ConwayLife.com

Posted: **September 1st, 2016, 8:19 pm**

From x3 SW and SE rakes I made one third of the gliders in a climber. There are already some scary signal crossings in this pattern so I don't know if it can be extended to make the missing two thirds.

Code: Select all

x = 1378, y = 1375, rule = B3/S23
1377bo$1375b2o$1376b2o72$bo$2bo$3o59$1320bo$1318b2o$1319b2o72$52bo$53b
o$51b3o59$1263bo$1261b2o$1262b2o72$103bo$104bo$102b3o59$1206bo$1204b2o
$1205b2o72$154bo$155bo$153b3o59$1149bo$1147b2o$1148b2o72$205bo$206bo$
204b3o59$1092bo$1090b2o$1091b2o72$256bo$257bo$255b3o59$1035bo$1033b2o$
1034b2o34$1024bo$1023b3o$1023bob2o$1024b3o$1024b2o5$1023b3o$1022bo2bo$
1025bo$1025bo$1022bobo14$1027bo$1026b3o$1026bob2o$1027b3o$1027b2o5$
1026b3o$1025bo2bo$307bo720bo$308bo719bo$306b3o716bobo14$1030bo$1029b3o
$1029bob2o$1030b3o$1030b2o5$1029b3o$1028bo2bo$1031bo$1031bo$1028bobo
14$1033bo$1032b3o$1032bob2o$1033b3o$1033b2o5$1032b3o$1031bo2bo$1034bo$
1034bo$1031bobo14$1036bo$1035b3o$1035bob2o$1036b3o$1036b2o5$1035b3o$
1034bo2bo$1037bo$1037bo$1034bobo14$1039bo$1038b3o$1038bob2o$1039b3o$
1039b2o5$1038b3o$1037bo2bo$1040bo$1040bo$1037bobo14$1042bo$1041b3o$
1041bob2o$1042b3o$1042b2o5$1041b3o$1040bo2bo$1043bo$1043bo$1040bobo19$
963b3o$963bo2bo$361bo601bo$360b3o600bo$355bo3b2obo601bobo$354b3o2b3o$
353b2obo3b2o$353b3o$354b2o608bo$963b3o$963bob2o$964b3o$964b2o15$966b3o
$966bo2bo$364bo601bo$363b3o600bo$358bo3b2obo601bobo$357b3o2b3o$356b2ob
o3b2o$356b3o$357b2o608bo$966b3o$966bob2o$967b3o$967b2o15$969b3o$969bo
2bo$367bo601bo$366b3o600bo$361bo3b2obo601bobo$360b3o2b3o$359b2obo3b2o$
359b3o$360b2o608bo$969b3o$969bob2o$970b3o$970b2o15$972b3o$972bo2bo$
370bo601bo$369b3o600bo$364bo3b2obo601bobo$363b3o2b3o$362b2obo3b2o$362b
3o25b3o$363b2o24bo2bo580bo$384b3o5bo579b3o$383bo2bo5bo579bob2o$386bo2b
obo581b3o$386bo586b2o$383bobo14$975b3o$975bo2bo$373bo601bo$372b3o600bo
$367bo3b2obo601bobo$366b3o2b3o$365b2obo3b2o641bo$365b3o25b3o618b3o$
366b2o24bo2bo580bo36b2obo$387b3o5bo579b3o35b3o$386bo2bo5bo579bob2o34b
3o$389bo2bobo581b3o35b2o$389bo586b2o$386bobo633b3o$1022bo2bo$1022bo$
1022bo$1023bobo10$978b3o$978bo2bo$376bo601bo$375b3o600bo$370bo3b2obo
601bobo$369b3o2b3o$368b2obo3b2o641bo$368b3o25b3o618b3o$369b2o24bo2bo
580bo36b2obo$390b3o5bo579b3o35b3o$389bo2bo5bo579bob2o34b3o$392bo2bobo
581b3o35b2o$392bo586b2o$389bobo633b3o$1025bo2bo$1025bo$1025bo$1026bobo
10$954b3o24b3o$953bo2bo24bo2bo$379bo576bo24bo$378b3o571bo3bo24bo$373bo
3b2obo575bo25bobo$372b3o2b3o573bobo$371b2obo3b2o583bo57bo$371b3o25b3o
560b3o55b3o$372b2o24bo2bo559b2obo17bo36b2obo$393b3o5bo559b3o17b3o35b3o
$392bo2bo5bo560b2o17bob2o34b3o$395bo2bobo581b3o35b2o$395bo586b2o$392bo
bo633b3o$1028bo2bo$1028bo$1028bo$1029bobo10$957b3o$956bo2bo$959bo$955b
o3bo$959bo$956bobo$966bo57bo$402b3o560b3o55b3o$401bo2bo559b2obo54b2obo
$396b3o5bo559b3o55b3o$395bo2bo5bo560b2o55b3o$398bo2bobo619b2o$398bo$
395bobo633b3o$1031bo2bo$1031bo$1031bo$1032bobo10$960b3o$959bo2bo$962bo
$958bo3bo$962bo$959bobo$969bo57bo$405b3o560b3o55b3o$404bo2bo559b2obo
54b2obo$399b3o5bo559b3o55b3o$398bo2bo5bo560b2o55b3o$401bo2bobo619b2o$
401bo$398bobo633b3o$1034bo2bo$1034bo$1034bo$1035bobo10$963b3o$962bo2bo
$965bo$961bo3bo$965bo$962bobo$972bo57bo$408b3o560b3o55b3o$407bo2bo559b
2obo54b2obo$402b3o5bo559b3o55b3o$401bo2bo5bo560b2o55b3o$404bo2bobo619b
2o$404bo$401bobo633b3o$1037bo2bo$1037bo$1037bo$1038bobo10$966b3o$965bo
2bo$968bo$964bo3bo$968bo$965bobo$975bo57bo$974b3o55b3o$973b2obo54b2obo
$973b3o55b3o$974b2o55b3o$1032b2o2$1040b3o$1040bo2bo$1040bo$1040bo$
1041bobo10$969b3o$968bo2bo$971bo$967bo3bo$971bo$968bobo$978bo$977b3o$
976b2obo$976b3o$977b2o17$972b3o$971bo2bo$974bo$970bo3bo$974bo$971bobo$
981bo$980b3o$979b2obo$979b3o$980b2o!

Posted: **September 1st, 2016, 9:27 pm**

That's a good start! The picture I had in mind involved some frozen tracks. An early duplicator split off the NE-traveling signal into NE and SE. The NE just travels a large distance as a delay mechanism, while the SE glider is repeatedly duplicated as in the original caterpillar to build a constellation with 2/3 density frozen tracks. The delayed glider is reflected back to provide the final 1/3, and the climber begins at the point where the streams cross.

Edit: No that doesn't make sense, there's no way to get the glider far enough NE not to just crash into the helix. Perhaps the final glider just comes from the nearby duplicators.

The crossings themselves should be fine by a 2d analog of the Chinese remainder theorem - just give it enough space and as long as there is a hole, there is a way to position the crossing that satisfies the modular arithmetic constraints and successfully passes through the hole. There is definitely a concern though for whether there even is a hole at points in my idea.

Posted: **September 2nd, 2016, 7:27 am**

It's possible to build an x1 climber pair using only kickbacks (as shown below) but you need to build one of the right sided gliders last (there would be a collision if you built all of the right sided gliders first). In the pattern posted above the right sided glider is always built first so you would need splitters with different phase in the left hand helix or use extra spaceships to rephase manually.

