A potential way to reflect p61 glider streams

p46beth · Post by **p46beth** » October 12th, 2010, 7:15 pm

I was recently looking at the game of life status page, and saw that p57, 58, and 61 glider streams can be reflected only if they have no gaps. I'd assume the p61 reflection could be accomplished by a p61 Herschel track, as shown in the p59 glider loop--

Code: Select all

x = 1457, y = 1359, rule = B3/S23
47$936bo49bo49bo49bo49bo49bo49bo$923bo10b3o36bo10b3o36bo10b3o36bo10b3o
36bo10b3o36bo10b3o36bo10b3o36bo$914b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo
30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o$898bo16bo4bo
12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo
4bo12b2o30bo4bo$896b3o16bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43b
obo3bo43bobo3bo43bobo3bo15b2o$880bo14bo20bobo3bo43bobo3bo43bobo3bo43bo
bo3bo43bob3obo43bobo3bo43bobo3bo43bobo3bo14bo$880b3o12b2o20bo3b2o44bo
3b2o44bo3b2o7b2o35bo3b2o44b3ob2o44bo3b2o7bobo34bo3b2o44bo3b2o12bobo$
883bo46b2o11bo49bo35bob2o10bo49bo49bo36bo2bo9bo49bo37b2o2b2o$882b2o47b
obo9b3o47b3o33bobo11b3o47b3o47b3o37bo9b3o47b3o35b2o$932bo13bo49bo15bob
o18b2o11bo49bo14bo34bo24bo8bobo13bo49bo12bo3b3o$899bo18b2o2b2o21b2o11b
o8b3o25b2o11b2o7b3o7bo3bo2bo10b2o11b2o35b2o14b2o32b2o11b2o9b2obo22b2o
22bo25b2o11bobo2b5o$883b2o12bo2bo17b2o2b3o33b2o7bo40bobo4b2o2bo7b2o2bo
26b2o7bo44b2o44b2o8bo4bo34bo9b2o38bo8b2o$883b2o11bo2b2o16b3o2b2o33bo2b
o7bo44b4ob2o8bo19bo5bo57bo17b3o39bo34b2o9bobo3b2o33b3o4b2o$897bo20b2o
2bo35b2o18bo36b3o11b3o16b2o2bo3bo11b2obo39bo17bo2bo15b2o18b4o34bobo15b
4o33b2o3bo$898bo75bobob2o50bo18b3o4bo13bobob2o31bobo18bo4b2o12bo2bo72b
o4bo54bo$974b3o2b2o69b2o5bo12b3ob2o29bobo25b2o15b2o70b4o2bo52b5o$938bo
35bobo2bo14bo3b2o50b2o2b3o15b2o49b3o3b3ob2o10bo3b2o71b2obob2o53bo2b2o$
937b4o14b2o15b2o3b2o13b2ob2ob2o32b3o20b2o33bob2o13bo14bob5o2bo12bo4bo
37b2o33b2o19bob4o31b3obo$935b5obo12b3o15b2ob3o13bo7bo31bo3bo18bo35bo3b
obo10bo16b2o5bo2bo9b3o39bo2b2o13b2o18b3o16b2o4bo30b2o$899b2o33bo6b2o
11bo2b2o16b2o6b2o7bo6b2o34bo47b2o11bo6bobo14bo2bo61b3o2bo13b2obo25b2o
8bo3bob2o29bo6b2o$877b2o20bo20b2o11bo3bob3o12b2o2bo11b2o11b2o9b2o2b2o
20b2o9b2ob2o5bobo26b2o11b2o9bobo4b2o5bo11bo12b2o35b2o13bo4bo14b3o12b2o
11b2o9b3obo20b2o9b2obo3bobo$878bo2b2o18bo19bo12bobo2b2o14bo2bo12bo22b
2o2b2o21bo11bo7b2o28bo18bobo13bobo12bo49bo13b5o16bo14bo34bo11bobo10b3o
5bo$878bobobo3b3o11b2o16b3o34b3o10b3o47b3o21bo25b3o47b3o47b3o15b2o30b
3o34bo12bo13bo6b2o$879bo7bo8b2o20bo49bo49bo49bo37bo11bo49bo49bo36bobo
9b2o4b2o$887b3o6bo45bo3b2o44bo3b2o44bo3b2o44bo3b2o7bo2bo33bo3b2o44bo3b
2o44bo3b2o8bo14bo2bo$881bo15b3o41bobo3bo43bobo3bo43bobo3bo43bobo3bo7bo
35bobo3bo43bobo3bo43bobo3bo23b2o$880bobo16bo40bobo3bo43bobo3bo43bobo3b
o43bobo3bo9bo2bo30bobo3bo43bobo3bo43bobo3bo33b2o$881bo58bo4bo12b2o30bo
4bo12b2o30bo4bo12b2o30bo4bo13bo30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o20b
2o$878b3o58b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo
30b2o5b3o9bo30b2o5b3o9bo$878bo69bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo
10b3o36bo10b3o36bo10b3o$961bo49bo49bo49bo49bo49bo49bo2$905b2o$905bo$
886b2o15bobo$886b2o15b2o3$1291bo$1283bo5b3o$1280b5o3bo$1279bo7bobo$
1270b2o16bo$891b2o378bo8bo3bo$890bobo378bobo7b3o6bo$889b2o13b2o366b2o
13bobobo$891bo8b2o2bo382b2o2bo$885b2o4bobo6bobobo386b2o$884bobo6b2o8bo
$884bo7b3o$883b2o16bo380bo$900bobo380bo$901bo381b2o$902b3o377b3o$904bo
373b3o2bo3b2o$1278b4obo3b2o$1278bobo2b2o2b2o$876b2o398b3o2b2obobo3b2o$
877bo398bo13bobo$877bobo15b2o376bob2o15bo$878b2o11bo3b2o376b3o16b2o$
890b3o381bo$889b2ob2o$889bo375bo$1265b3o4bo$204bo49bo49bo49bo49bo49bo
49bo49bo49bo49bo49bo49bo49bo86bo376bo4bo$191bo10b3o36bo10b3o36bo10b3o
36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b
3o36bo10b3o36bo10b3o36bo49b2o374bo$182b2o5b3o9bo30b2o5b3o9bo30b2o5b3o
9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b
3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o48bobo
375b3o14b2o$166bo16bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo
4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o
30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo446bo$164b3o16bobo3bo43bobo
3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bo
bo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo15b2o37bo371bo16bobo$148bo14b
o20bobo3bo7b3o33bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo
43bob3obo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo14bo21b
2o14b2o370bobobo13b2o$148b3o12b2o20bo3b2o7b3o34bo3b2o44bo3b2o44bo3b2o
44bo3b2o44bo3b2o7b2o35bo3b2o44b3ob2o44bo3b2o7bobo34bo3b2o44bo3b2o44bo
3b2o44bo3b2o44bo3b2o12bobo22bo2b2o10bo371bo2b2o10b2o$151bo8bo40bo9bo
49bo49bo36b2o11bo49bo35bob2o10bo49bo49bo36bo2bo9bo49bo36b3o10bo49bo22b
2o25bo37b2o2b2o23bobobo13b2o366b2o14b2o$150b2o7b2o50b3o47b3o47b3o35bob
o9b3o47b3o33bobo11b3o47b3o47b3o37bo9b3o47b3o34b3o10b3o47b3o12bo7b2o25b
3o35b2o28bo16bobo381b2o$159bobo22bo2bo8b2o2b2o12bo49bo14b2o33bo35bo13b
o49bo15bobo18b2o11bo49bo14bo34bo24bo8bobo13bo49bo12bo3b3o13bo3b2o11bo
21bobo25bo10bo2bo4b2o29bo83bo$158b2o4b2o17b2o3bo6b6o12b2o11b2o35b2o13b
2ob2o16bo13b2o11b2o8b2o2b2o21b2o11bo8b3o25b2o11b2o7b3o7bo3bo2bo10b2o
11b2o35b2o14b2o32b2o11b2o9b2obo22b2o22bo25b2o11bobo2b5o11b3o2bo10bo12b
2o8bobo3bo20b2o14bo5bo27b2o11b2o11bo41bo16b2o379bo$151b2o6b3o3b2o17bo
3bo5bo2bo3bo24b2o51bo2bo15b3o25b2o8b2o2b3o33b2o7bo40bobo4b2o2bo7b2o2bo
26b2o7bo44b2o44b2o8bo4bo34bo9b2o38bo8b2o9bo2b4o10bo3b3o6b2o7b2o37bo4bo
46b2o9b3o40bob3obo390bobo$151b2o6bob2ob2o4b2o12bo3bo10bobo13b3o19bobo
39bo2bo14bo2b2o15bo17b3o2b2o33bo2bo7bo44b4ob2o8bo19bo5bo57bo17b3o39bo
34b2o9bobo3b2o33b3o4b2o10b3obo17b4o14bo41b2o57bobo41bob3o392b2o$161b4o
5b2o12bo2bo10b3o14b3o6b2o10bo2bo40b2o15b5o14bob2o16b2o2bo35b2o18bo36b
3o11b3o16b2o2bo3bo11b2obo39bo17bo2bo15b2o18b4o34bobo15b4o33b2o3bo13bo
16bob2ob2o16bobobo55b2o16bo20bo40b3o4bo$185bo12b2o19b3o2bobo10bo2bob2o
55b3o14bo3bo71bobob2o50bo18b3o4bo13bobob2o31bobo18bo4b2o12bo2bo72bo4bo
70bo2bob2o11bo2bob3o32b3o16bo4b2o15b2o60bo397b2o$198b4o19bo4bo13bo2bo
30bo25b2o14b2o2bo71b3o2b2o69b2o5bo12b3ob2o29bobo25b2o15b2o70b4o2bo69b
2obo3b2o12bo3bo31bo21b2o3b2o12b2o2bo457bo2b2o$201bo18bo2bo2bo14b2o31bo
24bobobo12b2ob2o35bo35bobo2bo14bo3b2o50b2o2b3o15b2o49b3o3b3ob2o10bo3b
2o71b2obob2o69b2obobobo36bo11bobo19b2o3b2o11bo4b2o457bo3bo$201b3o19b3o
15b2o20bo30b2o3bob2o10bo3b2o36b4o14b2o15b2o3b2o13b2ob2ob2o32b3o20b2o
33bob2o13bo14bob5o2bo12bo4bo37b2o33b2o19bob4o34b2o17b3o37b3o12bo14b2o
7bo12b3o71b3o16b2o358b2o10b3o2b2o$203b2o56b2obo35b2o9b2o40b5obo12b3o
15b2ob3o13bo7bo31bo3bo18bo35bo3bobo10bo16b2o5bo2bo9b3o39bo2b2o13b2o18b
3o16b2o4bo32bo2bo17bo38b3o7bo3bo16b2o19b2o71bo2bo16bo358bobo15b2o$167b
2o35b2o45b2o9bob2o46b2o38bo6b2o11bo2b2o16b2o6b2o7bo6b2o34bo47b2o11bo6b
obo14bo2bo61b3o2bo13b2obo25b2o8bo3bob2o31bo2bo6bo40b2o6bo3bo5bo2bo2b2o
24b2o52b2o33bo5bobo4bobo358bo$145b2o20bo20b2o13b2o4bo28b2o11b2o11bo10b
o12b2o48b2o11bo3bob3o12b2o2bo11b2o11b2o9b2o2b2o20b2o9b2ob2o5bobo26b2o
11b2o9bobo4b2o5bo11bo12b2o35b2o13bo4bo14b3o12b2o11b2o9b3obo21b2o10bobo
7bobo25b2o11b2o6b4o7b3ob2obo10b2o11b2o34b2o10bo5bobo26bo5bo4bo3bo3b2o
358b2o$146bo2b2o18bo19bo18bo30bo35bo13bo49bo12bobo2b2o14bo2bo12bo22b2o
2b2o21bo11bo7b2o28bo18bobo13bobo12bo49bo13b5o16bo14bo34bo14bo20b2o27bo
19bob2o26bo46bobo9bobo6bo27bo4bo2bob2o3bo$146bobobo17b2o16b3o47b3o35bo
11b3o47b3o34b3o10b3o47b3o21bo25b3o47b3o47b3o15b2o30b3o34bo12b3o47b3o
34b2o2bo8b3o47bo10bo9b2o28bo4bobobobob2o$147bo16b2o20bo24bo24bo36b2o
11bo49bo49bo49bo49bo37bo11bo49bo49bo36bobo10bo49bo39bo9bo48b2o4b2o6bob
o39bo6bobo390bo$164bo46bo2b2o44bo3b2o9bo34bo3b2o44bo3b2o44bo3b2o44bo3b
2o44bo3b2o7bo2bo33bo3b2o44bo3b2o44bo3b2o8bo35bo3b2o44bo3b2o7b3o34bo3b
2o23bo2bo6b2o41bo2b2o392b3o$149bo5bo9b3o41bobo3bo43bobo3bo7b2o34bobo3b
o43bobo3bo43bobo3bo43bobo3bo43bobo3bo7bo35bobo3bo43bobo3bo43bobo3bo43b
obo3bo43bobo3bo8bo34bobo3bo23b2o55bo391bo$148bobo3b3o10bo40bobo3bo43bo
bo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo9bo2bo30bobo3bo43bob
o3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo79bobo390bobo$149bo4bob2o50bo
4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o
30bo4bo13bo30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b
2o30bo4bo12b2o67bo374b2o8bo7bo$146b3o4b2o52b2o5b3o9bo30b2o5b3o9bo30b2o
5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b
2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo444bo7bobo$
146bo6b2o61bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b
3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o441bobo16bo$
153b2o74bo49bo49bo49bo49bo49bo49bo49bo49bo49bo49bo49bo49bo74b2o366b2o
6b2o5bobobo$157bo742b2o2bo373b2o7b2o2bo$156b2o15b2o710b2o13bobobo371b
2o13b2o$154bobo16bo710bobo8bo7bo372b2obo$153bo2bo14bobo710bo8b2ob2o
380b2o$154b2o15b2o710b2o8b2ob2o3bo$167bo724b3obo3bobo$165bo2bo726b3o3b
o$166b2o691bo42b3o$857b3o44bo$856bo$849bo5bobo$838b2o8b4o4bo19b2o395b
2o15b2o$163bo675bo8b4o25bo395b2o15bobo$162b2o675bobo16bo18bobo15b2o
395bo$161bo2bo7b2o666b2o13bobobo18b2o15b2o395b2o$161bobo4b2o2bo675b4o
3b2o2bo$153b2o6bo2bo3bobobo676b3o7b2o$152bobo6bo2bo6bo678bo414bo$152bo
9bobo1100b3o$151b2o8b3o5bo1098bo$168bobo1096bobo$169bo1098bo6bo9b2o$
170b3o1101b2o9bo$172bo681bo31bo2b2o375bo9bo6bobo$853b2o22b2o11b2o373bo
bobo3b3o7b2o$852bo25bo2b2o6b2o374bo2b2o4bo$144b2o695bo11bo4b2o18bobobo
13b2o366b2o$145bo694bobo15bobo18bo5b2o2b2o5bobo$145bobo15b2o678bo16bo
30bo6bo$146b2o15b2o675bo2bo16b2o19bo3b4o9b2o$841bob2o35bobo4bo2bo$843b
3o35bo$833bo6b2ob2o33b3o$833b3o4b2o2bo33bo389bobo$158b3o675bo4b3o424bo
b2o5b2o$157bo2bo674bobo4bo426bo2b2o$157bo4bo673bo16b2o50b2o358b2o$156b
2ob2obo690bo51bo358bobo$156b2obo2bo671bo16bobo32b2o15bobo358bo18bo$
145b2o11b4o671bobobo13b2o33b2o15b2o358b2o16b4o$146bo2b2o8b3o671bo2b2o
442bo3bo$146bobobo13b2o666b2o57bo388bo2bo$147bo8bo7bobo723b3o388b3o7bo
$154b2o10bo723bo2bo395b3o$149bo5b2o9b2o720b2o2b3o393bo$148bobo737b3o2b
o393bobo$149bo737b2o2b2o377b2o16bo$146b3o692b3o43b3o381bo$146bo692b3ob
2o42bob4o378bobo16bo$839bo3b2o46b2o11b2o366b2o13bobobo$839bo2bo6bo39bo
10b2o2bo382b2o2bo$173b2o658b2o5b3o5bob2o33bo14bobobo386b2o$173bo658bob
o13bobo33bob2o15bo$171bobo658bo16bo34bo11bo$155b3o13b2o658b2o50b2o12bo
3bo374bo$156bo6b2o730b3o2bobo373bo$157bo6b2o735bo$162b3o694bo42b3o375b
2o$162b2o693b3o44bo375bobo$856bo419b2ob2ob2o$850b2o3bobo417bo2b5o$838b
2o9bobo4bo19b2o397b7o8b2o$839bo11bo25bo16b2o380bo13bobo$839bobo16bo18b
obo5b3o5bo2bo380bo14bo$172b2o666b2o13bobobo18b2o5bobo5bo398b2o$168b2o
2bo670b2o10b2o2bo23b2o2b2o5b3o$153b2o13bobobo670b2o14b2o22b2ob2o$152bo
bo16bo673b3o35b2obob2o375bo$152bo689b2o2bo38b2obo376b3o$151b2o16bo672b
2ob3o39b2o379bo$168bobo672b2o422bobo$169bo674bo2b2o419bo6bo9b2o$162b3o
5b3o672b3o426b2o9bo$162bo2bo6bo673bo419bo7bobo6bobo$161bo3bo711b2o386b
obobo13b2o$161bobob2o711bo2b2o382bo2b2o$144b2o16b2ob2o674b2o15b2o18bob
obo13b2o366b2o11b4o$145bo17b3o675b2o15bobo18bo16bobo377b3o2bo$145bobo
712bo37bo377bo3bo$146b2o3b2o707b2o19bo5bo10b2o377bo2bo$150bo2bo726bobo
3b3o388b3o$881bo4bob2o$150b2obo679bo44b3o4b2o$833b3o42bo6b2o$836bo6bo
41b2o$835bobo4bobo44bo$836bo7bo8b2o33b2o15b2o358b2o15b2o$840b2o3bo7bo
32bobo16bo358bobo15b2o$834bo5b2o2bo6bobo31bo2bo14bobo358bo$145b2o8bo
677bobobo6bo6b2o33b2o15b2o358b2o$146bo2b2o3bobo676bo2b2o61bo$146bobobo
2bo3bo6b2o666b2o6b2o2b2o51bo2bo$147bo6bo2bo6bobo673b6o52b2o391bo$154bo
2bo8bo675bo446b3o$149bo5bobo8b2o1120bo$148bobo1130bo5bobo$149bo1120b2o
8b4o4bo$146b3o746bo375bo8b4o$146bo747b2o375bobo16bo$893bo2bo7b2o366b2o
13bobobo$893bobo4b2o2bo375b4o3b2o2bo$173b2o658b2o15b2o33b2o6bo2bo3bobo
bo376b3o7b2o$173bo658bobo16bo32bobo6bo2bo6bo378bo$154b2o15bobo658bo17b
o33bo9bobo$154b2o15b2o658b2o50b2o8b3o5bo$852bo47bobo$849bo51bo$849bo2b
o6bo42b3o$848b3o6b3o44bo381bo$848b3o5bo428b2o$848bo2bo3bobo426bo$159bo
678b2o9bobo4bo19b2o395bo11bo4b2o$158b3o678bo9b3o25bo394bobo15bobo$157b
o2b2o677bobo16bo18bobo15b2o378bo16bo$157bo14b2o666b2o13bobobo18b2o15b
2o375bo2bo16b2o$158bo9b2o2bo682b2o2bo413bob2o$153b2o7bo5bobobo686b2o
