Belated POTY 2012 nomination thread

[atavoidirc]

The 2012 POTY competition is the last remaining skipped POTY, So i've decided to finish it

From the original thread:
#01 37P4H1V0 (by Josh Ball): The smallest known c/4 orthogonal spaceship.
#02 Statorless p3(by Jason Summers): The first Strictly volatile P3.
#03 444-tick glider-to-Herschel converter (by Sergey Petrov): This is the fastest known stable glider-to-Herschel converter/90-degree glider reflector known.
#04 G4 Herschel merge circuit (by Sergey Petrov) (1)(2)
#05 Ambidextrous G5 Herschel transceiver (by Arie Paap and Matthias Merzenich) (1)
#06 P4 glider reflector:The first fast period-4 90-degree reflector (by Karel Suhajda and Matthias Merzenich)
#07 Direct stable Herschel Duplicator(by Sergey Petrov)


In addition I'd like to add:
#07 HLx111R (by Matthias Merzenich)
#08 Slow salvo snyth of the Herschel transmitter (by Sergey Petrov)

Additional Nominees:
#09 Low density oprhan (by Marijn Heule, Christiaan Hartman, Kees Kwekkeboom, and Alain Noels)
#10 New smallest 3c/6 spaceship (by Matthias Merzenich and Josh Ball)
#11 New c/5 diagonal rake design that allows periods as low as 85 (by Matthias Merzenich)
#12 Herschel-less p62 gun (by Jason Summers)
#13 New c/4 diagonal spaceships (by Nicolay Beluchenko)
#14 New reflector periods (By Matthias Merzenich)
From the time of posting, I will allow a period of one month (until July 10th) for people to propose any additional entries before the voting starts, which may be extended with sufficient interest.

[atavoidirc]

[DELETED]

[Sokwe]

The 2012 POTY competition is the last remaining skipped POTY, So i've decided to finish it

There seems to be a tradition of new users trying to run PotY competitions only to have me lock their threads due to some mistake. Before you continue, I would like to give some advice to help avoid this.

From the time of posting, I will allow a period of three days for people to propose any additional entries before the voting starts.

Not enough time. Give at least two weeks for additional proposals. We've waited 9 years, we can wait a bit longer.

Also, do not create a voting thread until you have a complete list of entries with links and descriptions and you have community consensus approval for that list. Obtaining consensus means posting the final list in this thread and waiting several days (I'd say at least 5) to see if anyone objects in any way to that list.

#06 Period-52 glider gun (by Karel Suhajda, Matthias Merzenich)

No such gun was discovered in 2012. I originally nominated the p4 reflector by Karel Suhajda and myself which works at periods as low as 52 (included in the link for the p52 and p58 reflectors you posted above).

Requesting this be moved to general discussion

I believe all previous PotY nomination and voting threads have been in the patterns board. I'm fine with sticking to tradition and keeping it here.

[Sokwe]

Here are two nominations:

• The orphan with the lowest known density (by Marijn Heule, Christiaan Hartman, Kees Kwekkeboom and Alain Noels)
• New reflector periods: dependent p26 and independent p52 and p58 reflectors (by Matthias Merzenich):

  Code: Select all

  x = 294, y = 75, rule = B3/S23
  25b2obo6b2obo96bob2o6b2obo106bob2o6b2obo$25bob2o6bob2o96b2obo6bob2o
  106b2obo6bob2o$29b2o2b2o98b2o14b2o102b2o8b2o4b2o$29bo3bo100bo14bo104bo
  8bo5bo$30bo3bo98bo16bo102bo10bo5bo$29b2o2b2o98b2o14b2o102b2o8b2o4b2o$
  25b2obo6b2obo96bob2o6b2obo106bob2o6b2obo$25bob2o6bob2o96b2obo6bob2o
  106b2obo6bob2o$23b2o8b2o4b2o98b2o2b2o114b2o2b2o4b2o$23bo9bo5bo100bo2bo
  116bo2bo5bo$24bo9bo5bo98bo4bo114bo4bo5bo$23b2o8b2o4b2o98b2o2b2o114b2o
  2b2o4b2o$25b2obo6b2obo96bob2o6b2obo106bob2o6b2obo$25bob2o6bob2o96b2obo
  6bob2o106b2obo6bob2o4$234bobo$obo232b2o49b2o$b2o50b2o180bo51b2o$bo52b
  2o60bobo167bo$53bo63b2o$117bo2$7bo$8b2o37bo$7b2o38b2o119bo$46bobo119b
  2o$167bobo3$13bobo233bo$14b2o24b2o208b2o20bo$14bo26b2o86bobo117b2o21b
  2o$40bo89b2o139bobo$130bo2$20bo$21b2o11bo$20b2o12b2o112bo6bo$33bobo90b
  2o2b2o14b3o6b2o$126bo2bo2bo12bo8bobo$39b2o77bo8bob2obo12b2o124b2o$39bo
  78b3o3b4obo2b2o137bo$37bobo81bobo5bobo2bo134bobo$32bo4b2o77b3o2bob5o2b
  o2b2o134b2o$31bobo81bobobobo3bobo2bo3bo7bobo118bobo$31bobo81b2obo2bo2b
  3o7bo8b2o109b2o8b2o$30bo2bo83b2o7bobobo3bo8bo110b2o8bo$31b2o85bob6o4bo
  2bo$116bo2bo6b3o2bo10b2o3bobo113b2o6b2o$116b2obob2o2bo3b2o11b2o6b2o
  111b2o6b2o$119bo2bo3bo2bo5bo14b2o$34bo84b2o6bobo3b3o15bo94bo7bo20bo7bo
  $30b2obobo92bo3bo112bobo5bobo18bobo5bobo$28bo2bob2o100bo110bo7bo20bo7b
  o$28b2o2bo99bo3bo16b3o2b2o$33bobo97bobo7b3o7b2o4bo2bo$34b2o98b2o17bo5b
  obobo$127bobo4b2o9b3o8b2obo2bo83b3o3b3o3bo2b2o4b2o2bo3b3o3b3o$126bo3bo
  8b2o5b2o8bo2bo97bo3b3o2b3o3bo$126bo4b2o6b2o4bobo5bo4bo80b2o5bobo3bobo
  3bo2b2o4b2o2bo3bobo3bobo5b2o$125b2obob3o12bo7b5o81bo7bo5bo22bo5bo7bo$
  129bo16bo89b2obo50bob2o$143b3o9bo80bo2b3o46b3o2bo$143bo10bobo80b2o4bo
  13b2o12b2o13bo4b2o$133b2o20bo83b5o13bobo10bobo13b5o$133b2o104bo4b2o13b
  o10bo13b2o4bo$240b2o2bo7b2o5b2o8b2o5b2o7bo2b2o$242bobobo5b2o22b2o5bobo
  bo$242bobobo2bo30bo2bobobo$243b2ob4o30b4ob2o$245bo38bo$245bobo34bobo$
  246b2o34b2o!

Edit: another nomination:

• The smallest known 3c/6 spaceship (by Matthias Merzenich and Josh Ball)

[Macbi]

• The orphan with the lowest known density (by Marijn Heule, Christiaan Hartman, Kees Kwekkeboom and Alain Noels)

While it was the lowest density at the time, I'll clarify that it isn't the current record holder. As observed here, the pattern American Dream can be used to construct orphans of arbitrarily low density by placing two copies at right angles.

[Sokwe]

If we do eventually hold a vote, I think that the entries should be described as if it were the beginning of 2013, with a note at the top of the list saying that some of these records have since been broken. However, I'm willing to hear alternative perspectives on this.

Edit: three more nominations:

• New c/5 diagonal rake design that allows periods as low as 85 (by Matthias Merzenich)
• Herschel-less p62 gun (by Jason Summers):

  Code: Select all

  #C The first p62 gun not based on Herschel tracks
  #C Jason Summers, 25 Feb 2012
  x = 476, y = 419, rule = B3/S23
  291b3o2bo4bo2b3o$294b3o4b3o$291bo3b2o4b2o3bo$287b2o20b2o$287b2o3bo2bo
  6bo2bo3b2o$295b2o4b2o$292bo2bo6bo2bo$292bobo8bobo2$292bobo8bobo$292bo
  2bo6bo2bo$295b2o4b2o$287b2o3bo2bo6bo2bo3b2o$287b2o20b2o$291bo3b2o4b2o
  3bo$294b3o4b3o$291b3o2bo4bo2b3o8$296bobo$297b2o$281bo15bo$281b2o$280bo
  bo11$312bo$313b2o$312b2o$265b2o$266b2o$265bo11$327bobo$328b2o$250bo77b
  o$250b2o$249bobo8$319b4o6b4o$319bo2bo6bo2bo$322bo6bo$314b2o3bo12bo3b2o
  5bo$314bobob4o8b4obobo6b2o$315b4o3bo6bo3b4o6b2o$234b2o80b6o8b6o$235b2o
  83bo10bo$234bo$320bo10bo$316b6o8b6o$315b4o3bo6bo3b4o$314bobob4o8b4obob
  o$314b2o3bo12bo3b2o$322bo6bo$319bo2bo6bo2bo$319b4o6b4o3$315bo42bobo$
  315b2o42b2o$219bo94bobo42bo$219b2o$218bobo5$79b2o6b2o$79b2obo2bob2o$
  72b2o4bo4b2o4bo4b2o$72b2o5b4o2b4o5b2o234bobo$80b2o4b2o243b2o$331bo$
  374bo$299b2o74b2o$300b2o72b2o$203b2o94bo$80b2o4b2o116b2o$72b2o5b4o2b4o
  5b2o107bo$72b2o4bo4b2o4bo4b2o$79b2obo2bob2o$79b2o6b2o4$346bo$89bo257b
  2o$87b2o257b2o$88b2o$157b2o7b2o116bo104bobo$157b2o7b2o116b2o104b2o$
  188bo94bobo49bo4bo49bo$188b2o140b5o6b5o$187bobo137bo4b2o8b2o4bo$155bob
  o9bobo156bo22bo$155bobo9bobo156bo3bob2o8b2obo3bo$104b2o221b4o2bo8bo2b
  4o$103b2o49b2obo2b2ob2o2bob2o160b3o8b3o$105bo48bo2bo9bo2bo$156b2o9b2o$
  153b2ob2o9b2ob2o$153b2ob2o9b2ob2o159b3o8b3o16bobo$72bobo81b2o9b2o158b
  4o2bo8bo2b4o13b2o$72b2o80bo2bo9bo2bo155bo3bob2o8b2obo3bo12bo$73bo80b2o
  bo2b2ob2o2bob2o155bo22bo55bo$94b2o172b2o57bo4b2o8b2o4bo57b2o$90bob6obo
  55bobo9bobo99b2o59b5o6b5o59b2o$90bo8bo55bobo9bobo2b2o94bo66bo4bo$83b2o
  5bo8bo5b2o66b2o$83b2o6bo6bo6b2o65bo$92bo4bo$94b2o24bo36b2o7b2o$119b2o
  36b2o7b2o$119bobo$334bobo$94b2o239b2o$92bo4bo237bo41bo$58bo24b2o6bo6bo
  6b2o271b2o$56b2o25b2o5bo8bo5b2o212bo57b2o$57b2o31bo8bo219b2o$90bob6obo
  153bo64bobo99bobo$94b2o157b2o166b2o$218b2o7b2o23bobo166bo$187b2o29b2o
  7b2o$186b2o$188bo$218bo9bo$80b2o7b2o44b2o79b2ob2o5b2ob2o$80b2o7b2o43b
  2o83b2o5b2o$109b2o25bo78bo4bo5bo4bo118bo$108b2o105bo3bo7bo3bo119b2o$
  110bo103bo17bo117b2o$96bobo116bo4bo5bo4bo160bobo$41bobo35b2o9b2o5b2o
  294b2o$41b2o38bo7bo7bo205b2o88bo$42bo37b2o7b2o124bo4bo5bo4bo72b2o130bo
  $78bob2o7b2obo121bo17bo4b2o64bo133b2o$78bo13bo122bo3bo7bo3bo6b2o196b2o
  $203bo11bo4bo5bo4bo5bo$202b2o15b2o5b2o140b2o7b2o$78bo13bo109bobo11b2ob
  2o5b2ob2o33b2o7b2o93b2o7b2o$78bob2o7b2obo125bo9bo35b2o7b2o$80b2o7b2o
  60bo$81bo7bo60b2o$79b2o9b2o33bo24bobo65b2o7b2o$124b2o92b2o7b2o131bo6b
  3o7b3o$124bobo231b2o6bo2bo7bo2bo$112bo149b3o9b3o82b2o4bo2bo9bo2bo26bo$
  27bo85b2o150bo7bo92b3o9b3o28b2o$25b2o53b2o7b2o21b2o148bo3bo5bo3bo11bo
  77bo2b2o5b2o2bo27b2o$26b2o52b2o7b2o171bo13bo11b2o77bo11bo$261b2o4bo3bo
  4b2o9bobo77bo11bo71bobo$244b2o15b2o4bo3bo4b2o88bo2b2o5b2o2bo71b2o$243b
  2o17bo13bo89b3o9b3o71bo9b2o7b2o$3b2o7b2o204b2o25bo16bo3bo5bo3bo88bo2bo
  9bo2bo80b2o7b2o$3b2o7b2o203b2o46bo7bo92bo2bo7bo2bo$219bo42b3o9b3o90b3o
  7b3o2$166b2o$2bo11bo150b2o294b2o9b2o$bobo2b2ob2o2bobo124b2o25bo292bo2b
  2o5b2o2bo$4bo7bo126b2o202bobo22b2o7b2o81b2o11b2o$b3ob2o3b2ob3o125bo
  122b2o7b2o68b2o23b2o7b2o81b2o11b2o$3o3bo3bo3b3o110bobo134b2o7b2o69bo
  78bobo37b2o5b2o$bo4bo3bo4bo9bo102b2o168bo19b2o104b2o35b3o7b3o$bo13bo
  10b2o100bo157bo11b3o18bo104bo36b3o7b3o$bo13bo9b2o245bo12b2o14bo17bob2o
  140b2o5b2o$bo4bo3bo4bo244bo11b3o10bobo12b2o18bobo122bobo12b2o11b2o$3o
  3bo3bo3b3o229bo12b2o14bo31b2o136b2o13b2o11b2o$b3ob2o3b2ob3o218bo11b3o
  10bobo12b2o33bo136bo13bo2b2o5b2o2bo$4bo7bo207bo12b2o14bo31b2o26bob2o
  148b2o9b2o$bobo2b2ob2o2bobo191bo12b3o10bobo12b2o33bo22b3o4bo$2bo11bo
  179bo12b3o13bo31b2o26bob2o26bo$182bo11b3o13bo11b2o33bo22b3o4bo23b3o$
  168bo12b2o14bo11b2o18b2o26bob2o26bo45bo$156bo11b3o10bobo12b2o33bo22b3o
  4bo23b3o44bo2bo126b2o7b2o$3b2o7b2o141b2o14bo31b2o26bob2o26bo69bo4bo55b
  o2bo66b2o7b2o$3b2o7b2o141bobo12b2o33bo22b3o4bo23b3o69bo4bo23b4o27bo30b
  4o$143bo33b2o26bob2o26bo69b3o23b3obo24bo3bo26bo3bo26bo3bo$144b2o33bo
  22b3o4bo23b3o69bo27bo26bo30b4o27bo$40bobo100b2o6b2o26bob2o26bo69b3o23b
  o4b3o48bo2bo58bo2bo$41b2o110bo22b3o4bo23b3o69bo26b2obo$41bo24b2o60b2o
  23bob2o26bo69b3o23bo4b3o22bo$65b4o29b2o27b4o19b3o4bo23b3o69bo26b2obo
  26b2o$65b2ob2o26b2ob2o26b2ob2o25bo69b3o23bo4b3o22bo$67b2o27b4o29b2o13b
  2o9b3o69bo26b2obo26b2o18b2o156b2o7b2o$3b2o7b2o22b3o58b2o45b2o55b3o23bo
  4b3o22bo46bo157b2o7b2o$3b2o7b2o24bo162bo26b2obo26b2o18b2o25b3o$37bo
  137b3o23bo4b3o22bo46bo28bo133b2o$175bo26b2obo26b2o18b2o25b3o159bobo$
  42b3o130bo4b3o22bo46bo28bo56b3o100bo19bo11bo$42bo133b2obo26b2o18b2o25b
  3o82bo121bobo2b2ob2o2bobo$2b2o9b2o28bo94b3o38bo46bo28bo71bo11bo123bo7b
  o$bo2b2o5b2o2bo124bo39b2o18b2o25b3o98bo131b3ob2o3b2ob3o$b2o11b2o123bo
  60bo28bo71bo24b3o130b3o3bo3bo3b3o$b2o11b2o137bobo18b2o25b3o98bo157bo4b
  o3bo4bo$4b2o5b2o140b2obo17bo28bo71bo24b3o157bo13bo$2b3o7b3o141bo18b3o
  98bo183bo13bo$2b3o7b3o141b2o19bo71bo24b3o183bo4bo3bo4bo$4b2o5b2o188b2o
  7b2o38bo208b3o3bo3bo3b3o$b2o11b2o81b2o7b2o93b2o7b2o11bo24b3o209b3ob2o
  3b2ob3o$b2o11b2o5b2o74b2o7b2o116bo238bo7bo$bo2b2o5b2o2bo4bobo199b3o
  235bobo2b2ob2o2bobo$2b2o9b2o7bo171bo262bo3bo11bo$194bobo259bobo$58b2o
  134b2o158b2o99bo$58bobo35b3o7b3o90b3o9b3o140bobo100b2o$58bo36bo2bo7bo
  2bo13b2o77bo7bo143bo107b2o7b2o$3b2o7b2o80bo2bo9bo2bo11bobo74bo3bo5bo3b
  o129bo118b2o7b2o$3b2o7b2o81b3o9b3o14bo74bo13bo127bobo$95bo2b2o5b2o2bo
  88b2o4bo3bo4b2o102bo24b2o$96bo11bo89b2o4bo3bo4b2o100bobo$96bo11bo90bo
  13bo77bo24b2o67b2o7b2o$95bo2b2o5b2o2bo89bo3bo5bo3bo75bobo93b2o7b2o$95b
  3o9b3o92bo7bo54bo24b2o$94bo2bo9bo2bo88b3o9b3o49bobo$95bo2bo7bo2bo129bo
  24b2o$30b2o64b3o7b3o128bobo7b2o7b2o$30bobo146bo58b2o7b2o7b2o126b2o9b2o
  $30bo147bo207bo7bo$178b3o204b2o7b2o44b3o$73b3o125b2o7b2o35bo9bo111b3o
  11bob2o7b2obo44bo$73bo23b2o7b2o93b2o7b2o33b2ob2o5b2ob2o109bo13bo13bo
  43bo$74bo22b2o7b2o8b2o130b2o5b2o101bo11bo$116bobo125bo4bo5bo4bo98bo$
  116bo127bo3bo7bo3bo71bo24b3o23bo13bo$243bo17bo71bo49bob2o7b2obo$244bo
  4bo5bo4bo45bo24b3o51b2o7b2o$307bo78bo7bo$280bo24b3o76b2o9b2o$244bo4bo
  5bo4bo20bo$243bo17bo17b3o$229bo14bo3bo7bo3bo$45b3o181bobo12bo4bo5bo4bo
  $45bo117bo65b2o17b2o5b2o128b2o7b2o$46bo116bobo79b2ob2o5b2ob2o125b2o7b
  2o29b2o$89b2o72b2o82bo9bo166bobo$89bobo281b3o50bo$89bo285bo$131b3o113b
  2o7b2o116bo$131bo115b2o7b2o$132bo215bo31b2o$346bobo27bob6obo$322bo24b
  2o27bo8bo$320bobo46b2o5bo8bo5b2o$296bo24b2o46b2o6bo6bo6b2o$294bobo81bo
  4bo$214bo80b2o83b2o$61b2o150bo$61bobo84bo64b3o$61bo85bo160b2o7b2o$147b
  3o158b2o7b2o61b2o27b3o$104b3o271bo4bo27bo$104bo264b2o6bo6bo6b2o17bo$
  105bo263b2o5bo8bo5b2o$135bo4bo165bobo9bobo55bo8bo$130b5o6b5o160bobo9bo
  bo42bo12bob6obo$127bo4b2o8b2o4bo215bo15b2o$126bo22bo155b2obo2b2ob2o2bo
  b2o15bo24b3o$126bo3bob2o8b2obo3bo155bo2bo9bo2bo16bo$127b4o2bo8bo2b4o
  158b2o9b2o16b3o$131b3o8b3o149bo9b2ob2o9b2ob2o$294bobo7b2ob2o9b2ob2o$
  198bo95b2o11b2o9b2o$76b3o119bobo104bo2bo9bo2bo$76bo54b3o8b3o53b2o105b
  2obo2b2ob2o2bob2o$77bo49b4o2bo8bo2b4o245b2o$120b2o4bo3bob2o8b2obo3bo
  156bobo9bobo72bobo$120bobo3bo22bo156bobo9bobo74bo$120bo6bo4b2o8b2o4bo$
  130b5o6b5o$135bo4bo$308b2o7b2o60bo$308b2o7b2o58bobo$353bo24b2o$351bobo
  $279bo72b2o$278bo$183bo94b3o$92b2o88bo$92bobo87b3o$92bo294b2o6b2o$387b
  2obo2bob2o$135b3o242b2o4bo4b2o4bo4b2o$135bo244b2o5b4o2b4o5b2o$136bo
  251b2o4b2o4$368bo$369bo$367b3o18b2o4b2o$263bo116b2o5b4o2b4o5b2o$263bob
  o114b2o4bo4b2o4bo4b2o$167bo95b2o122b2obo2bob2o$107b3o57bobo217b2o6b2o$
  107bo59b2o$108bo$151b2o$151bobo$151bo5$384bo$382bobo$143b4o6b4o91bo
  134b2o$143bo2bo6bo2bo90bo$146bo6bo93b3o$123b2o13b2o3bo12bo3b2o$123bobo
  12bobob4o8b4obobo$123bo15b4o3bo6bo3b4o$140b6o8b6o$144bo10bo2$144bo10bo
  $140b6o8b6o$139b4o3bo6bo3b4o$138bobob4o8b4obobo$138b2o3bo12bo3b2o$146b
  o6bo$143bo2bo6bo2bo$143b4o6b4o75bo$232bobo$232b2o$138b3o$138bo$139bo
  10$217bo$216bo$216b3o$154b2o$154bobo$154bo11$201bo$201bobo$201b2o$169b
  3o$169bo$170bo10$186bo$185bo$185b3o3$169b3o2bo4bo2b3o$172b3o4b3o$169bo
  3b2o4b2o3bo$165b2o20b2o$165b2o3bo2bo6bo2bo3b2o$173b2o4b2o$170bo2bo6bo
  2bo$170bobo8bobo2$170bobo8bobo$170bo2bo6bo2bo$173b2o4b2o$165b2o3bo2bo
  6bo2bo3b2o$165b2o20b2o$169bo3b2o4b2o3bo$172b3o4b3o$169b3o2bo4bo2b3o!