Code: Select all

x = 3325, y = 2785, rule = B3/S23
3323b2o$3322b2o$3324bo2$518b2o$517bobo$519bo21$3266b2o$3265b2o$3267bo
2$569b2o$568bobo$570bo21$3209b2o$3208b2o$3210bo2$620b2o$619bobo$621bo
21$3152b2o$3151b2o$3153bo2$671b2o$670bobo$672bo21$3095b2o$3094b2o$
3096bo2$722b2o$721bobo$723bo21$3038b2o$3037b2o$3039bo2$773b2o$772bobo$
774bo21$2981b2o$2980b2o$2982bo2$824b2o$823bobo$825bo12$3247b2o$3246b2o
$3248bo2$442b2o$441bobo$443bo3$2924b2o$2923b2o$2925bo2$875b2o$874bobo$
876bo12$3190b2o$3189b2o$3191bo2$493b2o$492bobo$494bo3$2867b2o$2866b2o$
2868bo2$926b2o$925bobo$927bo12$3133b2o$3132b2o$3134bo2$544b2o$543bobo$
545bo3$2810b2o$2809b2o$2811bo2$977b2o$976bobo$978bo12$3076b2o$3075b2o$
3077bo2$595b2o$594bobo$596bo3$2753b2o$2752b2o$2754bo2$1028b2o$1027bobo
$1029bo12$3019b2o$3018b2o$3020bo2$646b2o$645bobo$647bo3$2696b2o$2695b
2o$2697bo2$1079b2o$1078bobo$1080bo12$2962b2o$2961b2o$2963bo2$697b2o$
696bobo$698bo3$2639b2o$2638b2o$2640bo2$1130b2o$1129bobo$1131bo12$2905b
2o$2904b2o$2906bo2$748b2o$747bobo$749bo3$2582b2o$2581b2o$2583bo2$1181b
2o$1180bobo$1182bo3$3171b2o$3170b2o$3172bo2$366b2o$365bobo$367bo3$
2848b2o$2847b2o$2849bo2$799b2o$798bobo$800bo3$2525b2o$2524b2o$2526bo2$
1232b2o$1231bobo$1233bo3$3114b2o$3113b2o$3115bo2$417b2o$416bobo$418bo
3$2791b2o$2790b2o$2792bo2$850b2o$849bobo$851bo3$2468b2o$2467b2o$2469bo
2$1283b2o$1282bobo$1284bo3$3057b2o$3056b2o$3058bo2$468b2o$467bobo$469b
o3$2734b2o$2733b2o$2735bo2$901b2o$900bobo$902bo3$2411b2o$2410b2o$2412b
o2$1334b2o$1333bobo$1335bo3$3000b2o$2999b2o$3001bo2$519b2o$518bobo$
520bo3$2677b2o$2676b2o$2678bo2$952b2o$951bobo$953bo3$2354b2o$2353b2o$
2355bo2$1385b2o$1384bobo$1386bo3$2943b2o$2942b2o$2944bo2$570b2o$569bob
o$571bo3$2620b2o$2619b2o$2621bo2$1003b2o$1002bobo$1004bo3$2297b2o$
2296b2o$2298bo2$1436b2o$1435bobo$1437bo3$2886b2o$2885b2o$2887bo2$621b
2o$620bobo$622bo3$2563b2o$2562b2o$2564bo2$1054b2o$1053bobo$1055bo3$
2240b2o$2239b2o$2241bo2$1487b2o$1486bobo$1488bo3$2829b2o$2828b2o$2830b
o2$672b2o$671bobo$673bo3$2506b2o$2505b2o$2507bo2$1105b2o$1104bobo$
1106bo3$2183b2o$2182b2o$2184bo2$1538b2o$1537bobo$1539bo3$2772b2o$2771b
2o$2773bo2$723b2o$722bobo$724bo3$2449b2o$2448b2o$2450bo2$1156b2o$1155b
obo$1157bo3$2126b2o$2125b2o$2127bo2$1589b2o$1588bobo$1590bo3$2715b2o$
2714b2o$2716bo2$774b2o$773bobo$775bo3$2392b2o$2391b2o$2393bo2$1207b2o$
1206bobo$1208bo3$2069b2o$2068b2o$2070bo2$1640b2o$1639bobo$1641bo3$
2658b2o$2657b2o$2659bo2$825b2o$824bobo$826bo3$2335b2o$2334b2o$2336bo2$
1258b2o$1257bobo$1259bo3$2012b2o$2011b2o$2013bo2$1691b2o$1690bobo$
1692bo3$2601b2o$2600b2o$2602bo2$876b2o$875bobo$877bo3$2278b2o$2277b2o$
2279bo2$1309b2o$1308bobo$1310bo3$1955b2o$1954b2o$1956bo2$1742b2o$1741b
obo$1743bo3$2544b2o$2543b2o$2545bo2$927b2o$926bobo$928bo3$2221b2o$
2220b2o$2222bo2$1360b2o$1359bobo$1361bo3$1898b2o$1897b2o$1899bo2$1793b
2o$1792bobo$1794bo3$2487b2o$2486b2o$2488bo2$978b2o$977bobo$979bo3$
2164b2o$2163b2o$2165bo2$1411b2o$1410bobo$1412bo8$1842bo$1842bobo$1842b
2o2$2430b2o$2429b2o$2431bo2$1029b2o$1028bobo$1030bo3$2107b2o$2106b2o$
2108bo2$1462b2o$1461bobo$1463bo12$2373b2o$2372b2o$2374bo2$1080b2o$
1079bobo$1081bo3$2050b2o$2049b2o$2051bo2$1513b2o$1512bobo$1514bo12$
2316b2o$2315b2o$2317bo2$1131b2o$1130bobo$1132bo3$1993b2o$1992b2o$1994b
o2$1564b2o$1563bobo$1565bo12$2259b2o$2258b2o$2260bo2$1182b2o$1181bobo$
1183bo3$1936b2o$1935b2o$1937bo2$1615b2o$1614bobo$1616bo12$2202b2o$
2201b2o$2203bo2$1233b2o$1232bobo$1234bo3$1879b2o$1878b2o$1880bo2$1666b
2o$1665bobo$1667bo8$1785bo$1785bobo$1785b2o2$2145b2o$2144b2o$2146bo2$
1284b2o$1283bobo$1285bo3$1822b2o$1821b2o$1823bo2$1717b2o$1716bobo$
1718bo12$2088b2o$2087b2o$2089bo2$1335b2o$1334bobo$1336bo8$1766bo$1766b
obo$1766b2o11$2031b2o$2030b2o$2032bo$2956b2o$1386b2o1568bobo$1385bobo
1568bo$1387bo$153bo$153b2o$152bobo18$1974b2o$1973b2o$1975bo$2899b2o$
1437b2o1460bobo$1436bobo1460bo$1438bo$204bo$204b2o$203bobo18$1917b2o$
1916b2o$1918bo$2842b2o$1488b2o1352bobo$1487bobo1352bo$1489bo$255bo$
255b2o$254bobo14$1728bo$1728bobo$1728b2o2$1860b2o$1859b2o$1861bo$2785b
2o$1539b2o1244bobo$1538bobo1244bo$1540bo$306bo$306b2o$305bobo18$1803b
2o$1802b2o$1804bo$2728b2o$1590b2o1136bobo$1589bobo1136bo$1591bo$357bo$
357b2o$356bobo5$1709bo$1709bobo$1709b2o11$1746b2o$1745b2o$1747bo$2671b
2o$1641b2o1028bobo$1640bobo1028bo$1642bo$408bo$408b2o$407bobo21$2614b
2o$2614bobo$1690bo923bo$1690bobo$459bo1230b2o$459b2o$458bobo12$2880b2o
$2880bobo$2880bo2$77bo$77b2o$76bobo3$2557b2o$2557bobo$2557bo2$510bo$
510b2o$509bobo12$2823b2o$2823bobo$1671bo1151bo$1671bobo$128bo1542b2o$
128b2o$127bobo3$2500b2o$2500bobo$2500bo2$561bo$561b2o$560bobo12$2766b
2o$2766bobo$2766bo2$179bo$179b2o$178bobo3$2443b2o$2443bobo$2443bo2$
612bo$612b2o$611bobo5$1652bo$1652bobo$1652b2o5$2709b2o$2709bobo$2709bo
2$230bo$230b2o$229bobo3$2386b2o$2386bobo$2386bo2$663bo$663b2o$662bobo
12$2652b2o$2652bobo$2652bo2$281bo$281b2o$280bobo3$2329b2o$2329bobo$
1633bo695bo$1633bobo$714bo918b2o$714b2o$713bobo12$2595b2o$2595bobo$
2595bo2$332bo$332b2o$331bobo3$2272b2o$2272bobo$2272bo2$765bo$765b2o$
764bobo12$2538b2o$2538bobo$1614bo923bo$1614bobo$383bo1230b2o$383b2o$
382bobo3$2215b2o$2215bobo$2215bo2$816bo$816b2o$815bobo3$2804b2o$2804bo
bo$2804bo2$bo$b2o$obo3$2481b2o$2481bobo$2481bo2$434bo$434b2o$433bobo3$
2158b2o$2158bobo$2158bo2$867bo$867b2o$866bobo3$2747b2o$2747bobo$1595bo
1151bo$1595bobo$52bo1542b2o$52b2o$51bobo3$2424b2o$2424bobo$2424bo2$
485bo$485b2o$484bobo3$2101b2o$2101bobo$2101bo2$918bo$918b2o$917bobo3$
2690b2o$2690bobo$2690bo2$103bo$103b2o$102bobo3$2367b2o$2367bobo$2367bo
2$536bo$536b2o$535bobo3$2044b2o$2044bobo$1576bo467bo$1576bobo$969bo
606b2o$969b2o$968bobo3$2633b2o$2633bobo$2633bo2$154bo$154b2o$153bobo3$
2310b2o$2310bobo$2310bo2$587bo$587b2o$586bobo3$1987b2o$1987bobo$1987bo
2$1020bo$1020b2o$1019bobo3$2576b2o$2576bobo$2576bo2$205bo$205b2o$204bo
bo3$2253b2o$2253bobo$1557bo695bo$1557bobo$638bo918b2o$638b2o$637bobo3$
1930b2o$1930bobo$1930bo2$1071bo$1071b2o$1070bobo3$2519b2o$2519bobo$
2519bo2$256bo$256b2o$255bobo3$2196b2o$2196bobo$2196bo2$689bo$689b2o$
688bobo3$1873b2o$1873bobo$1873bo2$1122bo$1122b2o$1121bobo3$2462b2o$
2462bobo$1538bo923bo$1538bobo$307bo1230b2o$307b2o$306bobo3$2139b2o$
2139bobo$2139bo2$740bo$740b2o$739bobo3$1816b2o$1816bobo$1816bo2$1173bo
$1173b2o$1172bobo3$2405b2o$2405bobo$2405bo2$358bo$358b2o$357bobo3$
2082b2o$2082bobo$2082bo2$791bo$791b2o$790bobo3$1759b2o$1759bobo$1519bo
239bo$1519bobo$1224bo294b2o$1224b2o$1223bobo3$2348b2o$2348bobo$2348bo
2$409bo$409b2o$408bobo3$2025b2o$2025bobo$2025bo2$842bo$842b2o$841bobo
3$1702b2o$1702bobo$1702bo2$1275bo$1275b2o$1274bobo3$2291b2o$2291bobo$
2291bo2$460bo$460b2o$459bobo3$1968b2o$1968bobo$1500bo467bo$1500bobo$
893bo606b2o$893b2o$892bobo3$1645b2o$1645bobo$1645bo2$1326bo$1326b2o$
1325bobo3$2234b2o$2234bobo$2234bo2$511bo$511b2o$510bobo3$1911b2o$1911b
obo$1911bo2$944bo$944b2o$943bobo3$1588b2o$1588bobo$1588bo2$1377bo$
1377b2o$1376bobo3$2177b2o$2177bobo$1481bo695bo$1481bobo$562bo918b2o$
562b2o$561bobo3$1854b2o$1854bobo$1854bo2$995bo$995b2o$994bobo3$1531b2o
$1531bobo$1531bo2$1428bo$1428b2o$1427bobo3$2120b2o$2120bobo$2120bo2$
613bo$613b2o$612bobo3$1797b2o$1797bobo$1797bo2$1046bo$1046b2o$1045bobo
5$1462bo$1462bobo$1462b2o3$1475bobo$1475b2o$1476bo586b2o$2063bobo$
2063bo2$664bo$664b2o$663bobo3$1740b2o$1740bobo$1740bo2$1097bo$1097b2o$
1096bobo12$2006b2o$2006bobo$2006bo2$715bo$715b2o$714bobo3$1683b2o$
1683bobo$1443bo239bo$1443bobo$1148bo294b2o$1148b2o$1147bobo12$1949b2o$
1949bobo$1949bo2$766bo$766b2o$765bobo3$1626b2o$1626bobo$1626bo2$1199bo
$1199b2o$1198bobo12$1892b2o$1892bobo$1424bo467bo$1424bobo$817bo606b2o$
817b2o$816bobo3$1569b2o$1569bobo$1569bo2$1250bo$1250b2o$1249bobo12$
1835b2o$1835bobo$1835bo2$868bo$868b2o$867bobo3$1512b2o$1512bobo$1512bo
2$1301bo$1301b2o$1300bobo5$1405bo$1405bobo$1405b2o3$1418bobo$1418b2o$
1419bo358b2o$1778bobo$1778bo2$919bo$919b2o$918bobo3$1455b2o$1455bobo$
1455bo2$1352bo$1352b2o$1351bobo12$1721b2o$1721bobo$1721bo2$970bo$970b
2o$969bobo5$1386bo$1386bobo$1386b2o3$1399bobo$1399b2o$1400bo9$1664b2o$
1664bobo$1664bo2$1021bo$1021b2o$1020bobo21$1607b2o$1607bobo$1367bo239b
o$1367bobo$1072bo294b2o$1072b2o$1071bobo21$1550b2o$1550bobo$1550bo2$
1123bo$1123b2o$1122bobo14$1348bo$1348bobo$1348b2o3$1361bobo$1361b2o$
1362bo130b2o$1493bobo$1493bo2$1174bo$1174b2o$1173bobo21$1436b2o$1436bo
bo$1436bo2$1225bo$1225b2o$1224bobo5$1329bo$1329bobo$1329b2o3$1342bobo$
1342b2o$1343bo9$1379b2o$1379bobo$1379bo2$1276bo$1276b2o$1275bobo23$
1310bo$1310bobo$1310b2o3$1323bobo$1323b2o$1324bo38$1291bo$1291bobo$
1291b2o3$1304bobo$1304b2o$1305bo38$1272bo$1272bobo$1272b2o3$1285bobo$
1285b2o$1286bo38$1253bo$1253bobo$1253b2o3$1266bobo$1266b2o$1267bo38$
1234bo$1234bobo$1234b2o3$1247bobo$1247b2o$1248bo38$1215bo$1215bobo$
1215b2o3$1228bobo$1228b2o$1229bo38$1196bo$1196bobo$1196b2o3$1209bobo$
1209b2o$1210bo38$1177bo$1177bobo$1177b2o3$1190bobo$1190b2o$1191bo38$
1158bo$1158bobo$1158b2o3$1171bobo$1171b2o$1172bo38$1139bo$1139bobo$
1139b2o3$1152bobo$1152b2o$1153bo38$1120bo$1120bobo$1120b2o3$1133bobo$
1133b2o$1134bo38$1101bo$1101bobo$1101b2o3$1114bobo$1114b2o$1115bo38$
1082bo$1082bobo$1082b2o3$1095bobo$1095b2o$1096bo38$1063bo$1063bobo$
1063b2o3$1076bobo$1076b2o$1077bo38$1044bo$1044bobo$1044b2o3$1057bobo$
1057b2o$1058bo38$1025bo$1025bobo$1025b2o3$1038bobo$1038b2o$1039bo38$
1006bo$1006bobo$1006b2o3$1019bobo$1019b2o$1020bo38$987bo$987bobo$987b
2o3$1000bobo$1000b2o$1001bo38$968bo$968bobo$968b2o3$981bobo$981b2o$
982bo!

It doesn't look possible to make the 3-glider track with kickbacks only though.

EDIT: Attaching an x3 rakes -> x1 climber trail pattern

gentrail.rle.gz: (16.19 KiB) Downloaded 558 times

Posted: **September 2nd, 2016, 7:04 pm**

Just checked out your attachment - that's good news, especially if it turns out the climber pair is capable of building up the other 3 to make a full cluster. That puts the total number of spaceships to synthesize at 23 on the right, and 20 plus the helix on the left. The helix would have to be adapted to drop SE instead of NE gliders to work with this - I had requested NE earlier assuming all fanouts would happen on the right but I doubt it would be cheaper not to use kickbacks, and that necessarily requires some fanouts on the left helix.