414b3o$152bobo5bobo8bo1093bo6b2ob2o$152bo8b2o1102b3o4b2o2bo$151b2o16bo
720b3o375bo4b3o$168bobo679b2o37bo2bo374bobo4bo$169bo679b2o38bo4bo373bo
16b2o$170b3o675bo4b2o33b2ob2obo390bo$172bo674b2o6bo32b2obo2bo371bo16bo
bo$841bobo4bob2ob3o21b2o11b4o371bobobo13b2o$841bo2bo9bo23bo2b2o8b3o
371bo2b2o$144b2o694bo3bo7bo5b2o18bobobo13b2o366b2o$145bo695bo2bo6b2o5b
obo18bo8bo7bobo$145bobo10b3obobo676b3o16bo25b2o10bo$146b2o10b3o3bo695b
2o19bo5b2o9b2o$156b2o722bobo$156bo3b3o718bo$156bo3bo672bo44b3o392b3o$
157bo2bo672b3o42bo392b3ob2o$158bo2bo674bo3b2o429bo3b2o$161bo673bobob2o
430bo2bo6bo$161bo674bo4bo11b2o50b2o358b2o5b3o5bob2o$160b3o690bo51bo
358bobo13bobo$160b3o671bo16bobo49bobo358bo16bo$145b2o13bo2bo669bobobo
13b2o34b3o13b2o358b2o$146bo2b2o10bo671bo2b2o50bo6b2o$146bobobo14bo666b
2o14b2o39bo6b2o$147bobo13b2obo680b2o45b3o394bo$149b2o15bo678b3o46b2o
393b3o$149b2o15b2o677b3o440bo$148bobo697bo433b2o3bobo$149bo1120b2o9bob
o4bo$146b3o694bobo3bo421bo11bo$146bo697b2o425bobo16bo$155bo688b2ob2o
55b2o366b2o13bobobo$154b3o689bo53b2o2bo370b2o10b2o2bo$153b2o2bo15b2o
658b2o15b2o33b2o13bobobo370b2o14b2o$173bo658bobo15b2o32bobo16bo373b3o$
158bo11b2obo658bo51bo389b2o2bo$164b2o2bo3bo658b2o50b2o16bo372b2ob3o$
158b2ob2o737bobo372b2o$165bobo2bo730bo374bo2b2o$159bo3bo4b2o689bo34b3o
5b3o372b3o$857b3o34bo2bo6bo373bo$163bo692bo36bo3bo$164bo685bo4bobo35bo
bob2o$164bo673b2o8bo7bo19b2o16b2ob2o374b2o15b2o$839bo8bo28bo17b3o375b
2o15bobo$839bobo4b2o10bo18bobo412bo$172b2o666b2o4bobo6bobobo18b2o3b2o
407b2o$168b2o2bo672b3o7b2o2bo22bo2bo$153b2o7b3o3bobobo672bo13b2o$152bo
bo16bo674b2o34b2obo379bo$152bo9bobo681b2o417b3o$151b2o8bo7bo1098bo6bo$
161bo3bo2bobo1096bobo4bobo$169bo1098bo7bo8b2o$161b2o2bo4b3o1099b2o3bo
7bo$172bo1093bo5b2o2bo6bobo$877b2o8bo377bobobo6bo6b2o$878bo2b2o3bobo
376bo2b2o$144b2o695b2o15b2o18bobobo2bo3bo6b2o366b2o6b2o2b2o$145bo695b
2o15bobo18bo6bo2bo6bobo373b6o$145bobo15b2o695bo25bo2bo8bo375bo$146b2o
15b2o695b2o19bo5bobo8b2o$880bobo$881bo$833bo44b3o$833b3o4bo2b2o33bo$
836bo$835bobo2bo3bo$836bo7bo8b2o50b2o358b2o15b2o$158b2o681bobo9bo51bo
358bobo16bo$158b2o674bo16bobo32b2o15bobo358bo17bo$145b2o13bo672bobobo
3b3o7b2o33b2o15b2o358b2o$146bo2b2o7b3o672bo2b2o446bo$146bobobo6bobo4b
2o666b2o447bo$147bo10b2o4bobo1114bo2bo6bo$157bo8bo1113b3o6b3o$149bo7bo
8b2o673bo438b3o5bo$148bobo4bo685bo438bo2bo3bobo$149bo692bo48bo378b2o9b
obo4bo$146b3o741b3o378bo9b3o$146bo689b2o4bo3bo42bo2b2o377bobo16bo$835b
o2bobo48bo14b2o366b2o13bobobo$843b2ob2o42bo9b2o2bo382b2o2bo$173b2o658b
o3bo2b2o43b2o7bo5bobobo386b2o$173bo658bob2o11bo36bobo5bobo8bo$154b2o
15bobo658bo51bo8b2o$154b2o15b2o658b2o15bo2b2o30b2o16bo$159bo689b3o48bo
bo379b2o$157b2ob2o688bo50bo379b2o$160b2o697bo42b3o375bo4b2o$156bo3bobo
694b3o44bo374b2o6bo$856bo416bobo4bob2ob3o$157bo697bobo415bo2bo9bo$158b
3o677b2o15b2o19b2o394bo3bo7bo5b2o$158b3o678bo15b2o20bo395bo2bo6b2o5bob
o$157b2o680bob2o13bobo18bobo10b3obobo376b3o16bo$156b2o14b2o666bo14bobo
bo18b2o10b3o3bo395b2o$168b2o2bo671bo10b2o2bo28b2o$153b2o13bobobo669bo
2bo13b2o27bo3b3o$152bobo16bo671b3o42bo3bo372bo$152bo690b3o43bo2bo372b
3o$151b2o11bo4bo674bo45bo2bo374bo3b2o$165b2obobo673bo48bo373bobob2o$
164b2o3bo674bo2bo45bo374bo4bo11b2o$170b3o672bo2bo43b3o390bo$172bo672bo
3bo42b3o371bo16bobo$843b3o3bo27b2o13bo2bo369bobobo13b2o$848b2o28bo2b2o
10bo371bo2b2o$144b2o695bo3b3o10b2o18bobobo14bo366b2o14b2o$145bo16b3o
676bobob3o10bobo18bobo13b2obo380b2o$145bobo5b2o6bo2bo695bo20b2o15bo
378b3o$146b2o5bo7bo3bo694b2o19b2o15b2o377b3o$151bo9bo2bo715bobo397bo$
150b3ob2obo4bobo716bo$150bo6b2o674bo44b3o394bobo3bo$151b2o4bo675b3o42b
o397b2o$155b2o679bo50bo388b2ob2o$154b2o679bobo48b3o389bo$836bo16b2o30b
2o2bo15b2o358b2o15b2o$843b2o8bo51bo358bobo15b2o$834bo8bobo5bobo36bo11b
2obo358bo$145b2o686bobobo5bo7b2o43b2o2bo3bo358b2o$146bo2b2o682bo2b2o9b
o42b2ob2o$146bobobo13b2o666b2o14bo48bobo2bo$147bo16bobo677b2o2bo42bo3b
o4b2o389bo$154b3o9bo678b3o441b3o$149bo4bobo9b2o678bo48bo392bo$148bobo
3bo2bo738bo385bo4bobo$149bo5b3o738bo373b2o8bo7bo$146b3o6b3o1113bo8bo$
146bo6bo2bo1114bobo4b2o10bo$156bo747b2o366b2o4bobo6bobobo$153bo746b2o
2bo372b3o7b2o2bo$173b2o658b2o15b2o33b2o7b3o3bobobo372bo13b2o$155bo17bo
658bobo15b2o32bobo16bo374b2o$154bo16bobo658bo51bo9bobo381b2o$154b2o15b
2o658b2o50b2o8bo7bo$893bo3bo2bobo$901bo$859bo33b2o2bo4b3o$857b3o44bo$
856bo$855bobo$838b2o8bobo5bo19b2o395b2o15b2o$163bo675bo8bo2bo25bo395b
2o15bobo$160b6o673bobo6bo2bo6bo18bobo15b2o395bo$160b2o2b2o6b2o666b2o6b
o3bo2bobobo18b2o15b2o395b2o$168b2o2bo676bobo3b2o2bo$153b2o6bo6bobobo
677bo8b2o$152bobo6bo2b2o5bo1093bo$152bo7bo3b2o1099b3o4bo2b2o$151b2o8bo
7bo1098bo$161bobo4bobo1096bobo2bo3bo$162bo6bo1098bo7bo8b2o$170b3o717b
2o381bobo9bo$172bo679bob2o34b2o374bo16bobo$877b2o13bo372bobobo3b3o7b2o
$852bo2bo22bo2b2o7b3o372bo2b2o$144b2o707b2o3b2o18bobobo6bobo4b2o366b2o
$145bo712bobo18bo10b2o4bobo$145bobo15b2o675b3o17bo28bo8bo$146b2o15b2o
674b2ob2o16b2o19bo7bo8b2o373bo$839b2obobo35bobo4bo385bo$840bo3bo36bo
392bo$159bo673bo6bo2bo34b3o$158b3o672b3o5b3o34bo389b2o4bo3bo$157b2o2bo
674bo430bo2bobo$161b2o672bobo437b2ob2o$158b3ob2o672bo16b2o50b2o358bo3b
o2b2o$159bo2b2o689bo51bo358bob2o11bo$158b3o673bo16bobo32b2o15bobo358bo
$145b2o14b2o670bobobo13b2o33b2o15b2o358b2o15bo2b2o$146bo2b2o10b2o670bo
2b2o53bo389b3o$146bobobo13b2o666b2o55b2ob2o388bo$147bo16bobo725b2o397b
o$154bo11bo721bo3bobo394b3o$149bo4bobo9b2o1120bo$148bobo3b2o733bo397bo
bo$149bo740b3o377b2o15b2o$146b3o693b2o46b3o378bo15b2o$146bo694b3o45b2o
380bob2o13bobo$840b2o6bo39b2o14b2o366bo14bobobo$841b2o6bo50b2o2bo371bo
10b2o2bo$173b2o658b2o13b3o34b2o13bobobo369bo2bo13b2o$156bo16bo658bobo
49bobo16bo371b3o$155bobo13bobo658bo51bo390b3o$154b2obo5b3o5b2o658b2o
50b2o11bo4bo374bo$156bo6bo2bo730b2obobo373bo$161b2o3bo729b2o3bo374bo2b
o$161b2ob3o692bo42b3o372bo2bo$162b3o692b3o44bo372bo3bo$856bo418b3o3bo$
855bobo422b2o$838b2o9b2o5bo19b2o395bo3b3o10b2o$839bo10b2o25bo16b3o376b
obob3o10bobo$839bobo7bo8bo18bobo5b2o6bo2bo395bo$172b2o666b2o13bobobo
18b2o5bo7bo3bo394b2o$168b2o2bo671b3o8b2o2bo23bo9bo2bo$153b2o13bobobo
671b4o11b2o21b3ob2obo4bobo$152bobo16bo671bo2bob2o32bo6b2o374bo$152bo
690bob2ob2o33b2o4bo375b3o$151b2o16bo673bo4bo38b2o379bo$163bo4bobo674bo
2bo37b2o379bobo$162b3o4bo675b3o420bo16b2o$161bo2b2o4b3o1102b2o8bo$161b
2ob2o6bo1093bo8bobo5bobo$160b3o714b2o386bobobo5bo7b2o$161b2obo713bo2b
2o382bo2b2o9bo$144b2o16bo2bo675b2o15b2o18bobobo13b2o366b2o14bo$145bo
16bo678b2o15bobo18bo16bobo377b2o2bo$145bobo15bobo694bo25b3o9bo378b3o$
146b2o4bo11bo695b2o19bo4bobo9b2o378bo$153bo726bobo3bo2bo$151b2o728bo5b
3o$151bo681bo44b3o6b3o$833b3o42bo6bo2bo$836bo51bo$835bobo47bo$836bo5b
3o8b2o50b2o358b2o15b2o$841bobo9bo33bo17bo358bobo15b2o$155bo678bo6bo2bo
6bobo32bo16bobo358bo$145b2o7b3o676bobobo3bo2bo6b2o33b2o15b2o358b2o$
146bo2b2o3b4o675bo2b2o4bobo$146bobobo13b2o666b2o7bo2bo$147bo16bobo675b
2o447bo$154b4o8bo675bo446b3o$149bo4b4o8b2o1120bo$148bobo5bo1130bobo$
149bo1120b2o8bobo5bo$146b3o746bo375bo8bo2bo$146bo691b2o52b6o373bobo6bo
2bo6bo$837bo2bo51b2o2b2o6b2o366b2o6bo3bo2bobobo$838bo61b2o2bo376bobo3b
2o2bo$833b2o15b2o33b2o6bo6bobobo377bo8b2o$832bobo14bo2bo31bobo6bo2b2o
5bo$832bo16bobo32bo7bo3b2o$831b2o15b2o33b2o8bo7bo$848bo44bobo4bobo$
176bo49bo49bo49bo49bo49bo49bo49bo49bo49bo49bo49bo49bo74b2o41bo6bo$176b
3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo
36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo61b2o6bo42b3o$179bo9b3o5b
2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o
5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b
3o5b2o52b2o4b3o44bo379bob2o$178b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o
12bo4bo30b2o12bo4bo30b2o12bo4bo30bo13bo4bo30b2o12bo4bo30b2o12bo4bo30b
2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo50b2obo4bo$191bo3bobo43bo
3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo30bo2bo9bo3bobo43bo3bobo43bo
3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo40bo10b3o3bobo426bo2bo$165b2o
23bo3bobo34bo8bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo35bo7bo3bobo
43bo3bobo43bo3bobo43bo3bobo43bo3bobo34b2o7bo3bobo43bo3bobo41b3o9bo5bo
19b2o407b2o3b2o$155b2o6bo2bo23b2o3bo34b3o7b2o3bo44b2o3bo35bo8b2o3bo44b
2o3bo44b2o3bo33bo2bo7b2o3bo44b2o3bo44b2o3bo44b2o3bo44b2o3bo34bo9b2o3bo
44b2o2bo46bo35bo412bobo$154bobo6b2o4b2o48bo9bo39bo49bo10bobo36bo49bo
49bo11bo37bo49bo49bo49bo49bo11b2o36bo24bo24bo20b2o16bo18bobo15b2o375b
3o17bo$147b2o9bo10bo47b3o8bo2b2o34b3o47b3o12bo34b3o30b2o15b3o47b3o47b
3o25bo21b3o47b3o10b3o34b3o47b3o11bo35b3o47b3o16b2o17bobobo18b2o15b2o
374b2ob2o16b2o$148bo6bobo9bobo46bo26b2obo19bo27b2o20bo14bo34bo14bo16b
5o13bo49bo12bobo13bobo18bo28b2o7bo11bo21b2o2b2o22bo12bo2bo14b2o2bobo
12bo49bo13bo35bo30bo18bo19bo18b2o2bo411b2obobo$148bobo5bo10b2o34b2o11b
2o10bob2ob3o7b4o6b2o11b2o25bobo7bobo10b2o21bob3o9b2o11b2o12b3o14bo4bo
13b2o35b2o12bo11bo5b2o4bobo9b2o11b2o26bobo5b2ob2o9b2o20b2o2b2o9b2o11b
2o11bo2b2o12b3obo3bo11b2o48b2o12bo10bo11b2o11b2o28bo4b2o13b2o20bo20b2o
411bo3bo$149b2o52b2o24b2o2bo2bo5bo3bo6b2o40bo6bo2bo31b2obo3bo8b2o25bob
2o13bo2b3o61bo2bo14bobo6bo11b2o47bo34b2o6bo7b2o6b2o16b2o2bo11b2o6bo38b
2o46b2obo9b2o45b2o35b2o52bo373bo6bo2bo$192b2o19b2o16bo3bo7b3o38bo17bo
2bo32bo4b2o16b3o18b2o13b2o2bo39b3o9bo2bo5b2o16bo10bobo3bo35bo18bo3bo
31bo7bo13b3ob2o15b3o12bob5o40b2o9b2o35bob2o56b2o87b3o372b3o5b3o$191b3o
12bo7b2o14bo12b3o37b3o17b2o34b4obo19b2o33b2o37bo4bo12bo2b5obo14bo13b2o
bo33b2o20b3o32b2ob2ob2o13b2o3b2o15b2o14b4o36b2o3bo10b2obo3b2o30bo20b2o
15b3o19b3o84b2o2bo374bo$187b2o4bo11b2o3b2o19bobo11bo36bobobob2o69b2obo
b2o71b2o3bo10b2ob3o3b3o49b2o15b3o2b2o50b2o3bo14bo2bobo35bo35b2ob2o12bo
bobo24bo31b2o14bo2bo2bo18bo88b2o372bobo$187bo2b2o12b2o3b2o21bo31bo3bo
12b2o3bob2o69bo2b4o70b2o15b2o25bobo29b2ob3o12bo5b2o69b2o2b3o71bo2b2o
14b2o25bo30bo2bo13bo4bo19b4o82b3ob2o372bo16b2o$188b2o15b2o4bo16b3o32b
3obo2bo11b2obo2bo70bo4bo72bo2bo12b2o4bo18bobo31b2obobo13bo4b3o18bo50b
2obobo71bo3bo14b3o55b2obo2bo10bobo2b3o19b2o12bo70bo2b2o389bo$168bo20bo
16b2o55bobobo16b2ob2obo16bo13bo3b2o33b4o15bobo34b4o18b2o15bo2bo17bo39b
ob2o11bo3bo2b2o16b3o11b3o36bo18b2o35bo2b2o16b2obo14b5o15b2o40bo2bo10b
2o6b3o14b3o10bo2bo12b2o5b4o45b3o373bo16bobo$166bobo57b2o41bo14b4o17bob
3o10b2o4b3o33b2o3bobo9b2o34bo39b3o17bo57bo5bo19bo8b2ob4o44bo7bo2bo33b
2o2b3o17bo15b2o2bo14bo2bo39bobo19b3o13bobo10bo3bo12b2o4b2ob2obo6b2o22b
2o14b2o370bobobo13b2o$166b3o9b2o46bo4bo37b2o7b2o6b3o3bo10b4o2bo9b2o8bo
38b2o9bo34bo4bo8b2o44b2o44bo7b2o26bo2b2o7bo2b2o4bobo40bo7b2o33b3o2b2o
8b2o25b3o15bo2bo51b2o24bo3bo2bo5bo3bo17b2o3b3o6b2o23bo2b2o10b2o370bo2b
2o$166bo11b2o11b2o27bo5bo14b2o20bo3bobo8b2o12bo10bo2b3o11b5o2bobo11b2o
25bo22b2o22bob2o9b2o11b2o32b2o14b2o35b2o11b2o10bo2bo3bo7b3o7b2o11b2o
25b3o8bo11b2o21b2o2b2o8b2o11b2o13bo16b2ob2o13b2o35b2o11b2o12b6o6bo3b2o
17b2o4b2o30bobobo13b2o366b2o$191bo29b2o4bo2bo10bo25bobo21bo11b2o3bo13b
3o3bo12bo49bo13bobo8bo24bo34bo14bo49bo11b2o18bobo15bo49bo13bo35bo33b2o
14bo49bo12b2o2b2o8bo2bo22bobo32bo16bobo$155b2o35b3o25b2o7bo12b3o47b3o
10b3o34b3o47b3o9bo37b3o47b3o47b3o11bobo33b3o47b3o9bobo35b3o47b3o47b3o
50b2o7b2o30bo11bo$151b2o2b2o37bo25b2o22bo49bo10b3o36bo49bo9bo2bo36bo
49bo49bo10b2obo35bo49bo11b2o36bo49bo49bo9bo40bo8bo26bo4bobo9b2o$150bob
o12b2o3bo44b2o3bo44b2o3bo44b2o3bo44b2o3bo34bobo7b2o3bo44b2ob3o44b2o3bo
35b2o7b2o3bo44b2o3bo44b2o3bo44b2o3bo44b2o3bo34b3o7b2o3bo20b2o12b3o22bo
bo3b2o$150bo14bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo
b3obo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo28bo14bo3bobo33b3o7b
o3bobo20bo14bo23bo$149b2o15bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo
43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo25b2o
16bo3bobo43bo3bobo16b3o36b3o393b2o$167bo4bo30b2o12bo4bo30b2o12bo4bo30b
2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo
30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo26b2o16bo4bo30b2o12bo4bo16bo38bo
394b3o$164b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo
9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o
30bo9b3o5b2o40b3o5b2o30bo9b3o5b2o448b2o6bo$164bo36b3o10bo36b3o10bo36b
