBerBruce

    cuBerBruce Member

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    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
        76     95,079 530,006,331
        77     59,450 530,065,781
        78     29,292 530,095,073
        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
        90    98,661 205,310,995
        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
    
     
  12. ben1996123

    ben1996123 Banned

    4,972
    4
    May 17, 2009
    Ponyville
    WCA:
    2009WHIT01
    YouTube:
    ben1996123
    oh ok, I just tried the basic 4x4 one before. I'm letting it compile the huge 8x8 project now.
     
  13. stannic

    stannic Member

    120
    0
    Jun 16, 2010
    The country of riddles
    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)?
     
    Last edited: Sep 30, 2012
  14. cuBerBruce

    cuBerBruce Member

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    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.
     
  15. stannic

    stannic Member

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    Jun 16, 2010
    The country of riddles
    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.
     
    Last edited: Sep 30, 2012
  16. ben1996123

    ben1996123 Banned

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

    stannic Member

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    Jun 16, 2010
    The country of riddles
    In the "tables\" subdirectory. There are *.t files (tables) and *.md5 files (hashsums used to verify tables).
     
  18. ben1996123

    ben1996123 Banned

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

    stannic Member

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    The country of riddles
    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.
     
  20. stannic

    stannic Member

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    The country of riddles
    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
    
     
    Last edited: Apr 13, 2017

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