Code: Select all

x = 2578, y = 2698, rule = B3/S23
o$b2o$2o133$51bo$52b2o$51b2o133$102bo$103b2o$102b2o67$126b3o$126bo2bo$
120b3o3bo$120bo2bo2bo$120bo6bobo$120bo$121bobo3$148b3o$150bo$149bo16$
129b3o$129bo2bo$123b3o3bo$123bo2bo2bo$123bo6bobo$123bo$124bobo3$199b3o
$201bo$200bo16$132b3o$132bo2bo$126b3o3bo$126bo2bo2bo$126bo6bobo$126bo$
127bobo3$250b3o$252bo$251bo3$156bo$157bo$155b3o11$135b3o$135bo2bo$129b
3o3bo$129bo2bo2bo$129bo6bobo$129bo$130bobo3$301b3o$303bo$302bo16$138b
3o$138bo2bo$132b3o3bo$132bo2bo2bo$132bo6bobo$132bo$133bobo3$352b3o$
354bo$353bo16$141b3o$141bo2bo$135b3o3bo$135bo2bo2bo$135bo6bobo$135bo$
136bobo3$403b3o$405bo$404bo16$144b3o$144bo2bo$138b3o3bo$138bo2bo2bo$
138bo6bobo$138bo$139bobo3$454b3o$456bo$455bo16$147b3o$147bo2bo$141b3o
3bo$141bo2bo2bo$141bo6bobo$141bo$142bobo3$505b3o$507bo$506bo3$207bo$
208bo$206b3o11$150b3o$150bo2bo$144b3o3bo$144bo2bo2bo$144bo6bobo$144bo$
145bobo3$556b3o$558bo$557bo16$153b3o$153bo2bo$147b3o3bo$147bo2bo2bo$
147bo6bobo$147bo$148bobo3$607b3o$609bo$608bo16$156b3o$156bo2bo$150b3o
3bo$150bo2bo2bo$150bo6bobo$150bo$151bobo3$658b3o$660bo$659bo16$159b3o$
159bo2bo$153b3o3bo$153bo2bo2bo$153bo6bobo$153bo$154bobo3$709b3o$711bo$
710bo16$162b3o$162bo2bo$156b3o3bo$156bo2bo2bo$156bo6bobo87bo$156bo96b
2o$157bobo92bobo3$760b3o$762bo$761bo6$259bobo$260b2o$255bo4bo$254b3o$
249bo3b2obo$248b3o2b3o$247b2obo3b2o$247b3o$248b2o2$165b3o$165bo2bo$
159b3o3bo$159bo2bo2bo$159bo6bobo135bo$159bo144b2o$160bobo140bobo3$811b
3o$813bo$812bo8$258bo$257b3o$252bo3b2obo$251b3o2b3o$250b2obo3b2o$250b
3o$251b2o2$168b3o$168bo2bo$162b3o3bo$162bo2bo2bo$162bo6bobo183bo$162bo
192b2o$163bobo188bobo3$862b3o$864bo$863bo8$261bo$260b3o$255bo3b2obo$
254b3o2b3o$253b2obo3b2o$253b3o$254b2o2$171b3o$171bo2bo$165b3o3bo$165bo
2bo2bo$165bo6bobo231bo$165bo240b2o$166bobo236bobo3$913b3o$915bo$914bo
8$264bo$263b3o$258bo3b2obo$257b3o2b3o$256b2obo3b2o$256b3o$257b2o2$174b
3o$174bo2bo$168b3o3bo$168bo2bo2bo$168bo6bobo279bo$168bo288b2o$169bobo
284bobo3$964b3o$966bo$965bo8$267bo$266b3o$261bo3b2obo$260b3o2b3o$259b
2obo3b2o$259b3o$260b2o2$177b3o$177bo2bo$171b3o3bo$171bo2bo2bo$171bo6bo
bo327bo$171bo336b2o$172bobo332bobo3$1015b3o$1017bo$1016bo3$306bo$307b
2o$306b2o3$270bo$269b3o31bo$264bo3b2obo30b3o$263b3o2b3o30b2obo$262b2ob
o3b2o30b3o$262b3o36b3o$263b2o37b2o2$180b3o$180bo2bo122bo$174b3o3bo124b
3o$174bo2bo2bo124bob2o$174bo6bobo122b3o250bo$174bo131b3o250b2o$175bobo
128b2o250bobo3$1066b3o$1068bo$1067bo8$273bo$272b3o31bo$267bo3b2obo30b
3o$266b3o2b3o30b2obo$265b2obo3b2o30b3o$265b3o36b3o$266b2o37b2o2$183b3o
$183bo2bo122bo$177b3o3bo124b3o$177bo2bo2bo124bob2o$177bo6bobo122b3o
298bo$177bo131b3o298b2o$178bobo128b2o298bobo3$1117b3o$1119bo$1118bo8$
276bo$275b3o31bo$270bo3b2obo30b3o$269b3o2b3o30b2obo$268b2obo3b2o30b3o$
268b3o36b3o$269b2o37b2o2$186b3o$186bo2bo122bo$180b3o3bo124b3o$180bo2bo
2bo124bob2o$180bo6bobo122b3o346bo$180bo131b3o346b2o$181bobo128b2o346bo
bo3$1168b3o$1170bo$1169bo8$279bo$278b3o31bo$273bo3b2obo30b3o$272b3o2b
3o30b2obo$271b2obo3b2o30b3o$271b3o36b3o$272b2o37b2o2$189b3o$189bo2bo
122bo$183b3o3bo124b3o$183bo2bo2bo124bob2o$183bo6bobo122b3o394bo$183bo
131b3o394b2o$184bobo128b2o394bobo3$1219b3o$1221bo$1220bo7$352b3o$282bo
71bo$281b3o31bo37bo$276bo3b2obo30b3o$275b3o2b3o30b2obo$274b2obo3b2o30b
3o$274b3o36b3o$275b2o37b2o$347b3o$192b3o152bo2bo$192bo2bo122bo22b3o3bo
$186b3o3bo124b3o21bo2bo2bo$186bo2bo2bo124bob2o20bo6bobo$186bo6bobo122b
3o20bo421bo$186bo131b3o21bobo418b2o$187bobo128b2o442bobo3$1270b3o$
1272bo$1271bo5$360bo$361bo$359b3o41b3o$285bo119bo$284b3o31bo85bo$279bo
3b2obo30b3o$278b3o2b3o30b2obo$277b2obo3b2o30b3o$277b3o36b3o$278b2o37b
2o$350b3o$195b3o152bo2bo$195bo2bo122bo22b3o3bo$189b3o3bo124b3o21bo2bo
2bo$189bo2bo2bo124bob2o20bo6bobo$189bo6bobo122b3o20bo469bo$189bo131b3o
21bobo466b2o$190bobo128b2o490bobo3$1321b3o$1323bo$1322bo7$454b3o$288bo
167bo$287b3o31bo133bo$282bo3b2obo30b3o$281b3o2b3o30b2obo$280b2obo3b2o
30b3o$280b3o36b3o$281b2o37b2o$353b3o$198b3o152bo2bo$198bo2bo122bo22b3o
3bo$192b3o3bo124b3o21bo2bo2bo$192bo2bo2bo124bob2o20bo6bobo$192bo6bobo
122b3o20bo517bo$192bo131b3o21bobo514b2o$193bobo128b2o538bobo3$1372b3o$
1374bo$1373bo7$505b3o$291bo215bo$290b3o31bo181bo$285bo3b2obo30b3o$284b
3o2b3o30b2obo$283b2obo3b2o30b3o$283b3o36b3o$284b2o37b2o$356b3o$201b3o
152bo2bo$201bo2bo122bo22b3o3bo$195b3o3bo124b3o21bo2bo2bo$195bo2bo2bo
124bob2o20bo6bobo$195bo6bobo122b3o20bo565bo$195bo131b3o21bobo562b2o$
196bobo128b2o586bobo3$1423b3o$1425bo$1424bo7$556b3o$294bo263bo$293b3o
31bo229bo$288bo3b2obo30b3o$287b3o2b3o30b2obo$286b2obo3b2o30b3o$286b3o
36b3o$287b2o37b2o$359b3o$204b3o152bo2bo$204bo2bo122bo22b3o3bo$198b3o3b
o124b3o21bo2bo2bo$198bo2bo2bo124bob2o20bo6bobo$198bo6bobo122b3o20bo
613bo$198bo131b3o21bobo610b2o$199bobo128b2o634bobo3$1474b3o$1476bo$
1475bo7$607b3o$297bo311bo$296b3o31bo277bo$291bo3b2obo30b3o$290b3o2b3o
30b2obo$289b2obo3b2o30b3o$289b3o36b3o$290b2o37b2o$362b3o$207b3o152bo2b
o$207bo2bo122bo22b3o3bo$201b3o3bo124b3o21bo2bo2bo$201bo2bo2bo124bob2o
20bo6bobo$201bo6bobo122b3o20bo661bo$201bo131b3o21bobo658b2o$202bobo
128b2o682bobo3$1525b3o$1527bo$1526bo5$411bo$412bo$410b3o245b3o$300bo
359bo$299b3o31bo325bo$294bo3b2obo30b3o$293b3o2b3o30b2obo$292b2obo3b2o
30b3o$292b3o36b3o$293b2o37b2o$365b3o$210b3o152bo2bo$210bo2bo122bo22b3o
3bo$204b3o3bo124b3o21bo2bo2bo$204bo2bo2bo124bob2o20bo6bobo$204bo6bobo
122b3o20bo709bo$204bo131b3o21bobo706b2o$205bobo128b2o730bobo3$1576b3o$
1578bo$1577bo5$2577bo2$709b3o$303bo407bo$302b3o31bo373bo$297bo3b2obo
30b3o$296b3o2b3o30b2obo$295b2obo3b2o30b3o$295b3o36b3o87bo$296b2o37b2o
86b3o$368b3o47bo3b2obo$213b3o152bo2bo45b3o2b3o$213bo2bo122bo22b3o3bo
47b2obo3b2o$207b3o3bo124b3o21bo2bo2bo47b3o$207bo2bo2bo124bob2o20bo6bob
o45b2o$207bo6bobo122b3o20bo757bo$207bo131b3o21bobo754b2o$208bobo128b2o
778bobo3$1627b3o$1629bo$1628bo6$457bo$457b2o301b3o$306bo149bobo303bo$
305b3o31bo421bo$300bo3b2obo30b3o$299b3o2b3o30b2obo$298b2obo3b2o30b3o$
298b3o36b3o87bo$299b2o37b2o86b3o$371b3o47bo3b2obo$216b3o152bo2bo45b3o
2b3o$216bo2bo122bo22b3o3bo47b2obo3b2o$210b3o3bo124b3o21bo2bo2bo47b3o$
210bo2bo2bo124bob2o20bo6bobo45b2o$210bo6bobo122b3o20bo805bo$210bo131b
3o21bobo802b2o$211bobo128b2o826bobo3$1678b3o$1680bo$1679bo6$508bo$508b
2o301b3o$309bo197bobo303bo$308b3o31bo469bo$303bo3b2obo30b3o$302b3o2b3o
30b2obo$301b2obo3b2o30b3o$301b3o36b3o87bo$302b2o37b2o86b3o$374b3o47bo
3b2obo$219b3o152bo2bo45b3o2b3o$219bo2bo122bo22b3o3bo47b2obo3b2o$213b3o
3bo124b3o21bo2bo2bo47b3o$213bo2bo2bo124bob2o20bo6bobo45b2o$213bo6bobo
122b3o20bo853bo$213bo131b3o21bobo850b2o$214bobo128b2o874bobo3$1729b3o$
1731bo$1730bo6$559bo$559b2o301b3o$312bo245bobo303bo$311b3o31bo517bo$
306bo3b2obo30b3o$305b3o2b3o30b2obo$304b2obo3b2o30b3o$304b3o36b3o87bo$
305b2o37b2o86b3o$377b3o47bo3b2obo$222b3o152bo2bo45b3o2b3o$222bo2bo122b
o22b3o3bo47b2obo3b2o$216b3o3bo124b3o21bo2bo2bo47b3o$216bo2bo2bo124bob
2o20bo6bobo45b2o$216bo6bobo122b3o20bo901bo$216bo131b3o21bobo898b2o$
217bobo128b2o922bobo3$1780b3o$1782bo$1781bo6$610bo$610b2o301b3o$315bo
147bobo143bobo303bo$314b3o31bo115b2o448bo$309bo3b2obo30b3o114bo$308b3o
2b3o30b2obo$307b2obo3b2o30b3o$307b3o36b3o87bo$308b2o37b2o86b3o$380b3o
47bo3b2obo$225b3o152bo2bo45b3o2b3o$225bo2bo122bo22b3o3bo47b2obo3b2o$
219b3o3bo124b3o21bo2bo2bo47b3o$219bo2bo2bo124bob2o20bo6bobo45b2o$219bo
6bobo122b3o20bo949bo$219bo131b3o21bobo946b2o$220bobo128b2o970bobo3$
1831b3o$1833bo$1832bo6$661bo$661b2o301b3o$318bo341bobo303bo$317b3o31bo
613bo$312bo3b2obo30b3o$311b3o2b3o30b2obo$310b2obo3b2o30b3o$310b3o36b3o
87bo$311b2o37b2o86b3o31bo$383b3o47bo3b2obo30b3o$228b3o152bo2bo45b3o2b
3o30b2obo$228bo2bo122bo22b3o3bo47b2obo3b2o30b3o$222b3o3bo124b3o21bo2bo
2bo47b3o36b3o$222bo2bo2bo124bob2o20bo6bobo45b2o37b2o$222bo6bobo122b3o
20bo997bo$222bo131b3o21bobo994b2o$223bobo128b2o119bo898bobo$474b3o$