3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo
36b3o10bo49bo36b3o10bo458b2o6bo$201bo49bo49bo49bo49bo49bo49bo49bo49bo
49bo49bo99bo103b2o358b2o13b3o$888bo16bo358bobo$887bobo13bobo358bo$886b
2obo5b3o5b2o358b2o$762bo125bo6bo2bo$761b2o130b2o3bo$761bobo129b2ob3o
392bo$894b3o392b3o$1288bo$1287bobo$734bo535b2o9b2o5bo$734bobo534bo10b
2o$734b2o535bobo7bo8bo$904b2o366b2o13bobobo$900b2o2bo371b3o8b2o2bo$
269bo49bo49bo49bo49bo49bo49bo315b2o13bobobo371b4o11b2o$256bo10b3o36bo
10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo277bobo16bo371bo
2bob2o$247b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo
30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o277bo390bob2ob2o$231bo16bo4bo12b2o30b
o4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o
30bo4bo279b2o16bo373bo4bo$229b3o16bobo3bo43bobo3bo43bobo3bo43bobo3bo
43bobo3bo43bobo3bo43bobo3bo43bobo3bo15b2o154b2o117bo4bobo374bo2bo$213b
o14bo20bobo3bo43bobo3bo43bobo3bo43bobo3bo43bob3obo43bobo3bo43bobo3bo
43bobo3bo14bo155bobo115b3o4bo375b3o$213b3o12b2o20bo3b2o44bo3b2o44bo3b
2o7b2o35bo3b2o44b3ob2o44bo3b2o7bobo34bo3b2o44bo3b2o12bobo155bo116bo2b
2o4b3o$216bo46b2o11bo49bo35bob2o10bo49bo49bo36bo2bo9bo49bo37b2o2b2o
273b2ob2o6bo$215b2o47bobo9b3o47b3o33bobo11b3o47b3o47b3o37bo9b3o47b3o
35b2o276b3o$265bo13bo49bo15bobo18b2o11bo49bo14bo34bo24bo8bobo13bo49bo
12bo3b3o294b2obo$232bo18b2o2b2o21b2o11bo8b3o25b2o11b2o7b3o7bo3bo2bo10b
2o11b2o35b2o14b2o32b2o11b2o9b2obo22b2o22bo25b2o11bobo2b5o118bobo154b2o
16bo2bo375b2o15b2o$216b2o12bo2bo17b2o2b3o33b2o7bo40bobo4b2o2bo7b2o2bo
26b2o7bo44b2o44b2o8bo4bo34bo9b2o38bo8b2o117b2o156bo16bo378b2o15bobo$
216b2o11bo2b2o16b3o2b2o33bo2bo7bo44b4ob2o8bo19bo5bo57bo17b3o39bo34b2o
9bobo3b2o33b3o4b2o119bo156bobo15bobo394bo$230bo20b2o2bo35b2o18bo36b3o
11b3o16b2o2bo3bo11b2obo39bo17bo2bo15b2o18b4o34bobo15b4o33b2o3bo278b2o
4bo11bo395b2o$231bo75bobob2o50bo18b3o4bo13bobob2o31bobo18bo4b2o12bo2bo
72bo4bo54bo268bo$307b3o2b2o69b2o5bo12b3ob2o29bobo25b2o15b2o70b4o2bo52b
5o264b2o$271bo35bobo2bo14bo3b2o50b2o2b3o15b2o49b3o3b3ob2o10bo3b2o71b2o
bob2o53bo2b2o263bo381bo$270b4o14b2o15b2o3b2o13b2ob2ob2o32b3o20b2o33bob
2o13bo14bob5o2bo12bo4bo37b2o33b2o19bob4o31b3obo647b3o$268b5obo12b3o15b
2ob3o13bo7bo31bo3bo18bo35bo3bobo10bo16b2o5bo2bo9b3o39bo2b2o13b2o18b3o
16b2o4bo30b2o653bo$232b2o33bo6b2o11bo2b2o16b2o6b2o7bo6b2o34bo47b2o11bo
6bobo14bo2bo61b3o2bo13b2obo25b2o8bo3bob2o29bo6b2o169b2o474bobo$210b2o
20bo20b2o11bo3bob3o12b2o2bo11b2o11b2o9b2o2b2o20b2o9b2ob2o5bobo26b2o11b
2o9bobo4b2o5bo11bo12b2o35b2o13bo4bo14b3o12b2o11b2o9b3obo20b2o9b2obo3bo
bo167b2o476bo5b3o8b2o$211bo2b2o18bo19bo12bobo2b2o14bo2bo12bo22b2o2b2o
21bo11bo7b2o28bo18bobo13bobo12bo49bo13b5o16bo14bo34bo11bobo10b3o5bo
169bo480bobo9bo$211bobobo3b3o11b2o16b3o34b3o10b3o47b3o21bo25b3o47b3o
47b3o15b2o30b3o34bo12bo13bo6b2o263bo378bo6bo2bo6bobo$212bo7bo8b2o20bo
49bo49bo49bo37bo11bo49bo49bo36bobo9b2o4b2o269b2o7b3o376bobobo3bo2bo6b
2o$220b3o6bo45bo3b2o44bo3b2o44bo3b2o44bo3b2o7bo2bo33bo3b2o44bo3b2o44bo
3b2o8bo14bo2bo97bo172bo2b2o3b4o375bo2b2o4bobo$214bo15b3o41bobo3bo43bob
o3bo43bobo3bo43bobo3bo7bo35bobo3bo43bobo3bo43bobo3bo23b2o98bo173bobobo
13b2o366b2o7bo2bo$213bobo16bo40bobo3bo43bobo3bo43bobo3bo43bobo3bo9bo2b
o30bobo3bo43bobo3bo43bobo3bo33b2o89b3o172bo16bobo375b2o$214bo58bo4bo
12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo13bo30bo4bo12b2o30bo4bo12b2o30bo4b
o12b2o20b2o271b4o8bo375bo$211b3o58b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo
30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo289bo4b4o8b2o$211bo69b
o10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o285bobo5bo
$294bo49bo49bo49bo49bo49bo49bo286bo$878b3o$238b2o638bo391b2o$238bo
1030bo2bo$219b2o15bobo566b3o462bo$219b2o15b2o567bo99b2o358b2o15b2o$
806bo98bo358bobo14bo2bo$886b2o15bobo358bo16bobo$624bo261b2o15b2o358b2o
15b2o$616bo5b3o66bo588bo$613b5o3bo67b2o592b2o$612bo7bobo67b2o591b2o6bo
$603b2o16bo661b2o4b3o$224b2o378bo8bo3bo662b2obo4bo$223bobo378bobo7b3o
6bo266b3o388b3o3bobo$222b2o13b2o366b2o13bobobo264bo2bo377b2o10bo5bo$
224bo8b2o2bo382b2o2bo264bo3bo377bo$218b2o4bobo6bobobo386b2o262bo2b3o
377bobo16bo$217bobo6b2o8bo584bo67b4o11b2o366b2o13bobobo$217bo7b3o592b
2o78b2o2bo382b2o2bo$216b2o16bo380bo204bobo62b2o13bobobo386b2o$233bobo
380bo267bobo6bobo7bo$234bo381b2o266bo9b2o$235b3o377b3o265b2o9bo6bo$
237bo373b3o2bo3b2o53bo224bobo$611b4obo3b2o53bobo223bo379b2o$611bobo2b
2o2b2o53b2o225b3o376bob2o$209b2o398b3o2b2obobo3b2o279bo375b2obob2o$
210bo398bo13bobo656b2ob2o$210bobo15b2o376bob2o15bo647b3o5b2o2b2o$211b
2o11bo3b2o376b3o16b2o249b2o398bo5bobo5b2o$223b3o381bo269bo14bo380bo2bo
5b3o5bobo$222b2ob2o650bobo13bo380b2o16bo$222bo375bo236b2o41b2o8b7o397b
2o$598b3o4bo229bobo49b5o2bo$224bo376bo4bo228bo50b2ob2ob2o$224b2o374bo
286bobo375bo$223bobo375b3o14b2o268b2o375b3o$618bo649bo$227bo371bo16bob
o41bobo230bo373bobo2b3o$210b2o14b2o370bobobo13b2o42b2o231bo374bo3bo12b
2o$211bo2b2o10bo371bo2b2o10b2o46bo611bo11bo$211bobobo13b2o366b2o14b2o
651bo15b2obo$212bo16bobo381b2o262b2o386bobobo14bo$231bo646bo2b2o382bo
2b2o10bo$214bo16b2o379bo265bobobo13b2o366b2o11b2o$213bob3obo390bobo
266bo16bobo378b4obo$214bob3o392b2o285bo381b3o$211b3o4bo631b2o29bo16b2o
377b2o2b2o$211bo397b2o238b2o29bobo393bo2b3o$609bo2b2o237bo29bo393b3o2b
2o$609bo3bo264b3o395bo2bo$219b3o16b2o358b2o10b3o2b2o261bo7b3o388b3o$
218bo2bo16bo358bobo15b2o29bo239bo2bo388bo$223bo5bobo4bobo358bo47bo239b
o3bo$217bo5bo4bo3bo3b2o358b2o47b3o237b4o16b2o358b2o15b2o$218bo4bo2bob
2o3bo652bo18bo358bobo15b2o$220bo4bobobobob2o668bobo358bo$224bo6bobo
390bo278b2o358b2o$225bo2b2o392b3o271b2o2bo$229bo391bo269b2o5b2obo$227b
obo390bobo276bobo389bo$228bo374b2o8bo7bo667b3o$604bo7bobo249b3o421bo$
604bobo16bo240bo414bo2bo4bobo$237b2o366b2o6b2o5bobobo240bo404b2o9b4o3b
o$233b2o2bo373b2o7b2o2bo646bo6bo$218b2o13bobobo371b2o13b2o645bobo5b2o
2b2o5bo$217bobo8bo7bo372b2obo19bo271b2o366b2o13bobobo$217bo8b2ob2o380b
2o17b2o263bo4b2o2bo374b2o6b2o2bo$216b2o8b2ob2o3bo396b2o252b2o7b3o3bobo
bo373b2o11b2o$225b3obo3bobo648bobo6bo9bo375b2o2bo$228b3o3bo649bo9b2o$
235b3o645b2o9bo6bo$237bo662bobo$901bo$902b3o$209b2o395b2o138b2obo6b2ob
o120bo23bo$210bo395b2o138bob2o6bob2o119b2o$210bobo15b2o514b2o8b2o4b2o
117bobo$211b2o15b2o514bo9bo5bo512b2o15b2o$621bobo121bo9bo5bo511b2o15bo
bo$622b2o120b2o8b2o4b2o133b2o395bo$598bo23bo123b2obo6b2obo135b2o395b2o
$598b3o145bob2o6bob2o$601bo148b2o8b2o$600bobo147bo9bo504bo$601bo6bo9b
2o131bo9bo503b3o$607b2o9bo131b2o8b2o506bo3b3o$219bo2b2o375bo9bo6bobo
127b2obo6b2obo507bobo3bob3o$210b2o11b2o373bobobo3b3o7b2o128bob2o6bob2o
110b2o396bo3b2ob2o8b2o$211bo2b2o6b2o374bo2b2o4bo263b2o17b2o380b2ob2o8b
o$211bobobo13b2o366b2o271bo19bob2o372bo7bo8bobo$212bo5b2o2b2o5bobo645b
2o13b2o371bobobo13b2o$224bo6bo646bo2b2o7b2o373bo2b2o$214bo3b4o9b2o404b
o240bobobo5b2o6b2o366b2o$213bobo4bo2bo414bo240bo16bobo$214bo421b3o249b
obo7bo$211b3o667bo7bo8b2o374bo$211bo389bobo276bobo390bobo$601bob2o5b2o
269bo391bo$602bo2b2o271b3o392b2o2bo$238b2o358b2o278bo390bobo6bo$238bo
358bobo668b2obobobobo4bo$219b2o15bobo358bo18bo652bo3b2obo2bo4bo$219b2o
15b2o358b2o16b4o237b3o47b2o358b2o3bo3bo4bo5bo$613bo3bo239bo47bo358bobo
4bobo5bo$224bo388bo2bo239bo29b2o15bobo358bo16bo2bo$223b3o388b3o7bo261b
2o2b3o10b2o358b2o16b3o$223bo2bo395b3o264bo3bo$221b2o2b3o393bo29bo237b
2o2bo$221b3o2bo393bobo29b2o238b2o397bo$220b2o2b2o377b2o16bo29b2o631bo
4b3o$220b3o381bo285b2o392b3obo$220bob4o378bobo16bo266bobo390bob3obo$
224b2o11b2o366b2o13bobobo265bo379b2o16bo$222bo10b2o2bo382b2o2bo646bo$
218bo14bobobo386b2o262b2o381bobo16bo$217bob2o15bo651b2o14b2o366b2o13bo
bobo$217bo11bo611bo46b2o10b2o2bo371bo10b2o2bo$216b2o12bo3bo374bo231b2o
42b2o13bobobo370b2o14b2o$228b3o2bobo373bo230bobo41bobo16bo371bo$234bo
649bo$235b3o375b2o268b2o14b3o375bobo$237bo375bobo286bo374b2o$609b2ob2o
b2o50bo228bo4bo376bo$608bo2b5o49bobo229bo4b3o$209b2o397b7o8b2o41b2o
236bo375bo$210bo16b2o380bo13bobo650b2ob2o$210bobo5b3o5bo2bo380bo14bo
269bo381b3o$211b2o5bobo5bo398b2o249b2o16b3o376b2o3bo11b2o$216b2o2b2o5b
3o647bo15b2obo376b2o15bobo$216b2ob2o656bobo13bo398bo$216b2obob2o375bo
279b2o3bobob2o2b3o398b2o$218b2obo376b3o225b2o53b2o2b2o2bobo$220b2o379b
o223bobo53b2o3bob4o$600bobo224bo53b2o3bo2b3o373bo$601bo6bo9b2o265b3o
377b3o$607b2o9bo266b2o381bo$599bo7bobo6bobo267bo380bobo$210b2o386bobob
o13b2o62bobo204bo380bo16b2o$211bo2b2o382bo2b2o78b2o592b3o7bo$211bobobo
13b2o366b2o11b4o67bo584bo8b2o6bobo$212bo16bobo377b3o2bo262b2o386bobobo
6bobo4b2o$231bo377bo3bo264bo2b2o382bo2b2o8bo$214bo5bo10b2o377bo2bo264b
obobo13b2o366b2o13b2o$213bobo3b3o388b3o266bo6b3o7bobo378bobo$214bo4bob
2o662bo3bo8bo378b2o$211b3o4b2o661bo16b2o$211bo6b2o591b2o67bobo7bo$218b
2o592b2o67bo3b5o$222bo588bo66b3o5bo$221b2o15b2o358b2o15b2o261bo$219bob
o16bo358bobo15b2o$218bo2bo14bobo358bo98bo$219b2o15b2o358b2o99bo567b2o
15b2o$232bo462b3o566bobo15b2o$230bo2bo1030bo$231b2o391bo638b2o$622b3o$
621bo286bo49bo49bo49bo49bo49bo49bo$614bo5bobo285b3o10bo36b3o10bo36b3o
10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo69bo$603b2o8b4o4bo289bo9b3o5b
2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o
5b2o58b3o$228bo375bo8b4o271b2o20b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30bo
13bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo58bo$227b2o375bobo16bo172b
3o89b2o33bo3bobo43bo3bobo43bo3bobo30bo2bo9bo3bobo43bo3bobo43bo3bobo43b
o3bobo40bo16bobo$226bo2bo7b2o366b2o13bobobo173bo98b2o23bo3bobo43bo3bob
o43bo3bobo35bo7bo3bobo43bo3bobo43bo3bobo43bo3bobo41b3o15bo$226bobo4b2o
2bo375b4o3b2o2bo172bo97bo2bo14bo8b2o3bo44b2o3bo44b2o3bo33bo2bo7b2o3bo
44b2o3bo44b2o3bo44b2o3bo45bo6b3o$218b2o6bo2bo3bobobo376b3o7b2o269b2o4b
2o9bobo36bo49bo49bo11bo37bo49bo49bo49bo20b2o8bo7bo$217bobo6bo2bo6bo
378bo263b2o6bo13bo12bo34b3o30b2o15b3o47b3o47b3o25bo21b3o47b3o10b3o34b
3o16b2o11b3o3bobobo$217bo9bobo480bo169bo5b3o10bobo11bo34bo14bo16b5o13b
o49bo12bobo13bobo18bo28b2o7bo11bo21b2o2b2o22bo12bo2bo14b2o2bobo12bo19b
o18b2o2bo$216b2o8b3o5bo476b2o167bobo3bob2o9b2o20bob3o9b2o11b2o12b3o14b
o4bo13b2o35b2o12bo11bo5b2o4bobo9b2o11b2o26bobo5b2ob2o9b2o20b2o2b2o9b2o
11b2o11bo2b2o12b3obo3bo11b2o20bo20b2o$233bobo474b2o169b2o6bo29b2obo3bo
8b2o25bob2o13bo2b3o61bo2bo14bobo6bo11b2o47bo34b2o6bo7b2o6b2o16b2o2bo
11b2o6bo33b2o$234bo653b2o30bo4b2o16b3o18b2o13b2o2bo39b3o9bo2bo5b2o16bo
10bobo3bo35bo18bo3bo31bo7bo13b3ob2o15b3o12bob5o$235b3o647bob3o31b4obo
19b2o33b2o37bo4bo12bo2b5obo14bo13b2obo33b2o20b3o32b2ob2ob2o13b2o3b2o
15b2o14b4o$237bo381bo263b2o2bo53b2obob2o71b2o3bo10b2ob3o3b3o49b2o15b3o
2b2o50b2o3bo14bo2bobo35bo$618b2o264b5o52bo2b4o70b2o15b2o25bobo29b2ob3o
12bo5b2o69b2o2b3o$617bo268bo54bo4bo72bo2bo12b2o4bo18bobo31b2obobo13bo
4b3o18bo50b2obobo75bo$209b2o395bo11bo4b2o278bo3b2o33b4o15bobo34b4o18b
2o15bo2bo17bo39bob2o11bo3bo2b2o16b3o11b3o36bo18b2o35bo2b2o20bo$210bo
394bobo15bobo156bo119b2o4b3o33b2o3bobo9b2o34bo39b3o17bo57bo5bo19bo8b2o
b4o44bo7bo2bo33b2o2b3o16b2o2bo11b2o$210bobo15b2o378bo16bo156b2o117b2o
8bo38b2o9bo34bo4bo8b2o44b2o44bo7b2o26bo2b2o7bo2b2o4bobo40bo7b2o33b3o2b
2o17bo2bo12b2o$211b2o15b2o375bo2bo16b2o154bobo118b5o2bobo11b2o25bo22b
2o22bob2o9b2o11b2o32b2o14b2o35b2o11b2o10bo2bo3bo7b3o7b2o11b2o25b3o8bo
11b2o21b2o2b2o18bo$606bob2o294b3o3bo12bo49bo13bobo8bo24bo34bo14bo49bo
11b2o18bobo15bo49bo13bo$608b3o276b2o35b3o47b3o9bo37b3o47b3o47b3o11bobo
33b3o47b3o9bobo47b2o$598bo6b2ob2o273b2o2b2o37bo49bo9bo2bo36bo49bo49bo
10b2obo35bo49bo11b2o46bo$598b3o4b2o2bo116bo155bobo12b2o3bo44b2o3bo34bo
bo7b2o3bo44b2ob3o44b2o3bo35b2o7b2o3bo44b2o3bo44b2o3bo20b2o12b3o$223b3o
375bo4b3o115bobo155bo14bo3bobo43bo3bobo43bo3bobo43bob3obo43bo3bobo43bo
3bobo43bo3bobo43bo3bobo20bo14bo$222bo2bo374bobo4bo117b2o154b2o15bo3bob
o43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo16b3o$
222bo4bo373bo16b2o279bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12b
o4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo16bo$221b2ob2obo390bo277b3o5b
2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o
5b2o30bo9b3o5b2o$221b2obo2bo371bo16bobo277bo36b3o10bo36b3o10bo36b3o10b
o36b3o10bo36b3o10bo36b3o10bo36b3o10bo$210b2o11b4o371bobobo13b2o315bo