• A very large collection of new c/4 diagonal spaceships (by Nicolay Beluchenko):

  Code: Select all

  #C New c/4 diagonal spaceships
  #C Nicolay Beluchenko, 2012
  x = 942, y = 1549, rule = B3/S23
  62b2o70bo42b3o16b3o44b2o52b2o43bo15b2o24bo19b3o16b3o46b2o36b2o$61b2o
  70b2o21bo20bo18bo45b2o52b2o43b2o14b2o24b2o19bo18bo47b2o36b2o$63bo69bob
  o19b2o21bo18bo46bo53bo42bobo15bo23bobo19bo18bo48bo37bo$24bobobo4bobo
  29b2o68bo19bobo22b2o17b2o45b2o52b2o41bo17bo4b3o38b2o17b2o47b2o36b2o$
  64bo71bo42b2o17b2o45bo53bo44bo16b3o4b2o16b2o18b2o17b2o47bo37bo$24bo7bo
  3bo57bobobo4bobo27bobob2o19b2o62bobobo3bo3bo34bobobo3bobobo34bobobo3bo
  bobo12bobob2o15b3obobo17b2o52bobobo4bobo37bobobo5bo$63bo2bo67bob4o18b
  2o18bo18bo46bo2bo50bo2bo40bob4o21bo35bo18bo44b3obo2bo20bo3bo9bo2bo$24b
  obo5bo3bo18b2o5b2o30bo7bo3bo63b3o5bo2bo7b3o5bo2bo21bo7bo3bo6b2obo24bo
  7bo12b2o5b2o17bo11bo33bobo12bo6b2o11b3o5bo2bo7b3o5bo2bo12bo7bo3bo16bo
  2bo16bo18b2obo$28bo25b2o5bo74bo12bo6b2o12bo7bo10bo7bo42b2o4bo42b2o5bo
  47bo16b2obo11b2o5bo2bo10bo7bo10bo7bo39b2o6bo2bo21bo3bo5b2o4bo$32bo3bo
  19bo4bobo30bobo8bo29bo2bo9b2o5bo2bo12bo2b5obo9bo2b5obo22bobo5bobobo7bo
  bo2bo6bo14bobo5bobo11bo4bobo17bobo8bo15bo2bo15bo13bobo3b2obo12bo2b5obo
  9bo2b5obo13bobo6bobo11b2o5bo18bobo7bo9bobo2bo6bo$28bo29b2o2bo35bo32b3o
  4bo9bobo3b2obo15bo18bo33bo20bo5b2o18bo7bo11b2o2bo22bo18b3o4bo13b2obo
  16bo19bo18bo24bo20bo4b4o19bo7bo12bo5b2o$24bobo6bobo22b2o43bo27bo2bo17b
  o21b2o17b2o39bo9bo2bo5bobo37b2o31bo12bo2bo5b2o13bo15bo21b2o17b2o26bo3b
  o14b2o4bobo35bo2bo5bobo$98bo33bobobo14bo47b3o24bo18bobo25bo7bo38bo19bo
  bobo2b2o12b2o16bo2bo2bo40b3o15bo22b2o24bo6bo11bobo$94bobo5bobobo28bo
  15bo2bo2bo20b3o18bo2b2o18bobo9bo10bobo8b2o11bobo5bobo36bobo7bo16bo5bo
  35bo19b3o18bo2b2o9bobo6bobo37bobo6bo13bobo8b2o$61b3o68bo24bo20bo2b2o
  15b2ob2o43b2o7b4o37b3o41bo23b3o17bo2b2o16bo2b2o15b2ob2o83b2o7b4o$61bo
  2b2o61b2o3b4o20bo2b2o16b2ob2o11b2o51bo5bobo41bo2b2o34b2o3b4o20bo2b2o
  15bob2obo14b2ob2o11b2o48b3o40bo5bobo$60b2ob2o61b2o4bo23bob2obo10b2o18b
  2o4bobo49b3o2bo39b2ob2o34b2o4bo22b2ob2o10b2o4b2o13b2o18b2o4bobo42bo2b
  2o42b3o2bo$55b2o71bo2bo4bo13b2o4b2o13b2o4bobo14bo2bob2o49bo3b2o34b2o
  44bo2bo4bo13b2o18bobo2b3o12b2o4bobo14bo2bob2o41b2ob2o43bo3b2o$54b2o4bo
  bo68b2o3bo13bobo2b3o15bo2bob2o16b2o52bobo36b2o4bobo41b2o3bo12b2o4bobo
  12bo3bo17bo2bob2o16b2o39b2o51bobo$56bo2bob2o67bo19bo3bo20b2o19b2o53b2o
  38bo2bob2o40bo20bo2bob2o15b2o3bo15b2o19b2o4bo33b2o4bobo46b2o4bobo$58b
  2o71bo3bo17b2o3bo16b2o20bo53bo41b2o44bo3bo17b2o18bo4bo15b2o4bo15bo5b2o
  33bo2bob2o46bo6bobo$58b2o70bo22bo4bo17bo116b2o4bo38bo22b2o25b2o13bo5b
  2o18bo37b2o56bo$59bo71bo2bo159bo5b2o37bo2bo19bo19b2o3b2o19bo21bo36b2o$
  132bo21b2o143bo40bo48bo19bo58bo$300bo9$55b3o23b2o30b3o28bo53b3o14b2o
  58bo27b2o37b2o48bo32b2o23b2o24b3o23b2o$55bo25bobo29bo9b2o18b2o53bo15b
  2o58b2o26b2o38bobo46b2o31b2o24bobo23bo25bobo$56bo24bo32bo6b3obo11bo5bo
  bo53bo16bo51bo5bobo27bo37bo42bo5bobo32bo23bo26bo24bo$58b2o24bo31b2o2b
  2o14b2o63b2o15bo4b3o41b2o37b2o31b2obo41b2o42b2o23bo25b2o24bo$59bo23bob
  o31bo18bobo3b2obobo52b2o16b3o4b2o40bobo3b2obobo26bo33bo4bo39bobo3b2obo
  bo31bo24bobo25bo23bobo$26bo5bobo18b2o28bobo13bo4bo16bo18bo7b2o23bo5bob
  o11b2o24b3obobo23bo4bobo14bo7b2o43bo4bo3bo5bob2o6b3o36bo7b2o21b2o31bob
  o19b2o28bobo$24bo28bo2b2o17b3o5bo13bo19b2o3bo16bo4bo5b2o19bo21bobo3bo
  26bo20bo10bo11bo4bo5b2o17b3obo2bo14bo21b3o4b2o34bo4bo5b2o19bo2b2o2bo2b
  o14b3o5bo21bo2b2o17b3o5bo$31bo3bo17bo3bo17bo7bo20bo11bobob2o17bo2bo2b
  6o27bo3bo10bo5bo19bobo48bo2bo2b6o18bo2bo25bo3bo11b3obobo18bo4bobobo7bo
  2bo2b6o20bob3o2bo17bo7bo21bo3bo17bo7bo$23bo31bo2bo11b2o6b2o3bo12bo19bo
  bo2bob2o45bo25bo2bo18b2obo24bo11bo36b2o6bo2bo14bo30bo15bo51bo4bo2bo10b
  2o6b2o3bo23bo2bo11b2o6b2o3bo$25bo5bo3bo19bo2bo11bobo3bo6bo14bo5bo10bo
  4b2o50bo8bo14b2o2bobo16bo28bo5bobo37b2o5bo21bo5bobobo11bobo27bo44bo6bo
  11bobo3bo6bo2b2o19bo2bo11bobo3bo6bo$23bo3bo30bo11bo5b2o4bo13bo3bo14b2o
  31b2obo18bo3bo42b2obo25bo3bo7bo37bo4b4o16bo3bo18b2obo19bo71bo5b2o4bo3b
  obo21bo11bo5b2o4bo$31bo3bo11b3o23bo4b3o23bo10b2o31bo2bo27bo7b3o30bo58b
  obo16b2o4bobo26bo11bo23bo5bobo36b3o7bo17bo4b3o5bo12b3o23bo4b3o$23bo3bo
  19bo9bo15b2o21bo3bo47bobo19bo3bo12bo9bo20b2o26bo3bo7bo19b4o16b2o21bo3b
  o17b2obo20bo3bo7bo17b2o15bo27b2o24bo9bo15b2o$25bo6bobo13bo2b6o41bo5bo
  17b3o47bo5bobobo5bo2b6o51bo5bobo21bo44bo9bo12bo49b2o17bo2b6o45bo2b6o$
  50bo71bo2b2o63bo30b3o120b2o21bo3bo7bo37bo53bo$51b2o27b3o38b2ob2o23b3o
  39b2o28bo2b2o54bo20b3o65bo5bobo17bo6bo15b2o29b3o20b2o27b3o$80bo2b2o31b
  2o31bo2b2o66b2ob2o55bo20bo2b2o41b3o46bob2ob2o46bo2b2o47bo2b2o$57b3o19b
  2ob2o31b2o4bobo24b2ob2o44b3o15b2o62bo2b2o16b2ob2o42bo2b2o45bo3bobo19b
  3o22b2ob2o25b3o19b2ob2o$57bo2b2o12b2o41bo2bob2o19b2o52bo2b2o12b2o4bobo
  56bob2obo10b2o49b2ob2o49b2o21bo2b2o15b2o33bo2b2o12b2o$56b2ob2o12b2o4bo
  bo37b2o21b2o4bobo45b2ob2o15bo2bob2o50b2o4b2o13b2o4bobo38b2o54b4o2bo18b
  2ob2o15b2o4bobo26b2ob2o12b2o4bobo$51b2o22bo2bob2o37b2o23bo2bob2o40b2o
  25b2o53bobo2b3o15bo2bob2o37b2o4bobo47b2obobo15b2o25bo2bob2o21b2o22bo2b
  ob2o$50b2o4bobo18b2o41bo25b2o42b2o4bobo19b2o4bo48bo3bo20b2o42bo2bob2o
  47bo4b2o13b2o4bobo21b2o23b2o4bobo18b2o$52bo2bob2o18b2o67b2o44bo2bob2o
  20bo5b2o49b2o3bo16b2o4bo39b2o51bo20bo2bob2o21b2o25bo2bob2o18b2o4bo$54b
  2o22bo68bo46b2o28bo51bo4bo17bo5b2o37b2o55b2o17b2o25bo27b2o22bo5b2o$54b
  2o138b2o29bo78bo40bo55bobo16b2o53b2o4bo22bo$55bo139bo81b2o26bo115bo54b
  o5b2o21bo$402b3o76bo$482bo14$55bo24bo27bo25b3o27b3o20b3o13b3o28bo49b3o
  34b3o49b3o13b3o32bo64bo31bo31bo30b3o13b2obo26b2o$54b2o23b2o26b2o25bo5b
  3o21bo22bo15bo9b2o18b2o49bo36bo51bo15bo9b2o22b2o63b2o30b2o30b2o30bo15b
  o3bo6b2o17bobo$54bobo22bobo25bobo25bo2b2ob2o22bo22bo15bo6b3obo11bo5bob
  o49bo36bo51bo15bo6b3obo15bo5bobo62bobo29bobo29bobo31bo13bo4bo4b2o18bo$
  56bo24bo27bo20b3o4bo29b2o21b2o14b2o2b2o14b2o56b3o37b2o50b2o14b2o2b2o
  18b2o72bo31bo31bo29bobo15b2o8bo14b2obo$57bo24bo27bo19bo7b2o26b2o21b2o
  16bo18bobo3b2obobo46b3ob2o33b2o43b2o5b2o16bo22bobo3b2obobo63bo31bo31bo
  28b2o18bobo3b2o15bo4bo$54bobob2o19bobob2o22bobob2o18bo2b3o45b2o27bo18b
  o7b2o76b2o26bo5bobo15bo2bo25bo5bo16bo7b2o58bobob2o26bobob2o26bobob2o
  26bobo20bo2b2o15bob2o6b3o$55bob4o19bob4o22bob4o19bo2bo23b3o2bo16bobo3b
  o18b2o3bo16bo4bo5b2o24bo4bobobo40bobo3bo19bo25bo2bo2bo18b2o3bo3b2o15bo
  4bo5b2o26bo6bo23bob4o26bob4o26bob4o46bo9b3o14b3o4b2o$25bo7bo102bo22bo
  5bo16bo5bo17bobob2o17bo2bo2b6o23bo22bo28bo5bo26bo3bo16b2o2bo17bobob2o
  4bobo14bo2bo2b6o25bo6bo3bo114b2o22bob3obo2bo17b3obobo$23bo7bo25bo24bo
  27bo14b3o30bo3bo2bo19bo2bo3bo13bobo2bob2o60bo10b2o31bo2bo18bo27bobo2bo
  2bo14bobo2bob2obo88bo31bo31bo23bo2b2ob2o20b3o2bo4bo22bo$56bo2bo21bo2bo
  24bo2bo12bo9bo22bo3b2o2bobo16b2o2bo3b2o10bo4b2o51bo22bo32b2o2bobo17bo
  7bo17b3o3bo15bo4b2o5bo51bo7bo3bo22bo2bo28bo2bo28bo2bo16b2ob2o3bo2bo25b
  obob2o16bobo$22bo7bo21b3o4bo17b3o4bo20b3o4bo13bo2b6o24b2o31bo12b2o31b
  2obo23bo8bo12b3o7b2o42bo3bo3bo3bo9b2o5b2o19b2o64bo7bo20b3o4bo24b3o4bo
  24b3o4bo15b2o3bo31b2o20b2obo$24bo7bo19bo2bo21bo2bo24bo2bo19bo34bo12b3o
  14bo11b2o31bo2bo21bo3bo27b3obo10b3o49b2o5b2o20b2o35bobo24bo3bo7bo18bo
  2bo28bo2bo28bo2bo21bobobo2b3o25bo22bo$22bo3bo3bo3bo18bobobo20bobobo23b
  obobo18b2o21b3o21bo9bo51bobo32bo13b2obo3b2o14bo9bo20bo3bo3bo3bo10bo4bo
  57b4o56bobobo27bobobo27bobobo54bo20b2obo$56bo24bo27bo42bo9bo14bo2b6o
  26b3o48bo3bo19b2o2bobo17bo2b6o23bo7bo14b2o2b2o26b3o26bo27bo3bo6bo23bo
  31bo31bo22b3o2bo30b3o18bo$22bo3bo3bo3bo18bo24bo27bo28b3o15bo2b6o17bo
  32bo2b2o48bo6bo16bo6bo16bo52b2o30bo2b2o54bo6bo22bo31bo31bo25b2o34bo2b
  2o14b2o$24bo7bo15b2o3b4o16b2o3b4o19b2o3b4o25bo2b2o15bo24b2o29b2ob2o23b
  3o49bo22b2o81b2ob2o27bo52b2o3b4o23b2o3b4o23b2o3b4o28b2o27b2ob2o$47b2o
  4bo18b2o4bo21b2o4bo27b2ob2o17b2o48b2o31bo2b2o48bo2bo96b2o35bo51b2o4bo
  25b2o4bo25b2o4bo31b4o20b2o26b3o$49bo2bo4bo16bo2bo4bo19bo2bo4bo18b2o55b
  3o16b2o4bobo24b2ob2o50b2o25b3o46b3o19b2o4bobo28bo2b2o50bo2bo4bo23bo2bo
  4bo23bo2bo4bo26bo4bo18b2o4bobo20bo2b2o$52b2o3bo19b2o3bo22b2o3bo17b2o4b
  obo25b3o21bo2b2o16bo2bob2o19b2o85bo2b2o44bo2b2o19bo2bob2o28bob2obo52b
  2o3bo26b2o3bo26b2o3bo21bo4bo4bo20bo2bob2o19b2ob2o$51bo24bo7bo19bo25bo
  2bob2o25bo2b2o18b2ob2o19b2o21b2o4bobo78b2ob2o44b2ob2o22b2o25b2o4b2o55b
  o8bo22bo7bo23bo26b2o3b2o27b2o17b2o$52bo3bob2o17bo3bo2b2o19bo3bo22b2o
  27b2ob2o14b2o27b2o4bo18bo2bob2o54b3o16b2o47b2o30b2o25bobo2b3o56bo3bob
  2o24bo3bo2bo24bo3bo21bobo3bo27b2o16b2o4bobo$51bo7bo16bo10b2o15bo27b2o
  22b2o21b2o4bobo22bo5b2o18b2o57bo2b2o13b2o4bobo40b2o4bobo25bo25bo3bo58b
  o9bo21bo6bo24bo7bo22b5o26bo18bo2bob2o$52bo2bo21bo2bo6b3o15bo2bob2o21bo
  21b2o4bobo17bo2bob2o27bo20b2o4bo51b2ob2o16bo2bob2o42bo2bob2o54b2o3bo
  55bo2bo6b3o19bo2bo4bo23bo2bob2o23b4o48b2o$53bo6b2ob3o12bo11bo15bo4bo
  45bo2bob2o19b2o31bo20bo5b2o44b2o26b2o47b2o57bo4bo56bo9bobo19bo7bob2o
  20bo6bo21b2o50b2o4bo$60b2o25bo2bo68b2o22b2o57bo45b2o4bobo20b2o4bo42b2o
  64b2o62bob2o27b2ob2o27b3o19bo51bo5b2o$61bo3bo21bo24b2ob3o41b2o23bo58bo
  46bo2bob2o21bo5b2o41bo58b2o3b2o63b3o28bob3o28bobo75bo$62b2o23bobo22b2o
  46bo131b2o29bo109bo63b2o29b2o29bob2o76bo$113bo3bo174b2o30bo234b3o$114b
  2o177bo266b2o13$62bo7b2o15b3o31b3o26b2o23b2o79bo30bo21b3o$61b2o5b3obo
  14bo33bo27b2o24bobo77b2o29b2o21bo$61bobo3b2o19bo33bo28bo23bo79bobo28bo
  bo21bo72b2o54b2o59bo49b2o31b2o8b2o$66bo23b2o32b2o27b2o23bo78bo30bo23b
  2o68b2o54b2o59b2o48b2obo29b2o8b2o$58bo5bo4bo21bo31b2o27bo24bobo78bo30b
  o23bo70bo55bo58bobo48bo33bo9bo$24bobobo5bo22b2o4b2o3bo75b2o31bobo75bob
  ob2o25bobob2o47bobobo6bo35b2o54b2o106bo3bo31b2o$32bo3bo20bobo2b2o29bo
  23b3o2bo21bo2b2o2bo2bo14b3o5bo78bob4o25bob4o17b2o36bo36bo55bo60b2o46bo
  3bo30bo9b3o$28bo32bo2b2o23bob2obo21bo5bo21bob3o2bo17bo7bo30bobobo4bobo
  90b2o2bo28bo68bobobo3bobobo44bobobo4bobo21b2o22bo7bo15bo3b2o37bob4o$
  32bo3bo23b2o21b2o3b3o4bo19bo3bo2bo3bo18bo4bo2bo10b2o6b2o3bo80bo30bo11b
  2o6bo2bo3b2o29bo36bo2bo52bo2bo80bo3bo3bo3bo17b3o27bo2bo3b6o$27bo33bob
  2o17b2o4bo2bo23bo3b2o2bo3b2o16bo6bo11bobo3bo6bo2b2o30bo3bo3bo36bo2bo
  27bo2bo9bobo3b2ob3o3bo25bo6bo33b2o31bo7bo7b2o5b2o32bo3bo3bo11bo6b2o49b
  ob2o21b2o5b2o4b2o4b2o$32bo3bo22b2o23bo31b2o8bo37bo5b2o4bo3bobo70b3o4bo
  17bo5b3o4bo9bo5b2o4b2o2bo29bo3bo30bo48b2o5bo53b2o5bo2bo21bo3bo3bo3bo
  16b2o20b2o5bo6b2o4bo$26bo31bobo28b2ob2obob2o21bo6bo11b3o7bo17bo4b3o5bo
  30bo7bo33bo2bo20b2o5bo2bo16bo36bo39bo2bo30bo7bo9bo4bobo31bo6bo12bobo3b