474bob2o$475b3o1404b3o$475b3o1406bo$475b2o1406bo6$712bo$712b2o301b3o$
321bo389bobo303bo$320b3o31bo661bo$315bo3b2obo30b3o$314b3o2b3o30b2obo$
313b2obo3b2o30b3o$313b3o36b3o87bo$314b2o37b2o86b3o31bo$386b3o47bo3b2ob
o30b3o$231b3o152bo2bo45b3o2b3o30b2obo$231bo2bo122bo22b3o3bo47b2obo3b2o
30b3o$225b3o3bo124b3o21bo2bo2bo47b3o36b3o$225bo2bo2bo124bob2o20bo6bobo
45b2o37b2o$225bo6bobo122b3o20bo1045bo$225bo131b3o21bobo1042b2o$226bobo
128b2o119bo946bobo$477b3o$477bob2o$478b3o1452b3o$478b3o1454bo$478b2o
1454bo6$763bo$763b2o301b3o$324bo437bobo303bo$323b3o31bo709bo$318bo3b2o
bo30b3o$317b3o2b3o30b2obo$316b2obo3b2o30b3o$316b3o36b3o87bo$317b2o37b
2o86b3o31bo$389b3o47bo3b2obo30b3o$234b3o152bo2bo45b3o2b3o30b2obo$234bo
2bo122bo22b3o3bo47b2obo3b2o30b3o$228b3o3bo124b3o21bo2bo2bo47b3o36b3o$
228bo2bo2bo124bob2o20bo6bobo45b2o37b2o$228bo6bobo122b3o20bo1093bo$228b
o131b3o21bobo1090b2o$229bobo128b2o119bo994bobo$480b3o$480bob2o$481b3o
1500b3o$481b3o1502bo$481b2o1502bo6$814bo$814b2o301b3o$327bo485bobo303b
o$326b3o31bo757bo$321bo3b2obo30b3o$320b3o2b3o30b2obo$319b2obo3b2o30b3o
$319b3o36b3o87bo$320b2o37b2o86b3o31bo$392b3o47bo3b2obo30b3o$237b3o152b
o2bo45b3o2b3o30b2obo$237bo2bo122bo22b3o3bo47b2obo3b2o30b3o$231b3o3bo
124b3o21bo2bo2bo47b3o36b3o$231bo2bo2bo124bob2o20bo6bobo45b2o37b2o$231b
o6bobo122b3o20bo1141bo$231bo131b3o21bobo1138b2o$232bobo128b2o119bo
1042bobo$483b3o$483bob2o$484b3o1548b3o$484b3o1550bo$484b2o1550bo5$510b
o$511b2o352bo$510b2o353b2o301b3o$330bo533bobo303bo$329b3o31bo805bo$
324bo3b2obo30b3o$323b3o2b3o30b2obo$322b2obo3b2o30b3o$322b3o36b3o87bo$
323b2o37b2o86b3o31bo$395b3o47bo3b2obo30b3o$240b3o152bo2bo45b3o2b3o30b
2obo$240bo2bo122bo22b3o3bo47b2obo3b2o30b3o$234b3o3bo124b3o21bo2bo2bo
47b3o36b3o$234bo2bo2bo124bob2o20bo6bobo45b2o37b2o$234bo6bobo122b3o20bo
126b3o1060bo$234bo131b3o21bobo123bo2bo1059b2o$235bobo128b2o119bo22b3o
3bo1061bobo$486b3o21bo2bo2bo$486bob2o20bo6bobo$487b3o20bo1575b3o$487b
3o21bobo1574bo$487b2o1598bo6$916bo$916b2o301b3o$333bo581bobo303bo$332b
3o31bo853bo$327bo3b2obo30b3o$326b3o2b3o30b2obo$325b2obo3b2o30b3o$325b
3o36b3o87bo$326b2o37b2o86b3o31bo$398b3o47bo3b2obo30b3o$243b3o152bo2bo
45b3o2b3o30b2obo$243bo2bo122bo22b3o3bo47b2obo3b2o30b3o$237b3o3bo124b3o
21bo2bo2bo47b3o36b3o$237bo2bo2bo124bob2o20bo6bobo45b2o37b2o$237bo6bobo
122b3o20bo126b3o34b3o1071bo$237bo131b3o21bobo123bo2bo35bo1071b2o$238bo
bo128b2o119bo22b3o3bo37bo1071bobo$489b3o21bo2bo2bo$489bob2o20bo6bobo$
490b3o20bo1623b3o$490b3o21bobo1622bo$490b2o1646bo6$967bo$967b2o301b3o$
336bo629bobo303bo$335b3o31bo901bo$330bo3b2obo30b3o$329b3o2b3o30b2obo$
328b2obo3b2o30b3o$328b3o36b3o87bo$329b2o37b2o86b3o31bo$401b3o47bo3b2ob
o30b3o$246b3o152bo2bo45b3o2b3o30b2obo$246bo2bo122bo22b3o3bo47b2obo3b2o
30b3o$240b3o3bo124b3o21bo2bo2bo47b3o36b3o$240bo2bo2bo124bob2o20bo6bobo
45b2o37b2o$240bo6bobo122b3o20bo126b3o82b3o1071bo$240bo131b3o21bobo123b
o2bo83bo1071b2o$241bobo128b2o119bo22b3o3bo85bo1071bobo$492b3o21bo2bo2b
o$492bob2o20bo6bobo$493b3o20bo1671b3o$493b3o21bobo1670bo$493b2o1694bo
6$1018bo$1018b2o301b3o$339bo677bobo303bo$338b3o31bo949bo$333bo3b2obo
30b3o$332b3o2b3o30b2obo$331b2obo3b2o30b3o$331b3o36b3o87bo$332b2o37b2o
86b3o31bo$404b3o47bo3b2obo30b3o$249b3o152bo2bo45b3o2b3o30b2obo$249bo2b
o122bo22b3o3bo47b2obo3b2o30b3o$243b3o3bo124b3o21bo2bo2bo47b3o36b3o$
243bo2bo2bo124bob2o20bo6bobo45b2o37b2o$243bo6bobo122b3o20bo126b3o130b
3o1071bo$243bo131b3o21bobo123bo2bo131bo1071b2o$244bobo128b2o119bo22b3o
3bo133bo1071bobo$495b3o21bo2bo2bo$495bob2o20bo6bobo$496b3o20bo1719b3o$
496b3o21bobo1718bo$496b2o1742bo6$1069bo$1069b2o301b3o$342bo725bobo303b
o$341b3o31bo997bo$336bo3b2obo30b3o$335b3o2b3o30b2obo$334b2obo3b2o30b3o
$334b3o36b3o87bo$335b2o37b2o86b3o31bo$407b3o47bo3b2obo30b3o$407bo2bo
45b3o2b3o30b2obo$378bo22b3o3bo47b2obo3b2o30b3o$377b3o21bo2bo2bo47b3o
36b3o$377bob2o20bo6bobo45b2o37b2o$378b3o20bo126b3o178b3o1071bo$378b3o
21bobo123bo2bo179bo1071b2o$378b2o119bo22b3o3bo181bo1071bobo$498b3o21bo
2bo2bo$498bob2o20bo6bobo$499b3o20bo$499b3o21bobo$499b2o6$1120bo$564bo
555b2o301b3o$345bo219bo553bobo303bo$344b3o31bo184b3o858bo$339bo3b2obo
30b3o1898b3o$338b3o2b3o30b2obo1897bo2bo$337b2obo3b2o30b3o1901bo$337b3o
36b3o87bo1813bo$338b2o37b2o86b3o31bo1777bobo$410b3o47bo3b2obo30b3o
1772b2o$410bo2bo45b3o2b3o30b2obo1772b2o$381bo22b3o3bo47b2obo3b2o30b3o$
380b3o21bo2bo2bo47b3o36b3o$380bob2o20bo6bobo45b2o37b2o$381b3o20bo126b
3o226b3o1071bo$381b3o21bobo123bo2bo227bo1071b2o$381b2o119bo22b3o3bo
229bo1071bobo$501b3o21bo2bo2bo$501bob2o20bo6bobo$502b3o20bo$502b3o21bo
bo$502b2o6$1171bo$1171b2o301b3o$348bo821bobo303bo$347b3o31bo1093bo$
342bo3b2obo30b3o1898b3o$341b3o2b3o30b2obo1897bo2bo$340b2obo3b2o30b3o
1901bo$340b3o36b3o87bo1813bo$341b2o37b2o86b3o31bo1777bobo$413b3o47bo3b
2obo30b3o$413bo2bo45b3o2b3o30b2obo$384bo22b3o3bo47b2obo3b2o30b3o$383b
3o21bo2bo2bo47b3o36b3o$383bob2o20bo6bobo45b2o37b2o$384b3o20bo126b3o
274b3o1071bo$384b3o21bobo123bo2bo275bo1071b2o$384b2o119bo22b3o3bo277bo
1071bobo$504b3o21bo2bo2bo$504bob2o20bo6bobo$505b3o20bo$505b3o21bobo$
505b2o6$1222bo$1222b2o301b3o$351bo869bobo303bo$350b3o31bo1141bo$345bo
3b2obo30b3o1898b3o$344b3o2b3o30b2obo1897bo2bo$343b2obo3b2o30b3o1901bo$
343b3o36b3o87bo1813bo$344b2o37b2o86b3o31bo1777bobo$416b3o47bo3b2obo30b
3o$416bo2bo45b3o2b3o30b2obo1736b2o$387bo22b3o3bo47b2obo3b2o30b3o1737bo
bo27b3o$386b3o21bo2bo2bo47b3o36b3o1737bo29bo2bo$386bob2o20bo6bobo45b2o
37b2o1767bo$387b3o20bo126b3o322b3o1071bo336bo3bo$387b3o21bobo123bo2bo
323bo1071b2o335bo$387b2o119bo22b3o3bo325bo1071bobo336bobo$507b3o21bo2b
o2bo$507bob2o20bo6bobo$508b3o20bo$508b3o21bobo$508b2o3$2273bo$2272b3o$
2271b2obo$1273bo997b3o$1273b2o301b3o693b2o$354bo917bobo303bo$353b3o31b
o1189bo$348bo3b2obo30b3o1898b3o$347b3o2b3o30b2obo1897bo2bo$346b2obo3b
2o30b3o1901bo$346b3o36b3o87bo1813bo$347b2o37b2o86b3o31bo1777bobo$419b
3o47bo3b2obo30b3o$419bo2bo45b3o2b3o30b2obo1676b2o$390bo22b3o3bo47b2obo
3b2o30b3o1677bobo87b3o$389b3o21bo2bo2bo47b3o36b3o87bo1589bo89bo2bo$
389bob2o20bo6bobo45b2o37b2o86b3o12bo1665bo$390b3o20bo126b3o47bo3b2obo
12b2o301b3o1071bo288bo3bo$390b3o21bobo123bo2bo45b3o2b3o12bobo303bo
1071b2o287bo$390b2o119bo22b3o3bo47b2obo3b2o317bo1071bobo288bobo$510b3o
21bo2bo2bo47b3o$510bob2o20bo6bobo45b2o$511b3o20bo$511b3o21bobo$511b2o
3$2276bo$2275b3o$2274b2obo$1324bo949b3o$1324b2o301b3o645b2o$357bo965bo
bo303bo$356b3o31bo1237bo$351bo3b2obo30b3o1898b3o$350b3o2b3o30b2obo
1897bo2bo$349b2obo3b2o30b3o1901bo$349b3o36b3o87bo1813bo$350b2o37b2o86b
3o31bo1777bobo$422b3o47bo3b2obo30b3o$422bo2bo45b3o2b3o30b2obo1616b2o$
393bo22b3o3bo47b2obo3b2o30b3o1617bobo112bobo32b3o$392b3o21bo2bo2bo47b
3o36b3o87bo1529bo114b2o33bo2bo$392bob2o20bo6bobo45b2o37b2o86b3o60bo
1583bo33bo$393b3o20bo126b3o47bo3b2obo60b2o301b3o1071bo240bo3bo$393b3o
21bobo123bo2bo45b3o2b3o60bobo303bo1071b2o239bo$393b2o119bo22b3o3bo47b
2obo3b2o365bo1071bobo240bobo$513b3o21bo2bo2bo47b3o$513bob2o20bo6bobo
45b2o$514b3o20bo$514b3o21bobo$514b2o2$2237bo$2236b3o40bo$2236bob2o38b
3o$2237b3o37b2obo$1375bo861b2o38b3o$1375b2o301b3o597b2o$360bo1013bobo
303bo$359b3o31bo1285bo$354bo3b2obo30b3o221bobo1623b3o48b3o$353b3o2b3o
30b2obo222b2o1622bo2bo47bo2bo$352b2obo3b2o30b3o223bo1626bo50bo$352b3o
36b3o87bo1762bo50bo$353b2o37b2o86b3o31bo1726bobo48bobo$425b3o47bo3b2ob
o30b3o$425bo2bo45b3o2b3o30b2obo$396bo22b3o3bo47b2obo3b2o30b3o1767b3o$
395b3o21bo2bo2bo47b3o36b3o87bo1679bo2bo$395bob2o20bo6bobo45b2o37b2o86b
3o108bo1569bo$396b3o20bo126b3o47bo3b2obo108b2o301b3o1264bo3bo$396b3o
21bobo123bo2bo45b3o2b3o108bobo303bo1264bo$396b2o119bo22b3o3bo47b2obo3b
2o413bo1266bobo$516b3o21bo2bo2bo47b3o$516bob2o20bo6bobo45b2o$517b3o20b
o$517b3o21bobo$517b2o2$2240bo$2239b3o40bo$2239bob2o38b3o$2240b3o37b2ob
o$1426bo813b2o38b3o$1426b2o301b3o549b2o$363bo1061bobo303bo341bobo$362b
3o31bo1333bo342b2o$357bo3b2obo30b3o1676bo170b3o48b3o$356b3o2b3o30b2obo