49bo49bo49bo49bo49bo49bo$211bo2b2o8b3o371bo2b2o$211bobobo13b2o366b2o$
212bo8bo7bobo535b2o$219b2o10bo534bobo$214bo5b2o9b2o535bo$213bobo$214bo
$211b3o392b3o$211bo392b3ob2o129bobo$604bo3b2o130b2o$604bo2bo6bo125bo$
238b2o358b2o5b3o5bob2o$238bo358bobo13bobo$236bobo358bo16bo$220b3o13b2o
358b2o103bo99bo49bo49bo49bo49bo49bo49bo49bo49bo49bo49bo$221bo6b2o458bo
10b3o36bo49bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b
3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo$222bo6b2o448b2o5b3o9bo30b2o
5b3o40b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o
5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b
2o5b3o$227b3o394bo38bo16bo4bo12b2o30bo4bo16b2o26bo4bo12b2o30bo4bo12b2o
30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b
2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo$227b2o393b3o36b3o16bobo
3bo43bobo3bo16b2o25bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3b
o43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo15b2o$621bo23bo
14bo20bobo3bo7b3o33bobo3bo14bo28bobo3bo43bobo3bo43bobo3bo43bobo3bo43bo
bo3bo43bob3obo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo
14bo$615b2o3bobo22b3o12b2o20bo3b2o7b3o34bo3b2o44bo3b2o44bo3b2o44bo3b2o
44bo3b2o7b2o35bo3b2o44b3ob2o44bo3b2o7bobo34bo3b2o44bo3b2o44bo3b2o44bo
3b2o44bo3b2o12bobo$603b2o9bobo4bo26bo8bo40bo9bo49bo49bo36b2o11bo49bo
35bob2o10bo49bo49bo36bo2bo9bo49bo36b3o10bo49bo22b2o25bo37b2o2b2o$604bo
11bo30b2o7b2o50b3o47b3o47b3o35bobo9b3o47b3o33bobo11b3o47b3o47b3o37bo9b
3o47b3o34b3o10b3o47b3o12bo7b2o25b3o35b2o$604bobo16bo32bobo22bo2bo8b2o
2b2o12bo49bo14b2o33bo35bo13bo49bo15bobo18b2o11bo49bo14bo34bo24bo8bobo
13bo49bo12bo3b3o13bo3b2o11bo21bobo25bo10bo2bo4b2o29bo$237b2o366b2o13bo
bobo30b2o4b2o17b2o3bo6b6o12b2o11b2o35b2o13b2ob2o16bo13b2o11b2o8b2o2b2o
21b2o11bo8b3o25b2o11b2o7b3o7bo3bo2bo10b2o11b2o35b2o14b2o32b2o11b2o9b2o
bo22b2o22bo25b2o11bobo2b5o11b3o2bo10bo12b2o8bobo3bo20b2o14bo5bo27b2o
11b2o11bo$233b2o2bo370b2o10b2o2bo23b2o6b3o3b2o17bo3bo5bo2bo3bo24b2o51b
o2bo15b3o25b2o8b2o2b3o33b2o7bo40bobo4b2o2bo7b2o2bo26b2o7bo44b2o44b2o8b
o4bo34bo9b2o38bo8b2o9bo2b4o10bo3b3o6b2o7b2o37bo4bo46b2o9b3o$218b2o13bo
bobo370b2o14b2o22b2o6bob2ob2o4b2o12bo3bo10bobo13b3o19bobo39bo2bo14bo2b
2o15bo17b3o2b2o33bo2bo7bo44b4ob2o8bo19bo5bo57bo17b3o39bo34b2o9bobo3b2o
33b3o4b2o10b3obo17b4o14bo41b2o57bobo$217bobo16bo373b3o45b4o5b2o12bo2bo
10b3o14b3o6b2o10bo2bo40b2o15b5o14bob2o16b2o2bo35b2o18bo36b3o11b3o16b2o
2bo3bo11b2obo39bo17bo2bo15b2o18b4o34bobo15b4o33b2o3bo13bo16bob2ob2o16b
obobo55b2o16bo20bo$217bo389b2o2bo70bo12b2o19b3o2bobo10bo2bob2o55b3o14b
o3bo71bobob2o50bo18b3o4bo13bobob2o31bobo18bo4b2o12bo2bo72bo4bo70bo2bob
2o11bo2bob3o32b3o16bo4b2o15b2o$216b2o16bo372b2ob3o82b4o19bo4bo13bo2bo
30bo25b2o14b2o2bo71b3o2b2o69b2o5bo12b3ob2o29bobo25b2o15b2o70b4o2bo69b
2obo3b2o12bo3bo31bo21b2o3b2o12b2o2bo$233bobo372b2o88bo18bo2bo2bo14b2o
31bo24bobobo12b2ob2o35bo35bobo2bo14bo3b2o50b2o2b3o15b2o49b3o3b3ob2o10b
o3b2o71b2obob2o69b2obobobo36bo11bobo19b2o3b2o11bo4b2o$234bo374bo2b2o
84b3o19b3o15b2o20bo30b2o3bob2o10bo3b2o36b4o14b2o15b2o3b2o13b2ob2ob2o
32b3o20b2o33bob2o13bo14bob5o2bo12bo4bo37b2o33b2o19bob4o34b2o17b3o37b3o
12bo14b2o7bo12b3o$227b3o5b3o372b3o87b2o56b2obo35b2o9b2o40b5obo12b3o15b
2ob3o13bo7bo31bo3bo18bo35bo3bobo10bo16b2o5bo2bo9b3o39bo2b2o13b2o18b3o
16b2o4bo32bo2bo17bo38b3o7bo3bo16b2o19b2o$227bo2bo6bo373bo52b2o35b2o45b
2o9bob2o46b2o38bo6b2o11bo2b2o16b2o6b2o7bo6b2o34bo47b2o11bo6bobo14bo2bo
61b3o2bo13b2obo25b2o8bo3bob2o31bo2bo6bo40b2o6bo3bo5bo2bo2b2o24b2o52b2o
$226bo3bo411b2o20bo20b2o13b2o4bo28b2o11b2o11bo10bo12b2o48b2o11bo3bob3o
12b2o2bo11b2o11b2o9b2o2b2o20b2o9b2ob2o5bobo26b2o11b2o9bobo4b2o5bo11bo
12b2o35b2o13bo4bo14b3o12b2o11b2o9b3obo21b2o10bobo7bobo25b2o11b2o6b4o7b
3ob2obo10b2o11b2o34b2o10bo5bobo$226bobob2o411bo2b2o18bo19bo18bo30bo35b
o13bo49bo12bobo2b2o14bo2bo12bo22b2o2b2o21bo11bo7b2o28bo18bobo13bobo12b
o49bo13b5o16bo14bo34bo14bo20b2o27bo19bob2o26bo46bobo9bobo6bo$209b2o16b
2ob2o374b2o15b2o18bobobo17b2o16b3o47b3o35bo11b3o47b3o34b3o10b3o47b3o
21bo25b3o47b3o47b3o15b2o30b3o34bo12b3o47b3o34b2o2bo8b3o47bo10bo9b2o$
210bo17b3o375b2o15bobo18bo16b2o20bo24bo24bo36b2o11bo49bo49bo49bo49bo
37bo11bo49bo49bo36bobo10bo49bo39bo9bo48b2o4b2o6bobo$210bobo412bo35bo
46bo2b2o44bo3b2o9bo34bo3b2o44bo3b2o44bo3b2o44bo3b2o44bo3b2o7bo2bo33bo
3b2o44bo3b2o44bo3b2o8bo35bo3b2o44bo3b2o7b3o34bo3b2o23bo2bo6b2o$211b2o
3b2o407b2o19bo5bo9b3o41bobo3bo43bobo3bo7b2o34bobo3bo43bobo3bo43bobo3bo
43bobo3bo43bobo3bo7bo35bobo3bo43bobo3bo43bobo3bo43bobo3bo43bobo3bo8bo
34bobo3bo23b2o$215bo2bo426bobo3b3o10bo40bobo3bo43bobo3bo43bobo3bo43bob
o3bo43bobo3bo43bobo3bo43bobo3bo9bo2bo30bobo3bo43bobo3bo43bobo3bo43bobo
3bo43bobo3bo43bobo3bo$646bo4bob2o50bo4bo12b2o30bo4bo12b2o30bo4bo12b2o
30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo13bo30bo4bo12b2o30bo4bo12b
2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o30bo4bo12b2o$215b2obo379bo44b3o
4b2o52b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o
5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b2o5b3o9bo30b
2o5b3o9bo30b2o5b3o9bo$598b3o42bo6b2o61bo10b3o36bo10b3o36bo10b3o36bo10b
3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo10b3o36bo
10b3o36bo10b3o$601bo6bo41b2o74bo49bo49bo49bo49bo49bo49bo49bo49bo49bo
49bo49bo49bo$600bobo4bobo44bo$601bo7bo8b2o33b2o15b2o$605b2o3bo7bo32bob
o16bo$599bo5b2o2bo6bobo31bo2bo14bobo$210b2o8bo377bobobo6bo6b2o33b2o15b
2o$211bo2b2o3bobo376bo2b2o61bo$211bobobo2bo3bo6b2o366b2o6b2o2b2o51bo2b
o$212bo6bo2bo6bobo373b6o52b2o691bo$219bo2bo8bo375bo746b3o$214bo5bobo8b
2o1120bo$213bobo1130bo5bobo$214bo1120b2o8b4o4bo$211b3o446bo675bo8b4o$
211bo447b2o675bobo16bo$658bo2bo7b2o666b2o13bobobo$658bobo4b2o2bo675b4o
3b2o2bo$238b2o358b2o15b2o33b2o6bo2bo3bobobo676b3o7b2o$238bo358bobo16bo
32bobo6bo2bo6bo678bo$219b2o15bobo358bo17bo33bo9bobo$219b2o15b2o358b2o
50b2o8b3o5bo$617bo47bobo$614bo51bo$614bo2bo6bo42b3o$613b3o6b3o44bo681b
o$613b3o5bo728b2o$613bo2bo3bobo726bo$224bo378b2o9bobo4bo19b2o695bo11bo
4b2o$223b3o378bo9b3o25bo694bobo15bobo$222bo2b2o377bobo16bo18bobo15b2o
678bo16bo$222bo14b2o366b2o13bobobo18b2o15b2o675bo2bo16b2o$223bo9b2o2bo
382b2o2bo713bob2o$218b2o7bo5bobobo386b2o714b3o$217bobo5bobo8bo1093bo6b
2ob2o$217bo8b2o1102b3o4b2o2bo$216b2o16bo420b3o675bo4b3o$233bobo379b2o
37bo2bo674bobo4bo$234bo379b2o38bo4bo673bo16b2o$235b3o375bo4b2o33b2ob2o
bo690bo$237bo374b2o6bo32b2obo2bo671bo16bobo$606bobo4bob2ob3o21b2o11b4o
671bobobo13b2o$606bo2bo9bo23bo2b2o8b3o671bo2b2o$209b2o394bo3bo7bo5b2o
18bobobo13b2o666b2o$210bo395bo2bo6b2o5bobo18bo8bo7bobo$210bobo10b3obob
o376b3o16bo25b2o10bo$211b2o10b3o3bo395b2o19bo5b2o9b2o$221b2o422bobo$
221bo3b3o418bo$221bo3bo372bo44b3o692b3o$222bo2bo372b3o42bo692b3ob2o$
223bo2bo374bo3b2o729bo3b2o$226bo373bobob2o730bo2bo6bo$226bo374bo4bo11b
2o50b2o658b2o5b3o5bob2o$225b3o390bo51bo658bobo13bobo$225b3o371bo16bobo
49bobo658bo16bo$210b2o13bo2bo369bobobo13b2o34b3o13b2o658b2o$211bo2b2o
10bo371bo2b2o50bo6b2o$211bobobo14bo366b2o14b2o39bo6b2o$212bobo13b2obo
380b2o45b3o694bo$214b2o15bo378b3o46b2o693b3o$214b2o15b2o377b3o740bo$
213bobo397bo733b2o3bobo$214bo1120b2o9bobo4bo$211b3o394bobo3bo721bo11bo
$211bo397b2o725bobo16bo$220bo388b2ob2o55b2o666b2o13bobobo$219b3o389bo
53b2o2bo670b2o10b2o2bo$218b2o2bo15b2o358b2o15b2o33b2o13bobobo670b2o14b
2o$238bo358bobo15b2o32bobo16bo673b3o$223bo11b2obo358bo51bo689b2o2bo$
229b2o2bo3bo358b2o50b2o16bo672b2ob3o$223b2ob2o437bobo672b2o$230bobo2bo
430bo674bo2b2o$224bo3bo4b2o389bo34b3o5b3o672b3o$622b3o34bo2bo6bo673bo$
228bo392bo36bo3bo$229bo385bo4bobo35bobob2o$229bo373b2o8bo7bo19b2o16b2o
b2o674b2o15b2o$604bo8bo28bo17b3o675b2o15bobo$604bobo4b2o10bo18bobo712b
o$237b2o366b2o4bobo6bobobo18b2o3b2o707b2o$233b2o2bo372b3o7b2o2bo22bo2b
o$218b2o7b3o3bobobo372bo13b2o$217bobo16bo374b2o34b2obo679bo$217bo9bobo
381b2o717b3o$216b2o8bo7bo1098bo6bo$226bo3bo2bobo1096bobo4bobo$234bo
1098bo7bo8b2o$226b2o2bo4b3o1099b2o3bo7bo$237bo1093bo5b2o2bo6bobo$642b
2o8bo677bobobo6bo6b2o$643bo2b2o3bobo676bo2b2o$209b2o395b2o15b2o18bobob
o2bo3bo6b2o666b2o6b2o2b2o$210bo395b2o15bobo18bo6bo2bo6bobo673b6o$210bo
bo15b2o395bo25bo2bo8bo675bo$211b2o15b2o395b2o19bo5bobo8b2o$645bobo$
646bo$598bo44b3o$598b3o4bo2b2o33bo$601bo$600bobo2bo3bo$601bo7bo8b2o50b
2o658b2o15b2o$223b2o381bobo9bo51bo658bobo16bo$223b2o374bo16bobo32b2o
15bobo658bo17bo$210b2o13bo372bobobo3b3o7b2o33b2o15b2o658b2o$211bo2b2o
7b3o372bo2b2o746bo$211bobobo6bobo4b2o366b2o747bo$212bo10b2o4bobo1114bo
2bo6bo$222bo8bo1113b3o6b3o$214bo7bo8b2o373bo738b3o5bo$213bobo4bo385bo
738bo2bo3bobo$214bo392bo48bo678b2o9bobo4bo$211b3o441b3o678bo9b3o$211bo
389b2o4bo3bo42bo2b2o677bobo16bo$600bo2bobo48bo14b2o666b2o13bobobo$608b
2ob2o42bo9b2o2bo682b2o2bo$238b2o358bo3bo2b2o43b2o7bo5bobobo686b2o$238b
o358bob2o11bo36bobo5bobo8bo$219b2o15bobo358bo51bo8b2o$219b2o15b2o358b
2o15bo2b2o30b2o16bo$224bo389b3o48bobo679b2o$222b2ob2o388bo50bo679b2o$
225b2o397bo42b3o675bo4b2o$221bo3bobo394b3o44bo674b2o6bo$621bo716bobo4b
ob2ob3o$222bo397bobo715bo2bo9bo$223b3o377b2o15b2o19b2o694bo3bo7bo5b2o$
223b3o378bo15b2o20bo695bo2bo6b2o5bobo$222b2o380bob2o13bobo18bobo10b3ob
obo676b3o16bo$221b2o14b2o366bo14bobobo18b2o10b3o3bo695b2o$233b2o2bo
371bo10b2o2bo28b2o$218b2o13bobobo369bo2bo13b2o27bo3b3o$217bobo16bo371b
3o42bo3bo672bo$217bo390b3o43bo2bo672b3o$216b2o11bo4bo374bo45bo2bo674bo
3b2o$230b2obobo373bo48bo673bobob2o$229b2o3bo374bo2bo45bo674bo4bo11b2o$
235b3o372bo2bo43b3o690bo$237bo372bo3bo42b3o671bo16bobo$608b3o3bo27b2o
13bo2bo669bobobo13b2o$613b2o28bo2b2o10bo671bo2b2o$209b2o395bo3b3o10b2o
18bobobo14bo666b2o14b2o$210bo16b3o376bobob3o10bobo18bobo13b2obo680b2o$
210bobo5b2o6bo2bo395bo20b2o15bo678b3o$211b2o5bo7bo3bo394b2o19b2o15b2o
677b3o$216bo9bo2bo415bobo697bo$215b3ob2obo4bobo416bo$215bo6b2o374bo44b
3o694bobo3bo$216b2o4bo375b3o42bo697b2o$220b2o379bo50bo688b2ob2o$219b2o
379bobo48b3o689bo$601bo16b2o30b2o2bo15b2o658b2o15b2o$608b2o8bo51bo658b
obo15b2o$599bo8bobo5bobo36bo11b2obo658bo$210b2o386bobobo5bo7b2o43b2o2b
o3bo658b2o$211bo2b2o382bo2b2o9bo42b2ob2o$211bobobo13b2o366b2o14bo48bob
o2bo$212bo16bobo377b2o2bo42bo3bo4b2o689bo$219b3o9bo378b3o741b3o$214bo
4bobo9b2o378bo48bo692bo$213bobo3bo2bo438bo685bo4bobo$214bo5b3o438bo
673b2o8bo7bo$211b3o6b3o1113bo8bo$211bo6bo2bo1114bobo4b2o10bo$221bo447b
2o666b2o4bobo6bobobo$218bo446b2o2bo672b3o7b2o2bo$238b2o358b2o15b2o33b
2o7b3o3bobobo672bo13b2o$220bo17bo358bobo15b2o32bobo16bo674b2o$219bo16b
obo358bo51bo9bobo681b2o$219b2o15b2o358b2o50b2o8bo7bo$658bo3bo2bobo$
666bo$624bo33b2o2bo4b3o$622b3o44bo$621bo$620bobo$603b2o8bobo5bo19b2o
695b2o15b2o$228bo375bo8bo2bo25bo695b2o15bobo$225b6o373bobo6bo2bo6bo18b
obo15b2o695bo$225b2o2b2o6b2o366b2o6bo3bo2bobobo18b2o15b2o695b2o$233b2o
2bo376bobo3b2o2bo$218b2o6bo6bobobo377bo8b2o$217bobo6bo2b2o5bo1093bo$
217bo7bo3b2o1099b3o4bo2b2o$216b2o8bo7bo1098bo$226bobo4bobo1096bobo2bo
3bo$227bo6bo1098bo7bo8b2o$235b3o417b2o681bobo9bo$237bo379bob2o34b2o
674bo16bobo$642b2o13bo672bobobo3b3o7b2o$617bo2bo22bo2b2o7b3o672bo2b2o$
209b2o407b2o3b2o18bobobo6bobo4b2o666b2o$210bo412bobo18bo10b2o4bobo$
210bobo15b2o375b3o17bo28bo8bo$211b2o15b2o374b2ob2o16b2o19bo7bo8b2o673b
o$604b2obobo35bobo4bo685bo$605bo3bo36bo692bo$224bo373bo6bo2bo34b3o$
223b3o372b3o5b3o34bo689b2o4bo3bo$222b2o2bo374bo730bo2bobo$226b2o372bob
o737b2ob2o$223b3ob2o372bo16b2o50b2o658bo3bo2b2o$224bo2b2o389bo51bo658b
ob2o11bo$223b3o373bo16bobo32b2o15bobo658bo$210b2o14b2o370bobobo13b2o
33b2o15b2o658b2o15bo2b2o$211bo2b2o10b2o370bo2b2o53bo689b3o$211bobobo
13b2o366b2o55b2ob2o688bo$212bo16bobo425b2o697bo$219bo11bo421bo3bobo
694b3o$214bo4bobo9b2o1120bo$213bobo3b2o433bo697bobo$214bo440b3o677b2o
15b2o$211b3o393b2o46b3o678bo15b2o$211bo394b3o45b2o680bob2o13bobo$605b
2o6bo39b2o14b2o666bo14bobobo$606b2o6bo50b2o2bo671bo10b2o2bo$238b2o358b
2o13b3o34b2o13bobobo669bo2bo13b2o$221bo16bo358bobo49bobo16bo671b3o$
220bobo13bobo358bo51bo690b3o$219b2obo5b3o5b2o358b2o50b2o11bo4bo674bo$
221bo6bo2bo430b2obobo673bo$226b2o3bo429b2o3bo674bo2bo$226b2ob3o392bo
42b3o672bo2bo$227b3o392b3o44bo672bo3bo$621bo718b3o3bo$620bobo722b2o$