  2obo24bo21b2o27bo4bobo5bo$32bo3bo21bobo24b3ob3obobobobo9b3o27bo27b2o
  85bobobo18bobo5bobobo14b2o3bob2o34bo3bo29bo53b2o2bo37bo3bo14bo27bo3bo
  3bo3bo11bo2b2o26b2o2bo6bo$26bo7bo22bo31b2o4bobo11bo9bo20bo2b6o61bo6bo
  39bo30bo20bo2bo28bo7bo31bo32bo7bo12b2o34bo23bo52bo3bo26b2o10b2o$57b2o
  51bo2b6o23bo111bo25b2o3bo86b3o4b2o96bo3bo13bo2bo25bo3bo3bo3bo12b2o$57b
  2o2b3o48bo30b2o29b3o33bo5bobobo33b4o22b2o3b4o22bo60bo2b3o35bo7bo49bo7b
  o46bo7bo14b2obo$61bo2b2o29b3o15b2o59bo2b2o75bo30bo88bo5bo57b3o58b2o43b
  o3b2o2bo29b3o$60b2ob2o30bo2b2o48b3o22b2ob2o76bo3bo12bo6b2o4bo4bo22b2o
  59b2o63bo2b2o56b4o40b2o6bo5bo24bo2b2o$55b2o37b2ob2o20b3o26bo2b2o15b2o
  83bo4bo11b2o5bo2bo3b2o3bo22b4o57b2o2b2o58b2ob2o56bo4bo39bobobo3b2o3b2o
  23b2ob2o$54b2o4bobo26b2o28bo2b2o23b2ob2o15b2o4bobo76b2obo14bobo3b2obo
  3bo27bo4bo56b2o57b2o59bo4bo4bo46bo5bobo17b2o$56bo2bob2o25b2o4bobo21b2o
  b2o19b2o25bo2bob2o76b2o20bo9bo3bo17bo4bo4bo53b2o2bo56b2o4bobo52b2o3b2o
  48bobo25b2o4bobo$58b2o30bo2bob2o16b2o26b2o4bobo21b2o79b3o18bo9bo21b2o
  3b2o57b2o62bo2bob2o52bobo3bo47bo2bo9b2o16bo2bob2o$58b2o32b2o18b2o4bobo
  22bo2bob2o21b2o4bo70b3ob2o19bo2bo7bo2bo17bobo3bo52b2ob2obo64b2o59b5o
  45bo2bo8b4o17b2o$59bo32b2o20bo2bob2o24b2o25bo5b2o67bo2bo34bo23b5o50bob
  5o64b2o58bo2b3o3bo44bo5bobo21b2o$93bo22b2o27b2o4bo25bo68bo62b4o51bo71b
  o4bo54bo5bobo2b2o38b2o4b3o2bo21bo$116b2o28bo5b2o24bo67bo62b2o52b2o6b2o
  68bo58b2o4b3o44bo3b2o$117bo33bo87b2o7bo61bo49b2o4b2o72bo2b2o55b2o5bo
  45bobo$152bo85b2o6bobo110b2o3bob2o72bob2obo54b2o52b2o$240bo2b2o116bo3b
  2o67b2o4b2o58b2o3b2o47bo$242b2o2b2o113bo2bobo67bobo2b3o59bo3bobo$242b
  2o117b2o71bo3bo$364b2o71b2o3bo63b3o$437bo4bo2$438b2o12$364bo$56bo39bo
  127bo138b2o$55b2o38b2o126b2o75bo62bobo$55bobo37bobo58bo66bobo73b2o64bo
  $57bo39bo57b2o68bo73bobo64bo$58bo39bo56bobo68bo74bo61bobob2o$25bo7bo
  21bobob2o34bobob2o56bo65bobob2o31bo4bobo4bobobo25bo61bob4o$23bo3bo3bo
  3bo20bob4o34bob4o56bo65bob4o69bobob2o$155bobob2o30bo5bobobo58bo3bo3bo
  3bo27bob4o60bo$23bo3bo3bo3bo22bo39bo33bo8bo14bob4o27bo3bo32bo138bo2bo$
  25bo31bo2bo36bo2bo3bo6bo18bo3bo4bo61bo23bo2bo31bo3bo3bo3bobo27bo58b3o
  4bo$27bo3bo3bo17b3o4bo32b3o4bo2bob3o2b2o46bo30bo3bo27b3o4bo47bo24bo2bo
  56bo2bo$53bo2bo36bo2bo5bo7bobo17bo3bo3bo18bo2bo30bo8bo20bo2bo35bo3bo3b
  o28b3o4bo28bo5bo5bo16bobobo$26bo4bo3bo18bobobo35bobobo4b2o5b2o20bo7bo
  12b3o4bo32bo28bobobo49bo20bo2bo36bo3bo23bo$24bo8bo23bo39bo10bo2b2o21bo
  3bo3bo10bo2bo42bo25bo34bo4bobo4bobo23bobobo30bo11bo16bo$54bo39bo11b2o
  2bob2o40bobobo33bo29bo78bo39bo15b2o3b4o$49b2o3b4o31b2o3b4o8b3obobob2o
  17bo4bo3bo14bo32bo8bo17b2o3b4o72bo34bo11bo10b2o4bo6b3o$48b2o4bo33b2o4b
  o11bobobobob2o15bo8bo13bo61b2o4bo70b2o3b4o38bo17bo2bo4bo2bo$50bo2bo4bo
  3bo6bo20bo2bo4bo18bo31b2o3b4o3b2o55bo2bo4bob3o61b2o4bo7b2o25bo4bo6bo
  15b2o3bo3bo$53b2o3bo2bob3o2b2o23b2o3bo18bo30b2o4bo6bobo57b2o3bobo2b3o
  60bo2bo4bo2b2o53bo11b2o$52bo7bo7bobo21bo57bo2bo4bo2bo58bo8bobo65b2o3bo
  4bo25bo3bobobo3bo15bo3bo7bo$53bo3bo3b2o5b2o23bo3bo55b2o3bo5bo56bo3bo8b
  o61bo12bo50bo$52bo13bo2b2o21bo59bo10bobo54bo11bo64bo3bo6bobo50bo2bobob
  o6b2o$53bo2bo7b2o2bob2o21bo2bo56bo3bo5bobo55bo2bobobo5bobo59bo9bobo53b
  o3bob5ob2o$54bo9b3obobob2o20bo57bo9bo59bo3bob2obo65bo2bo3b6o56bo4b2o$
  64bobobobob2o79bo2bob3ob2o62bo4bo2b3o61bo3b2o4b2o61b3o$75bo78bo7b3o65b
  o3bo67b2o4b2ob4o$75bo88b3o65b2o69bo7b5o57bo$166b2o63bo2bobo66bo6bo63b
  3obo$167bo65bo4bo65b2o71b4o$162b2o2b5o61bo5bo70b2o65bo$161b2o3b4o63bo
  4bob2o72b2o$163bobobo66bo4bo71bo2bo2bo59bo2bo$166bo70b2o71b3o2bobo58bo
  2b4o$165b2o71bo71b2o5bo58bo4b3o$238bo137bobo2b2o2bo$383bob3o$385b3obo
  2$387b3o$387bobo$388b3o$390bo11$139bo$138b2o179bo$138bobo53bo3bobo4bob
  o27b2o48bo3bobobo2bobobo17b2o83b2o$54bo85bo61bo6bo24b2obo80bobo51bo6bo
  3bobobo14b2obo$53b2o86bo52bo40bo49bo3bo10bo19bo56bo25bo$53bobo82bobob
  2o58bo6bo25bo3bo81bo50bo10bo19bo3bo$55bo83bob4o49bo5bo6bo27bo3bo45bo3b
  obo7bo18bobob2o52bo26bo3bo$56bo145bo6bo25bo3b2o52bo25bob4o47bo5bo4bobo
  17bo3b2o$53bobob2o82bo52bo44b3o43bo12bo77bo3bo6bo19b3o$54bob4o80bo2bo
  58bo6bo26bob2o53bo27bo50bo31bob2o$136b3o4bo50bo3bobo4bobo30b2o45bo3bob
  o6bo21bo2bo52bo3bo6bo18b2o$56bo41bo3bobo7bo23bo2bo93b2o81b3o4bo48bo5bo
  4bobo15b2o$55bo2bo47bo3bo3bo22bobobo91bo2b2o78bo2bo81bo2b2o$51b3o4bo
  39bo41bo92bo3bo79bobobo79bo3bo$51bo2bo51bo7bo22bo96b2o84bo81b2o$24bo5b
  o5bobobo11bobobo41bo5bo27b2o3b4o93b2obo79bo84b2obo$28bo3bo22bo50bo6bo
  17b2o4bo91bo3b2o2bo74b2o3b4o76bo3b2o2bo$24bo11bo15bo45bo12bo21bo2bo4bo
  86b2o6bo74b2o4bo78b2o6bo$32bo14b2o3b4o50bo29b2o3bo86bobobo3b2o5bo69bo
  2bo4bo74bobobo3b2o$24bo11bobo7b2o4bo6b3o36bo3bobo5bobobo20bo10b3o86bo
  5bo2bo71b2o3bo3b2o76bo6bo$31bo8bo7bo2bo4bo2bo76bo3bo5bo85bobo5b2o3bo
  69bo8b2o74bobo6b2o$24bo4bo21b2o3bo3bo74bo12bo82bo2bo5bo4b2o69bo3bo4bob
  o71bo2bo6bobo$40bo9bo11b2o72bo2bobobo2bobo82bo2bo11bob3o64bo6b6o71bo2b
  o$24bo3bobobo3bobo12bo3bo7bo73bo3bob3o2b2o84bo12bo3b2o63bo2bo2bobo3b2o
  72bo3b3o2b3o$50bo90bo5bob2o81b2o15b4o64bo4bo5b2ob3o66b2o4bo8bob2o$51bo
  2bobobo6b2o83bo94bo83b2o3bo72b2o5b2o$52bo3bob5ob2o84bo3bo91b3obo79bo
  85bo2bo$56bo4b2o88b4obo91b2o2bo76b2ob2o80b3obo$61b3o82b2o4b2o95bo3b2o
  159bo$145b2o5bobobobo94b2o73bo2bo82bo5b3o$63bo83bo4b3o3bo92bo79b2o5b2o
  73bo3bo2bo$64b3obo80b2o2bo5bo93b2o73b2ob2o4b2o74b3o5bo$67b4o78b2o5bo3b
  o93bo73bobob2o5bo72bo2bo7b3o$66bo93bobo93b2o71bo4bo78bob4o5b3o$154bobo
  95bobo78bobo4b2o72bob2obo5b3o$67bo2bo83bobo5b2o90bo3bo74bo2bo2b2o2b2o
  73bobo4bo$66bo2b4o82bo6bo91bo4b2o76bob2o2bo75bo3b2o3b2o$66bo4b3o80bo6b
  2o92b2o2bo74bobo5bo76bo3bo4bo$66bobo2b2o2bo79bo6b2o94b3o2bo72b2ob3o77b
  o10bo$73bob3obo180b2obo73b2ob2o80bob2o3b2o$75b3o2bo83bo96bo3bo72bo81b
  3obo$79bo83bo2b2o95bo74bob2o80bo3bo3b2obo$74b3o87bob2o97bob2o70bo83bob
  2o6b2o$74b2obo90bo99bo72bobo80b2o2b3o2bo$78bo87bobo101bo74b3o77bo7bo$
  77bobo86bo95b3o6bo71bo2bo88bo$80b2o85bobo92bo2b2o4bo73bo3b3o83b2o$169b
  o93bo2bo83b2o86b2o$265bo2bo81b2ob2o81bob2o$266b2o85bobo80bo3bo$351bob
  3o81bo3bo$355b2o84bo82$162b2ob2o42bobobo3bobobo11bo$162bob3o65b2o$162b
  o2b2o3b2o37bo7bo3bo10bobo$88bobobo3bobobo8b3o32bobobo3bobobo12b2obob2o
  $26bo3bo3bobobo11bo58bo56bo5bob2o33bobobo3bobobo13b2o$49b2o37bo11bo9bo
  33bo7bo13bo5bo3bo58b2o$26bo3bo7bo10bobo57b3o62bo38bo3bo3bo$51bo36bobob
  o3bobobo8b3ob2o29bobobo3bobobo19bobo52bob2o$26bobobo3bobobo13bo125bo
  30bobobo3bobobo8b4o$49bob2o39bo7bo47bo3bo3bo21bobo49bo3b2o$30bo7bo11bo
  61bo122bo2bo$88bobobo3bobobo10b2o5bo25bobobo3bobobo23bobo$30bo3bobobo
  12b2o58bo4bo2bo114b2o3bo$51b2o59bob3o3bo60bobo50b2o4bobo$51bobo2b2o62b
  2o59b2o52bo4bo2bo$56b2ob2o52bo2b2o2bobo58bo53bo11bo$53b3o3bobo174b2o2b
  3o3b2o$114bo3b5o56bo2bo59bo3bobo$55bo2bo54b2obobobo50b2o5b2o2bo57bobo$
  55b3o55bo5bo50b2o5bo62bobo3bo2bo$55b2o55b2o5b2o51bo4bobo60bobo5b2o$56b
  2o54bo6b2o53b2o2bo62b2o8bo$53b2ob2o55bo60b2o65bo9bo$53bo$54bo25$445bob
  obo3bobobo15bo$243bobobo3bobobo17b2o28b2o24b3o24b3o30bobobo3bobobo16bo
  53b2o$272b2o28b2o25bo26bo60b2o30bo3bo3bo8bo5bobo$172bobobo3bobobo15b2o
  41bo7bo3bo18bo29bo25bo26bo31bo7bo3bo15bobo45b2o$135b3o61b2o75b2o28b2o
  24b2o25b2o87bo4bo3bo7bobo3b2obobo$26bobobo3bobobo12b2o82bo36bo7bo20bo
  41bobobo3bobobo13bo5bo23bo5bo25b2o25b2o29bobobo3bobobo18b2o47bo7b2o$
  50b2o33bobobo3bobobo12b2o26bo64b2o63b2o28b2o120b2o25bo5bo3bo10bo4bo5b
  2o$26bo11bo13bo56b2o24bo2bo33bobobo3bobobo17bo40bo3bo3bo3bo12bobo2bo3b
  o20bobo2bo3bo22bo26bo31bo3bo7bo66bo2bo2b6o$54b2o29bo7bo17bo24bo2bo132b
  2o28b2o18b3o5bo2bo15b3o5bo2bo50bo6b2o27bo5bobobo$26bobobo3bobobo14bo
  59b2o22bo34bo3bo3bo3bo16bo2bo38bobobo3bobobo15b2o2bo25b2o2bo16bo7bo18b
  o7bo31bobobo3bobobo8b2o5bo2bo$85bobobo3bobobo14bo26bobo51b2o5b2o66bo
  29bo24bo2b5obo17bo2b5obo50bobo3b2obo61b3o$26bo3bo7bo13bo2bo85b2o29bobo
  bo3bobobo7b2o5bo67b2o3b2o23b2o3b2o21bo26bo61bo66bo2b2o$49b2obo32bo3bo
  7bo17bo26bo51bo4bobo65bobo27bobo26b2o25b2o58bo66b2ob2o$26bobobo3bobobo
  9b2o4bo59bobo24b2o53b2o2bo67b2o28b2o59b3o51bo2bo2bo55b2o$50bobo2bo5bo
  23bobobo3bobobo7b2o3b3ob3o23b3o53b2o132b3o26bo2b2o55bo54b2o4bobo$55bo
  4b2o43bobo2bo2bob2o18b2ob2ob2o124b3o27b3o30bo2b2o23b2ob2o55bo2b2o53bo
  2bob2o$52bo2bo4bobo42bo5bo3bo19bo3bob2o120b2o3bo24b2o3bo30b2ob2o19b2o
  63bob2obo54b2o$53bobo52bo5b2obo2bo14bob3o2bo56b3o61bo3bo25bo3bo26b2o
  26b2o4bobo51b2o4b2o58b2o4bo$53bobo4b2o46bo2b2o4b3obo18b2o57bo2b2o59bo
  4bo24bo4bo2b3o19b2o4bobo22bo2bob2o51bobo2b3o59bo4bo$54b2o4bo47bo3bo3bo
  2bobo17b3o56b2ob2o62bobo27bobo5b2o20bo2bob2o24b2o54bo3bo67b2o$54bo9b2o
  127b2o71bo3bo25bo9b2o19b2o27b2o4bo52b2o3bo64bo$61b2ob4o54b2o19b3o46b2o
  4bobo64bo4b3o22bo10b3o18b2o4bo23bo4bo52bo4bo$60bo7bo53b2o14b3o4b2o47bo
  2bob2o63bobo4b2o21bobo12bo18bo4bo28b2o58bo63b2ob3o$61bo6bo69b3o7b2o46b
  2o66bobo6b2obo17bobo9bo2bo23b2o28bo52b2o4bo63b2o$113bo6b2o26b3o45b2o4b
  o60bo10bobo16bo12bo27bo86bo65bo3bo$64b2o46b2o5bo2bo14b2o12bo45bo4bo60b
  2o9bo2bo15b2o11bobo55b2ob3o53bo64b2o$62bo49bobo3b2obo15bo10bo2bo50b2o
  59b2o28b2o40b2ob3o23b2o58bob2o$61b3o52bo31bo54bo69b2o60b2o28bo3bo54b2o
  b2o$61bo2b2o49bo32bobo124bo60bo3bo25b2o56bob3o$64bobo48bo2bo85b2ob3o
  127b2o86b2o$204b2o$65b3o137bo3bo$206b2o17$151bobobo3bobobo17b2o$180b2o
  $28bobobo3bo16b2o31bobobo3bobobo12b2o42bo7bo18bo$52b2o56b2o72b2o$32bo
  3bo17bo35bo7bo13bo41bo4bobobo19bo$56b2o56b2o$31bo4bo18bo33bo4bobobo14b
  o39bo9bo22bo$185bobo$30bo5bo21bo29bo5bo21bo36bo5bobobo12b2o3b3ob3o$57b
  obo55bobo58bobo2bo2bob2o$30bo5bo11b2o3b3ob3o28bo5bobobo7b2o3b3ob3o58bo
  5bo3bo$48bobo2bo2bob2o46bobo2bo2bob2o61bo5b2obo2bo$48bo5bo3bo47bo5bo3b
  o62bo2b2o4b3obo$51bo5b2obo2bo45bo5b2obo2bo57bo3bo3bo2bobo$51bo2b2o4b3o
  bo44bo2b2o4b3obo$51bo3bo3bo2bobo44bo3bo3bo2bobo70b2o$130bo62b2o$65b2o
  56b2o3bobobo55b2o$65b2o57b2ob3o2bo55bo2b2o$124b2o4b2o51bo4bo3bo$61bob
  2o60bob2o53b2o5b2obo$60b4o118bobo3bo3b2o$60bo3b2o57bobo60bo$65bo2bo54b
  o61bo4bo2bo$123b3o59bo2bo$64b2o3bo54bobo$64b2o3bo$65bo$65bo$66b2o21$
  384b2o62b3o29b3o36bobobo3bobobo15b2o$150b2o165b3o32bobobo3bobobo18b2ob
  o6b2o29bobobo3bobobo11bo9b2o20bo9b2o54b2o$52b2o2bo34bobobo3bobobo15b2o
  28b2obo60b2o43b2o34bobobo3bobobo10bo66bo7b2o55bo6b3obo20bo6b3obo26bo3b
  o3bo3bo8b2o5bo$51b2o4bo60b2o30bo36bobobo3bobobo13bobo21bobobo3bobobo7b
  2o59bo33bo3bo3bo23bo2bo6bo29bo3bo7bo14b2o2b2o26b2o2b2o50b2o5b2o$53b2ob
  o2b3o29bo3bo7bo8b2o5bo30bo2bo59bo45bo34bo3bo3bo3bo13b2o62bo3bo63bo31bo