1846bo2bo47bo2bo$355b2obo3b2o30b3o1850bo50bo$355b3o36b3o87bo1762bo50bo
$356b2o37b2o86b3o31bo1726bobo48bobo$428b3o47bo3b2obo30b3o$428bo2bo45b
3o2b3o30b2obo$399bo22b3o3bo47b2obo3b2o30b3o1767b3o$398b3o21bo2bo2bo47b
3o36b3o87bo1679bo2bo$398bob2o20bo6bobo45b2o37b2o86b3o156bo1521bo$399b
3o20bo126b3o47bo3b2obo156b2o301b3o1216bo3bo$399b3o21bobo123bo2bo45b3o
2b3o156bobo303bo1216bo$399b2o119bo22b3o3bo47b2obo3b2o461bo1218bobo$
519b3o21bo2bo2bo47b3o$519bob2o20bo6bobo45b2o$520b3o20bo$520b3o21bobo$
520b2o2$2243bo$2242b3o40bo$2242bob2o38b3o$2243b3o37b2obo$1477bo765b2o
38b3o$1477b2o301b3o501b2o$366bo1109bobo303bo$365b3o31bo1381bo$360bo3b
2obo30b3o1847b3o48b3o$359b3o2b3o30b2obo1846bo2bo47bo2bo$358b2obo3b2o
30b3o1850bo50bo$358b3o36b3o87bo1762bo50bo$359b2o37b2o86b3o31bo1726bobo
48bobo$431b3o47bo3b2obo30b3o$431bo2bo45b3o2b3o30b2obo$402bo22b3o3bo47b
2obo3b2o30b3o1767b3o$401b3o21bo2bo2bo47b3o36b3o87bo1679bo2bo$401bob2o
20bo6bobo45b2o37b2o86b3o204bo1473bo$402b3o20bo126b3o47bo3b2obo204b2o
301b3o1168bo3bo$402b3o21bobo123bo2bo45b3o2b3o204bobo303bo1168bo$402b2o
119bo22b3o3bo47b2obo3b2o509bo1112b2o56bobo$522b3o21bo2bo2bo47b3o1628b
2o$522bob2o20bo6bobo45b2o$523b3o20bo$523b3o21bobo$523b2o2$2246bo$2245b
3o40bo$2245bob2o38b3o$2246b3o37b2obo$1528bo717b2o38b3o$1528b2o301b3o
453b2o$369bo1157bobo303bo$368b3o31bo1429bo399bo$363bo3b2obo30b3o1827b
3o17b3o48b3o$362b3o2b3o30b2obo1827bob2o15bo2bo47bo2bo$361b2obo3b2o30b
3o1829b3o18bo50bo$361b3o36b3o87bo1741b3o18bo50bo$362b2o37b2o86b3o31bo
1708b2o16bobo48bobo$434b3o47bo3b2obo30b3o$434bo2bo45b3o2b3o30b2obo$
405bo22b3o3bo47b2obo3b2o30b3o1767b3o$404b3o21bo2bo2bo47b3o36b3o87bo
1679bo2bo$404bob2o20bo6bobo45b2o37b2o86b3o31bo220bo1425bo$405b3o20bo
126b3o47bo3b2obo30b3o219b2o301b3o1120bo3bo$405b3o21bobo123bo2bo45b3o2b
3o30b2obo218bobo303bo1120bo$405b2o119bo22b3o3bo47b2obo3b2o30b3o524bo
1122bobo$525b3o21bo2bo2bo47b3o36b3o1585b3o$525bob2o20bo6bobo45b2o37b2o
1585bo2bo$526b3o20bo1680bo$526b3o21bobo1677bo$526b2o119bo1583bobo$646b
3o$646bob2o1531bo67bo$647b3o1530b2o66b3o40bo$647b3o1530bobo65bob2o38b
3o$647b2o1600b3o37b2obo$1579bo669b2o38b3o$1579b2o301b3o405b2o$372bo
1205bobo303bo$371b3o31bo1477bo351bo$366bo3b2obo30b3o1827b3o17b3o48b3o$
365b3o2b3o30b2obo1827bob2o15bo2bo47bo2bo$364b2obo3b2o30b3o1829b3o18bo
50bo$364b3o36b3o87bo1741b3o18bo50bo$365b2o37b2o86b3o31bo1708b2o16bobo
48bobo$437b3o47bo3b2obo30b3o$437bo2bo45b3o2b3o30b2obo$408bo22b3o3bo47b
2obo3b2o30b3o1767b3o$407b3o21bo2bo2bo47b3o36b3o87bo1679bo2bo$407bob2o
20bo6bobo45b2o37b2o86b3o31bo268bo1377bo$408b3o20bo126b3o47bo3b2obo30b
3o267b2o301b3o1072bo3bo$408b3o21bobo123bo2bo45b3o2b3o30b2obo266bobo
303bo1072bo$408b2o119bo22b3o3bo47b2obo3b2o30b3o572bo1074bobo$528b3o21b
o2bo2bo47b3o36b3o1585b3o$528bob2o20bo6bobo45b2o37b2o1585bo2bo$529b3o
20bo1680bo$529b3o21bobo1677bo$529b2o119bo1583bobo$649b3o$649bob2o1471b
o127bo$650b3o1470b2o126b3o40bo$650b3o1470bobo125bob2o38b3o$650b2o1600b
3o37b2obo$1630bo621b2o38b3o$663bo966b2o301b3o357b2o$375bo288b2o963bobo
303bo$374b3o31bo254b2o1269bo303bo$369bo3b2obo30b3o1827b3o17b3o48b3o$
368b3o2b3o30b2obo1827bob2o15bo2bo47bo2bo$367b2obo3b2o30b3o1829b3o18bo
50bo$367b3o36b3o87bo1741b3o18bo50bo$368b2o37b2o86b3o31bo1708b2o16bobo
48bobo$440b3o47bo3b2obo30b3o$440bo2bo45b3o2b3o30b2obo$411bo22b3o3bo47b
2obo3b2o30b3o1767b3o$410b3o21bo2bo2bo47b3o36b3o87bo1679bo2bo$410bob2o
20bo6bobo45b2o37b2o86b3o31bo316bo1329bo$411b3o20bo126b3o47bo3b2obo30b
3o315b2o301b3o1024bo3bo$411b3o21bobo123bo2bo45b3o2b3o30b2obo314bobo
303bo1024bo$411b2o119bo22b3o3bo47b2obo3b2o30b3o620bo1026bobo$531b3o21b
o2bo2bo47b3o36b3o1585b3o$531bob2o20bo6bobo45b2o37b2o1585bo2bo$532b3o
20bo1680bo$532b3o21bobo1677bo$532b2o119bo1583bobo$652b3o1549b3o$652bob
2o1411bo135bo2bo48bo$653b3o1410b2o138bo47b3o40bo$653b3o1410bobo137bo
47bob2o38b3o$653b2o1548bobo49b3o37b2obo$1681bo573b2o38b3o$1681b2o301b
3o309b2o$378bo1301bobo303bo29bobo192bo$377b3o31bo1573bo30b2o192b3o28bo
$372bo3b2obo30b3o1604bo191b2obo27b3o17b3o48b3o$371b3o2b3o30b2obo1796b
3o28bob2o15bo2bo47bo2bo$370b2obo3b2o30b3o1798b2o29b3o18bo50bo$370b3o
36b3o87bo1741b3o18bo50bo$371b2o37b2o86b3o31bo1708b2o16bobo48bobo$443b
3o47bo3b2obo30b3o$443bo2bo45b3o2b3o30b2obo$414bo22b3o3bo47b2obo3b2o30b
3o1767b3o$413b3o21bo2bo2bo47b3o36b3o87bo1679bo2bo$413bob2o20bo6bobo45b
2o37b2o86b3o31bo364bo1281bo$414b3o20bo126b3o47bo3b2obo30b3o363b2o301b
3o976bo3bo$414b3o21bobo123bo2bo45b3o2b3o30b2obo362bobo303bo976bo$414b
2o119bo22b3o3bo47b2obo3b2o30b3o668bo876b2o100bobo$534b3o21bo2bo2bo47b
3o36b3o1545b2o38b3o$534bob2o20bo6bobo45b2o37b2o1585bo2bo$535b3o20bo
1680bo$535b3o21bobo1677bo$535b2o119bo1583bobo$655b3o1549b3o$655bob2o
1547bo2bo48bo$656b3o1550bo47b3o40bo$656b3o1550bo47bob2o38b3o$656b2o
1548bobo49b3o37b2obo$1732bo525b2o38b3o$1732b2o565b2o$381bo1349bobo480b
o$380b3o31bo1784b3o11b3o28bo$375bo3b2obo30b3o1783bo2bo9b2obo27b3o17b3o
48b3o$374b3o2b3o30b2obo1783bo12b3o28bob2o15bo2bo47bo2bo$373b2obo3b2o
30b3o1784bo3bo9b2o29b3o18bo50bo$373b3o36b3o87bo1696bo44b3o18bo50bo$
374b2o37b2o86b3o31bo1664bobo41b2o16bobo48bobo$446b3o47bo3b2obo30b3o$
446bo2bo45b3o2b3o30b2obo$417bo22b3o3bo47b2obo3b2o30b3o1767b3o$416b3o
21bo2bo2bo47b3o36b3o87bo1679bo2bo$416bob2o20bo6bobo45b2o37b2o86b3o31bo
412bo1233bo$417b3o20bo126b3o47bo3b2obo30b3o411b2o301b3o928bo3bo$417b3o
21bobo123bo2bo45b3o2b3o30b2obo410bobo303bo928bo$417b2o119bo22b3o3bo47b
2obo3b2o30b3o716bo825bo104bobo$537b3o21bo2bo2bo47b3o36b3o1541b3o41b3o$
537bob2o20bo6bobo45b2o37b2o1540b2obo41bo2bo$538b3o20bo126b3o1506b3o42b
o$538b3o21bobo123bo2bo1506b2o42bo$538b2o119bo22b3o3bo1554bobo$658b3o
21bo2bo2bo1521b3o$658bob2o20bo6bobo1456b2o59bo2bo48bo$659b3o20bo1328bo
136bobo61bo47b3o40bo$659b3o21bobo1324bo137bo63bo47bob2o38b3o$659b2o
1349b3o196bobo49b3o37b2obo$709b3o1071bo477b2o38b3o$711bo1071b2o517b2o$
384bo325bo1071bobo432bo$383b3o31bo1784b3o11b3o28bo$378bo3b2obo30b3o
1783bo2bo9b2obo27b3o17b3o48b3o$377b3o2b3o30b2obo1783bo12b3o28bob2o15bo
2bo47bo2bo$376b2obo3b2o30b3o1784bo3bo9b2o29b3o18bo50bo$376b3o36b3o87bo
1696bo44b3o18bo50bo$377b2o37b2o86b3o31bo1664bobo41b2o16bobo48bobo$449b
3o47bo3b2obo30b3o$449bo2bo45b3o2b3o30b2obo$420bo22b3o3bo47b2obo3b2o30b
3o1767b3o$419b3o21bo2bo2bo47b3o36b3o87bo1679bo2bo$419bob2o20bo6bobo45b
2o37b2o86b3o31bo460bo1185bo$420b3o20bo126b3o47bo3b2obo30b3o459b2o301b
3o880bo3bo$420b3o21bobo123bo2bo45b3o2b3o30b2obo458bobo303bo880bo$420b
2o119bo22b3o3bo47b2obo3b2o30b3o764bo777bo104bobo$540b3o21bo2bo2bo47b3o
36b3o1541b3o41b3o$540bob2o20bo6bobo45b2o37b2o1540b2obo41bo2bo$541b3o
20bo126b3o1506b3o42bo$541b3o21bobo123bo2bo1506b2o42bo$541b2o119bo22b3o
3bo1554bobo$661b3o21bo2bo2bo1521b3o$661bob2o20bo6bobo1396b2o119bo2bo
48bo$662b3o20bo1405bobo121bo47b3o40bo$662b3o21bobo1402bo123bo47bob2o
38b3o$662b2o1548bobo49b3o37b2obo$760b3o1071bo429b2o38b3o$762bo1071b2o
469b2o$387bo373bo1071bobo384bo$386b3o31bo1784b3o11b3o28bo$381bo3b2obo
30b3o1783bo2bo9b2obo27b3o17b3o48b3o$380b3o2b3o30b2obo1783bo12b3o28bob
2o15bo2bo47bo2bo$379b2obo3b2o30b3o1784bo3bo9b2o29b3o18bo50bo$379b3o36b
3o87bo1696bo44b3o18bo50bo$380b2o37b2o86b3o31bo1664bobo41b2o16bobo48bob
o$452b3o47bo3b2obo30b3o$452bo2bo45b3o2b3o30b2obo$423bo22b3o3bo47b2obo
3b2o30b3o1767b3o$422b3o21bo2bo2bo47b3o36b3o87bo1679bo2bo$422bob2o20bo
6bobo45b2o37b2o86b3o31bo508bo1137bo$423b3o20bo126b3o47bo3b2obo30b3o
507b2o301b3o832bo3bo$423b3o21bobo123bo2bo45b3o2b3o30b2obo506bobo303bo
832bo$423b2o119bo22b3o3bo47b2obo3b2o30b3o812bo729bo104bobo$543b3o21bo
2bo2bo47b3o36b3o1541b3o41b3o$543bob2o20bo6bobo45b2o37b2o1540b2obo41bo
2bo$544b3o20bo126b3o1506b3o42bo$544b3o21bobo123bo2bo1506b2o42bo$544b2o
119bo22b3o3bo1554bobo$664b3o21bo2bo2bo1521b3o$664bob2o20bo6bobo1336b2o
179bo2bo48bo$665b3o20bo1345bobo181bo47b3o40bo$665b3o21bobo1342bo183bo
47bob2o38b3o$665b2o1548bobo49b3o37b2obo$811b3o1071bo381b2o38b3o$813bo