603b2o9b2o5bo19b2o695bo3b3o10b2o$604bo10b2o25bo16b3o676bobob3o10bobo$
604bobo7bo8bo18bobo5b2o6bo2bo695bo$237b2o366b2o13bobobo18b2o5bo7bo3bo
694b2o$233b2o2bo371b3o8b2o2bo23bo9bo2bo$218b2o13bobobo371b4o11b2o21b3o
b2obo4bobo$217bobo16bo371bo2bob2o32bo6b2o674bo$217bo390bob2ob2o33b2o4b
o675b3o$216b2o16bo373bo4bo38b2o679bo$228bo4bobo374bo2bo37b2o679bobo$
227b3o4bo375b3o720bo16b2o$226bo2b2o4b3o1102b2o8bo$226b2ob2o6bo1093bo8b
obo5bobo$225b3o414b2o686bobobo5bo7b2o$226b2obo413bo2b2o682bo2b2o9bo$
209b2o16bo2bo375b2o15b2o18bobobo13b2o666b2o14bo$210bo16bo378b2o15bobo
18bo16bobo677b2o2bo$210bobo15bobo394bo25b3o9bo678b3o$211b2o4bo11bo395b
2o19bo4bobo9b2o678bo$218bo426bobo3bo2bo$216b2o428bo5b3o$216bo381bo44b
3o6b3o$598b3o42bo6bo2bo$601bo51bo$600bobo47bo$601bo5b3o8b2o50b2o658b2o
15b2o$606bobo9bo33bo17bo658bobo15b2o$220bo378bo6bo2bo6bobo32bo16bobo
658bo$210b2o7b3o376bobobo3bo2bo6b2o33b2o15b2o658b2o$211bo2b2o3b4o375bo
2b2o4bobo$211bobobo13b2o366b2o7bo2bo$212bo16bobo375b2o747bo$219b4o8bo
375bo746b3o$214bo4b4o8b2o1120bo$213bobo5bo1130bobo$214bo1120b2o8bobo5b
o$211b3o446bo675bo8bo2bo$211bo391b2o52b6o673bobo6bo2bo6bo$602bo2bo51b
2o2b2o6b2o666b2o6bo3bo2bobobo$603bo61b2o2bo676bobo3b2o2bo$238b2o358b2o
15b2o33b2o6bo6bobobo677bo8b2o$238bo358bobo14bo2bo31bobo6bo2b2o5bo$219b
2o15bobo358bo16bobo32bo7bo3b2o$219b2o15b2o358b2o15b2o33b2o8bo7bo$613bo
44bobo4bobo$616b2o41bo6bo$616b2o6bo42b3o$616b2o4b3o44bo679bob2o$613b2o
bo4bo$223b3o388b3o3bobo726bo2bo$222bo2bo377b2o10bo5bo19b2o707b2o3b2o$
222bo3bo377bo37bo712bobo$221bo2b3o377bobo16bo18bobo15b2o675b3o17bo$
222b4o11b2o366b2o13bobobo18b2o15b2o674b2ob2o16b2o$233b2o2bo382b2o2bo
711b2obobo$218b2o13bobobo386b2o711bo3bo$217bobo6bobo7bo419bo673bo6bo2b
o$217bo9b2o426b3o672b3o5b3o$216b2o9bo6bo419b2o2bo674bo$233bobo422b2o
672bobo$234bo379b2o39b3ob2o672bo16b2o$235b3o376bob2o38bo2b2o689bo$237b
o375b2obob2o35b3o673bo16bobo$615b2ob2o22b2o14b2o670bobobo13b2o$606b3o
5b2o2b2o23bo2b2o10b2o670bo2b2o$209b2o398bo5bobo5b2o18bobobo13b2o666b2o
$210bo14bo380bo2bo5b3o5bobo18bo16bobo$210bobo13bo380b2o16bo25bo11bo$
211b2o8b7o397b2o19bo4bobo9b2o$220b5o2bo417bobo3b2o$219b2ob2ob2o419bo$
220bobo375bo44b3o693b2o$221b2o375b3o42bo694b3o$601bo735b2o6bo$226bo
373bobo2b3o730b2o6bo$226bo374bo3bo12b2o50b2o658b2o13b3o$606bo11bo34bo
16bo658bobo$599bo15b2obo33bobo13bobo658bo$210b2o386bobobo14bo33b2obo5b
3o5b2o658b2o$211bo2b2o382bo2b2o10bo39bo6bo2bo$211bobobo13b2o366b2o11b
2o46b2o3bo$212bo16bobo378b4obo42b2ob3o692bo$231bo381b3o43b3o692b3o$
214bo16b2o377b2o2b2o737bo$213bobo393bo2b3o737bobo$214bo393b3o2b2o720b
2o9b2o5bo$211b3o395bo2bo723bo10b2o$211bo7b3o388b3o723bobo7bo8bo$219bo
2bo388bo57b2o666b2o13bobobo$218bo3bo442b2o2bo671b3o8b2o2bo$218b4o16b2o
358b2o15b2o33b2o13bobobo671b4o11b2o$219bo18bo358bobo15b2o32bobo16bo
671bo2bob2o$236bobo358bo51bo690bob2ob2o$236b2o358b2o50b2o16bo673bo4bo$
229b2o2bo426bo4bobo674bo2bo$224b2o5b2obo424b3o4bo675b3o$232bobo389bo
33bo2b2o4b3o$622b3o33b2ob2o6bo$621bo35b3o$612bo2bo4bobo35b2obo$603b2o
9b4o3bo19b2o16bo2bo675b2o15b2o$604bo6bo30bo16bo678b2o15bobo$604bobo5b
2o2b2o5bo18bobo15bobo694bo$237b2o366b2o13bobobo18b2o4bo11bo695b2o$228b
o4b2o2bo374b2o6b2o2bo25bo$218b2o7b3o3bobobo373b2o11b2o22b2o$217bobo6bo
9bo375b2o2bo31bo681bo$217bo9b2o1101b3o$216b2o9bo6bo1098bo$233bobo1096b
obo$234bo1098bo5b3o8b2o$235b3o1100bobo9bo$237bo414bo678bo6bo2bo6bobo$
642b2o7b3o676bobobo3bo2bo6b2o$643bo2b2o3b4o675bo2b2o4bobo$209b2o395b2o
15b2o18bobobo13b2o666b2o7bo2bo$210bo395b2o15bobo18bo16bobo675b2o$210bo
bo15b2o395bo25b4o8bo675bo$211b2o15b2o395b2o19bo4b4o8b2o$645bobo5bo$
646bo$598bo44b3o$598b3o42bo691b2o$601bo3b3o726bo2bo$600bobo3bob3o724bo
$601bo3b2ob2o8b2o710b2o15b2o$223b2o380b2ob2o8bo710bobo14bo2bo$223bob2o
372bo7bo8bobo710bo16bobo$210b2o13b2o371bobobo13b2o710b2o15b2o$211bo2b
2o7b2o373bo2b2o742bo$211bobobo5b2o6b2o366b2o74bo49bo49bo49bo49bo49bo
49bo49bo49bo49bo49bo49bo49bo74b2o$212bo16bobo441b3o10bo36b3o10bo36b3o
10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b
3o10bo36b3o10bo36b3o10bo61b2o6bo$221bobo7bo444bo9b3o5b2o30bo9b3o5b2o
30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b
2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o52b2o4b
3o$214bo7bo8b2o374bo67b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo
30b2o12bo4bo30b2o12bo4bo30bo13bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4b
o30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo50b2obo4bo$213bobo390bobo79bo3bob
o43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo30bo2bo9bo3bobo43bo3bobo
43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo40bo10b3o3bobo$214bo391bo
55b2o23bo3bobo34bo8bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo35bo7bo
3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo34b2o7bo3bobo43bo3bobo41b3o9b
o5bo$211b3o392b2o2bo41b2o6bo2bo23b2o3bo34b3o7b2o3bo44b2o3bo35bo8b2o3bo
44b2o3bo44b2o3bo33bo2bo7b2o3bo44b2o3bo44b2o3bo44b2o3bo44b2o3bo34bo9b2o
3bo44b2o2bo46bo$211bo390bobo6bo39bobo6b2o4b2o48bo9bo39bo49bo10bobo36bo
49bo49bo11bo37bo49bo49bo49bo49bo11b2o36bo24bo24bo20b2o16bo$601b2obobob
obo4bo28b2o9bo10bo47b3o8bo2b2o34b3o47b3o12bo34b3o30b2o15b3o47b3o47b3o
25bo21b3o47b3o10b3o34b3o47b3o11bo35b3o47b3o16b2o17bobobo$602bo3b2obo2b
o4bo27bo6bobo9bobo46bo26b2obo19bo27b2o20bo14bo34bo14bo16b5o13bo49bo12b
obo13bobo18bo28b2o7bo11bo21b2o2b2o22bo12bo2bo14b2o2bobo12bo49bo13bo35b
o30bo18bo19bo18b2o2bo$238b2o358b2o3bo3bo4bo5bo26bobo5bo10b2o34b2o11b2o
10bob2ob3o7b4o6b2o11b2o25bobo7bobo10b2o21bob3o9b2o11b2o12b3o14bo4bo13b
2o35b2o12bo11bo5b2o4bobo9b2o11b2o26bobo5b2ob2o9b2o20b2o2b2o9b2o11b2o
11bo2b2o12b3obo3bo11b2o48b2o12bo10bo11b2o11b2o28bo4b2o13b2o20bo20b2o$
238bo358bobo4bobo5bo33b2o52b2o24b2o2bo2bo5bo3bo6b2o40bo6bo2bo31b2obo3b
o8b2o25bob2o13bo2b3o61bo2bo14bobo6bo11b2o47bo34b2o6bo7b2o6b2o16b2o2bo
11b2o6bo38b2o46b2obo9b2o45b2o35b2o$219b2o15bobo358bo16bo2bo71b2o19b2o
16bo3bo7b3o38bo17bo2bo32bo4b2o16b3o18b2o13b2o2bo39b3o9bo2bo5b2o16bo10b
obo3bo35bo18bo3bo31bo7bo13b3ob2o15b3o12bob5o40b2o9b2o35bob2o56b2o$219b
2o2b3o10b2o358b2o16b3o71b3o12bo7b2o14bo12b3o37b3o17b2o34b4obo19b2o33b
2o37bo4bo12bo2b5obo14bo13b2obo33b2o20b3o32b2ob2ob2o13b2o3b2o15b2o14b4o
36b2o3bo10b2obo3b2o30bo20b2o15b3o19b3o$222bo3bo457b2o4bo11b2o3b2o19bob
o11bo36bobobob2o69b2obob2o71b2o3bo10b2ob3o3b3o49b2o15b3o2b2o50b2o3bo
14bo2bobo35bo35b2ob2o12bobobo24bo31b2o14bo2bo2bo18bo$222b2o2bo457bo2b
2o12b2o3b2o21bo31bo3bo12b2o3bob2o69bo2b4o70b2o15b2o25bobo29b2ob3o12bo
5b2o69b2o2b3o71bo2b2o14b2o25bo30bo2bo13bo4bo19b4o$225b2o397bo60b2o15b
2o4bo16b3o32b3obo2bo11b2obo2bo70bo4bo72bo2bo12b2o4bo18bobo31b2obobo13b
o4b3o18bo50b2obobo71bo3bo14b3o55b2obo2bo10bobo2b3o19b2o12bo$617bo4b3o
40bo20bo16b2o55bobobo16b2ob2obo16bo13bo3b2o33b4o15bobo34b4o18b2o15bo2b
o17bo39bob2o11bo3bo2b2o16b3o11b3o36bo18b2o35bo2b2o16b2obo14b5o15b2o40b
o2bo10b2o6b3o14b3o10bo2bo12b2o5b4o$223b2o392b3obo41bobo57b2o41bo14b4o
17bob3o10b2o4b3o33b2o3bobo9b2o34bo39b3o17bo57bo5bo19bo8b2ob4o44bo7bo2b
o33b2o2b3o17bo15b2o2bo14bo2bo39bobo19b3o13bobo10bo3bo12b2o4b2ob2obo6b
2o$223bobo390bob3obo40b3o9b2o46bo4bo37b2o7b2o6b3o3bo10b4o2bo9b2o8bo38b
2o9bo34bo4bo8b2o44b2o44bo7b2o26bo2b2o7bo2b2o4bobo40bo7b2o33b3o2b2o8b2o
25b3o15bo2bo51b2o24bo3bo2bo5bo3bo17b2o3b3o6b2o$223bo379b2o16bo41bo11b
2o11b2o27bo5bo14b2o20bo3bobo8b2o12bo10bo2b3o11b5o2bobo11b2o25bo22b2o
22bob2o9b2o11b2o32b2o14b2o35b2o11b2o10bo2bo3bo7b3o7b2o11b2o25b3o8bo11b
2o21b2o2b2o8b2o11b2o13bo16b2ob2o13b2o35b2o11b2o12b6o6bo3b2o17b2o4b2o$
604bo83bo29b2o4bo2bo10bo25bobo21bo11b2o3bo13b3o3bo12bo49bo13bobo8bo24b
o34bo14bo49bo11b2o18bobo15bo49bo13bo35bo33b2o14bo49bo12b2o2b2o8bo2bo
22bobo$221b2o381bobo16bo28b2o35b3o25b2o7bo12b3o47b3o10b3o34b3o47b3o9bo
37b3o47b3o47b3o11bobo33b3o47b3o9bobo35b3o47b3o47b3o50b2o7b2o$221b2o14b
2o366b2o13bobobo23b2o2b2o37bo25b2o22bo49bo10b3o36bo49bo9bo2bo36bo49bo
49bo10b2obo35bo49bo11b2o36bo49bo49bo9bo40bo8bo$221b2o10b2o2bo371bo10b
2o2bo22bobo12b2o3bo44b2o3bo44b2o3bo44b2o3bo44b2o3bo34bobo7b2o3bo44b2ob
3o44b2o3bo35b2o7b2o3bo44b2o3bo44b2o3bo44b2o3bo44b2o3bo34b3o7b2o3bo20b
2o12b3o$218b2o13bobobo370b2o14b2o21bo14bo3bobo43bo3bobo43bo3bobo43bo3b
obo43bo3bobo43bo3bobo43bob3obo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo
3bobo43bo3bobo33b3o7bo3bobo20bo14bo$217bobo16bo371bo37b2o15bo3bobo43bo
3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo
43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo16b3o$217bo446bo4bo30b2o
12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b
2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo
30b2o12bo4bo16bo$216b2o14b3o375bobo48b3o5b2o30bo9b3o5b2o30bo9b3o5b2o
30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b
2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o$235bo
374b2o49bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o
10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo$229bo4bo
376bo86bo49bo49bo49bo49bo49bo49bo49bo49bo49bo49bo49bo49bo$230bo4b3o$
237bo375bo$609b2ob2o$228bo381b3o$209b2o16b3o376b2o3bo11b2o$210bo15b2ob
o376b2o15bobo$210bobo13bo398bo$211b2o3bobob2o2b3o398b2o$214b2o2b2o2bob
o$214b2o3bob4o$214b2o3bo2b3o373bo$218b3o377b3o$218b2o381bo$219bo380bob
o$220bo380bo16b2o$608b3o7bo$599bo8b2o6bobo$210b2o386bobobo6bobo4b2o$
211bo2b2o382bo2b2o8bo$211bobobo13b2o366b2o13b2o$212bo6b3o7bobo378bobo$
218bo3bo8bo378b2o$214bo16b2o$213bobo7bo$214bo3b5o$211b3o5bo$211bo3$
598b2o15b2o$597bobo15b2o$597bo$596b2o2$241bo49bo49bo49bo49bo49bo49bo$
241b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo69bo$
244bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o
5b2o30bo9b3o5b2o58b3o$221b2o20b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30bo
13bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo58bo$221b2o33bo3bobo43bo3bo
bo43bo3bobo30bo2bo9bo3bobo43bo3bobo43bo3bobo43bo3bobo40bo16bobo$230b2o
23bo3bobo43bo3bobo43bo3bobo35bo7bo3bobo43bo3bobo43bo3bobo43bo3bobo41b
3o15bo$228bo2bo14bo8b2o3bo44b2o3bo44b2o3bo33bo2bo7b2o3bo44b2o3bo44b2o
3bo44b2o3bo45bo6b3o$228b2o4b2o9bobo36bo49bo49bo11bo37bo49bo49bo49bo20b
2o8bo7bo$212b2o6bo13bo12bo34b3o30b2o15b3o47b3o47b3o25bo21b3o47b3o10b3o
34b3o16b2o11b3o3bobobo$213bo5b3o10bobo11bo34bo14bo16b5o13bo49bo12bobo
13bobo18bo28b2o7bo11bo21b2o2b2o22bo12bo2bo14b2o2bobo12bo19bo18b2o2bo$
213bobo3bob2o9b2o20bob3o9b2o11b2o12b3o14bo4bo13b2o35b2o12bo11bo5b2o4bo
bo9b2o11b2o26bobo5b2ob2o9b2o20b2o2b2o9b2o11b2o11bo2b2o12b3obo3bo11b2o
20bo20b2o$214b2o6bo29b2obo3bo8b2o25bob2o13bo2b3o61bo2bo14bobo6bo11b2o
47bo34b2o6bo7b2o6b2o16b2o2bo11b2o6bo33b2o$221b2o30bo4b2o16b3o18b2o13b
2o2bo39b3o9bo2bo5b2o16bo10bobo3bo35bo18bo3bo31bo7bo13b3ob2o15b3o12bob
5o$218bob3o31b4obo19b2o33b2o37bo4bo12bo2b5obo14bo13b2obo33b2o20b3o32b
2ob2ob2o13b2o3b2o15b2o14b4o$216b2o2bo53b2obob2o71b2o3bo10b2ob3o3b3o49b
2o15b3o2b2o50b2o3bo14bo2bobo35bo$217b5o52bo2b4o70b2o15b2o25bobo29b2ob
3o12bo5b2o69b2o2b3o$219bo54bo4bo72bo2bo12b2o4bo18bobo31b2obobo13bo4b3o
18bo50b2obobo75bo$236bo3b2o33b4o15bobo34b4o18b2o15bo2bo17bo39bob2o11bo
3bo2b2o16b3o11b3o36bo18b2o35bo2b2o20bo$235b2o4b3o33b2o3bobo9b2o34bo39b
3o17bo57bo5bo19bo8b2ob4o44bo7bo2bo33b2o2b3o16b2o2bo11b2o$234b2o8bo38b
2o9bo34bo4bo8b2o44b2o44bo7b2o26bo2b2o7bo2b2o4bobo40bo7b2o33b3o2b2o17bo
2bo12b2o$235b5o2bobo11b2o25bo22b2o22bob2o9b2o11b2o32b2o14b2o35b2o11b2o
10bo2bo3bo7b3o7b2o11b2o25b3o8bo11b2o21b2o2b2o18bo$237b3o3bo12bo49bo13b
obo8bo24bo34bo14bo49bo11b2o18bobo15bo49bo13bo$220b2o35b3o47b3o9bo37b3o
47b3o47b3o11bobo33b3o47b3o9bobo47b2o$216b2o2b2o37bo49bo9bo2bo36bo49bo
49bo10b2obo35bo49bo11b2o46bo$215bobo12b2o3bo44b2o3bo34bobo7b2o3bo44b2o
b3o44b2o3bo35b2o7b2o3bo44b2o3bo44b2o3bo20b2o12b3o$215bo14bo3bobo43bo3b
obo43bo3bobo43bob3obo43bo3bobo43bo3bobo43bo3bobo43bo3bobo20bo14bo$214b
2o15bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo3bobo43bo
3bobo16b3o$232bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b2o12bo4bo30b
2o12bo4bo30b2o12bo4bo30b2o12bo4bo16bo$229b3o5b2o30bo9b3o5b2o30bo9b3o5b
2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o30bo9b3o5b2o$229bo
36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo36b3o10bo$266bo
49bo49bo49bo49bo49bo49bo!