  34bobobo3bobobo9bo4bobo2b2o$55b2o2b2obob2o45b2o5b2o30bo3bo32bo3bo3bo
  20bo20bo3bo7bo11b2o56b2o31bobobo3bobobo19bo2bo4b4obo26bobobo7bo19bo31b
  o54b2o3b2ob4o$30bobobo3bobobo19bobobo24bobobo3bobobo9bo4bobo2b2o25bo2b
  o62b2o42bo33bobobo3bobobo82bob2o2bo2bo53b2o3bo26b2o3bo33bo3bo3bo11b2o
  10bo$64bo50b2o3b2ob4o60bobobo3bobobo16b2o19bobobo7bo68bo37bo7bo20b3o4b
  o4bo30bo7bo14bobob2o26bobob2o66bo$30bo3bo7bo22bobo23bo3bo7bo11b2o10bo
  87b2o42bo2bo31bo3bo3bo3bo3b3o5bo2bo64b3ob2obo57bobo2bob2o23bobo2bob2o
  27bobobo3bobobo17bo$67bo59bo23b3o33bo3bo3bo3bo6b2o6b2o21bo3bo7bo6b2obo
  50bo7bo33bobobo3bobobo21b2o2bo3b2o28bobobo7bo13bo4b2o25bo4b2o62bo$30bo
  bobo3bobobo25bo22bobobo3bobobo17bo29bo5b3o46bobo3b2o2bo38b2o4bo32bobob
  o3bobobo4bo2b5obo67bo61b2o30b2o68b2obob3o$69bo53bo28bobob4o27bobobo3bo
  bobo6bo5b3o22bobobo7bo7bobo2bo50bo136b2o30b2o71bo4b2o$30bo3bo3bo30bobo
  52b2obob3o21b2o5bo48bo52bo51b2o71b2o103bo59bo2b6o$127bo4b2o20b5o2b2o4b
  o41b2o48bo2bo58bo65b3o4bo59bo33b2ob4o58bo$30bobobo3bobobo28b2o51bo2b6o
  22bo5b2o3b2o92bobo54b2ob4o65b2o2bobo54b2ob4o30b2o2b2obo$71bo53bo29b7o
  4bobo43bobo45bobo53b2o2b2obo69bobo53b2o2b2obo30bobob3o$70b2o82bobobo
  52bo3b2o44b2o53bobob3o70b2o54bobob3o30bo2bo65b2obo$71b2o80b2o14b2o40bo
  3bob2o42bo53bo2bo74bo54bo2bo38bo3bo59b2o$127b2obo22bobo3b2o7b4o38bo4bo
  103bo3bo68bo2bo6b2o48bo3bo29bo2bo4bo61bo2bo$68b2o56b2o24bo6bo5bobo42b
  3obo47bobo50bo2bo4bo76b3obo43bo2bo4bo28bo72b2o$60b3o5b2o58bo2bo21b2o8b
  3o2bo41b2o5b2o42bo3b2o47bo78bobo3b2o46bo37bo2b2o71bo$60bo6bobo60b2o31b
  o3b2o42b2o3bo44bo3bob2o45bo2b2o76b2o50bo2b2o33bobo2b2o8b2o59bo$61bo4b
  2o65bo29bobo43b2o49bo4bo48bobo2b2o8b2o65bo3bo46bobo2b2o8b2o36bobo54b2o
  $63b4obo64bo30b2o42b5o47b3obo64bobo130bobo23bo3bobo5bo55bo2bo$64b2o63b
  2o33bo43bo4bo10bo35b2o5b2o48bo3bobo5bo68bo51bo3bobo5bo26bobob2o3b2o55b
  o3bo$68bo59bo2bo80b2obo7b2o36b2o3bo51bobob2o3b2o67b2o53bobob2o3b2o27b
  2o4b2obo55bo2bo$67bobo57bo3bo80b2obo7bobo33b2o57b2o4b2obo68bo54b2o4b2o
  bo29b5o52b2o5bo$67bo58bo2bo82bo3b3obo37b5o56b5o73bo54b5o35b3o51b2o6bob
  o$68bobo55bo86bo7b2o35bo4bo10bo46b3o74bo55b3o35b2o54bo2bo3bo$119b2o7bo
  83bo5bo43b2obo7b2o46b2o131b2o94b3o$70bobo45b2o6bobo85b4o3b2o39b2obo7bo
  bo122b2ob2o147b2o$70bobo47bo2b2o137bo3b3obo129b2obo138b2o5b2o$71bo50b
  2o2b2o135bo7b2o127b2obo137b2o6b2o$70bo51b2o138bo5bo274bo2b2ob2o$70b2o
  192b4o3b2o128bobo141b2o$68b4o331bo141b2o$67b2o334bo$67bobo2$69bo$68b2o
  5$309bo$308b2o$308bobo2$311b2o$311b2o2$302bo6b2o3bo$301b2o5bo2bobobo$
  301bobo3b2obo3bobo$305bo9bobo$188bo3bobobo3bobobo14b2o83bo11bobo$110bo
  3bobobo3bobobo8b2ob2o79bobo82bo2bo9bobo$135bob3o48bo7bo3bo3bo14bo98bob
  o$75b2o33bo3bo3bo3bo12bo2b2o3b2o77bo96b2o2b2o$32bo3bobobo3bobobo25b2ob
  o64b2obo42bo3bobobo3bo3bo17b2o2b2o95bobo$75bo34bo3bo3bo3bobobo12bo7bo
  5bo72bobo94bo$32bo3bo3bo3bo3bo26bo2bo60bo5bo2bo3b2o34bo3bo7bo3bo21bo
  96bo$75bo3bo30bo3bo3bo7bo18bo6bobo71bo$32bo3bo3bo3bo3bo26bo2bo68bob4o
  35bo3bobobo3bobobo117bo2b2o$110bo3bobobo3bobobo17b2obobo3bo71bo2b2o91b
  2obobobo$32bo3bo3bo3bo3bo95b2o3bo74b2obobobo90b2o4b2o$76b3o66bo79b2o4b
  2o89b2o3b3o$32bo3bobobo3bobobo27bo68bo79b2o3b3o88bo2bob3o$77b2o67b2o
  76bo2bob3o89bobo$78b2o144bobo92bobo4b2o$78bobo68b2o71bobo4b2o87b5o$78b
  obo64b4o3bo68b5o92bo3bo$78bo66bo6bo68bo3bo96b3o$81b2o61b2obobobo73b3o
  101b2o$59b2o2bo82b2ob3o80b2o90b4obo$58b2o4bo17bobo62b2o78b4obo91b2obo$
  60b2obo2b3o158b2obo93b2o2bo$62b2o2b2obob2o10bo59b2ob2o79b2o2bo92b2o4bo
  $69bobobo6b4o2b3o53b2o2b3o78b2o4bo92bobo2bo$71bo7b2o6b2o55bob3o9b2o69b
  obo2bo94bo2bob3o$72bobo6b4o64bo7b2o73bo2bob3o92bo$74bo3b3ob2obo64bobo
  5b2o75bo92bo3b4o$75bobo2bo4bo60b2ob4o2b3o73bo3b4o88b5o4bo$76bob2o5bo
  61bo5bob3o72b5o4bo87bo3b2o4bo$78b6obo61b2o81bo3b2o4bo87bo9bo$79bo2bo
  148bo9bo96bobo$79bo2bob2o64bobo88bobo92bo3bo$78bo160bo3bo91bo6bo$79bo
  158bo6bo88b2o2bo3bo$237b2o2bo3bo88bo2bo5bo$237bo2bo5bo86b2o5bobo$236b
  2o5bobo87bo5b2o$236bo5b2o90bo4bobo$237bo4bobo$341bo$244bo95b2o$243b2o
  12$73bo$72b2o$72bobo39bo3bobobo3bobobo9bo$74bo64b2o$32bo3bobobo3bobobo
  26bo38bo7bo7bo8bobo43bo3bobobo3bobobo29b2o$72bobob2o65bo86b2o37bo3bobo
  bo3bobobo24bob2o84bo$32bo7bo3bo28bob4o35bo3bobobo7bo11bo3b3o36bo7bo3bo
  3bo22b2o5bo76b3ob2obo39bo3bobobo3bobobo22bobobo$142bo3b3o74b2o5b2o37bo
  7bo3bo3bo22bo3bo2bo76b2obo3bo$32bo3bobobo3bobobo26bo38bo3bo11bo54bo3bo
  bobo3bobobo23bo4bobo2b2o71bo4b2o40bo7bo7bo20bo2b3obo42bo3bobobo3bo3bo
  9bo$74bo2bo67bo81b2o3b2ob4o30bo3bobobo3bo3bo19b2obo2bo2bobo77bobo70b2o
  $32bo3bo11bo21b3o4bo36bo3bobobo7bo14bobo37bo3bo11bo25b2o10bo65bo12bo
  36bo3bobobo3bobobo17b4obo2bo2b2o40bo7bo3bo3bo8bobo$70bo2bo165bo29bo7bo
  3bo3bo18bo2b3o2bo2bo2bo70bo4b2o4b2obo67bo$32bo3bobobo3bobobo22bobobo
  69bobo37bo3bobobo3bobobo16b2o13bo71b2o2bobo3bo3bo35bo7bo3bo20b2o13bo
  38bo3bobobo3bobobo11bo3b3o$74bo69b3o70b2o16bo33bo3bobobo3bobobo18bob2o
  10b4o70bo2bo4bob3o65bo3b3o$71bo68b2ob2o74bo16b2obob3o62bobo5b2obo2b2o
  33bo3bobobo3bobobo16b3o3bo4bobo40bo7bo7bo$66b2o3b4o65bob2o3b2o2bo69b2o
  16bo4b2o57b2o8bobo4bo67b2obo6b2obo2bobo66bo$65b2o4bo68bo5bob2obo68bo
  15bo2b6o60b2o5b3obo5b2o67b2o4bobo42bo3bobobo7bo14bobo$67bo2bo4bo70bob
  2ob2o84bo70b2obo3b2obo14b2o54b2o3b2ob2obobo3b2o$70b2o3bo66bo8b3o65bo2b
  o85b2o2b2o9bobo6b2o3bo54bo6b2obo5bo64bobo$69bo72b2o72b2obo91bo3b3o14bo
  bob2o59bo4bo6bo62b3o$61b2o7bo3bo67b2o6b2o2bo60b2o4bo17b2obo66b3o13bob
  2ob3o60b2obo3bo7bo59b2ob2o$60b2o7bo78b3o66bobo2bo15b2o71bobo15bob2o62b
  2o10bob2o2bo54bob2o3b2o2bo$62bo7bo2bo74bo8bo64bo17bo2bo83b2o67b3o6bobo
  b4obo53bo5bob2obo$65b2o4bo2b3o71bob2o3b2o2bo59bo2bo19b2o69bobo80b2o6b
  2ob2obo63bob2ob2o$62bobo3bo5b3o75bo2b2o3bo59bobo3bo18bo69bo83bo4bobo3b
  o59bo8b3o$55b3o2bo7bo2b4o75bo2bo3bob2o59bobo3b2o17bo70bo82bobo2bob2o2b
  3o57b2o$47bo7bo2b3o3b4o3bobo79bo4b2ob3o57b2o2bo2bo12b2o74bo85b2ob2o2bo
  59b2o6b2o2bo$46b6o6b2o3bo6bobo76bo3bo2b3o3b2o57bo4bobo3b2o6bo2bo73bobo
  81bo4bo5bo63b3o$46bo6bo2bo4b2o85b6ob2obo67bo4b2o6bo3bo163b4obo63bo8bo$
  47bo8b2ob2obo5b2o78bo3bo2b2o75bo5bo2bo77b2o83bo71bob2o3b2o2bo$53b2o13b
  o80bo6b2o67b2o3bo2b2o3bo80bo84b2o74bo2b2o3bo$49b6o14bo86bo68b2o3bo2bob
  o2bobo77b2o84b2o72bo2bo3bob2o$51b2o103bobo67bo12bo79b2o160bo4b2ob3o$
  52bo105bo67bo7b3o240bo3bo2b3o3b2o$159b2o66b2o87b2o158b6ob2obo$159bo11b
  o143b2o159bo3bo2b2o$161b2o7b2o144b2o159bo6b2o$161bo3bo4bobo143b3o165bo
  $162bo4bo148bo167bobo$163bobo2b2o147b2o167bo$164bo322b2o$168b2o317bo$
  489b2o$489bo3bo$490bo4b2o$491bobo3b2o$492bo5b3o$495b3o$497bo$498bo3bo$
  497bo$498bo2bo$499bo5$278bo3bo3bo3bobobo17b2o205bo3bobobo3bobobo10b3o$
  145b2o49bo3bo3bo3bo15bo87bobo46bo3bo3bo3bobobo11b2o155bo$118bo3bobobo
  3bobobo9b2o77b2o53bo3bo3bo7bo17bo75b2o49bo3bo3bo3bobobo9b2o52bo3bo7bo
  3bo11bo$39bo3bobobo3bobobo14bob2o72bo49bo3bo3bo3bo14bobo89bo4bo40bo3bo
  3bo3bo16bo74bobo81b3o3bo$68b3ob2obo42bo7bo7bo13b2o3bo73bo50bo3bobobo3b
  obobo20b2o2bobo70b2o3bo41bo3bo3bo7bo9bo53bo3bobobo3bobobo14b5obo$39bo
  7bo3bo16bo3bo2bo72b2o2bobo41bo3bobobo3bo17bo3b3o86bobo39bo3bobobo3bobo
  bo14b2o2bobo69bo4bo78bo$68bo4b2o43bo3bobobo7bo16b2obo71bo3b3o45bo7bo3b
  o28b2o74b2obo40bo3bobobo7bo12b2o2bobo44bo7bo7bo16bo$39bo3bobobo3bobobo
  9b2obo2bo2bobo74b2o43bo7bo3bo110bo41bo7bo7bo17b2o75bobo78b2o$65bo12bo
  39bo7bo7bo16b2o76bo48bo7bo3bobobo24bo75b2o42bo7bo7bo16b2o45bo3bobobo3b
  obobo17b2o$39bo7bo7bo8bo2b3o2bo2bo2bo117bo7bo3bo20bobo129bo7bo3bobobo
  94bo79b2o$65b2o2bobo3bo3bo38bo3bobobo7bo16bo165b2o76bo43bo7bo7bo16bo
  79bo$39bo3bobobo3bobobo8bob2o10b4o68b2o77bobo84bo2bo74b2o152bo2bo3bo$
  66bobo5b2obo2b2o68bob2o74b3o82b2o4b2o73bob2o72b2o75b4o6b2o$63b2o8bobo
  4bo64b3o2b3o2bo68b2ob2o83b2ob3o2b4o65b3o2b3o2bo69bo2bo74bo5b2ob3o$65b
  2o5b3obo5b2o61bo2b2obo2b3o67bob2o3b2o2bo78bo4bo4bo64bo2b2obo2b3o65b2o
  4b2o74bo3bo3bo$68b2obo3b2obo67b4o74bo5bob2obo85b2o3bo63b4o71b2ob3o2b4o
  82b2o$68b2o2b2o9bobo62bo6bobo72bob2ob2o78b2o6b2obo65bo6bobo65bo4bo4bo
  71b2o6bob2o$71bo3b3o70bo7b2ob2o65bo8b3o76bo8bo2bo65bo7b2ob2o69b2o3bo
  69b2o7b4o$69b3o13bob2ob2o55bo7bo70b2o87b2o6b2o66bo7bo68b2o6b2obo76bo$
  71bobo15bo58bo9bo67b2o6b2o2bo82bob2o67bo9bo64bo8bo2bo75b2o3b2o$87b2o2b
  3o59b2o3bo73b3o85b2o2bo4bo67b2o3bo65b2o6b2o77bob2o4b3o$73bobo17b2o58b
  2o2b2o3bo69bo8bo80bobo3bobo66b2o2b2o3bo67bob2o79bo5b4o$75bo20b2o57bob
  2ob2ob2o67bob2o3b2o2bo78b2obob2ob2obo65bob2ob2ob2o64b2o2bo4bo74b2ob2o
  4b2o$76bo17bob2o57b2obo5bo71bo2b2o3bo80b3ob2o4bo63b2obo5bo66bobo3bobo
  74b2o9b2o$77bo16bo3bo65bo2b2o65bo2bo3bob2o80b3obo4bobo71bo2b2o62b2obob
  2ob2obo71bo5b2o3bo$77bobo15bo3bo57bo9bobo67bo4b2ob3o73b2obobob2o4bobo
  64bo9bobo64b3ob2o4bo66b3ob2o2b2o$99bo54b2obo3b3o69bo3bo2b3o3b2o73bob2o
  bo4bo66b2obo3b3o70b3obo4bobo65bo5bobo$79b2o72b2ob2o3bo70b6ob2obo78bo3b
  3o69b2ob2o3bo68b2obobob2o4bobo66b2obo12b2o$79bo75bob4o71bo3bo2b2o89bo
  68bob4o69bob2obo4bo77b2o7bo$78b2o79b2obo70bo6b2o86bobo72b2obo67bo3b3o
  81b4o4bo3bo$79b2o82bo76bo88bo77bo75bo82bo2bo2b2o$161bo2bo75bobo86b3o2b
  2o69bo2bo72bobo80b5o$81bo80b2o2b3o73bo90b2obob2o66b2o2b3o69bo82b2o3bo$
  80bo2b2o78bo2b2o75b2o91bob2o67bo2b2obob2o65b3o2b2o77bo10b3o$81bob2o83b
  obo5b2o65bo11bo80bo3bo72bobobo68b2obo6b2o68bob2ob2o4bo$85bo84bo5bobo
  66b2o7b2o82bo76bo75bo2b3obo68bo5bo4bo$83bobo84bob3o70bo3bo4bobo83bobo
  73bobo70bo3b2o73bo3bo2bo4b2o$83bo84b2o3b4o69bo4bo90bo75bo70bo80bob2o7b
  o$84bobo81b2o3bob2o70bobo2b2o88bobo74bo68b2obo2bo76bo$86bo85bo75bo171b
  o70bo78bo2b2obo$169b2o81b2o90bobo73bobo64bo5b2o78bob6o$169bo82b6o230bo
  4bob3o73b2o6b2o$170bo81b2obo89bobo74b2o65b3ob2ob2o$252b2o2bo88b2o75bo
  67bo2bo$256bo88bo75b2o68bobo$257bo164b2o$342b2o2bo$342bo81bo$342bo80bo
  2b2o$343bo80bob2o$343b2o83bo$343b2o81bobo$426bo$427bobo$429bo2$161b3o$
  161bo$162bo$164b2o$165bo$160bo$159b4o$159bo2b2o$161bo$160bo2bo$157bob
  6o$156b6ob2o$156bo2bo$158b2o$159bo2b2o$152b3obo4b2o$152bo4bobob2o$154b
  o4b2obo2bo$152bobo5bo4bo$148b3obo12bo$148bo4b2o5bobo4b3o$150bo11b2obo$
  148bobo14bo$144b3obo$144bo4b2o$146bo$144bobo$140b3obo$140bo4b2o$142bo$
  140bobo$136b3obo$136bo4b2o$138bo$136bobo$132b3obo$132bo4b2o$134bo$132b
  obo$128b3obo$128bo4b2o$130bo$128bobo$124b3obo$124bo4b2o$126bo$124bobo$
  120b3obo$120bo4b2o$122bo$120bobo$116b3obo$116bo4b2o$118bo$116bobo$112b
  3obo$112bo4b2o$114bo$112bobo$108b3obo$108bo4b2o$110bo$108bobo$104b3obo
  $104bo4b2o$106bo$104bobo$100b3obo$100bo4b2o$102bo$100bobo$96b3obo$96bo