1071b2o421b2o$390bo421bo1071bobo336bo$389b3o31bo293bo1490b3o11b3o28bo$
384bo3b2obo30b3o293bo1489bo2bo9b2obo27b3o17b3o48b3o$383b3o2b3o30b2obo
291b3o1489bo12b3o28bob2o15bo2bo47bo2bo$382b2obo3b2o30b3o1784bo3bo9b2o
29b3o18bo50bo$382b3o36b3o87bo1696bo44b3o18bo50bo$383b2o37b2o86b3o31bo
1664bobo41b2o16bobo48bobo$455b3o47bo3b2obo30b3o$455bo2bo45b3o2b3o30b2o
bo$426bo22b3o3bo47b2obo3b2o30b3o1767b3o$425b3o21bo2bo2bo47b3o36b3o87bo
1679bo2bo$425bob2o20bo6bobo45b2o37b2o86b3o31bo556bo1089bo$426b3o20bo
126b3o47bo3b2obo30b3o555b2o301b3o784bo3bo$426b3o21bobo123bo2bo45b3o2b
3o30b2obo554bobo303bo638bo145bo$426b2o119bo22b3o3bo47b2obo3b2o30b3o
860bo638b3o40bo104bobo$546b3o21bo2bo2bo47b3o36b3o1499bob2o38b3o41b3o$
546bob2o20bo6bobo45b2o37b2o1500b3o37b2obo41bo2bo$547b3o20bo126b3o1466b
2o38b3o42bo$547b3o21bobo123bo2bo1506b2o42bo$547b2o119bo22b3o3bo1554bob
o$667b3o21bo2bo2bo1521b3o$667bob2o20bo6bobo1276b2o181b2o9b3o44bo2bo48b
o$668b3o20bo1285bobo180b2o8bo2bo47bo47b3o40bo$668b3o21bobo1282bo195bo
47bo47bob2o38b3o$668b2o1503bo44bobo49b3o37b2obo$862b3o1071bo233bobo97b
2o38b3o$864bo1071b2o373b2o$393bo469bo1071bobo21bobo264bo$392b3o31bo
1532b2o250b3o11b3o28bo$387bo3b2obo30b3o1532bo250bo2bo9b2obo27b3o17b3o
48b3o$386b3o2b3o30b2obo1783bo12b3o28bob2o15bo2bo47bo2bo$385b2obo3b2o
30b3o1784bo3bo9b2o29b3o18bo50bo$385b3o36b3o87bo1696bo44b3o18bo50bo$
386b2o37b2o86b3o31bo1664bobo41b2o16bobo48bobo$458b3o47bo3b2obo30b3o$
458bo2bo45b3o2b3o30b2obo$429bo22b3o3bo47b2obo3b2o30b3o1767b3o$428b3o
21bo2bo2bo47b3o36b3o87bo1679bo2bo$428bob2o20bo6bobo45b2o37b2o86b3o31bo
604bo1041bo$429b3o20bo126b3o47bo3b2obo30b3o603b2o301b3o736bo3bo$429b3o
21bobo123bo2bo45b3o2b3o30b2obo602bobo303bo590bo145bo$429b2o119bo22b3o
3bo47b2obo3b2o30b3o908bo590b3o40bo104bobo$549b3o21bo2bo2bo47b3o36b3o
1499bob2o38b3o41b3o$549bob2o20bo6bobo45b2o37b2o1500b3o37b2obo41bo2bo$
550b3o20bo126b3o1466b2o38b3o42bo$550b3o21bobo123bo2bo1506b2o42bo$550b
2o119bo22b3o3bo1554bobo$670b3o21bo2bo2bo1521b3o$670bob2o20bo6bobo1470b
3o44bo2bo48bo$671b3o20bo1478bo2bo47bo47b3o40bo$671b3o21bobo1478bo47bo
47bob2o38b3o$671b2o1503bo44bobo49b3o37b2obo$913b3o1257bobo97b2o38b3o$
915bo1398b2o$396bo517bo1314bo$395b3o31bo1784b3o11b3o28bo$390bo3b2obo
30b3o1783bo2bo9b2obo27b3o17b3o48b3o$389b3o2b3o30b2obo1783bo12b3o28bob
2o15bo2bo47bo2bo$388b2obo3b2o30b3o1784bo3bo9b2o29b3o18bo50bo$388b3o36b
3o87bo1696bo44b3o18bo50bo$389b2o37b2o86b3o31bo1664bobo41b2o16bobo48bob
o$461b3o47bo3b2obo30b3o$461bo2bo45b3o2b3o30b2obo$432bo22b3o3bo47b2obo
3b2o30b3o1767b3o$431b3o21bo2bo2bo47b3o36b3o87bo1679bo2bo$431bob2o20bo
6bobo45b2o37b2o86b3o31bo652bo993bo$432b3o20bo126b3o47bo3b2obo30b3o651b
2o301b3o688bo3bo$432b3o21bobo123bo2bo45b3o2b3o30b2obo650bobo303bo542bo
145bo$432b2o119bo22b3o3bo47b2obo3b2o30b3o956bo542b3o40bo104bobo$552b3o
21bo2bo2bo47b3o36b3o1499bob2o38b3o41b3o$552bob2o20bo6bobo45b2o37b2o
1500b3o37b2obo41bo2bo$553b3o20bo126b3o1466b2o38b3o42bo$553b3o21bobo
123bo2bo1506b2o42bo$553b2o119bo22b3o3bo1554bobo$673b3o21bo2bo2bo1521b
3o$673bob2o20bo6bobo1470b3o44bo2bo48bo$674b3o20bo1256bo221bo2bo47bo47b
3o40bo$674b3o21bobo1252bo225bo47bo47bob2o38b3o$674b2o1277b3o223bo44bob
o49b3o37b2obo$964b3o1209bobo97b2o38b3o$966bo1350b2o$399bo565bo1266bo$
398b3o31bo1784b3o11b3o28bo$393bo3b2obo30b3o1783bo2bo9b2obo27b3o17b3o
48b3o$392b3o2b3o30b2obo1783bo12b3o28bob2o15bo2bo47bo2bo$391b2obo3b2o
30b3o1784bo3bo9b2o29b3o18bo50bo$391b3o36b3o87bo1696bo44b3o18bo50bo$
392b2o37b2o86b3o31bo1664bobo41b2o16bobo48bobo$464b3o47bo3b2obo30b3o
1588bo$464bo2bo45b3o2b3o30b2obo1587b2o$435bo22b3o3bo47b2obo3b2o30b3o
1588bobo176b3o$434b3o21bo2bo2bo47b3o36b3o87bo1679bo2bo$434bob2o20bo6bo
bo45b2o37b2o86b3o31bo700bo945bo$435b3o20bo126b3o47bo3b2obo30b3o699b2o
301b3o640bo3bo$435b3o21bobo123bo2bo45b3o2b3o30b2obo698bobo303bo494bo
145bo$435b2o119bo22b3o3bo47b2obo3b2o30b3o1004bo494b3o40bo104bobo$555b
3o21bo2bo2bo47b3o36b3o1499bob2o38b3o41b3o$555bob2o20bo6bobo45b2o37b2o
1500b3o37b2obo41bo2bo$556b3o20bo126b3o1466b2o38b3o42bo$556b3o21bobo
123bo2bo1506b2o42bo$556b2o119bo22b3o3bo1554bobo$676b3o21bo2bo2bo1454bo
66b3o$676bob2o20bo6bobo1450b3o17b3o44bo2bo48bo$677b3o20bo1459bob2o15bo
2bo47bo47b3o40bo$677b3o21bobo1457b3o18bo47bo47bob2o38b3o$677b2o1482b3o
18bo44bobo49b3o37b2obo$1015b3o1143b2o16bobo97b2o38b3o$1017bo1302b2o$
402bo613bo1218bo$401b3o31bo1784b3o11b3o28bo$396bo3b2obo30b3o1783bo2bo
9b2obo27b3o17b3o48b3o$395b3o2b3o30b2obo1783bo12b3o28bob2o15bo2bo47bo2b
o$394b2obo3b2o30b3o1784bo3bo9b2o29b3o18bo50bo$394b3o36b3o87bo1696bo44b
3o18bo50bo$395b2o37b2o86b3o31bo1664bobo41b2o16bobo48bobo$467b3o47bo3b
2obo30b3o1528bo72b3o$467bo2bo45b3o2b3o30b2obo1527b2o72bo2bo$438bo22b3o
3bo47b2obo3b2o30b3o1364bobo161bobo71bo164b3o$437b3o21bo2bo2bo47b3o36b
3o87bo1276b2o221bo14bo164bo2bo$437bob2o20bo6bobo45b2o37b2o86b3o31bo
748bo495bo220bo16bobo161bo$438b3o20bo126b3o47bo3b2obo30b3o747b2o301b3o
411b3o178bo3bo$438b3o21bobo123bo2bo45b3o2b3o30b2obo746bobo303bo446bo
145bo$438b2o119bo22b3o3bo47b2obo3b2o30b3o1052bo446b3o40bo104bobo$558b
3o21bo2bo2bo47b3o36b3o1499bob2o38b3o41b3o$558bob2o20bo6bobo45b2o37b2o
1500b3o37b2obo41bo2bo$559b3o20bo126b3o1466b2o38b3o42bo$559b3o21bobo
123bo2bo1506b2o42bo$559b2o119bo22b3o3bo1554bobo$679b3o21bo2bo2bo1454bo
66b3o$679bob2o20bo6bobo1450b3o17b3o44bo2bo48bo$680b3o20bo1459bob2o15bo
2bo47bo47b3o40bo$680b3o21bobo1457b3o18bo47bo47bob2o38b3o$680b2o1482b3o
18bo44bobo49b3o37b2obo$1066b3o1095b2o16bobo97b2o38b3o$1068bo1254b2o$
405bo661bo1170bo$404b3o31bo329bo1454b3o11b3o28bo$399bo3b2obo30b3o329bo
1453bo2bo9b2obo27b3o17b3o48b3o$398b3o2b3o30b2obo327b3o1453bo12b3o28bob
2o15bo2bo47bo2bo$397b2obo3b2o30b3o1784bo3bo9b2o29b3o18bo50bo$397b3o36b
3o87bo1696bo44b3o18bo50bo$398b2o37b2o86b3o31bo1664bobo41b2o16bobo48bob
o$470b3o47bo3b2obo30b3o1468bo132b3o$470bo2bo45b3o2b3o30b2obo1467b2o
132bo2bo$441bo22b3o3bo47b2obo3b2o30b3o1468bobo131bo164b3o$440b3o21bo2b
o2bo47b3o36b3o87bo1514bo164bo2bo$440bob2o20bo6bobo45b2o37b2o86b3o31bo
796bo685bobo161bo$441b3o20bo126b3o47bo3b2obo30b3o795b2o301b3o347b3o
194bo3bo$441b3o21bobo123bo2bo45b3o2b3o30b2obo794bobo303bo346bo2bo48bo
145bo$441b2o119bo22b3o3bo47b2obo3b2o30b3o1100bo350bo47b3o40bo104bobo$
561b3o21bo2bo2bo47b3o36b3o1451bo47bob2o38b3o41b3o$561bob2o20bo6bobo45b
2o37b2o1448bobo49b3o37b2obo41bo2bo$562b3o20bo126b3o1466b2o38b3o42bo$
562b3o21bobo123bo2bo1506b2o42bo$562b2o119bo22b3o3bo1424bo129bobo$682b
3o21bo2bo2bo1423b3o28bo66b3o$682bob2o20bo6bobo1419b2obo27b3o17b3o44bo
2bo48bo$683b3o20bo1428b3o28bob2o15bo2bo47bo47b3o40bo$683b3o21bobo1426b
2o29b3o18bo47bo47bob2o38b3o$683b2o1482b3o18bo44bobo49b3o37b2obo$1117b
3o1047b2o16bobo97b2o38b3o$1119bo1206b2o$408bo709bo783bobo336bo$407b3o
31bo1460b2o322b3o11b3o28bo$402bo3b2obo30b3o1460bo322bo2bo9b2obo27b3o
17b3o48b3o$401b3o2b3o30b2obo1783bo12b3o28bob2o15bo2bo47bo2bo$400b2obo
3b2o30b3o1784bo3bo9b2o29b3o18bo50bo$400b3o36b3o87bo1696bo44b3o18bo50bo
$401b2o37b2o86b3o31bo1664bobo41b2o16bobo48bobo$473b3o47bo3b2obo30b3o
1408bo192b3o$473bo2bo45b3o2b3o30b2obo1407b2o192bo2bo$444bo22b3o3bo47b
2obo3b2o30b3o1408bobo191bo164b3o$443b3o21bo2bo2bo47b3o36b3o87bo1514bo
164bo2bo$443bob2o20bo6bobo45b2o37b2o86b3o31bo844bo637bobo161bo$444b3o
20bo126b3o47bo3b2obo30b3o843b2o301b3o299b3o194bo3bo$444b3o21bobo123bo
2bo45b3o2b3o30b2obo842bobo303bo298bo2bo48bo145bo$444b2o119bo22b3o3bo
47b2obo3b2o30b3o1148bo302bo47b3o40bo104bobo$564b3o21bo2bo2bo47b3o36b3o
1451bo47bob2o38b3o41b3o$564bob2o20bo6bobo45b2o37b2o1448bobo49b3o37b2ob
o41bo2bo$565b3o20bo126b3o1466b2o38b3o42bo$565b3o21bobo123bo2bo1506b2o
42bo$565b2o119bo22b3o3bo1424bo129bobo$685b3o21bo2bo2bo1423b3o28bo66b3o
$685bob2o20bo6bobo1419b2obo27b3o17b3o44bo2bo48bo$686b3o20bo1428b3o28bo
b2o15bo2bo47bo47b3o40bo$686b3o21bobo1426b2o29b3o18bo47bo47bob2o38b3o$
686b2o1482b3o18bo44bobo49b3o37b2obo$1168b3o999b2o16bobo97b2o38b3o$