Then I realized the only reason a gap in the glider stream isn't allowed is because the Herschel will create unwanted debris unless it is deterred by a glider (or eater, but of course that would mean it couldn't reflect gliders at that point). Then I thought that a glider-stream with gaps COULD be reflected if the Herschel stream also had corresponding gaps. But that would mean that that reflector could only reflect a specific binary sequence of gliders: not very useful.
That's when I had an idea--would if the p61 glider stream with or without gaps were duplicated, and one of the duplications was converted into Herschel, which would be used to reflect the original glider stream? The Herschel track should NOT loop around, it should end with a Herschel-eater. The only source of new Herschels would be the duplicated glider stream. Thus, a Herschel would always be present to reflect gliders, but would not be present when there is a gap in the glider stream.

I was half-asleep when I thought of this, so I didn't see the potential problems that I thought of. The main obstacle is that we need a mechanism which can convert gliders to Herschels and can recover fast enough to convert a p61 glider stream.

Axaj · Post by **Axaj** » October 12th, 2010, 7:54 pm

The mechanism you describe would reflect the glider stream anyways; there'd be no point.

p46beth · Post by **p46beth** » October 14th, 2010, 8:03 am

The mechanism you describe would reflect the glider stream anyways; there'd be no point.

Not necessarily. Its possible that a device could allow the stream to pass through, and reflect the duplicated stream 180 degrees (translated some number of cells). I am assuming we are trying to find a 90 degree reflector.

However, this gets us into a hypothetical discussion of whether we are more likely to find a glider duplicator which reflects gliders 90 degrees or one that reflects gliders 180 degrees.

Post by **apg** » October 14th, 2010, 1:38 pm

I think that the easiest way is to engineer a p61 gun, and use that as a reflector. (This is how p59 streams are reflected, using the behemoth p59 gun Jason and I made.)

Basically, the entire thing boils down to trying to create a positive-gain component, e.g. a component to split a Herschel into two gliders at p61. One of these glider streams can be converted directly into Herschels via known (at least, to me!) technology, and the remaining stream can escape as the output of the gun.

Additionally, a way to extract 2c/3 signals from the symmetrical TL eater would facilitate a p61 gun.

knightlife · Post by **knightlife** » October 16th, 2010, 3:31 pm

137ben wrote:I was recently looking at the game of life status page, and saw that p57, 58, and 61 glider streams can be reflected only if they have no gaps.