  4b2o$98bo$96bobo$92b3obo$92bo4b2o$94bo$89bo$88b2o$88bob5o$84bo6bo4bo$
  83b4o3bo5bo$83bo2b2o10bo$77b3o5bo6b2ob2o2bo$77bo6bo2bo3b2o2b2o3bo$78bo
  4b6o4bobo$80b4obob2o6bo2bobo$81b2o12b2o3bo$96b3o$96bo$98bo$98bo85$27bo
  bobo3bobobo8bo23b3o26bobobo3bo3bo15bo17bobobo3bobobo16b3o9b2obo17bo31b
  obobo3bobobo7b3o24bobobo3bobobo15bo8b3o25bobobo3bobobo7b2o25bobobo3bob
  obo10b2o23bobobo3bo15bo23bobobo3bobobo8b2o26bobobo3bobobo17bo18bobobo
  3bobobo14bo29bo20b3o11b2o2bo28bo37bobobo3bobobo7b2ob2o$47b5o20bo2b3o
  50b2o46bo11bo3bo15b6o47bo2b3o48b2o8bo2b3o42bobo4bo41b2o47b2o43b2o3bo
  52b2o44b2o28b2o20bo12b2o4bo26b5o54bob3o$27bo11bo7bo2b2o21bobo25bo7bo3b
  o14bobo16bo7bo21bo10bo4bo14bo7b2o23bo11bo8bobo23bo7bo3bo14bobo8bobo24b
  o7bo3bo7bo5bo20bo7bo3bo11bo23bo7bo14bobo22bo11bo9bob2o23bo7bo20bobo17b
  o7bo3bo13bobo27bobo20bo13b2obo2b3o22bo2b2o34bo7bo3bo7bo2b2o3b2o$49b2ob
  o25bo100b2o9b2o17bo6bobo48bo63bo44bob2o2b2o42b2o45bo46b3o152b2o12b2o2b
  2obob2o20b2obo60b2obob2o$27bobobo3bobobo36bo6b2o16bobobo3bobobo17b2o
  14bobobo3bobobo20bo11bobo4bo11bobo2bob6o17bobobo7bo11bo6b2o14bobobo3bo
  bobo17b2o9bo6b2o15bobobo3bobobo9bob2o4bo16bobobo3bo3bo12bo22bobobo3bo
  17bo21bobobo3bobobo11bo6b2o16bobobo3bobobo19b2o15bobobo3bobobo16b2o28b
  2o21bo19bobobo56bobobo3bobobo11bo5bob2o$52bobo2b3o18bob2ob2o34b2o9b3o
  38b2o25b2o12bo6bo4bo42bob2ob2o44b2o11bob2ob2o37bo42b3o50bobob2o45b3obo
  2bo47b2o44b2o28b2o43bo24bobo2b3o50bo5bo3bo$31bo7bo16bo25b2o21bo7bo5bob
  o8bo20bo7bo10b2o3bo18b2ob2obo19bo4bo19bo7bo17b2o19bo3bo3bo12b2o20b2o
  20bo7bo9bo2bob2o18bo3bo3bo3bo5bo5bo2bo20bo3bo3bo15bob4o18bo3bo3bo18b2o
  20bo3bo7bo14b2o20bo3bo3bo3bo10b2obo50bobo25bobo25bo29bo3bo7bo19bo$54b
  2o3bo19bo2bo36bo51bobob5o15b3o23bo46bo2bo41bo2b2o14bo2bo39bo2bobo38bo
  2b2o94bo4b2ob2o44bo2b2o40bo3b2o21bo6b2o17b3ob2o25bo23b2o3bo60bobo$27bo
  bobo3bobobo15bo24b3o18bobobo7bo6b2o7b3obo13bobobo3bobobo11b2obo3b2o42b
  o2b2o14bobobo7bo15b3o16bobobo3bobobo12bo3bo15b3o17bobobo3bobobo15bo18b
  obobo3bobobo8bo3bo22bobobo3bo17bo21bobobo3bobobo8b2o6bo19bobobo3bobobo
  14bo3bo17bobobo3bobobo10bo5b2o18b2o5bo2bo18b2o28bo23bo30bobobo3bobobo
  23bo$54b2obo22bo39bo2bo5b2ob2o37b3o51bo43bo44b2obo15bo41b3o44bobo48bo
  2bo40bobo53b2obo42b2obobo18bobo3b2obo16b2o30bo2bo12b2o6b2obo64bobo$54b
  2o23bo40bo8bo3bobo58bo3b2o24b2obo40bo44bo3b2o13bo42bob2o38b3o4bo44b3o
  4bo44bob2o47bo3b2o69bo23bo26b2obo3bo11bobo5b2o$54bo3bo19bo43bobo10bo
  58b2o2b2o24bo42bo42b2o19bo47bo37bo4b2o45bo2bo47bo4bo37b3o3b2o44b2obo
  27bo22bobo25b2o18bo7bo69bobo$54bo2bobo20bo45bo7bo38bo20b2o2bo24bo3bo
  41bo34bo5bo7bo14bo44bo2bo36bo5bo45bobobo45bo4b2o36bo5bo7bo37bo3bo26bo
  2b2o18bobo27bobobo14b2o5bo$54bo25bo43bo2b3obo40b2o17bo3bo26b2obo43bo
  33b2o5bo22bo47bobo36b2o3bo47bo57b2o32bo3bo45bo4bo30bo17bo2b2o27b3o14bo
  2bo3bo70bobo$56bo2bob2o61bo2bo2b2o40bo17b2o3b3o23b3o79bobo6b3o69bo34b
  3o48bo54bobo3bobo26b4obo5b3o43b2o31bo22b2o25bo4bo12bo77b2o$62bo16b3o
  43b3o44bobo15bobo5bo22b2o45b3o61b3o45b2o33b2ob2o3b2o45b4o51bo5bo28bo
  58bobo28bobo18bo25b3obo18bobob2o3b3o64bo$64bo13bo4bo39b3o41b3o4bo19bo
  72bo4bo33b2o3bo19bo4bo43bo2bobo29bo4bo49bo55bobo3bobo26bo2bobo3bo101bo
  24bo5bobobo21bo$56b3o6bo12bo4bo39b2o42bo2b2o2bo19bo2bo23bo2bo42bo4bo
  34b2ob4o17bo4bo47b4ob2o24bob3o50bo3bo57b2obo30b2ob4o47bob2o28bobo11b3o
  5b2o22bo3bo19bo3bo5bo60b2o2bo$56bo2b2o4bo12bo5bob2o80bobo23bo25bo2bo
  43bo5bob2o30b2o4bo17bo5bob2o45b2o3bo27b3o47bo4bo53bo6bo30b2o4bo46b3o
  44bo4b2o2bo30bobo14b4o3bo2bo59bo$57bo2bo19b2o3b2obo84bo22bo23bo2bo45b
  2o3b2obo30bob2o21b2o3b2obo44bo4bo77bobo56b2o4bo32bob2o47bo2bo31bobo11b
  o2bo2bo32b2o22bo3bo53b2o3bo$59bo2bo23bobo108bo25bo51bobo61bobo48bo30bo
  49bo146bo34b2o15b3o33bo20b2o2b2o55bobo3bo$60b2o107bo2bo22b2o24b2o83bob
  o78b3o77b2o61bo34bobo46b2o2b2o33bo16b3o56bo58bo5b2o$86b2o80b2obo22b4o
  77b2o29bo32b2o47b2o30b2o45b2o62b2o32bo48bo56bo31b2o2bo19b3o53bo5bobo2b
  2o$86b2o80bo25bo80b2o29b3o30b2o79bo43bo4bo95b3o46bo3bo31b2o2bo12b2ob2o
  bo29bo25bo52b2o5bo$86bo80b2o106bo31bobo29bo77b3o43b2o4b3o94bobo47bob2o
  30bo15b2o2bo3bo28bo78bobo3bobo$167bo110b2o62b3o72bo45bobo151b2obo24b2o
  3bo17bo2b2o31bo81bo3bo$168bo109bobo62b2o73bo48bo4bo146bo25bobo3bo19bob
  o30b2o79bo$466bo4bo144b2ob2o24bo5b2o51b2o79bo3b2o$466bo2bo145b3ob2o19b
  o5bobo2b2o16b2o$639b2o5bo22bo$614b2o23bobo3bobo22bo$614bo28bo3bo$642bo
  $642bo3b2o26$obobo3bobobo7b2ob2o33bobobo3bo20bo19bo23b2o19b2o10bobobo
  3bobobo7b2ob2o31bobobo3bobobo9b2o37b2o33b2o20bobobo3bo3bo24bo14b2o52b
  2o17bobobo3bobobo11b2o33b2o23b2o2bo33bobobo3bobobo8bo34b2o2bo44b3o24b
  3o22bobobo3bobobo7b3o28b2o2bo38bobobo3bobobo8bo36bobobo3bobobo8b3o$20b
  ob3o61b2o18b2o22b2o19b2o31bob3o52b2obo35b2obo31b2o57b2o13b2obo51bobo
  39b2o33b2o23b2o4bo52b6o29b2o4bo43bo26bo44bo7b2o20b2o4bo57b2o57bo2b3o$
  4bo3bo3bo7bo2b2o3b2o32bo3bo19bobo17bobo23bo20bo14bo7bo7bo2b2o3b2o30bo
  7bo9bo38bo3b2o30bo24bo3bo3bo23bobo13bo53bo22bo3bo16bo27bo6bo24b2obo2b
  3o32bo3bo11bo7b2o27b2obo2b3o40bo26bo27bo7bo8bo6bobo21b2obo2b3o37bo3bo
  3bo7bobo39bo3bo3bo9bobo$27b2obob2o100b2o19b2o34b2obob2o44bo2bo35bo3b2o
  32b2o69bo2bo53bo35b2o5b2o23b2o8b2o23b2o2b2obob2o45bo6bobo28b2o2b2obob
  2o38b2o25b2o43b2o3bo25b2o2b2obob2o51bo62bo$4bo3bo3bo11bo5bob2o28bo3bo
  22b2o18b2o22bo20bo13bo3bobobo11bo5bob2o26bo3bobobo9bo3bo33bo37bo23bo3b
  obobo26b2o11bo3bo51bobo18bo3bobobo7bobo3bo25bobo6bo32bobobo27bo3bobobo
  10bobo2bob5o31bobobo38bo26bo24bo7bo11bo36bobobo32bo3bobobo10bo38bo3bob
  obo12bo$24bo5bo3bo54b2o18b2o36b3o38bo5bo3bo43bo2bo32b2o3bo92b3o11bo2bo
  52bobo34bo35bo39bo49bo6bo36bo35bo25bo50bo3b2o2b2o29bo50bob2o61bobo$4bo
  3bo3bo19bo29bo3bo65bo2bo11bo5bo2bo11bo3bo23bo27bo7bo45bo3bo30b3obo2bo
  21bo7bo25bo69bo20bo7bo12bo2bo26bo3bo3bo33bobo26bo3bo3bo19b2o35bobo31b
  4o22b5o27bo7bo11bo2b2o2b2o31b2o32bo3bo3bo8bo40bo7bo8b2o$34bobo47b2ob2o
  16bob2o20b2obo15bo2b2o45bobo78b2o32bo2bo129bo38b2obo29bo3b2o38bo57bo
  35bo31bo2b2o21bo2b2ob2o44bobo6bo138b2o7b2o$4bo3bobobo23bo25bo3bo15b2ob
  3obo14b4o20b2o4bo15bo3bo13bo3bobobo23bo23bo3bobobo10b3o35b2obo31bo2bo
  22bo7bo21b2obobo13b3o48bo3bo20bo3bobobo9bo4bo32b2o38bo25bo3bobobo22bob
  o34bo24b3o5bo25b2obobo24bo7bo11bo2bo37bobo30bo3bobobo9b2o38bo3bobobo9b
  o2b2obo$36bobo43bo2b2o2bo14bo3b2o20bobo2bo15bobo46bobo40bo70bo56bo5bo
  13bo49b3obo39bob2o3bo28b2ob2o36bo2bo92bo23bo6bo2bo75b3o38b2o47b2o58b2o
  2b4o$78bo5bo24bo2bo22bo17bo90b2o34b2o32b4o43b2o7bo3b2o16b2o37bo8b2o50b
  o2b2o2b3o24bo32b2obo3bo55bobo33bobo22bo4b6o19bo56bo33b3o2b2o47bo59b2o
  2b2obobo$37bobo37b6obo50bo15b2o49bobo40b2o29bo3bo3bo26b2o4bobo41bobo6b
  o22b2o35b2o7b2o51bo2b2o2bo23b3o2bo29b2o125b4obob2o18b5o53b2o7b2o23b3o
  52b2o62bo$38bo38bo6b2o21b3o3bo16b3ob2o10b2o5bo91bobo27b2o3b3o13b2o12b
  2obo47bo8b2o21bobo9b2o23bobo7bo60bo26bo31bobobo59bobo33b2o24b2o24bo2b
  2o51b2ob2o6bobo85bo3b2o52bobobo$33b2o4bo64b2o3bo18b2obo3bo9b2o4bo51bob
  o39bobo7b3o17bobob2o14b2o6b2o6bo52bo6bo21bobo9bobo26bo59b2ob2o28bo3bo
  30b3o96bo52b2obo50bo4bo5bo23b2o5b3o46b3o4b2o3bobo51bobo3bobobo$32b2o3b
  3o34b3o4bo3bo18bo2bobob2o15bo4bobobo9bo2bo53bo40bo9bo25bo14bobo3b2o5bo
  54b2o2bobo22bo11bo27bo2bo2bobo50b2o6b2o26bobobo4bo23bo4bo50b3o5bob2o
  31b3o26b3o76bob2o31bo6b3o46bo2bo3bobo2bo55b3obo2bo2bo$34bo3b2obo32bo3b
  2o24bobo22b2o3b3o12bobo47b2o4bo42b2o6bo22b2o15b3o5bo2b2o44b3o12bo27b2o
  10bo14b2o8bo3b4o51bo5bo29bob2o4b2o20b3obo54bo7bo3bo30bo2bo53bobo2b3o
  48bobo2b2o30bo49bo9bo61bo4bo$42b2o32bo4bo29bo23bo12b2obobo44b2o3b3o49b
  3o21bo16b2o8bo3bo42bo10b2o2bo2bo36b2o12b2o14b2o54b5o29b3o5bobo19bo5bob
  obo49bo7b3obo29b4o20b2o35bo52b2o2bobo3b2o29b2o45b2ob2ob2obo59b2o5b2o$
  35bo4bob2o37bo29bo37bo2bo47bo3b2obo41bobo3b3ob2o37bobo5b4o44bo8b3o31bo
  b2o2bo5bo14bo8b2o61bo3b2o29b2o26bo3bo56b2o4b2obobo23b2o4bobobo17b2o5bo
  4b3o21b2o3bo49b5o4b2o25b3ob2obo46bo4bo3bo57b2o3bobobo$35b2o38b2ob2o2bo
  26bo24bo13bo59b2o68b2o76b2o7bo35bobo5bo2bo13bo4bob2o61b3o32bobo5b2o26b
  obo51bo33bobo3b2o3b2o17bo2bob2o3bo24bo58b2o3b2o25b3o54b2o2bo60bobo3b2o
  $38bo3b2o30bo3bo30bobo21b2o13bobo50bo4bob2o41bobo27b2o17bobob2o51bo2b
  6o33b2o2bo2b2o4bo13b3o3bo63bob4o28b2ob2obo2b2o26b2o56bo2bo26bo5b2o4bob
  2o16b2o2bo6bo20b2obo56b2o3bo26bo3bo49bo73b2o$38bobo27b3o2b3ob3o29bobo
  24bo8bob2o52b2o55bob2o12b2o4b2o20b5o50bo2bo6bo35b3obo3bo15b3obo3bo60bo
  6b2o26bo4bo30bo54bo3bo2b5o24bo12bo15b2o2bo4bo2bo19b2o60bo2bo25b2o4bo
  49bo3bobo66bo$38bo3b2o24bo7b2o32b3o24bo6b4o56bo3b2o43bobob2ob2ob2o8b2o
  5bobo18bo5bo50bob2o5bo35b4o29b2o64bo29bo3b3o83b2o2bo2b2ob2o24bo2b2o5b
  2o23bo2bo3bo18bo3bo53bobo30bo2bobo56bo65bobo$42bo26bo2bo2bo32bo23b2o3b
  o6bo2bo56bobo46bo5bobo2bo10bo4bo19bo3bo52b2o46b2o20bobo102bo5b2o29bo
  56bo31bo10bo22bobo2b2o20bo2bobo53bo31bobob3o56bo64b2o$39bo4bo27bo34b3o
  21b2obo11bobob2o52bo3b2o44bo3bo18bob2o19bo56b2o46bo20b2obo71b2o3bo26bo
  4b2o29b3o52bob2o32b2o7b2o24bo23bo154bo62bo$40b2o3bo26bobo31b2o2bo19b2o
  bo13b2o59bo46bo3bobobo13b5o18bobo53bo48bobo19bo73b2o3bo27bo34b3obo50bo
  b2o33bo6bo24b3o25bo2bob2o87b2o57bobo61bo2bo$43b2o60b2o22b2o18bo55bo4bo
  52b2o92bobo65b2obo73bo31bo134b2o24bo31bo87bo121bo$104b2o24bo16b3o56b2o
  3bo50b2o92bo2bo46b2o3b2o15bo73bo68b3o155bo88bo57b2o60bo2bo$105bo15b3o
  21b2o2bo59b2o51bo2bo7b2ob3o79bo47b2obobo14b2o75b2o66bobo147b3o6bo86bo
  58bo62bo$96b3o22bo8bo14bo3bo113b2o8bo3bo130bo3bo159b3o146bo2b2o4bo86bo
  57b2o$96bo8bo16bo2b5o14b2o127bob2obo295bo147bo2bo150b2o$97bo2b5o19bo
  19bo579bo2bo$99bo25b2o18bo579b2o151bo$100b2o775bo2b2o$878bob2o$882bo$
  880bobo$880bo$881bobo$883bo4$99bobobo3bobobo14b2o49bo18bobobo3bo6b2o
  36b2o45bobobo3bobobo22b3o10b2ob2o37bobobo3bo3bo7b2o38bobobo3bobobo7b2o
  31bobobo3bobobo11b2o33bobobo3bobobo19bo20b2o31bo40bobobo3bobobo22b2o
  22bo9bo$125b2o49b2o33bobo4bo29b2obo79bo12bob3o57bobo57bobo4bo48b2o65b
  2o20bobo4bo24b6o70b2o22b2o8b2o$99bo3bo3bo3bo8bo6bo48bobo17bo3bo3bo6bo
  5bo31bo46bo3bo7bo16b2o5bo11bo2b2o3b2o32bo3bo3bo3bo7bo6b3o30bo3bo3bo11b
  o5bo26bo3bo3bo15bo34bo3bo3bo3bo18bobo19bo5bo25bo7b2o32bo3bo3bo3bo23bo
  21bobo7bobo$119b2o8b2o83bob2o2b2o27bo2bo71b2o8b2o15b2obob2o51bo3bo55bo
  b2o2b2o43b3obo4b2o68bo14bob2o2b2o22bo6bobo69b2o$99bobobo3bo3bo7bobo6bo
  50b2o15bobobo3bo8bob2o4bo27bo3bo42bobobo3bobobo17bo8bo12bo5bob2o28bobo
  bo3bobobo10b3obobo30bobobo3bobobo9bob2o4bo22bobobo3bobobo7b2o2b2o4bobo
  26bobobo3bobobo21b2o3bobobo11bob2o4bo24bobo2bob5o27bobobo3bobobo24bo
  23b2o8b2o$123bo55b2o32bo35bo2bo95bo5bo3bo53b2o4bo49bo52bo2b2o3bo63b2ob