1170bo1158b2o$411bo757bo1074bo$410b3o31bo1784b3o11b3o28bo$405bo3b2obo
30b3o1783bo2bo9b2obo27b3o17b3o48b3o$404b3o2b3o30b2obo1783bo12b3o28bob
2o15bo2bo47bo2bo$403b2obo3b2o30b3o1784bo3bo9b2o29b3o18bo50bo$403b3o36b
3o87bo1696bo44b3o18bo50bo$404b2o37b2o86b3o31bo1664bobo41b2o16bobo48bob
o$476b3o47bo3b2obo30b3o1348bo194b2o56b3o$476bo2bo45b3o2b3o30b2obo1347b
2o194bobo55bo2bo$447bo22b3o3bo47b2obo3b2o30b3o1348bobo193bo57bo164b3o$
446b3o21bo2bo2bo47b3o36b3o87bo1514bo164bo2bo$446bob2o20bo6bobo45b2o37b
2o86b3o31bo892bo589bobo161bo$447b3o20bo126b3o47bo3b2obo30b3o891b2o301b
3o251b3o194bo3bo$447b3o21bobo123bo2bo45b3o2b3o30b2obo890bobo303bo250bo
2bo48bo145bo$447b2o119bo22b3o3bo47b2obo3b2o30b3o1196bo254bo47b3o40bo
104bobo$567b3o21bo2bo2bo47b3o36b3o1451bo47bob2o38b3o41b3o$567bob2o20bo
6bobo45b2o37b2o1448bobo49b3o37b2obo41bo2bo$568b3o20bo126b3o1466b2o38b
3o42bo$568b3o21bobo123bo2bo1506b2o42bo$568b2o119bo22b3o3bo1424bo129bob
o$688b3o21bo2bo2bo1409b3o11b3o28bo66b3o$688bob2o20bo6bobo1406bo2bo9b2o
bo27b3o17b3o44bo2bo48bo$689b3o20bo1184bo230bo12b3o28bob2o15bo2bo47bo
47b3o40bo$689b3o21bobo1180bo231bo3bo9b2o29b3o18bo47bo47bob2o38b3o$689b
2o1205b3o229bo44b3o18bo44bobo49b3o37b2obo$1219b3o907bobo41b2o16bobo97b
2o38b3o$1221bo1110b2o$414bo805bo1026bo$413b3o31bo1784b3o11b3o28bo$408b
o3b2obo30b3o1783bo2bo9b2obo27b3o17b3o48b3o$407b3o2b3o30b2obo1783bo12b
3o28bob2o15bo2bo47bo2bo$406b2obo3b2o30b3o1784bo3bo9b2o29b3o18bo50bo$
406b3o36b3o87bo1696bo44b3o18bo50bo$407b2o37b2o86b3o31bo1559bo104bobo
41b2o16bobo48bobo$479b3o47bo3b2obo30b3o1483b2o72b3o41b3o$479bo2bo45b3o
2b3o30b2obo1483bobo70b2obo41bo2bo$450bo22b3o3bo47b2obo3b2o30b3o1484bo
72b3o42bo164b3o$449b3o21bo2bo2bo47b3o36b3o87bo1470b2o42bo164bo2bo$449b
ob2o20bo6bobo45b2o37b2o86b3o31bo940bo480bobo58bobo161bo$450b3o20bo126b
3o47bo3b2obo30b3o939b2o479b2o26b3o194bo3bo$450b3o21bobo123bo2bo45b3o2b
3o30b2obo938bobo480bo25bo2bo48bo145bo$450b2o119bo22b3o3bo47b2obo3b2o
30b3o1451bo47b3o40bo104bobo$570b3o21bo2bo2bo47b3o36b3o1451bo47bob2o38b
3o41b3o$570bob2o20bo6bobo45b2o37b2o1448bobo49b3o37b2obo41bo2bo$571b3o
20bo126b3o1466b2o38b3o42bo$571b3o21bobo123bo2bo1506b2o42bo$571b2o119bo
22b3o3bo1424bo129bobo$691b3o21bo2bo2bo1409b3o11b3o28bo66b3o$691bob2o
20bo6bobo1406bo2bo9b2obo27b3o17b3o44bo2bo48bo$692b3o20bo1415bo12b3o28b
ob2o15bo2bo47bo47b3o40bo$692b3o21bobo1412bo3bo9b2o29b3o18bo47bo47bob2o
38b3o$692b2o1437bo44b3o18bo44bobo49b3o37b2obo$1270b3o859bobo41b2o16bob
o97b2o38b3o$1272bo1062b2o$1271bo978bo$450bo1784b3o11b3o28bo$449b3o
1783bo2bo9b2obo27b3o17b3o48b3o$448b2obo1783bo12b3o28bob2o15bo2bo47bo2b
o$448b3o1784bo3bo9b2o29b3o18bo50bo$448b3o87bo1696bo44b3o18bo50bo$449b
2o86b3o31bo1559bo104bobo41b2o16bobo48bobo$482b3o47bo3b2obo30b3o1423b2o
132b3o41b3o$482bo2bo45b3o2b3o30b2obo1423bobo130b2obo41bo2bo$453bo22b3o
3bo47b2obo3b2o30b3o1292bobo129bo132b3o42bo164b3o$452b3o21bo2bo2bo47b3o
36b3o87bo1204b2o264b2o42bo164bo2bo$452bob2o20bo6bobo45b2o37b2o86b3o31b
o988bo183bo309bobo161bo$453b3o20bo126b3o47bo3b2obo30b3o987b2o459b3o
194bo3bo$453b3o21bobo123bo2bo45b3o2b3o30b2obo986bobo458bo2bo48bo145bo$
453b2o119bo22b3o3bo47b2obo3b2o30b3o1451bo47b3o40bo104bobo$573b3o21bo2b
o2bo47b3o36b3o1451bo47bob2o38b3o41b3o$573bob2o20bo6bobo45b2o37b2o1448b
obo49b3o37b2obo41bo2bo$574b3o20bo126b3o1466b2o38b3o42bo$574b3o21bobo
123bo2bo1506b2o42bo$574b2o119bo22b3o3bo1424bo129bobo$694b3o21bo2bo2bo
1409b3o11b3o28bo66b3o$694bob2o20bo6bobo1406bo2bo9b2obo27b3o17b3o44bo2b
o48bo$695b3o20bo1415bo12b3o28bob2o15bo2bo47bo47b3o40bo$695b3o21bobo
1412bo3bo9b2o29b3o18bo47bo47bob2o38b3o$695b2o1437bo44b3o18bo44bobo49b
3o37b2obo$1321b3o811bobo41b2o16bobo97b2o38b3o$1323bo1014b2o$1322bo930b
o$453bo365bo1418b3o11b3o28bo$452b3o365bo1417bo2bo9b2obo27b3o17b3o48b3o
$451b2obo363b3o1417bo12b3o28bob2o15bo2bo47bo2bo$451b3o1784bo3bo9b2o29b
3o18bo50bo$451b3o87bo1550bo145bo44b3o18bo50bo$452b2o86b3o31bo1516b3o
40bo104bobo41b2o16bobo48bobo$485b3o47bo3b2obo30b3o1363b2o150bob2o38b3o
41b3o$485bo2bo45b3o2b3o30b2obo1363bobo150b3o37b2obo41bo2bo$456bo22b3o
3bo47b2obo3b2o30b3o1364bo152b2o38b3o42bo164b3o$455b3o21bo2bo2bo47b3o
36b3o87bo1470b2o42bo164bo2bo$455bob2o20bo6bobo45b2o37b2o86b3o31bo1036b
o445bobo161bo$456b3o20bo126b3o47bo3b2obo30b3o1035b2o411b3o194bo3bo$
456b3o21bobo123bo2bo45b3o2b3o30b2obo1034bobo363b3o44bo2bo48bo145bo$
456b2o119bo22b3o3bo47b2obo3b2o30b3o1400bo2bo47bo47b3o40bo104bobo$576b
3o21bo2bo2bo47b3o36b3o1403bo47bo47bob2o38b3o41b3o$576bob2o20bo6bobo45b
2o37b2o1403bo44bobo49b3o37b2obo41bo2bo$577b3o20bo126b3o1366bobo97b2o
38b3o42bo$577b3o21bobo123bo2bo1506b2o42bo$577b2o119bo22b3o3bo1424bo
129bobo$697b3o21bo2bo2bo1409b3o11b3o28bo66b3o$697bob2o20bo6bobo1406bo
2bo9b2obo27b3o17b3o44bo2bo48bo$698b3o20bo1415bo12b3o28bob2o15bo2bo47bo
47b3o40bo$698b3o21bobo1412bo3bo9b2o29b3o18bo47bo47bob2o38b3o$698b2o
1437bo44b3o18bo44bobo49b3o37b2obo$1372b3o763bobo41b2o16bobo97b2o38b3o$
1374bo966b2o$1373bo471bobo408bo$456bo1388b2o394b3o11b3o28bo$455b3o
1388bo394bo2bo9b2obo27b3o17b3o48b3o$454b2obo1783bo12b3o28bob2o15bo2bo
47bo2bo$454b3o1402bo381bo3bo9b2o29b3o18bo50bo$454b3o87bo1313bo236bo
145bo44b3o18bo50bo$455b2o86b3o31bo1280b3o233b3o40bo104bobo41b2o16bobo
48bobo$488b3o47bo3b2obo30b3o1303b2o210bob2o38b3o41b3o$488bo2bo45b3o2b
3o30b2obo1303bobo210b3o37b2obo41bo2bo$459bo22b3o3bo47b2obo3b2o30b3o
1304bo212b2o38b3o42bo164b3o$458b3o21bo2bo2bo47b3o36b3o87bo1470b2o42bo
164bo2bo$458bob2o20bo6bobo45b2o37b2o86b3o31bo1084bo397bobo161bo$459b3o
20bo126b3o47bo3b2obo30b3o1083b2o363b3o194bo3bo$459b3o21bobo123bo2bo45b
3o2b3o30b2obo1082bobo315b3o44bo2bo48bo145bo$459b2o119bo22b3o3bo47b2obo
3b2o30b3o1400bo2bo47bo47b3o40bo104bobo$579b3o21bo2bo2bo47b3o36b3o1403b
o47bo47bob2o38b3o41b3o$579bob2o20bo6bobo45b2o37b2o1403bo44bobo49b3o37b
2obo41bo2bo$580b3o20bo126b3o1366bobo97b2o38b3o42bo$580b3o21bobo123bo2b
o1506b2o42bo$580b2o119bo22b3o3bo1424bo129bobo$700b3o21bo2bo2bo1409b3o
11b3o28bo66b3o$700bob2o20bo6bobo1406bo2bo9b2obo27b3o17b3o44bo2bo48bo$
701b3o20bo1415bo12b3o28bob2o15bo2bo47bo47b3o40bo$701b3o21bobo1412bo3bo
9b2o29b3o18bo47bo47bob2o38b3o$701b2o1437bo44b3o18bo44bobo49b3o37b2obo$
1423b3o715bobo41b2o16bobo97b2o38b3o$1425bo918b2o$1424bo834bo$2086b2o
156b3o11b3o28bo$2086b2o156bo2bo9b2obo27b3o17b3o48b3o$2244bo12b3o28bob
2o15bo2bo47bo2bo$2244bo3bo9b2o29b3o18bo50bo$547bo1550bo145bo44b3o18bo
50bo$546b3o31bo1516b3o40bo104bobo41b2o16bobo48bobo$541bo3b2obo30b3o
1515bob2o38b3o41b3o$540b3o2b3o30b2obo1516b3o37b2obo41bo2bo$539b2obo3b
2o30b3o1517b2o38b3o42bo164b3o$539b3o36b3o87bo1470b2o42bo164bo2bo$540b
2o37b2o86b3o31bo1482bobo161bo$612b3o47bo3b2obo30b3o1448b3o194bo3bo$
612bo2bo45b3o2b3o30b2obo1400b3o44bo2bo48bo145bo$583bo22b3o3bo47b2obo3b
2o30b3o1400bo2bo47bo47b3o40bo104bobo$582b3o21bo2bo2bo47b3o36b3o1403bo
47bo47bob2o38b3o41b3o$582bob2o20bo6bobo45b2o37b2o1403bo44bobo49b3o37b
2obo41bo2bo$583b3o20bo126b3o1366bobo97b2o38b3o42bo$583b3o21bobo123bo2b
o1089bobo414b2o42bo$583b2o119bo22b3o3bo1092b2o330bo129bobo$703b3o21bo
2bo2bo1093bo315b3o11b3o28bo66b3o$703bob2o20bo6bobo1406bo2bo9b2obo27b3o
17b3o44bo2bo48bo$704b3o20bo1112bo302bo12b3o28bob2o15bo2bo47bo47b3o40bo
$704b3o21bobo1108bo303bo3bo9b2o29b3o18bo47bo47bob2o38b3o$704b2o1133b3o
301bo44b3o18bo44bobo49b3o37b2obo$1474b3o667bobo41b2o16bobo97b2o38b3o$
1476bo870b2o$1475bo786bo$2247b3o11b3o28bo$2247bo2bo9b2obo27b3o17b3o48b
3o$2247bo12b3o28bob2o15bo2bo47bo2bo$2247bo3bo9b2o29b3o18bo50bo$550bo
1550bo145bo44b3o18bo50bo$549b3o31bo1516b3o40bo104bobo41b2o16bobo48bobo
$544bo3b2obo30b3o1515bob2o38b3o41b3o$543b3o2b3o30b2obo1516b3o37b2obo
41bo2bo$542b2obo3b2o30b3o1517b2o38b3o42bo164b3o$542b3o36b3o87bo1470b2o
42bo164bo2bo$543b2o37b2o86b3o31bo1482bobo161bo$615b3o47bo3b2obo30b3o
1381bo66b3o194bo3bo$615bo2bo45b3o2b3o30b2obo1380b3o17b3o44bo2bo48bo
145bo$586bo22b3o3bo47b2obo3b2o30b3o1381bob2o15bo2bo47bo47b3o40bo104bob