There is a simple way reflect a p61 glider stream with gaps. Here is an example:

Code: Select all

x = 448, y = 318, rule = B3/S23
324b2o$324bo2b2o$325b2ob3o$331bo37bo14b2o$325b2ob4o2bo5b2o6b2o17b3o14b
o24b2o$325b2obo3b3o5bo2bo4b2o16bo18b3o6b2o13bo17b2o$331bo5b2obob2o22b
2o19bo6b2o11bobo17bo$303b2o26b2o3bobobo66b2o19bo$304bo17bo13bo3bob2o
83b2o$304bobo14b2o12b2o2bo2b2o92bo$305b2o14bobo15b2o9b3o30bo50b3o$312b
3o66b2ob2o47bo$312bobo35bo2bo27bo4bo3bo35b2o5b2o$313b3ob2o32b2o23b2o3b
o3bobo2b2o33b2obo$317bo2bo30bo24b2o4b4o5bo33bo2bo$299bob2o17bo26b3o36b
o2b2o29b3ob2ob2o$299b2obo15bobo27b3o36b2o31bo2b2o2bo$348b2o70bo5bo$
308b2o31b2o78b2o2bo$308b2o30bo2bo79b2o$340bo2bo35b2o$340b2ob2o13b2o20b
o$342b2o14bo20bo13b2o3b2o14b2o$359b3o17b2o13bo3bo15bo$320b2o3b2o34bo
29b3o5b3o13b3o$321bo3bo65bo9bo15bo$318b3o5b3o12b2o74bobo$318bo9bo12bo
76b2o6b3o$316bobo23b3o80bo3bo$316b2o26bo80bo2b2o$425b2o15b2o$312b2o
104b2o18b2obobo$311bobo103bobo7b2o9b2obo$313bo103bo8bo2bo12bo$416b2o
10b2o8b2ob2o$439bobo$294b2o143bobo$295bo6b2o132b2ob2o$295bobo4b2o126b
2o4bobo$293b2ob2o132b2o6bo$292bobo143b2o$292bobo$291b2ob2o8b2o10b2o$
291bo12bo2bo8bo103bo$292bob2o9b2o7bobo103bobo$290bobob2o18b2o104b2o$
290b2o15b2o$304b2o2bo80bo26b2o$304bo3bo80b3o23bobo$305b3o6b2o76bo12bo
9bo$314bobo74b2o12b3o5b3o$316bo15bo9bo65bo3bo$316b3o13b3o5b3o29bo34b2o
3b2o$319bo15bo3bo13b2o17b3o$318b2o14b2o3b2o13bo20bo14b2o$353bo20b2o13b
2ob2o$353b2o35bo2bo$309b2o79bo2bo30b2o$308bo2b2o78b2o31b2o$307bo5bo70b
2o$306bo2b2o2bo31b2o36b3o27bobo15bob2o$305b2ob2ob3o29b2o2bo36b3o26bo
17b2obo$305bo2bo33bo5b4o4b2o24bo30bo2bo$305bob2o33b2o2bobo3bo3b2o23b2o
32b2ob3o$299b2o5b2o35bo3bo4bo27bo2bo35bobo$300bo47b2ob2o66b3o$297b3o
50bo30b3o9b2o15bobo14b2o$297bo92b2o2bo2b2o12b2o14bobo$305b2o83b2obo3bo
13bo17bo$305bo19b2o66bobobo3b2o26b2o$306bo17bobo11b2o6bo43b2obob2o5bo$
305b2o17bo13b2o6b3o16bo18b2o4bo2bo5b3o3bob2o$323b2o24bo13b2o19b2o6b2o
5bo2b4ob2o$263bo20bo63b2o14b2o36bo$262bobo7bo11b3o12b2o102b3ob2o$263bo
6b3o14bo11bo105b2o2bo$252bo16bo16b2o12bo107b2o$252b3o14b2o28b2o115b2o$
255bo6bo47bo102b2o2bo$254b2o5bobo44b3o100b3ob2o$273bo33bo102bo$264bo2b
2o4b2o32b2o7b2o89bo2b4ob2o$272bo3bo39bo90b3o3bob2o$195b2o52b2o9bo4bo6b
obo2bo36bobo93bo$192b2o2bo53bo9bo2b3ob2o3b3o2bo36b2o93b2o26b2o$190b3ob
2o54bobo8b2o174bo$135b2o14bo37bo61b2o59bo18bo54b2o47bobo$30b2o78b2o24b
o14b3o17b2o6b2o5bo2b4ob2o111b2o22b3o53bo47b2o$30bo2b2o57b2o17bo13b2o6b
3o18bo16b2o4bo2bo5b3o3bob2o110bo3bo23bo51bo$31b2ob3o56bo17bobo11b2o6bo
19b2o22b2obob2o5bo74b2o44bo22b2o51b2o24b2o$37bo54bo19b2o58bo7bobobo3b
2o26b2o46bobo6b2o36b2o65bo30b2ob3o$31b2ob4o2bo51b2o77bobo3b2obo3bo31bo
49bo6bo20b2o15bo7bo58b3o28b2o3b2o15bo$31b2obo3b3o43bo85bo5b3o2bo2b2o
28bobo49b2o6bo20bo14bo7bobo60bo29bobo2bo12bo4bo4b2obo$37bo46b3o41bo41b
o3b3o3b2o13b3o2b2o2b2o8b2o57b2o17b3o8b2o14bo60b2o29b3o2b2o10bo5bo4bob
2o$9b2o26b2o48bo40bo4bo35b2obo3bo15b3obo5b2o2bo85bo11bo27bo78bobob2o
17bo$10bo75b2o39bo4b2o2b2o31bo5bo11b5ob2ob3o2bo2b2o95b3o26b3o56b2o24bo
13bo2bo$10bobo47b2o66bo3bo4bo5b2o24bobobo13b5o3bob4o100bo27bo59b2o14bo
24b3o$11b2o47bo31b3o40b2o6b2o26b2o21bo4bo120b2o7b2o73bo$37bo23bo29bo3b
o37b3o56b2o24b2obo40b2o52b2o2bo47b2o34b3o$39bo20b2o33bo97bo24bob2o40bo
bo51bobobo47bo$38b2o29bo21b2ob2o98b2o68bo53bobobo43bobo$30bo36b3o23bo
80b2o18b3obo12b2o51b2o52bo2b2o4b2o33b2o2b2o14bo32b2o3b2o$5bob2o4b2o13b
2o3b3o30bo106bo2bo18b2obo12b2o87bob2o13b2o7bo2bo3bobo26b2o17bobo32bo3b
o$5b2obo3bo2bo12bo4bo32b2o72b2o30b2ob2o20bo102b2obo23b2o4b2o12bob2o29b
2ob2o14b2o12b3o5b3o$12b2ob2o11bo2bo2b2o104bo20b2o11bo159bo4b2o6b4o29bo
3bo15bo12bo9bo$15bobo11bo27b2o46b2o14b2o3b2o13bo20bo146b2o28b2o6bo3bo
28bo3bo12b3o23bobo$17b2o11bo26b2o47bo15bo3bo13b2o17b3o147b2o37b3o30bo
15bo26b2o$14bo3bo84b3o13b3o5b3o29bo34b2o3b2o147b3o31b2obo9bobo$14bo2bo
26bo58bo15bo9bo65bo3bo52b3o73bo19bo33bo2bo9b2o$15b3o24bobo56bobo74b2o
12b3o5b3o48bo2bo72bobo$43b2o19b3o34b2o76bo12bo9bo42b2o4bo2bo72bobo41b
2o7b3o7b2o51bo$26b2o3b2o31bo111b3o23bobo40bo4bo2bo74bo42bo8b3o58b3o$
27bo3bo31bo112bo26b2o41bo3bo2bo2b2o115bob2o4b2o2bo9b2o43bo$24b3o5b3o
12b2o12bo15b2o166b2o4bobo71b2o3b2o36b2o2b2ob2o3b3o12bobo42b2o$24bo9bo
12bo15bo13bobob2o10bo7b2o149bob2o70bo3bo19b2o16bobo10b3o4bo8bo$22bobo
23b3o9bo2bo15bob2o9b3o6bobo151bobo65b3o5b3o15bobo18bob2ob2o4b2o5bo8b2o
$22b2o26bo9b2o16bo12b2o2bo7bo149b2o68bo9bo15bo20b2obobo5b2o$50bobo9bo
15b2ob2o9b2obo7b2o104b3o39b5o7b2o83b2o4b2o19bo5b2o2b2o$51b2o13bo12bobo
7b2ob2o115bo41bo11bo89bobo18b2ob2o2b6o$66b2o11bobo8bo5bo113bo14b2o24bo
b2o2bo3bobo89bo22bobo3bo2bo36b2o$4bo60bobo12b2ob2o5bo4bo119bo9bo31bo3b
2o4b2o42b3o38b2o7b2o13bo6b2o38bo$4b3o68b2o5bobo6bo2bo118bo2bo6bobo19b
2o20bo45bo6bobo38b2o12b2o46bobo$7bo43b2o18b2obobo5bo9bo119bo4bo5b2ob2o
18bo18bobo44bo6bob2o57bo43b2o$6b2o42bobo18b2obo6b2o14bo113bo5bo8bobo
17bobo16b2o13b2o35b3o58b3o$50bo24bo22bo115b2ob2o7bobo18b2o31b2o34bo4b
2o54bo$49b2o16bo3b2ob2o20b3o104b2o7bob2o9b2ob2o74b2o10b5obo54b2o62b2o$
67bo4bobo129bo7bo2b2o12bo73b2o2b2o11bo59b2o42b2o15b2o$72bobo129bobo6b
3o9b2obo57b2o15bob4o7b2o3bo15b2o36b5obo41bobo9b2o$69b2ob2o131b2o7bo10b
2obobo55b2o15b3o10bobo3bo14bo33b2o2bo21b2o24bo11b2o$24b2o43bobo157b2o
51b2o19b2o2b2o8bo3b2o12bobo33bo5b2o18bobo22b2o$24bo46bo31b2o26bo150b2o
20b3o2bo21b2o2b2o32bobo4b2ob2o18bo$22bobo46b2o30bobo23b3o165b2o5b2o2b
3o20b2o36b2o19b3o6b2o34bo$22b2o43bo37bo9bo12bo76b2o71bo18b2o7bo2bo71bo
7bo2bo40bo2bo$67b3o35b3o5b3o12b2o74bobo70b3o26b3o80bo3bo38b2o2bo4b2o$
70bo37bo3bo65bo9bo15bo71bo2bo7b2o18bo68b4o9bo2bo38bo10bo$5b2o62b2o36b
2o3b2o34bo29b3o5b3o13b3o48b2o20b3o2b2o5b2o86bo3b2ob2obo4bobo41bo7bobo$
5b2o15b2o42b2o78b3o17b2o13bo3bo15bo47b2o2b2o21bo2b3o20b2o47b2o8b3o11bo
9b2o45bo2bo7b2o$12bo9bobo41bob5o72bo20bo13b2o3b2o14b2o45bobo12b2o3bo8b
2o2b2o19b2o48bo7bo3b2o10bo2b2o4bo47b3o$13bo10bo24b2o4b3o14bo60bo11b2o
20bo80bo14bo3bobo10b3o15b2o52bobo28b2o$12b3o9b2o22bobo3bo2bo9b2obo39bo
20b2ob2o30b2o79b2o15bo3b2o7b4obo15b2o53b2o5bo21b2o$11bobo34bo5b2obo9b
2ob2o23b2o12bob2o18bo2bo130bo11b2o2b2o78bo3bo58bob2o$15bo31b2o46b2o12b
ob3o18b2o80bo48bob5o10b2o80b3o59b2obo$11b2obobo95b2o98b2ob2o46b2o4bo
34b2o31b2o11bo$5b2o7bobo42bobo24b2obo24bo97bo53b3o35b2o13b2o16bobo9bob
o81b2o$5bo9bo45bo24bob2o24b2o56b3o37bo3bo46b2obo6bo44bobo18bo9bobo81b
2o$3bobo6bo46bo3bo7b2o35bo4bo21b2o26b2o6b2o40b3o47bobo6bo45bo20b2o6b3o
b2o39b2o$3b2o7b2o46bo3bo6b2o34b4obo3b5o13bobobo24b2o5bo4bo3bo92b3o42b
2o4b2o3bo17bo45bobo$11bo2bo45bo6bo34b2o2bo2b3ob2ob5o11bo5bo31b2o2b2o4b
o39b2o100bobo3bo2b2obo12b3ob2o41bo$12bobo47b5o34bo2b2o5bob3o15bo3bob2o
35bo4bo40bo101bo11bo14bob2o41b2o$12b2o78b2o8b2o2b2o2b3o13b2o3b3o3bo41b
o41b3o97b2o7b5o$20b2obo67bobo28b2o2bo2b3o5bo85bo43b2o62b2o11b2o$20bob
2o67bo31bo3bob2o3bobo77b2o50bobo59bobo14bo18b2o77b2o$90b2o26b2o3bobobo
7bo16bobo39b2o19bo50bo63b2obo11bobo16bobo76bo$13b2o103bo5b2obob2o22b2o
19bo6b2o11bobo17bo50b2o65bobo4b2o5b2o18bo9bobo62bobo$13b2o97b2obo3b3o
5bo2bo4b2o16bo18b3o6b2o13bo17b2o112b2o2bo2bo3bo26b2o8b2o63b2o$54b2o56b
2ob4o2bo5b2o6b2o34bo24b2o134bo2bo4bo36bo$53bobo62bo53bo158bo2bo4b2o$
53bo58b2ob2o52b3o159bo2bo$52b2o56bo2bobo12bo38b3o161b3o$110b2o4bo11b3o
35bo256b2o$114b3o14bo34b2o107b2o147bo$3b2o93bo14bo16b2o143b2o147bobo$
4bo93b3o12b2o241bo68b2o$4bobo94bo52bo127bob2o69bobo26b2o$5b2o64bo28b2o
50b3o127b2obo69bobo26b2o$72b2o65bo11bo114b2o52b2o34bo$71b2o64b2obo10b
2o114bo53bo29b2o17b2o19bob2o$101b2o33bo4bo27bo97bobo51bobo26bobo17bobo
18b2obo$101b2o17b2o18bo26bobo98b2o52b2o26bo10bo10bo62b2o$23b2o95b2o14b
4o28b2o179b2o10bobo8b2o60b2o$23bo260bo76b2o10bo9b3o47bo4b2o2bo$21bobo
258b3o88bobo7bo2bo45b2o9bo$21b2o258bo11bo80bobo7bo41bobo4bob2ob2o3bo$
62b2o99b2o101bo14b2o8b3o17b2o63bo10bo38bo2bo9b4o$62b2o98bo2bo99bobo7bo
14bo20bo6b2o56b2o4bo2b2o38bo3bo$117b2o44b2o101bo7bo15b2o20bo6bo62bo2bo
40bo2bo7bo$53b2obo60bo20b2o133b2o36b2o6bobo61bo34b2o6b3o$53bob2o61b3o
18bo135bo44b2o97bo18b2ob2o$63b2o55bo15b3o6bob2o17b2o107bo3bo115b2o22bo
bo18b2o$10b5o47bobo49b2o20bo6b3ob2o17bo110b2o103b2o11bo24b2o21bo$9bo6b
o45bo2bo38b3o7bo27bo24b3o103bo59b2o47b2o9bobo41bob5o$4b2o6bo3bo46b2o7b
2o30bobo8b3o25b3ob2o20bo153b2o8bobo40b2o15b2o42b2o$4b2o7bo3bo46bo6bobo
30bo2bo9bo27bobo35bo86b2o36bo2b3o3b2ob3o2bo9bo40b2o62b2o$15bo45bo9bo
33b3o37bobo4b2o30b2o83bobo36bo2bobo6bo4bo9b2o10bo93bo$15bobo42bobo7b2o
33b3o38bo6bo29b2o84bo39bo3bo31b2o91b3o$60bobob2o37bo2bo43b3o115b2o7b2o
32b2o4b2o2bo24b2o45b2o43bo$28b2o31bo44bo43bo127bo33bo80bobo46b2o$5b2ob
2o9bob2o5bo34bobo37bo171b3o44bobo5b2o63bo38b2o6bo$6bob2o9bo2bo3bobo22b
2o9b3o210bo47bo6bo64b2o36bo2bo3bobo$4bo14b3o4b2o24bo10bo41bo209b2o14b
3o98b6o2b2ob2o$4b5obo41bobo9bo39bo40bo7bob2o141b2o16bo16bo98b2o2b2o5bo
bo$9b2o42b2o15b2o32b2o37b3o7b2obo141bo14b3o6bo113b2o5bobo$6b2o62b2o55b
o14bo156b3o11bo7bobo96b2o8bo5b2o4b2ob2o$6bo120b3o12b2o157bo20bo98bo8bo
4b3o8bo$7b3o120bo52bo193b2o42bobo12b3o3b2obo$9bo43b2o46bobo25b2o50b3o
194bo43b2o9bo2b2o4b2obobo$4b2o46bobo33b2o12b2o43b3o4b2o24bo194b3o58b3o
7b2o$5bo46bo34bobo12bo12b2o36b2ob2o22b2o7b2o8bo175bo51b2o7b3o$5bobo43b
2o34bo6b2o19bo14b2o16bo8bo31bo10bo130bo$3b2ob2o78b2o7bo17bobo14b2o16bo
bobo4bo29bobo8b3o129bo91b2o9bo2bo$2bobo90bobo15b2o32bo8bo30b2o141b3o
88bobo9bob2o$2bobo4bo86b2o4bo6b2o36bo4b3o238b2o26bo15bo$b2ob2o3bo16b2o
73bobo4bo2bo34bo4bobo239bobo23b3o12bo3bo$bo24bo74bobo5b2o35bo3bo244bo
9bo12bo15bo3bo$2bob2o18bobo42b2o31bo10b2o34bo245b3o5b3o12b2o14b2ob2o$o
bob2o18b2o43bo43bobo282bo3bo32bobo$2o68b3o42bo30b2o33b3o2bo210b2o3b2o
32bo$9bobo60bo42b2o29bo20b2o14bo2b2o4bo$9b2o89b2o19b2ob2o2b2o17b3o18bo
12bo2bo2bo3bobo$10bo13b2o71bo3bo20bobo2bobo19bo15b3o8b2o5b2obo5bo219b
3o$14bo9bobo65bo4b4o20bo3b2o16b2o20bo11bo236bo$15b2o9bo26b2o36bobo28b
2obo17bo30b3o5bo203b3o24bo14b2o$13bo2bo9b3o23bobo37bo6b4o20bobo2bo15b
3o27bo7bob2o200bo2bo13bo24b2o$13bo15bo12bo9bo28bo16bo3bo20bobobobo16bo
34bo3bo27bobo168bo17b2obobo$15bo12b2o12b3o5b3o28b3o14b2o24b2ob2o60b2o
23b2o99bobo58b2obo4bo5bo10b2o2b3o29b2o$13bo31bo3bo34bo104bobo22bo100b
2o59bob2o4bo4bo12bo2bobo29bo$12bo31b2o3b2o32b2o106bo124bo70bo15b2o3b2o
28b3o$10b3o19b2o50b3o95b2o2bo4b2o211b3ob2o30bo$32bobo24b3o23b2o33b3o
50bob2o6b3o219b2o24b2o$32bo26bo2bo22bob2ob2o28bo52b2obo7bo247bo$58bo3b
o15b2o10b2o13b2o14bo260b2o47bo$18b2o26bo11b2o19bo10b2o13b2o24bo50b2o
197bobo47b2o$18b2o27bo11bobo17bobo5b3o37bobob2o49b2o197bo$41b2o2bo2bo
11b2ob2o15b2o5b3o37b3o2b2o246b2o26b2o$9b2o32bo4bo12bo2bo3bob2o55bobo2b
o275bo$10bo30b3o3b2o13b2o4b2obo53b2o3b2o10b2o258b2obo3b3o$7b3o36bo46b
2o30b2ob3o11b2o258b2ob4o2bo$7bo29b2o54bobo6b2o24b2o6b2o270bo$15b2o20bo
57bo6bo33b2o92bo171b2ob3o$15bo23bo55b2o6bo88b2o34bobo69bo100bo2b2o$16b
o47b2o8bob2o24b2o88bo36b2o69bobo98b2o$15b2o47bobo7b2obo60b2o50bobo107b
2o$66bo64b2o5b2o50b2o$38b2o26b2o63b2o$39bo$36b3o3bob2o45b2o$36bo2b4ob
2o45bobo$39bo53bo78b2o$40b3ob2o47b2o78bo$42b2o2bo126bobo$45b2o127b2o2$
134b2o$75b2o50b2o5b2o108bo$74bobo50b2o116b2o39bo$74bo88b2o79b2o38b2o$
73b2o88bo6b2o113b2o$129b2o33bo6bo$129b2o6b2o24b2o6bobo$123b2o11b3ob2o
30b2o$123b2o10b2o3b2o$134bo2bobo$133b2o2b3o37b3o5b2o$83b2o49b2obobo37b
3o5bobo$83b2o50bo24b2o13b2o10bo$145bo14b2o13b2o10b2o$82bo7bob2o52bo28b
2ob2obo$81b3o6b2obo50b3o33b2o$74b2o4bo2b2o95b3o77bo$75bo106b2o77bo8bo$
75bobo104bo76b3o7bo$76b2o60b2ob2o24b2o14b3o83b3o$81bo3bo34bo16bobobobo
6b2o16bo16bo$81b2obo7bo27b3o15bo2bobo6bo14b3o6bo$84bo5b3o30bo17bob2o6b
3o11bo7bobo$89bo11bo20b2o16b2o3bo7bo20bo$74bo5bob2o5b2o8b3o15bo19bobo
2bobo$73bobo3bo2bo2bo12bo18b3o17b2o2b2ob2o$74bo4b2o2bo14b2o20bo$80bo2b
3o33b2o$272b3o$117bo154bo$116bo3bo152bo$113bobo4bo$112b3o4bo$78b2o30bo
8bo$77bobo29bo4bobobo16b2o$77bo31bo8bo16b2o$76b2o7b2o22b2ob2o$86bo24b
2o4b3o$83b3o50b2o$83bo52bo$123b2o12b3o$124bo14bo$110bob2o7b3o$110b2obo
7bo166b2o$287b2o$289bo28$319bo$318b2o$318bobo!