  3o2bo11bo33bo6bo91b2o7b4o$99bo3bo3bo3bo10bo3bo3bo65bo3bo3bo8bo2bob2o
  76bo3bo3bo22b2o27bo29bo3bo7bo18b2o27bo3bo7bo9bo2bob2o24bo3bo3bo3bo13bo
  32bo3bo3bo3bo22b2o4b2o12bo2bob2o35b2o28bo3bo7bo19b3obo2bo27bobo$122bo
  3b2o42b2o5b2o34bo2bobo107b2obob4o23bobo47bo8bobo48bo2bobo51bo3b2o2b2o
  53b2o4bob2o15bo2bobo39bo58bo2bo16bo6b2o4b3o2bo$99bobobo3bobobo15b2o40b
  2o5bo2bo16bobobo3bo14bo30b3o43bobobo3bobobo15b5obo2b2o25bo25bobobo7bo
  10b3o34bobobo3bobobo15bo24bobobo3bobobo13bo2b2o2b2o24bobobo3bobobo17bo
  bo28bo4b3o31bobo24bobobo3bobobo22bo2bo12b2o5bo2bo3bo3b2o$125b2ob2o41bo
  3b2obo34b3o34bo70b2ob2obo32bobo48bo2b2o52b3o54bobo6bo53bo3bobo18b3o8bo
  93bo17bobo3b2obo4bobo$130bo42bo39bob2o34b2o67bo4bo87bo54bob2o53bo2bo
  54b2o4b2obo2bo17bob2o8bo34bobo55b4o18bo10b2o4b3o$127b3o2bo39bo44bo34b
  2o65bo4b2obo2bo25b2o4bobo107bo8bo45b3o53bo2b2o3b3o23bo6b3o33bobo51b3o
  4bobo15bo11bo7bo$132bo38b2o43bo2bo32bobo63bo2b2o4bobo26bobo56b2o54bo2b
  o5b2o47bo53bo3bo3bo24bo2bo4b3ob2o22b2ob2o4bo46b2o4bo2bo21bo2bo$131bo3b
  o35b2o46bobo30bobo7b3o53bo2bo5bo28bo6bobo45b3ob2o57bobo3bobo46b2o7b2o
  44b2obo31bobo30bob3o50b2o6bobo42b2o$132bobobo4bo29b2ob2o46bo29bo9bo62b
  obo29bobo3b2o46bo2bo2b2o3b3o52bo49b2ob2o6bobo42bo3b2o33bo29bo2b2o3bobo
  bob3o40bo8b2o39b3o$132bob2o4b2o26b2o48b2o35b2o6bo53b2obo36b3o3bo48bo4b
  2o2bo2b2o47b2o5bo46bo4bo5bo41b2o36b2o5bo33b2o3bo46bo4b3o28b3o6bo2b2o$
  132b3o5bobo10b2o12b2obo47bo2bobo9bo28b3o52b4o3bo96bo5b2o44bo2bob3ob2o
  43bob2o43bo5bo7bo29bo2bob4o2bo26bo5bob4o43b3o4bo28bo6b2obo2b2o$135b2o
  15b2o6b2o6bo53b4ob2o3b2o22bobo3b3ob2o50bo4b2o31bo2bobo59b2o4b3o47b6o
  49bobo2b2o34b2o5bo41b3ob2obo26bo6bo5b2o41b3obo31bo2b3o3bo3bo$135bobo5b
  2o8bobo3b2o5bo57b2o3bo2bobo81b3o4bobo31bob3o3b3o50b3o9bo55b2o45b2o2bob
  o3b2o28bobo6b3o42bo3bo34b4obo45bo32bo3b2o4b2o$134b2ob2obo2b2o8b3o5bo2b
  2o58bo4bo28bobo48b2o4bo42bobo3b4o49bo2bo6bo2bo48b2ob2ob2obo44b5o4b2o
  85bo35b2o39b3o3bobo36b2o4bo$135bo4bo12b2o8bo3bo60bo3b2o31bob2o39b2o5bo
  2bo44bo53bo9bo51bo3bobo52b2o3b2o31b2o3bo49bob2o31b2o38bo4b2obo40b3o$
  136bo3b3o12bobo5b4o58b3o4bo27bobob2ob2ob2o38bo4b2o49b2o49b2o8bobo49bo
  7bo50b2o3bo33b2ob4o50bo30b3o5bo35bo2bo$136bo5b2o82b2o8b2o22bo5bo2b2obo
  39b2o51bo52bo61bo2bo56bo2bo33b2o4bo52bo35b2o27b3obo3bo2b2o44bo$137bo4b
  2o13bobob2o70b2ob4o21bo3bo46b2o52b2o112bo2b2o2bo48bobo39bob2o46b3o6bo
  29bobo2bobo26bo2bo4bo$138bo20b5o68bo7bo21bo2b2o102b3o47b2ob3o63bo48bo
  90bo2b2o4bo30b2ob2o23b2o6bo$138bo3b2o14bo5bo68bo6bo23b3o5bo95bobo2bo
  45b2o64bo3bo86bobo50bo2bo35bo4bo21b2o5bo$142bobo12bo3bo109b2o95bo4bo
  46bo3bo64bo86bo54bo2bo62bo4b4o$142bo14bo78b2o28bobo2bobo147b2o62b2o89b
  3o53b2o65b2o4bobo$157bobo107b2ob2o96b2o2bo114bo89bobo119b2o$267bo4bo
  97bo14$72bobobo3bobobo7b2o33b2o30b2ob2o31bobobo3bo8b2o31bobobo3bobobo
  6b2o38bo39bobobo3bo3bo23bo33bobobo3bobobo24b3o13b3o36b2ob2o39bobobo3bo
  bobo8b2o2bo26b2o34bobobo3bobobo25b2o21bobobo3bobobo7b2obo34b2o2bo$92bo
  bo4bo27bobo4bo24bob3o47b2o51bobo4bo31b2o74b5o67bo15bo6bo31bob3o59b2o4b
  o24b2o73bobo40bo3bo32b2o4bo$72bo3bo3bo3bo7bo5bo28bo5bo25bo2b2o3b2o26bo
  3bo3bo8bobo30bo3bo7bo6bo5bo32bobo38bo3bo3bo3bo22bo2b2o30bo3bo3bo22b2o
  5bo15bo4b3o30bo2b2o3b2o34bo3bo3bo13b2obo2b3o21bobo33bo3bo7bo25bo22bo3b
  o3bo3bo7bo4bo33b2obo2b3o$95bob2o2b2o27bob2o2b2o28b2obob2o39b3o52bob2o
  2b2o26bobo77b2obo59b2o8b2o14b2o4b3o34b2obob2o54b2o2b2obob2o17b3o72bobo
  41b2o37b2o2b2obob2o$72bobobo3bo3bo9bob2o4bo26bob2o4bo25bo5bob2o22bobob
  o3bo8b2o31bobobo3bobobo8bob2o4bo25b3obo4b3o32bobobo3bobobo57bobobo3bob
  obo19bo8bo13b2o4bob2o31bo5bob2o30bobobo3bobobo18bobobo16b2o34bobobo7bo
  20b2o4b3o19bobobo3bobobo11bobo4bo36bobobo$94bo34bo33bo5bo3bo40bobo49bo
  33bo2b3o3bo74bobo2b3o84b2o32bo5bo3bo62bo20bobo63b2o7bo49b2o38bo$76bo3b
  o3bo9bo2bob2o28bo2bob2o35bo27bo3bo45bo7bo8bo2bob2o32b3obobo36bo7bo31bo
  29bo7bo20b2o20bob3ob2o41bo35bo3bo3bo21bobo55bo7bo20bobo2bo26bo3bo3bo
  13b2ob2obo38bobo$94bo2bobo29bo2bobo38bobo40bobob5o41bo2bobo36b2o4bo66b
  o4b2o3bo54b2obob4o14bo5b2o43bobo63bo19bobob5o56b2obobo3b2o44b3o43bo$
  72bobobo3bobobo15bo34bo4b3o32bo19bobobo3bo14b4o23bobobo3bobobo14bo40b
  2o29bobobo7bo23b2o5bo26bobobo3bobobo17b5obo2b2o17b2o48bo27bobobo3bobob
  o13b3o8bo20b4o26bobobo7bo18bob2ob2o4b2o17bobobo3bobobo50b3o8bo$94b3o
  32b3o8bo34bobo39bo7bo2b2o36b3o35bo8bobo64bobo3b2obo51b2ob2obo21b2o42bo
  7bo54bo2b2obo4bo2bo16bo7bo2b2o47b3o92bo2b2obo4bo2bo$94bob2o31bob2o8bo
  25b2o2bo44bo3bo2bo4bobo35bob2o35b3o78b2o52bo4bo28bo37b2o7bobo53bo2bo2b
  o2bo19bo3bo2bo4bobo46bo6bo2bo47bo2bo34bo2bo2bo2bo$98bo8bo25bo6b3o23b2o
  4bo2bo2b2o36bo5bo5bo41bo36bo2b2o71b2o2bo51bo4b2obo2bo20b2obo37bobo2b3o
  3bo55b2obo4bo18bo5bo5bo48bo4bo52b2o3bo34b2obo4bo$97bo2bo5b2o24bo2bo4b
  3ob2o22b2obo2b2o2b3o35bobo4bobo3bobo37bo2bo36bo72bobo3bo49bo2b2o4bobo
  26bo39b5o6b2o54bob2o3bo15bobo4bobo3bobo40b2obobo2bob3o50b3o2bo5b2o31bo
  b2o3bo$100bobo3bobo26bobo32b2o2b2o3b2o48b2obo39bobo107bobo53bo2bo5bo
  27bob2o36bo3bo2b2ob3obo58bo30b2obo38b2o8b2o54bo2bobo3bobo35bo$103bo34b
  o36b2obo2bo43bo6bo42bo9bo25b2o68bo2bo60bobo27bob2o37bo5b2obo89bo6bo39b
  obob3o63b3o3bo$99b2o5bo27b2o5bo33bo3bo2bo42b2o4bo39b2o11b2o21b3ob2o66b
  o3bo48bo4b2obo33bo50bo56b3o30b2o4bo37b3o3bo2b2o63b4o31b3o9bo$99bo2bob
  3ob2o24bo2bob4o2bo30bobo92bo2bobo7bobo20bo2bo2b2o3b3o43bo13b3o50b2o4b
  4o2bo31b2o2b2o43bo5bo51bo2b3o71bo2bo70bobob2o29bo2b3o5b2o$103b6o29b3ob
  2obo31bo2bo37b2o2bo4bo47b4ob2o26bo4b2o2bo2b2o41b2o6bo6bo52bobo2b2o44b
  3obo34b2o6b2o52bobo22b2o2bo4bo41bobo68b2obo2bo3bo28bobo7bobo$112b2o29b
  o5b3o27bo2bo34b2o4bo4b2o47b2o3bo3b2o29bo5b2o38bobo4b2o7bo55b4ob4o37bob
  o3bo34b2o5bobo56bo18b2o4bo4b2o44b2o63b2o2bo2bo3b3o31bo$105b2ob2ob2obo
  29b2o3bo27b2ob2o37b2obo2b3o3b2o44bo4bo2b3o29b2o4b3o44bobo2b3o57bobo43b
  o3bo100bo22b2obo2b3o3b2o37bobo2b2o64bo6bob3o29bo2bo3bobo$105bo3bobo33b
  o6bo23bo6b2o36b2o2bo4bo50bo4b2o26b3o9bo38b3o6b4o58bo4bo45bo36b3ob2obob
  o54bobo20b2o2bo4bo38b2ob5o71bo35b2o2b3o3b2o$105bo7bo32bo3bo2bo30bob2o
  38bo4bo46b3o4bo27bo2bo6bo2bo37b3o6bo63bo2bo40b2o3bo37b2o8b2o51bo2bo25b
  o4bo31b2o3bob2o2bo113bo5bobo$106bo2bo37bo2bo3bo23b2o8bo43bo46b2o8bo23b
  o9bo42bobo8bo51b2o5bo50b3o35bo4bo5b2o48b2obo32bo30bobob2o75b2o39bobo2b
  3o$106bo2b2o2bo32bobo2b2o25bo6b2o41bo3bo51b3o2b2o22b2o8bobo42b3o2bo3bo
  51bobo4bo46b2obob2o35bo5b6o48b3o30bo3bo30bo4bob2o72bobo3b4o32b3o2b4o$
  114bo3b2o29bo29bo6bo40b4ob2o49bo6b4o20bo53b3o58bo6b2o48bo2bo4b3o29b2o
  57bo31b4ob2o32b2o76bo3bo5bo32b2o4b2o$111bo3bo2bobo26b3o36b2o39bo4bo50b
  o5bo3bo77bob3o56bo3b2o48bob2o4bo2b3o81b3o33bo4bo34bo79b2o6b2o30bo3bo$
  115bo2bo30bo35bo43bo2bo50bo4b2o2bo22b2ob3o47bobo61b2o53bob3o6b2o81bo2b
  o3bo30bo2bo34bo79bo40b2o$111b2o73b2o40bo3bo52bo8bo20b2o50bo2bo121bo89b
  o2bobo30bo3bo118b2o4b2o$113bo114bo3bo61bo21bo3bo46bo125bobo88b2obo30bo
  3bo2b2o114b2obo3b2o$231bo85b2o49bo124bobo125bo3bobo116bobo$494bo89b2o
  39bo120bob2o$583bob2o$582b2o2bo$582bobo$581bo$582b2o10$234bo3bobobo3bo
  bobo4b2o37bo3bobobo3bo3bo15bo36bo3bobobo3bobobo26bo15bo4b3o30bo59bo3bo
  bobo3bobobo6b2o42bo3bobobo3bo25b3o$254b2o3bo65b2o78b2o14b2o4bo31b2o81b
  2o81bo$234bo3bo3bo3bo3bo5bob2o34bo3bo3bo3bo3bo8bo5bobo35bo3bo3bo3bo29b
  obo2bo10bobo4bo30bobo58bo3bo3bo3bo3bo6bobo41bo7bo3bo26bo$258b3o57b2o
  86bo2bobo18b2o29bo81b3o82b2o$234bo3bo3bo3bo3bo7bo6b2o27bo3bo3bo3bobobo
  7bobo3b2obobo33bo3bo3bo3bobobo24bobo2bobo11b3o3b2o31bo57bo3bo3bo3bobob
  o6b2o42bo3bobobo3bo29bo$260b3obo2bo54bo7b2o71bo2bo15b3o34bob2o82bobo
  76bo$234bo3bo3bo3bo3bo10b2o31bo3bo3bo7bo10bo4bo5b2o29bo3bo3bo7bo23bo
  20bobobo31bo59bo3bo3bo3bo3bo50bo3bo7bo23b4o$261b2ob2o2bo52bo2bo2b6o70b
  ob2o19b2o3bo115bobob5o67bo2b2o$234bo3bobobo3bobobo12bo4bobo23bo3bobobo
  7bo52bo3bobobo3bobobo17b3o7bo18b3ob2o29b2o57bo3bobobo3bobobo12b4o34bo
  3bobobo3bo25bo$267bo2bo126bo10bo19bobo2b2o26b2o85bo7bo2b2o63bo2bo$261b
  2o9bo50b2o73bo6bo2bo21bo30bo85bo3bo2bo4bobo59bob6o$260bo4b3o3b2o50bobo
  2b2obob3o65b2o2b4o21bo3bo27b2o83bo5bo5bo54b3o3b6ob2o$261bobob2o5b3o48b
  o3bo2b3o67b3o2bo2bo26bo34bo3b2o71bobo4bobo3bobo51bo5bo2bo$263bo3bob2o
  4bo50b2o3bo64b3obo2bo2bo24b2obobo25b3o4b2o3bobo83b2obo52bo5b2o$274bo
  51bo5b2obo59bo2bo3b3ob2o54bo2bo3bobo2bo81bo6bo47b4obo6bo2b2o$271bob2ob
  o55b4o58bo4bo2bobobo27bo2bo25bo9bo82b2o4bo48bo2bo3bobo4b2o$266b2o3bo3b
  o118bo3b2o7bo29bo6bo20b2ob2ob2obo137bo5bo2bobob2o$266bobo68b3o49bo6bo
  37b2obo5b2o22bo4bo3bo72b2o2bo4bo54bo2bo6b2obo2bo$266bo3bo6bo59bo50b2o
  3b2obo2bo38bo4bobo25b2o2bo72b2o4bo4b2o42bo10bobobo5bo4bo$269b2o3bo2bo
  55b3o52bobobo5bo36b5o7bo20bo81b2obo2b3o3b2o38b2o11b2obo10bo$270bo3b2o
  58bobob2obo47bo2b4o39b2ob2o7bo21bo3bobo76b2o2bo4bo40bobo8bo3bo6bobo4b
  3o$270bo2b2o65bo50bobo3bo37b3o9bo27bo81bo4bo49bo13b2obo$270b2o2bo2b3o
  55bob2o49b3obo2bo40bo6b2o31bo86bo41b2o3bobobo14bo$272bo2bo60bo2b2o41b
  3o3bob2o4bo41bo3b2o2b3o26bo2bo83bo43b2ob3o2bo$270b3o5bobo58b2o3bo37bo
  5bobo46bobo3bo2b3o23b2obo3bo74b3o8b2o39b2o4b2o$272bo7bo2bo54b2obob3o2b
  o34bo2b2ob2o47b2o2bobo2bo23b2o81bo10bobo39bob2o$280b2ob3o53b3obobob2o
  36bo56bo3bo26bobobo77bo2b6o$282bo57bo2bo3b3o38bo52bo4b2o27b3o79bo47bob
  o$281bo64bob2o36b2o54bo31bo4bo78b2o4bo40bo$281bo64bo4bo91bo2b3o22b3obo
  86b2obo39b3o$347bo3bo119bo5bob2o81bo2b5o36bobo$348bo97b3o23bo3bo4bo80b
  2o2bo$446bo35b2o83b2o$447bo39bo$483bob4o$485bo2bo2bo$490bobo2$491b2ob
  2o$491b2o3bo$493b2o$496b2o53$11bo3bo3bobobo20b3o$44bo$11bo3bo3bo3bo21b
  o$47b2o$11bobobo3bobobo22b2o$39b3o$15bo3bo3bo15bo5bo$40bo4bo$15bo3bobo
  bo12b2o4bo2bo$36bobo2b3o2bobo$36bo$39bo$39bo3bo$39bo$41bo$31b3o$31bo9b
  o$32bo2b6o$34bo$35b2o14$263bo$191bobobo3bobobo16b3o11bobobo3bobobo15b
  2o92bobobo3bobobo19b3o$19bobobo3bobobo15b3o24bobobo3bobobo19b3o20bobob
  o3bobobo20b3o55bo41bobo35bobobo3bobobo20b3o52bo$47bo58bo55bo28bo7bo21b
  o12bo7bo90bo22bo11bo20bo$19bo11bo16bo25bo11bo20bo21bo11bo21bo59b2o40b
  2o33bo11bo21bo60bo$50b2o113b2o24bobobo3bobobo18b2o10bobobo3bobobo18b2o
  69b2o18bobobo7bo19b3o3b2o$19bobobo3bobobo17b2o23bobobo3bobobo19b3o20bo
  bobo3bobobo22b2o134bobobo7bo22b2o50b5o2bobo$42b3o60b5o47b3o35bo7bo17bo
  16bo7bo9bo6b2o63b3o29bo7bo16b2o4bo$23bo3bo14bo5bo29bo3bo20b2o4bo23bo7b
  o15bo5bo49b3o5bo2bo30b2o5bo2bo38bo7bo15bo5bo46bo3b2obobo$43bo4bo50bo3b
  2obobo49bo4bo27bobobo3bobobo9bo7bo12bobobo3bobobo8bobo3b2obo64bo4bo21b
  obobo7bo11b2o3bo3b2o$19bobobo3bobobo7b2o4bo2bo3bo21bobobo3bobobo11b2o
  3bo3b2o20bobobo3bobobo12b2o4bo2bo50bo2b5obo35bo40bobobo7bo12b2o4bo2bo
  3bo41bobo2bobo$39bobo2b3o2bo3b2o43bobo2bobo48bobo2b3o2bobo49bo41bo66bo
  bo2b3o2bo3b2o44bobo$39bo12bo50bobo48bo60b2obo39bo2b2o62bo12bo45b3o$42b
  o10bo48b3o52bo48b2o55bo64bo10bo$42bo3bo110bo3bo44bobo3b2o2b2o44bo65bo
  3bo$42bo114bo48bo3bo6bo44bobo63bo55bo$44bo57bo56bo49b2o3bo115bo46bo5b
  2obo$34b3o58bo5b2obo44b3o61b2o49bobo53b3o53b2o4b2o2bo$34bo9bo49b2o4b2o
  2bo44bo9bo50bo109bo9bo45bobo$35bo2b6o50bobo53bo2b6o51bo54bobo53bo2b6o
  50bo3bo$37bo60bo3bo49bo53b3o56b2o56bo55bo$38b2o57bo55b2o51bo58bo58b2o
  53bo2bo$97bo2bo57b3o48bo119b3o$158bo47bo2bo53bo2bo62bo$159bo47bo47b2o
  5b2o2bo63bo$208bo45b2o5bo$256bo4bobo$258b2o2bo$258b2o9$242bobobo3bo3bo
  16b2o$9bobobo3bobobo17b3o10bobobo3bo27b2o11bobobo3bo25bo63bobobo3bo3bo
  18b2o39bobo22bobobo3bo3bo10b2o$39bo48bobo43b2o14bobobo3bobobo23b3o40b
  2o11bo7bo3bo16bo8b3o35b2o$9bo7bo3bo18bo11bo7bo27bo12bo7bo24bobo49bo12b
  o7bo3bo19bo42bo3b2ob2o13bo7bo3bo11bo$42b2o47bo58bo11bo24bo45b2o7bobobo
  3bobobo19b2obo44b2o$9bobobo3bo3bo19b2o9bobobo3bo29bobo8bobobo3bo27b2o
  50b2o8bobobo3bobobo10b2o8bo44b3o16bobobo3bobobo12bo$34b3o46b2o5bobo43b
  3o11bobobo3bobobo27bo30b2o19bo3bo7bo$9bo3bo3bo3bo12bo5bo11bo3bo3bo22bo
  bo4bo10bo3bo3bo26bo62bo3bo7bo11bo6bo3bo39bo3bobo15bo3bo7bo11bo2bo3bo$
  35bo4bo42bo6bo59bo3bo3bo18b2obo2bobo43b2o11bobobo7bo18b2obob3o36b2obo
  5b2o$9bobobo3bobobo15bo2bo11bobobo3bo25bo3bo10bobobo3bo22b2obobo38b2o
  3bobob5o9bobobo7bo13bo2b2o2bo40bo3bo18bobobo7bo7b2o4bo3bobo$31b3o2b3o
  2bobo41bo4bo40bo5bo12bobobo3bobobo14bo2bo3bo3b2o30b6o46b2o5bo38bobo2bo
  $31bo53bo3bo34b3o3bo3b2o41bo2bo39b2o3bo3b2o41bo6bo43bo4bobo$32bo52bobo
  36bo5bo46bo7b2o32bo3b2o49bo45bo2bo6bo$34bo3bo38b2o5bobo38bo3bobo52bo
  29b2o2b2obo40b2o8bobo46bobo6bobo$33b2obo40bobo3b3o33b2o7b2o47bo7b2o27b
  obob2o2bo39bobo3b3o50bobo$24b2o51bo3bo3bo33bobo5b3o47b3o34bo3b2ob2o39b
  o3bo5bo49b2o8bobo$24bobo3b2o2b2o44b2o5bo31bo3b3o2bo48bo3b2o36b2o44b2o
  5bo49bo$24bo3bo6bo45bob4o35b2o2bo50bo3b2o86b2o62bobo$27b2o3bo39b2o11b
  2o35b2o46b3o43b2o48bo66b2o$31b2o39bobo3b3o36bo52bo6bobo35b2o49bo66bo$
  28bo43bo3bo4bo34b2o6bo46bo4b2obo36b2o44b3o$28bo46b2o39bobo3b2o49b4obo
  37b3o43bo68bo2bo$24b3o48bo5bo38bo4bo48b2o40bo48bo57b2o5b2o2bo$24bo94bo
  4bo92b2o43bo2bo56b2o5bo$27bo91bo2bo140bo60bo4bobo$24bo2bo236bo61b2o2bo
  $25bo300b2o$26bo15$175bobobo3bobobo24b3o$98bobobo3bobobo13b3o25b3o57bo
  35bobobo3bobobo22b3o27b3o$124bo27bo22bo7bo29bo69bo29bo$9bobobo3bobobo
  18b2o28b3o25bo7bo18bo27bo61b2o31bo11bo23bo29bo$40bobo27bo56b2o26b2o18b
  obobo3bobobo26b2o70b2o28b2o$9bo7bo22bo30bo26bobobo3bobobo17bo27bo50b3o
  38bobobo7bo24b2o28b2o$43bo29b2o47b2o26b2o23bo3bo3bo3bo19bo5bo94b3o$9bo
  bobo3bobobo20bobo27b2o24bo3bo3bo3bo11bo2b2o23bo2b2o53bo4bo34bo3bo7bo
  23bo23bo5bo$35b2o5bobo20b3o54bo3bo23bo3bo20bobobo3bobobo22bo2bo62b3o5b
  o2bo21bo4bo$9bo3bo7bo13bobo4bo22bo5bo26bobobo3bobobo13bo2bo24bo2bo48b
  3o2b3o2bobo31bobobo7bo15bo7bo20b2o4bo2bo$35bo6bo23bo4bo52bo2bo24bo2bo
  48bo72bo2b5obo18bobo2b3o2bobo$9bobobo3bobobo16bo3bo25bo2bo3bo51bo27bo
  49bo73bo25bo$37bo4bo24b3o2bo3b2o38b3o25b3o60bo3bo66b2obo26bo$37bo3bo
  33bo40bo9bo17bo9bo51b2obo61b3o34bo3bo$37bobo26bo2bo6bo40bo2b6o19bo2b6o
  52bo64bo5bo30bo$29b2o5bobo20b3o4bo2bo49bo27bo57b2o65bo4bo32bo$29bobo3b
  3o21bo6b2ob2o49b2o26b2o6bo48bo62b2o4bo2bo22b3o$29bo3bo3bo22bo2b3o2b2o
  57b2o26b2o50bo60bobo2b3o2bobo19bo9bo$32b2o5bo22bo3bob2o56b2obo25bo5b2o
  32b2o8bobo60bo32bo2b6o$33bob4o26bo65bo5bo18bob2ob4o30bobo3b3o67bo31bo$
  24b2o11b2o15b3o72bo2bo3b2o27bo29bo3bo5bo65bo3bo26b2obo$24bobo3b3o21bo
  9bo64bo6bobo18bo2b2o3bo32b2o5bo65bo$24bo3bo4bo21bo2b6o67bob4o21bo43b2o
  69bo27bo$27b2o28bo70b2obobo3bo22b3o36bo63b3o27b3o5bo2bo$27bo30b2o68b2o
  3bo26bo38bo63bo9bo19bo7bo$32bobo94bo30bo34b3o66bo2b6o21bo2b5obo$33bobo
  93bo28b3o34bo70bo29bo$33bo96b2o25b2o2bo36bo68b2o28b2o$159bo35bo2bo$
  196bo$197bo21$253bobobo3bobobo7b3o$273bo2b3o$93bobobo3bobobo14bo12bobo
  bo3bobobo6b2o2bo96bo7bo3bo8bobo$119b2o30b2o4bo19bobobo3bobobo14b2o24b
  2o47bo$13bobobo3bobobo15b2o25b2o23bo7bo3bo13bobo2bo8bo7bo3bo7b2obo2b3o
  42bobo3b2o18bobo3b2o15bobobo3bobobo11bo$41bobo24bobo49bo2bobo29b2o2b2o
  bob2o11bo7bo3bo14bo3b3obo17bo3b3obo40bobo$13bo7bo3bo15bo26bo24bobobo3b
  obobo12bobo2bobo7bobobo3bobobo16bobobo33b2o5b2o17b2o5b2o18bo3bo7bo16bo
  $44bo26bo45bo2bo43bo12bobobo3bobobo10bobo23bobo50bo2bo$13bobobo3bobobo
  17bobo24bobo20bo3bo3bo3bo11bo15bo3bo3bo3bo19b2o33bo3bo3bo17bo3bo3bo18b
  obobo3bobobo13bo2bo$43bobo24bobo44bob2o56bo3bo7bo13b2o24b2o48bo2bo$13b
  o3bo3bo3bo9b3o5bo18b3o5bo22bobobo3bobobo15bo11bobobo3bobobo20bobo35bo
  2bo22bo2bo49b2o$35bo7bo18bo7bo51bo45b2o7bobobo3bobobo5b2o24b2o57bo2b2o
  $13bobobo3bobobo10bo6bo19bo6bo47bo2bo41b3o2b2o25bobo3b3o17bobo3b3o54bo
  bo$38b2o3bo21b2o3bo47b2obo41b3o29bo3bo4bo16bo3bo4bo50b2o$39bo2bo23bo2b
  o48b3o77b2o24b2o55bo4bobo$30b2o25b2o58b3o2b2o38b2o34bo5bo19bo5bo51bo5b
  o$30bobo3b3o18bobo3b3o96bo43b2o24bo56bo$30bo3bo4bo17bo3bo4bo48b2o3bo
  84bo2bo22bobo48b2o6bo$33b2o25b2o53b2o3bo31b2o5bo3bo42bo4b3o17bo2bo47bo
  bo5bobo$33bo5bo20bo5bo49bo34b2o6bobobo43b2o3bob2o16bobo6b2o$41bo26b2o
  46bobo34bo2b2obobo47b3ob2o20bo2bob2o50b2o$40bobo24bo2bo84b2o4bo48bo24b
  3o3b2o49bo$40bo2bo24bo4b3o42bobo34b2o53bobo20bobo5bo49b2o$41bobo6b2o
  17b2o3bob2o131bo2bo20b2o2b2o2bo50b2o$44bo2bob2o20b3ob2o42bobo31bobo77b
  obo$44b3o3b2o20bo46b2o31b2o55bo24b2o53b2o$42bobo5bo21bobo44bo32bobo53b
  5o21bo46b3o5b2o$42b2o2b2o2bo20bo2bo133bobo70bo6bobo$42bobo72bo2bo33bo
  127bo4b2o$43b2o26bo37b2o5b2o2bo32b2o129b4obo$43bo26b5o33b2o5bo169b2o$
  70bobo37bo4bobo$112b2o2bo$112b2o18$304b2o$192b3o109bobo$192bo111bo8b3o
  $193bo113bo3b2ob2o$108bobobo3bobobo18b2o54b2o23bobobo3bo30bo47b2obo$
  139bobo52b2o62b2o19bobobo3bo22b3o$59bobobo3bobobo19b2o19bo3bo3bo18bo
  17bobobo3bobobo17b3o34bo3bo29bobo56b2o$10bobobo3bobobo21bo46bobo48bo
  44bo5bo89bo3bo19bo3bobo2b2o$43b2o18bo3bo3bo19bo20bo3bo3bo20bobo17bo3bo
  3bo18bo4bo30bo3bo32b2o43b2obob3o3bo$14bo3bo3bo20bobo41bo46b2o5bobo46bo
  2bo3bo63b2o20bo3bo18bo3bo5b2o$63bo3bo3bo14b2o6b4o14bo3bo3bo13bobo4bo
  19bo3bo3bo14b3o2b3o2bo3b2o24bo3bo24b2o50b2o5bo$14bo3bo3bo23b2o38bobo2b
  4ob3o35bo6bo42bo12bo54b2o5b2o22bo3bo17bo6bo$45b3o15bo3bo3bo18b3o2bo16b
  o3bobobo16bo3bo19bo3bo3bo15bo12bo25bo3bo25bo3bo2bo45bo$14bo3bo3bo22bo
  44bobo43bo4bo2b2o41bo3bo65b2obo22bo3bo7b2o8bobo$63bo3bobobo16b2o46bo3b
  o3bobo14bo3bobobo16b2obo62bo42bobo3b3o$14bo3bobobo18b2obobo40b2o47bobo
  5bo41bo64bob3o39bo3bo5bo$40bo5bo40bob2o37b2o5bobo47b2o63bo3bo43b2o5bo$
  39bo3b2o83bobo3b3o48bo63b2ob2o48b2o$38bo2bo46bobo37bo3bo3bo50bo56b3o2b
  o2b2o45bo$32b2o3bo2bo47b2o41b2o5bo36b2o8bobo56bo5b2o3b2o42bo$31b2obo2b
  o50bobo41bob4o37bobo3b3o61bo3bobo43b3o$27b3o2bo3b2obo45b2o36b2o11b2o
  37bo3bo5bo62bo46bo$27bo4bo3bobo39b2o4bo38bobo3b3o46b2o5bo63bo2bo45bo$
  29bobo6bo38b2o5bo2bo35bo3bo4bo49b2o111bo2bo$31bo3b2o42bo4bobo39b2o51bo
  68bo47bo$26b2o53b2o43bo52bo68b3o46bo$25b2obob3o42b2o4bo3bo45bobo41b3o
  62b3o4bo2bo$27bobo2bobo39b2o3b2o2bo48bobo40bo64bo5b2o$76bo3bo51bo45bo
  62bo4b3o$29bo48bo96bo2bo64b4o$27b2o49bo97bo67b2o$29bo49b2o96bo2$26b2ob
  o$26bo2bo$26bobo32$414b2o$413b2o$256bobobo3bobobo8bo42bobobo3bobobo18b
  2o22bobobo3bobobo19b2o5bo$111b2o16bobobo3bobobo7b2ob2o122b6o69bobo52b
  2o5b2o$110b2o37bob3o106bo7bo7bo7b2o38bo3bo3bo18bo27bo3bo3bo20bo4bobo2b
  2o$112bo20bo7bo7bo2b2o3b2o33bobobo3bobobo8b2o2bo59bo6bobo67bo55b2o3b2o
  b4o$76bobobo3bobobo25b2o40b2obob2o49b2o4bo41bo7bo10bobo2bob6o32bo3bobo
  bo20bobo23bo3bobobo22b2o10bo$19bobobo3bobobo18b2o61bo19bo3bobobo11bo5b
  ob2o33bo3bo13b2obo2b3o3bo53bo6bo4bo60bobo46b2o18bo$50bobo27bo7bo64bo5b
  o3bo52b2o2b2obobo2bo31bo7bo19bo4bo30bo3bo3bo12b3o5bo25bo3bo3bo13b2o9bo
  3bo$23bo7bo18bo61bo2bo17bo7bo19bo34bo3bobobo18bobo3bo59bo55bo7bo49bo7b
  2o5b2o$53bo26bo3bobobo15b2o5b2o50bobo59bo3bo30bo7bo21bo2b2o29bo3bobobo
  7b2o6b2o3bo25bo3bobobo17bo4bo2bo$23bo3bobobo20bobo48b2o5bo22bo3bobobo
  23bo30bo7bo21b5o62bo46bobo3bo6bo51b3ob3o$52bobo25bo3bo20bo4bobo52bobo
  62b2o60b2obo44bo5b2o4bo3bo49b5o$23bo3bo16b3o5bo54b2o2bo84bo3bobobo25b
  2o60bo50bo4b3o5b2o39bo$44bo7bo27bo3bobobo18b2o58bobo59bo61bo3bo47b2o
  10bo3bo36b2o6b2o$23bo3bobobo7b2o6b2o3bo46b2o127bo2bo58b2obo65bobo34bob
  o4bo$39bobo3bo6bo45b2o9bo58bobo56bo3bo57b3o63bobo4bo37b2o$39bo5b2o4bo
  48bo7b2o50b2o6b2o57b2obo58b2o64bo2b2o39b3o2bo$42bo4b3o4b3o45bo4bo2bo
  49bobo3bobo58b2o127bobob5o32b2obo2bo$42b2o10b3o45b3ob3o51bo3bo62bo61bo
  2bo3bo60b2o5bo30b2obo$54bo48b5o55b2o2b2o57bobo59bo2bo3b2o61b2o35bo5bo$
  59b2o33bo68bo3bo58b2o60bo2bo3bobo61bobo34b2o$54b3ob2obo31b2o6b2o63bo
  58bo65bo67bobo$55b3o35bobo4bo61bo3bo59bo2bo59b2o4b2o57b2o4b3o$55bo3bo
  37b2o60b2obo62bo69bo58bo2b2o$54b2o4bo35b3o2bo56b2o4bo61bo72b2o53bo4bo$
  54bo2bobo34b2obo2bo59bobo2bo61bobo66b2ob4o53bo2bo$54bobob3o31b2obo69bo
  62bo5b4o57bo7bo53bo$92bo5bo63bo2bo63b6ob3o57bo6bo54bo$59b2o32b2o68bobo
  68b2o$59bo103bobo63bo3bo65b2o$62bo101b2o64bo$61bo102bo$61bo22$272b2o$
  159bobobo3bobobo18b2o40bo3bobobo3bobobo23bobo$97bobobo3bobobo8b2o2bo
  67bobo79bo$27bobobo3bobobo8bo68b2o4bo35bo3bo7bo18bo41bo3bo3bo3bo3bo26b
  o$47b6o44bo3bo3bo13b2obo2b3o3bo61bo80bobo$27bo3bo3bo11bo7b2o64b2o2b2ob
  obo2bo25bobobo7bo20bobo37bo3bo3bo3bo3bo18b2o5bobo$48bo6bobo39bobobo3bo
  bobo18bobo3bo50b2o5bobo72bobo4bo$27bobobo3bobobo10bobo2bob6o67bo3bo28b
  o7bo13bobo4bo39bo3bo3bo3bo3bo18bo6bo$51bo6bo4bo37bo7bo21b5o49bo6bo77bo
  3bo$27bo3bo3bo3bo19bo4bo70b2o22bobobo7bo16bo3bo39bo3bobobo3bobobo20bo
  4bo$60bo36bobobo3bobobo25b2o50bo4bo76bo3bo$27bobobo3bobobo21bo2b2o68bo
  52bo3bo77bobo$64bo68bo2bo50bobo71b2o5bobo$63b2obo65bo3bo42b2o5bobo72bo
  bo3b3o$63bo68b2obo43bobo3b3o73bo3bo3bo$62bo3bo65b2o45bo3bo3bo76b2o5bo$
  61b2obo67bo49b2o5bo75bob4o$60b3o68bobo49bob4o67b2o11b2o$60b2o69b2o41b
  2o11b2o67bobo3b3o$130bo6bo36bobo3b3o73bo3bo4bo$60bo2bo67bo2bobobo35bo
  3bo4bo75b2o16b2o$59bo2bo67bo5bobo38b2o80bo5bo11bobo$59bo2bo68bo2bob2o
  3b3o33bo5bo2b3o3b2o72b2ob3o5bo$62bo69bo4b2o2bo43b4o3bobo74b3o6bobo$60b
  2o75b2o3bo41bo2b2o2bo2bo71bo4bo6b2obo$65b2o71b2o4b2o39bo5b2o74b3obo2bo
  6bo$64b2obo66bo10bo43bobo3bo78b2o4bo$69bo5bo57b2o53bo3bo3bo72bo$67bo2b
  o3b2o57bobo2b3ob2o43bo2bobobo2bo71b2o5bo$67bo6bobo60b3o3bo44bobo5b3o
  72bo5b2o$69bob4o61bo6bo54bo72bo$66b2obobo3bo61bo3bo130b2o$66b2o3bo$67b
  o$67bo$68b2o!