The reaction can be used to reflect any period-N glider stream 90 degrees for N>16 if a glider gun of that period is known. It doesn't matter if there are gaps or if the glider gun is a pseudo-period gun. Maybe the status page could use a different color for periods greater than 16 (that have a gun) or a note that trivial reflector examples are known if a gun exists. Red means "No examples are known" which is misleading.

There is another way to reflect 90 degrees using an LWSS stream that also works all the way down to p17 if the LWSS stream is possible (three guns or an unusual reaction).
Both ways are shown here using p17.

Code: Select all

x = 147, y = 37, rule = B3/S23
109bo$110b2o31bo$54b2o53b2o30b2o$54bo87b2o$52bobo59bo$o2bo23b2o5bo2bo
14b2o61bo22bo$4bo6b2o5b4o4b4o8bo6b2o66b3o21bo$o3bo4b2ob2o3bo3bo4b2ob2o
3bo3bo4b2ob2o89b3o$b4o4b4o8bo6b2o5b4o4b4o$10b2o5bo2bo23b2o71bobo$118b
2o13bobo$118bo14b2o$134bo$123bo$121bobo5bo$122b2o5bobo$129b2o5$63b2o
67b2o$62b2o68bobo$64bo67bo2$67b2o68bo$67bobo66b2o$67bo68bobo2$36bo2b3o
73bo2b3o$35b2o4bo72b2o4bo$36bo4bo73bo4bo$36bo4bo73bo4bo$36bo4bo73bo4bo
$35b3o3bo33b3o36b3o3bo24b2o$75bo68b2o$76bo69bo!

MWSS streams can be used instead of LWSS streams and they work also.

p46beth · Post by **p46beth** » October 16th, 2010, 10:18 pm

The "trivial" solutions you give are counted as nontrivial solutions (green) on the status page...assuming that the gun in question is TRUE period. That's probably because if you have a true period gun, you can build an oscillator of that period. As such, a pseudo-period 19 gun would allow you to reflect p19 glider streams, but would not allow you to build a p19 oscillator, so the p19 reflector is red. That said, you are right in that there should probably be a different color for such periods.

Given that, and the fact that p61 oscillators are already known, there would be almost no use for my potential idea for reflecting p57, p58, or p61 glider streams. The p61 glider splitting device would be nice if it exists, but that would require finding such a device, and would deserve a completely new topic, not related to reflecting p61 glider streams.

So there's not much use for this idea...

Post by **Sokwe** » October 17th, 2010, 4:30 am

Thanks to the tub-with-tail eater, only one glider stream is needed to reflect another glider stream non-trivially at periods greater than 16:

Code: Select all

x = 38, y = 28, rule = B3/S23
36bo$35bo$35b3o$bo$2bo$3o3$4bobo$5b2o20bo$5bo21bobo$27b2o$10bo$8bobo
13bo$9b2o11b2o$23b2o$13bo$14b2o$13b2o4$11b2o$11b2o3bo$15bobo$16bobo$
18bo$18b2o!

There is also a spark that works at period-14, but I am not sure that it can be created with the proper orientation by period-14 glider streams:

Code: Select all

x = 12, y = 14, rule = B3/S23
bo$2bo$3o2$5bo$3bobo$4b2o$8bo$9bo$7b3o2$10bo$10bo$11bo!

knightlife wrote:Maybe the status page could use a different color for periods greater than 16 (that have a gun) or a note that trivial reflector examples are known if a gun exists.

I don't think that it would be very helpful to include glider stream reflectors as some sort of trivial reflector on Jason's Life status page. It would be somewhat like including infinite oscillators (wicks and agars) in the oscillator period section. Also, the status page does say, "if you have a gun, you can build a reflector" (although I'm not sure if this is true for periods 14, 15, and 16).

knightlife wrote:There is another way to reflect 90 degrees using an LWSS stream that also works all the way down to p17 if the LWSS stream is possible (three guns or an unusual reaction).

Unfortunately, no known LWSS syntheses work to turn period-17 glider streams into a period-17 LWSS stream (see gun pseudo-periods on the Life status page). In fact, Adam P. Goucher (Calcyman) constructed the first pseudo-period p22 LWSS, MWSS, and HWSS guns earlier this year (there are still no known true-period p22 standard spaceship guns).

calcyman wrote:[A] way to extract 2c/3 signals from the symmetrical TL eater would facilitate a p61 gun.

Alternatively, extracting a 2c/3 signal from a glider using the tub-with-tail eater would also be sufficient. There are already some known ways to set off drifters in this manner:

Code: Select all

x = 41, y = 20, rule = B3/S23
33b2o$34bo$29bo2bo$11bob2o14b5o$11b2obo$7b2o22bo$8bo2b3o3b2o11bobo3b2o
$8bobobobobobo11b2o5bo$7b2obo3bobo18bobob2o$10bo2b2ob2o15b3obobo$7b2ob
obo2bo16bo4bobo$3b2o2b2obob2obo12b2o2b4o2bo$3b2o6bo2bo13b2o6b2o$13bo
20b2o$14b3o18bo$bo3bo10bo9bo3bo4bobo$2bobobo20bobobo4b2o$3o2bo19b3o2bo
$6b3o22b3o$8bo24bo!

Obviously, such a discovery would have several other implications.

p46beth · Post by **p46beth** » October 17th, 2010, 9:48 am

Also, the status page does say, "if you have a gun, you can build a reflector" (although I'm not sure if this is true for periods 14, 15, and 16).

It also says "if you have a reflector, you can build an oscillator." This is only true, however, if the reflector is itself period n, or some factor of n. A pseudo-period 19 gun can reflect p19 glider streams, but does not allow the construction of a p19 oscillator.

knightlife · Post by **knightlife** » October 17th, 2010, 1:48 pm

Thank you very much for all the responses, I really appreciate the helpful answers. Why would I possibly want to use two guns when I can use just one? I didn't know it was that easy to convert a pN gun into a pN reflector (easy only when you know the clever tub-with-tail solution). Being a beginner in the area of implementing reflectors, I didn't pick up on the idea that you shouldn't use guns to build reflectors, you should always use oscillators to build reflectors, I assumed that some of the reflector periods in green included guns: I am probably completely wrong on that. I am thinking now that the status page is indicating solutions for "non-trivial" reflectors that do not include entire guns of the same period.

Sokwe wrote:There is also a spark that works at period-14

If I find a gun solution that produces that 3-cell spark (at a p14, p15, or p16 rate) and it can be made into a complete pattern to reflect glider streams with gaps, have I found a p14, p15, or p16 reflector where there were none known before? Is it excluded from the chart as a gun solution versus a non-gun solution?

Sorry for nitpicking, I do understand the intention of the chart, more or less. It is always nice to have a reflector be as small as possible, without guns.

BTW, I have the utmost respect for Jason, his web page, and the awesome patterns he comes up with. I just want to clarify what the chart means so I don't go off on a tangent, when I do search for reflectors.

Post by **Sokwe** » October 17th, 2010, 4:19 pm

knightlife wrote:I am thinking now that the status page is indicating solutions for "non-trivial" reflectors that do not include entire guns of the same period.

Actually, the status page does include gun solutions provided that the true-period gun is known (to my knowledge, this is the only way to create period-22 and period-59 reflectors).

For those interested, here are all of the reflectors necessary for showing that the status page is correct (excluding periods 57, 58, 59, and 61):

Code: Select all

x = 390, y = 67, rule = B3/S23
184bo120bo$182b3o120b3o$181bo126bo$181b2o124b2o2$179bo139b2o$178bobo
138b2o$177bo3bo44bo6bo79bobo$177bo2bo44bo2bo2bo2bo80bo$177bo2bo37b2o
15bo$178b2o35bob4ob2ob2ob4ob2o74b3o$214bo14b2o71b2o5bo2bo$15b2o75b2o
119bo3bo2bo2bo78b2o5bo3bo$14bo2bo73bo2bo119b2o6bo69b2o19bo56b2o$13bob
2obo2b2o65bo3bobo197b2o15bo3bo39b2o15bobo7b2o$13bobo2bo3bo63b6obo215bo
2bo8b2o30b2o17bo7b2o$12b2o3bob3o63bo5bo88b2o127b3o9b2o47b3o$12bo2bobob
o65bob2obo2bo85bo2bo$13b3o3bo66bo3bob2o85bo2bo12bo98b2o36b2o$88bobo36b
o50bo3bo10b3o29bo2bo103bo$9b2o2b4o2bo7b2o58b2o3b2o32bobo50bobo10bo26bo
5bo2bo65bo4b3o28bobo37b3o$9bo2bo6bo8bo57bo2b2obo32bo3bo50bo11b2o24b2o
4bo3bo69bo3bo27b2o21b2o17bo7b2o$10bob2o3b2o5bo2bo38bo17bo2bo3bo2bo9bo
21bo3bo8bo78b2o5b3o4b3o10b2o50bo5bo13b3ob3o29b2o15bobo7b2o$7b3obo5bo6b
2o26b2o10b3o17b2obo3bob2o7b3o22bo3bo5b3o37b2o4bo36bo4b3o4b3o10b2o50bo
5bo13bo5bo46b2o$6bo4bo8b2o3bo25bo2bo8bo21bobob2obo8bo26bo3bo3bo41bo3bo
6b3o39bo3bo61b3ob3o13bo5bo$4b3ob2ob2o8bo4bo23bobobo8b2o20bob3o2bo8b2o
26bobo4b2o37b3o4b3o3bob2o39bo2bo54b2o27bo3bo$3bo3bob2o3bo10b2o23bobob
2o30bo3bob2o36bo44bo12bo2bo39bo2bo53bobo28b3o4bo$2bo2bo5bo6bo29b2obobo
2bo4bo25b4o2bo5bo34bo54b2o3bo93bo$2bob3o4bo3bobobo28bo2bo3b3o2bobo28bo
6bobo32bobo53b2o96b2o36b2o$obo4bo2bo7b2o2b2o21b2obo2bobo2bo4b2o2b2o20b
4o2bo5b2o2b2o29b2o2b2o37bo198b2o$2obobobob3obo8b2o21bo2b2o4b2o9b2o20bo
2bob2o9b2o33b2o29b2o6bobo118b2o9b3o63b2o$3bo3bobo36b2o4bobo37bo76b2o6b
2o68b2ob3o45b2o8bo2bo65bo$3bobobo2b2o36bobobobo35bobo154bo3bo4bo50bo3b
o15b2o$4bobobobo37bo4bo36b2o155bo3bo3bobo5bo43bo19b2o$5bo2bobo38b4o
115bo3bo18b2o55bobo3bo3bo3bobo42bo3bo5b2o$8b2o40bo116bobobo15bo3b2o56b
o4bo3bo3bo45bo2bo5b2o$22b3o23bo16b3o35b3o32b3o27bo2b3o16bo2bo59b3ob2o
4b2o44b3o$22bo25b2o15bo37bo34bo26b3o22b2obo43b3o$23bo42bo37bo34bo25bo
24b3o44bo67bo$238bo66bobo$300b2o86bo$188b2o110b2o85b2o$29b2o40b3o70b3o
42bo197bobo$28b2o41bo38b3o31bo41b3o63bo59b2o$30bo41bo37bo34bo40bo64bob
o58bo$111bo134b2o4bob2o2b5o3bo2bo43b3o$245b2o8bo2bo7bo2bo2bo42bo$247bo
7bo2bo3b5o2b3obo$272bo2$185b3o$185bo$186bo2$314bo$191b2o120b2o$191bobo
119bobo$191bo7$322b3o$322bo$323bo!

The first four reflectors (periods 5, 6, 7, and 8) can only work at periods above 21.

knightlife wrote:If I find a gun solution that produces that 3-cell spark (at a p14, p15, or p16 rate) and it can be made into a complete pattern to reflect glider streams with gaps, have I found a p14, p15, or p16 reflector where there were none known before?

I'm not sure if there is already a known way to create this spark using glider streams (the spark has been known for a long time, see buckaroo); however, for it to be considered a "proper" reflector it would need to be a finite oscillator with a period equal to or some factor of the period of the glider stream it is reflecting.

ConwayLife.com

A potential way to reflect p61 glider streams

A potential way to reflect p61 glider streams

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Re: A potential way to reflect p61 glider streams

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Re: A potential way to reflect p61 glider streams

Re: A potential way to reflect p61 glider streams

Re: A potential way to reflect p61 glider streams

Re: A potential way to reflect p61 glider streams

Re: A potential way to reflect p61 glider streams