Edit: corrected Nicolay's c/4 diagonal collection based on the three comments below.

[atavoidirc]

[*] A very large collection of new c/4 diagonal spaceships (by Nicolay Beluchenko):

Code: Select all

(rle)

One of the spaceships does not work.

[dvgrn]

One of the spaceships does not work.

If you're looking at the same one I'm looking at, it works fine... but it's a boat-eater, so once it runs out of long^N boat it crashes.

Code: Select all

x = 51, y = 52, rule = B3/S23
2$10bo$9bobo$10bobo$11bobo$12bobo$13bobo$14b2o2b2o$18bobo$18bo$18bo2$
17bo2b2o$16b2obobobo$17b2o4b2o$17b2o3b3o$16bo2bob3o$16bobo$14bobo4b2o$
13b5o$13bo3bo$17b3o$24b2o$19b4obo$19b2obo$19b2o2bo$19b2o4bo$21bobo2bo$
24bo2bob3o$27bo$23bo3b4o$22b5o4bo$22bo3b2o4bo$23bo9bo$33bobo$31bo3bo$
30bo6bo$29b2o2bo3bo$29bo2bo5bo$28b2o5bobo$28bo5b2o$29bo4bobo2$36bo$35b
2o!

[May13]

A very large collection of new c/4 diagonal spaceships (by Nicolay Beluchenko):

Code: Select all

(rle)

146-cell spaceship actually consists of 2 non-interacting parts - 141-cell spaceship and glider:

Code: Select all

x = 62, y = 45, rule = DoubleB3S23
C3.C3.C3.C.C.C11.C$27.2C$C3.C3.C3.C14.C.C$31.C$C3.C.C.C3.C.C.C13.C3.
3C$30.C3.3C$C7.C3.C3.C$33.C$C7.C3.C.C.C16.C.C2$33.C.C$32.3C$28.2C.2C$
28.C.2C3.2C2.C$28.C5.C.2C.C$34.C.2C.2C$30.C8.3C$30.2C$30.2C6.2C2.C$
36.3C$36.C8.C$36.C.2C3.2C2.C$40.C2.2C3.C$38.C2.C3.C.2C$41.C4.2C.3C$
37.C3.C2.3C3.2C$36.6C.2C.C$36.C3.C2.2C$37.C6.2C4.2A$44.C5.A.A$44.C.C
3.A$46.C$47.2C$47.C11.C$49.2C7.2C$49.C3.C4.C.C$50.C4.C$51.C.C2.2C$52.
C$56.2C$56.6C$56.2C.C$56.2C2.C$60.C$61.C!

[atavoidirc]

The nomination period is over! Now we must begin writing descriptions of the patterns. Voting will begin 24 hours after all descriptions have been written and judged to be satisfactory.

[Sokwe]

The nomination period is over! Now we must begin writing descriptions of the patterns. Voting will begin 24 hours after all descriptions have been written and judged to be satisfactory.

Here's a first draft of the list:

• #01 37P4H1V0 (by Josh Ball): the smallest known c/4 orthogonal spaceship.
• #02 Statorless p3 (by Jason Summers): the first strictly volatile period-3 oscillator.
• #03 444-tick glider-to-Herschel converter (by Sergey Petrov): the fastest known stable glider-to-Herschel converter/90-degree glider reflector.
• #04 G4 Herschel merge circuit (by Sergey Petrov and Adam P. Goucher): a spartan Herschel transceiver that allows two independent transmitters to feed into the same receiver.
• #05 Ambidextrous G5 Herschel transceiver (by Sergey Petrov and Paul Callahan): a spartan Herschel transmitter by Sergey Petrov that can connect to Paul Callahan's spartan Herschel receiver in either of the two possible orientations.
• #06 p4 glider reflector (by Karel Suhajda and Matthias Merzenich): the first fast period-4 90-degree reflector. It works at periods as low as 52.
• #07 Direct stable Herschel duplicator (by Sergey Petrov and Adam P. Goucher): a conduit with a single Herschel input and two independent Herschel outputs.
• #08 HLx111R (by Matthias Merzenich): a versatile H-to-R conduit that can be used to construct several new Herschel conduits.
• #09 Slow two-sided synthesis of the Herschel transmitter (by Sergey Petrov): two-sided syntheses of the standard Herschel transmitter in every orientation where only two gliders interact at any step in the synthesis.
• #10 86P6H3V0 (by Matthias Merzenich and Josh Ball): the smallest known 3c/6 orthogonal spaceship.
• #11 New c/5 diagonal rake design (by Matthias Merzenich): a c/5 diagonal rake design that allows rakes of periods as low as 85.
• #12 Herschel-less p62 gun (by Jason Summers): the first period-62 glider gun that does not rely on Herschels.
• #13 New c/4 diagonal spaceships (by Nicolay Beluchenko): a very large collection of new c/4 diagonal spaceships found with Nicolay Beluchenko's modification of WLS.
• #14 New reflector periods (by Matthias Merzenich): The first p26 dependent reflector and p52 and p58 independent reflectors.
• #15 Low density orphan (by Marijn Heule, Christiaan Hartman, Kees Kwekkeboom, and Alain Noels): an orphan with 92 set cells and only 45 on cells, giving it the lowest density of any known orphan.

I made a few corrections to the list in the first post:

• I added Adam P. Goucher to the credits for the G4 Herschel merge circuit and the direct stable Herschel duplicator.
• The ambidextrous G5 Herschel transceiver was found by Sergey Petrov, not Arie Paap and Matthias Merzenich. I also added Paul Callahan to the credits for this entry for discovering the Herschel receiver back in 1996.
• The entry labeled "slow salvo synth of the Herschel transmitter" is (I think) actually a slow two-sided synthesis (is this the correct nomenclature?).

[pzq_alex]

[*] #15 Low density orphan (by Marijn Heule, Christiaan Hartman, Kees Kwekkeboom, and Alain Noels): an orphan with 92 set cells and only 45 on cells, giving it the lowest density of any known orphan.

Can’t we just add arbitrarily add dead cells to an orphan to create orphans with arbitrarily low density?

[atavoidirc]

Can’t we just add arbitrarily add dead cells to an orphan to create orphans with arbitrarily low density?

that would no longer be considered an orphan, as you could remove cells and still have a pattern with no parents

[pzq_alex]

Can’t we just add arbitrarily add dead cells to an orphan to create orphans with arbitrarily low density?

that would no longer be considered an orphan, as you could remove cells and still have a pattern with no parents

I don’t think the definition of orphans concerns removing cells from the orphan:

A related concept to Gardens of Eden is that of orphans, which are finite patterns that cannot occur as part of the evolution of another pattern. That is, they are Gardens of Eden that can be extended in any way to form other Gardens of Eden.

[dvgrn]

I don’t think the definition of orphans concerns removing cells from the orphan...

Yeah, I think an orphan with a bajillion OFF cells added around it is still a (lower-density) orphan. So there's something implied but not stated in that description of the "lowest-density known" orphan.

Probably we could say "minimal orphan" instead of "orphan" and fix the problem -- a "minimal orphan" being an orphan that, if any subset of its cells is removed, is no longer an orphan.

[Book]

Looking at the list, I wonder how it would have looked if made in early 2013. How does the perspective of nearly a decade affect the judgements? I also wonder how the votes might be different.

[atavoidirc]

• #01 37P4H1V0 (by Josh Ball): the smallest known c/4 orthogonal spaceship.
• #02 Statorless p3 (by Jason Summers): the first strictly volatile period-3 oscillator.
• #03 444-tick glider-to-Herschel converter (by Sergey Petrov): the fastest known stable glider-to-Herschel converter/90-degree glider reflector.
• #04 G4 Herschel merge circuit (by Sergey Petrov and Adam P. Goucher): a spartan Herschel transceiver that allows two independent transmitters to feed into the same receiver.
• #05 Ambidextrous G5 Herschel transceiver (by Sergey Petrov and Paul Callahan): a spartan Herschel transmitter by Sergey Petrov that can connect to Paul Callahan's spartan Herschel receiver in either of the two possible orientations.
• #06 p4 glider reflector (by Karel Suhajda and Matthias Merzenich): the first fast period-4 90-degree reflector. It works at periods as low as 52.
• #07 Direct stable Herschel duplicator (by Sergey Petrov and Adam P. Goucher): a conduit with a single Herschel input and two independent Herschel outputs.
• #08 HLx111R (by Matthias Merzenich): a versatile H-to-R conduit that can be used to construct several new Herschel conduits.
• #09 Slow two-sided synthesis of the Herschel transmitter (by Sergey Petrov): two-sided syntheses of the standard Herschel transmitter in every orientation where only two gliders interact at any step in the synthesis.
• #10 86P6H3V0 (by Matthias Merzenich and Josh Ball): the smallest known 3c/6 orthogonal spaceship.
• #11 New c/5 diagonal rake design (by Matthias Merzenich): a c/5 diagonal rake design that allows rakes of periods as low as 85.
• #12 Herschel-less p62 gun (by Jason Summers): the first period-62 glider gun that does not rely on Herschels.
• #13 New c/4 diagonal spaceships (by Nicolay Beluchenko): a very large collection of new c/4 diagonal spaceships found with Nicolay Beluchenko's modification of WLS.
• #14 New reflector periods (by Matthias Merzenich): The first p26 dependent reflector and p52 and p58 independent reflectors.
• #15 Low density orphan (by Marijn Heule, Christiaan Hartman, Kees Kwekkeboom, and Alain Noels): an orphan with 92 set cells and only 45 on cells, giving it the lowest density of any known orphan.

if there are no objections within seven days this will be the final draft.

[pzq_alex]

<list of patterns>

if there are no objections within seven days this will be the final draft.

I’d say that the low density orphan item needs to be fixed as per this post — but has someone done the fact-checking to make sure that the statement with minimal orphans is correct.

[dvgrn]

I’d say that the low density orphan item needs to be fixed as per this post — but has someone done the fact-checking to make sure that the statement with minimal orphans is correct.

I haven't done an independent check, but I'm happy to see after actually following the link for the first time this morning, that I found the same exact wording that Achim used:

fewest number of totally needed cells for a minimal Orphan 92
smallest rectangular bounding box 10x10
lowest density of living cells for minimal Orphan 0.3203

[atavoidirc]

Updated:
#15 Low density orphan (by Marijn Heule, Christiaan Hartman, Kees Kwekkeboom, and Alain Noels): an orphan with 92 set cells and only 45 on cells, giving it the lowest density of any known irreducible orphan.

[atavoidirc]

Second draft of list:

• #01 37P4H1V0 (by Josh Ball): the smallest known c/4 orthogonal spaceship.
• #02 Statorless p3 (by Jason Summers): the first strictly volatile period-3 oscillator.
• #03 444-tick glider-to-Herschel converter (by Sergey Petrov): the fastest known stable glider-to-Herschel converter/90-degree glider reflector.
• #04 G4 Herschel merge circuit (by Sergey Petrov): a spartan Herschel transceiver that allows two independent transmitters to feed into the same receiver.
• #05 Ambidextrous G5 Herschel transceiver (by Sergey Petrov and Paul Callahan): a spartan Herschel transmitter by Sergey Petrov that can connect to Paul Callahan's spartan Herschel receiver in either of the two possible orientations.
• #06 p4 glider reflector (by Karel Suhajda and Matthias Merzenich): the first fast period-4 90-degree reflector. It works at periods as low as 52.
• #07 Direct stable Herschel duplicator (by Sergey Petrov): a conduit with a single Herschel input and two independent Herschel outputs.
• #08 HLx111R (by Matthias Merzenich): a versatile H-to-R conduit that can be used to construct several new Herschel conduits.
• #09 Slow two-sided synthesis of the Herschel transmitter (by Sergey Petrov): two-sided syntheses of the standard Herschel transmitter in every orientation where only two gliders interact at any step in the synthesis.
• #10 86P6H3V0 (by Matthias Merzenich and Josh Ball): the smallest known 3c/6 orthogonal spaceship.
• #11 New c/5 diagonal rake design (by Matthias Merzenich): a c/5 diagonal rake design that allows rakes of periods as low as 85.
• #12 Herschel-less p62 gun (by Jason Summers): the first period-62 glider gun that does not rely on Herschels.
• #13 New c/4 diagonal spaceships (by Nicolay Beluchenko): a very large collection of new c/4 diagonal spaceships found with Nicolay Beluchenko's modification of WLS.
• #14 New reflector periods (by Matthias Merzenich): The first p26 dependent reflector and p52 and p58 independent reflectors.
• #15 Low density orphan (by Marijn Heule, Christiaan Hartman, Kees Kwekkeboom, and Alain Noels): an orphan with 92 set cells and only 45 on cells, giving it the lowest density of any known irreducible orphan.

If there are no objections within five days this will become the final list.

[calcyman]

• #04 G4 Herschel merge circuit (by Sergey Petrov and Adam P. Goucher): a spartan Herschel transceiver that allows two independent transmitters to feed into the same receiver.
• #07 Direct stable Herschel duplicator (by Sergey Petrov and Adam P. Goucher): a conduit with a single Herschel input and two independent Herschel outputs.

I wasn't involved in either of these discoveries; it was entirely Sergey Petrov. I just made some observations about the patterns that he'd already discovered, and that's not really sufficient to include my name on either of those entries.