o$585b3o21bo2bo2bo47b3o36b3o1382b3o18bo47bo47bob2o38b3o41b3o$585bob2o
20bo6bobo45b2o37b2o1382b3o18bo44bobo49b3o37b2obo41bo2bo$586b3o20bo126b
3o1348b2o16bobo97b2o38b3o42bo$586b3o21bobo123bo2bo1506b2o42bo$586b2o
119bo22b3o3bo1424bo129bobo$706b3o21bo2bo2bo1311bo97b3o11b3o28bo66b3o$
706bob2o20bo6bobo1307b2o97bo2bo9b2obo27b3o17b3o44bo2bo48bo$707b3o20bo
1316bobo96bo12b3o28bob2o15bo2bo47bo47b3o40bo$707b3o21bobo1412bo3bo9b2o
29b3o18bo47bo47bob2o38b3o$707b2o1437bo44b3o18bo44bobo49b3o37b2obo$
1525b3o619bobo41b2o16bobo97b2o38b3o$1527bo557b3o262b2o$1526bo558bo2bo
176bo$2085bo164b3o11b3o28bo$2085bo164bo2bo9b2obo27b3o17b3o48b3o$2086bo
bo161bo12b3o28bob2o15bo2bo47bo2bo$2250bo3bo9b2o29b3o18bo50bo$2104bo
145bo44b3o18bo50bo$2103b3o40bo104bobo41b2o16bobo48bobo$2103bob2o38b3o
41b3o$2104b3o37b2obo41bo2bo$1807bobo294b2o38b3o42bo164b3o$674bo1132b2o
336b2o42bo164bo2bo$673b3o31bo1100bo381bobo161bo$668bo3b2obo30b3o1381bo
66b3o194bo3bo$667b3o2b3o30b2obo1380b3o17b3o44bo2bo48bo145bo$666b2obo3b
2o30b3o1381bob2o15bo2bo47bo47b3o40bo104bobo$666b3o36b3o1382b3o18bo47bo
47bob2o38b3o41b3o$667b2o37b2o1382b3o18bo44bobo49b3o37b2obo41bo2bo$739b
3o1348b2o16bobo97b2o38b3o42bo$739bo2bo1506b2o42bo$710bo22b3o3bo1424bo
129bobo$709b3o21bo2bo2bo1251bo157b3o11b3o28bo66b3o$709bob2o20bo6bobo
1247b2o157bo2bo9b2obo27b3o17b3o44bo2bo48bo$710b3o20bo1256bobo156bo12b
3o28bob2o15bo2bo47bo47b3o40bo$710b3o21bobo1412bo3bo9b2o29b3o18bo47bo
47bob2o38b3o$710b2o1437bo44b3o18bo44bobo49b3o37b2obo$1576b3o571bobo41b
2o16bobo97b2o38b3o$1578bo509b3o262b2o$1577bo510bo2bo176bo$870bo1217bo
164b3o11b3o28bo$871bo1216bo164bo2bo9b2obo27b3o17b3o48b3o$869b3o1217bob
o161bo12b3o28bob2o15bo2bo47bo2bo$2253bo3bo9b2o29b3o18bo50bo$2107bo145b
o44b3o18bo50bo$2106b3o40bo104bobo41b2o16bobo48bobo$2106bob2o38b3o41b3o
$2107b3o37b2obo41bo2bo$2107b2o38b3o42bo164b3o$2148b2o42bo164bo2bo$
2193bobo161bo$2093bo66b3o194bo3bo$2092b3o17b3o44bo2bo48bo145bo$2092bob
2o15bo2bo47bo47b3o40bo104bobo$2093b3o18bo47bo47bob2o38b3o41b3o$2093b3o
18bo44bobo49b3o37b2obo41bo2bo$2093b2o16bobo97b2o38b3o42bo$2252b2o42bo$
2167bo129bobo$1934bo217b3o11b3o28bo66b3o$1933b2o217bo2bo9b2obo27b3o17b
3o44bo2bo48bo$1933bobo216bo12b3o28bob2o15bo2bo47bo47b3o40bo$2152bo3bo
9b2o29b3o18bo47bo47bob2o38b3o$2152bo44b3o18bo44bobo49b3o37b2obo$1627b
3o523bobo41b2o16bobo97b2o38b3o$1629bo461b3o262b2o$1628bo159bobo300bo2b
o176bo$1788b2o301bo164b3o11b3o28bo$1789bo301bo164bo2bo9b2obo27b3o17b3o
48b3o$2092bobo161bo12b3o28bob2o15bo2bo47bo2bo$1802bo453bo3bo9b2o29b3o
18bo50bo$1801bo308bo145bo44b3o18bo50bo$1801b3o305b3o40bo104bobo41b2o
16bobo48bobo$2109bob2o38b3o41b3o$2110b3o37b2obo41bo2bo$2110b2o38b3o42b
o164b3o$2151b2o42bo164bo2bo$2049bo146bobo161bo$2048bo47bo66b3o194bo3bo
$2048b3o44b3o17b3o44bo2bo48bo145bo$2095bob2o15bo2bo47bo47b3o40bo104bob
o$2096b3o18bo47bo47bob2o38b3o41b3o$2096b3o18bo44bobo49b3o37b2obo41bo2b
o$2096b2o16bobo97b2o38b3o42bo$2255b2o42bo$2170bo129bobo$1877bo277b3o
11b3o28bo66b3o$1876b2o277bo2bo9b2obo27b3o17b3o44bo2bo48bo$1876bobo276b
o12b3o28bob2o15bo2bo47bo47b3o40bo$2155bo3bo9b2o29b3o18bo47bo47bob2o38b
3o$2155bo44b3o18bo44bobo49b3o37b2obo$1678b3o475bobo41b2o16bobo97b2o38b
3o$1680bo413b3o262b2o$1679bo414bo2bo176bo$2094bo164b3o11b3o28bo$2094bo
164bo2bo9b2obo27b3o17b3o48b3o$2095bobo161bo12b3o28bob2o15bo2bo47bo2bo$
2259bo3bo9b2o29b3o18bo50bo$2113bo145bo44b3o18bo50bo$2112b3o40bo104bobo
41b2o16bobo48bobo$2112bob2o38b3o41b3o$2113b3o37b2obo41bo2bo$2113b2o38b
3o42bo164b3o$2154b2o42bo164bo2bo$2199bobo161bo$2099bo66b3o194bo3bo$
2098b3o17b3o44bo2bo48bo145bo$2098bob2o15bo2bo47bo47b3o40bo104bobo$
2099b3o18bo47bo47bob2o38b3o41b3o$2099b3o18bo44bobo49b3o37b2obo41bo2bo$
2099b2o16bobo97b2o38b3o42bo$1769bobo486b2o42bo$1769b2o402bo129bobo$
1770bo49bo337b3o11b3o28bo66b3o$1819b2o337bo2bo9b2obo27b3o17b3o44bo2bo
48bo$1783bo35bobo336bo12b3o28bob2o15bo2bo47bo47b3o40bo$1782bo375bo3bo
9b2o29b3o18bo47bo47bob2o38b3o$1782b3o373bo44b3o18bo44bobo49b3o37b2obo$
1729b3o427bobo41b2o16bobo97b2o38b3o$1731bo365b3o262b2o$1730bo366bo2bo
176bo$2097bo164b3o11b3o28bo$2097bo164bo2bo9b2obo27b3o17b3o48b3o$2098bo
bo161bo12b3o28bob2o15bo2bo47bo2bo$2262bo3bo9b2o29b3o18bo50bo$2116bo
145bo44b3o18bo50bo$2115b3o40bo104bobo41b2o16bobo48bobo$2115bob2o38b3o
41b3o$2116b3o37b2obo41bo2bo$2116b2o38b3o42bo164b3o$2157b2o42bo164bo2bo
$2202bobo161bo$2102bo66b3o194bo3bo$2101b3o17b3o44bo2bo48bo145bo$2101bo
b2o15bo2bo47bo47b3o40bo104bobo$2102b3o18bo47bo47bob2o38b3o41b3o$2102b
3o18bo44bobo49b3o37b2obo41bo2bo$2102b2o16bobo97b2o38b3o42bo$2261b2o42b
o$2176bo129bobo$2161b3o11b3o28bo66b3o$2161bo2bo9b2obo27b3o17b3o44bo2bo
48bo$2161bo12b3o28bob2o15bo2bo47bo47b3o40bo$2161bo3bo9b2o29b3o18bo47bo
47bob2o38b3o$2161bo44b3o18bo44bobo49b3o37b2obo$2162bobo41b2o16bobo97b
2o38b3o$2100b3o262b2o$2100bo2bo176bo$2100bo164b3o11b3o28bo$2100bo164bo
2bo9b2obo27b3o17b3o48b3o$2101bobo161bo12b3o28bob2o15bo2bo47bo2bo$2265b
o3bo9b2o29b3o18bo50bo$2119bo145bo44b3o18bo50bo$2118b3o40bo104bobo41b2o
16bobo48bobo$2118bob2o38b3o41b3o$2119b3o37b2obo41bo2bo$1750bobo366b2o
38b3o42bo164b3o$1750b2o408b2o42bo164bo2bo$1751bo453bobo161bo$2105bo66b
3o194bo3bo$1764bo339b3o17b3o44bo2bo48bo145bo$1763bo340bob2o15bo2bo47bo
47b3o40bo104bobo$1763b3o339b3o18bo47bo47bob2o38b3o41b3o$2105b3o18bo44b
obo49b3o37b2obo41bo2bo$2105b2o16bobo97b2o38b3o42bo$2264b2o42bo$2179bo
129bobo$2164b3o11b3o28bo66b3o$2164bo2bo9b2obo27b3o17b3o44bo2bo48bo$
2164bo12b3o28bob2o15bo2bo47bo47b3o40bo$2164bo3bo9b2o29b3o18bo47bo47bob
2o38b3o$2164bo44b3o18bo44bobo49b3o37b2obo$2165bobo41b2o16bobo97b2o38b
3o$2103b3o262b2o$2103bo2bo176bo$2103bo164b3o11b3o28bo$2103bo164bo2bo9b
2obo27b3o17b3o48b3o$2104bobo161bo12b3o28bob2o15bo2bo47bo2bo$2268bo3bo
9b2o29b3o18bo50bo$2122bo145bo44b3o18bo50bo$2121b3o40bo104bobo41b2o16bo
bo48bobo$2121bob2o38b3o41b3o$2122b3o37b2obo41bo2bo$2122b2o38b3o42bo
164b3o$2163b2o42bo164bo2bo$2208bobo161bo$2108bo66b3o194bo3bo$2107b3o
17b3o44bo2bo48bo145bo$2107bob2o15bo2bo47bo47b3o40bo104bobo$2108b3o18bo
47bo47bob2o38b3o41b3o$2108b3o18bo44bobo49b3o37b2obo41bo2bo$2108b2o16bo
bo97b2o38b3o42bo$2267b2o42bo$2182bo129bobo$2167b3o11b3o28bo66b3o$2167b
o2bo9b2obo27b3o17b3o44bo2bo48bo$2167bo12b3o28bob2o15bo2bo47bo47b3o40bo
$2167bo3bo9b2o29b3o18bo47bo47bob2o38b3o$2167bo44b3o18bo44bobo49b3o37b
2obo$2168bobo41b2o16bobo97b2o38b3o$2106b3o262b2o$1731bobo372bo2bo176bo
$1731b2o373bo164b3o11b3o28bo$1732bo373bo164bo2bo9b2obo27b3o17b3o48b3o$
2107bobo161bo12b3o28bob2o15bo2bo47bo2bo$1745bo525bo3bo9b2o29b3o18bo50b
o$1744bo380bo145bo44b3o18bo50bo$1744b3o377b3o40bo104bobo41b2o16bobo48b
obo$2124bob2o38b3o41b3o$2125b3o37b2obo41bo2bo$2125b2o38b3o42bo164b3o$
2166b2o42bo164bo2bo$1992bo218bobo161bo$1991bo119bo66b3o194bo3bo$1991b
3o116b3o17b3o44bo2bo48bo145bo$2110bob2o15bo2bo47bo47b3o40bo104bobo$
2111b3o18bo47bo47bob2o38b3o41b3o$2111b3o18bo44bobo49b3o37b2obo41bo2bo$
2111b2o16bobo97b2o38b3o42bo$2270b2o42bo$2185bo129bobo$2170b3o11b3o28bo
66b3o$2170bo2bo9b2obo27b3o17b3o44bo2bo48bo$2170bo12b3o28bob2o15bo2bo
47bo47b3o40bo$2170bo3bo9b2o29b3o18bo47bo47bob2o38b3o$2170bo44b3o18bo
44bobo49b3o37b2obo$2171bobo41b2o16bobo97b2o38b3o$2109b3o262b2o$2109bo
2bo176bo$2109bo164b3o11b3o28bo$2109bo164bo2bo9b2obo27b3o17b3o$2110bobo
161bo12b3o28bob2o15bo2bo$2274bo3bo9b2o29b3o18bo$2128bo145bo44b3o18bo$
2127b3o40bo104bobo41b2o16bobo$2127bob2o38b3o41b3o$2128b3o37b2obo41bo2b
o$2128b2o38b3o42bo$2169b2o42bo$2214bobo$2114bo66b3o$2113b3o17b3o44bo2b
o48bo$2113bob2o15bo2bo47bo47b3o$2114b3o18bo47bo47bob2o$2114b3o18bo44bo
bo49b3o$2114b2o16bobo97b2o$1712bobo$1712b2o474bo$1713bo459b3o11b3o28bo
$2173bo2bo9b2obo27b3o17b3o$1726bo446bo12b3o28bob2o15bo2bo$1725bo447bo
3bo9b2o29b3o18bo$1725b3o445bo44b3o18bo$2174bobo41b2o16bobo$2112b3o$
2112bo2bo$2112bo$2112bo$2113bobo2$2131bo$2130b3o40bo$2130bob2o38b3o41b
3o$2131b3o37b2obo41bo2bo$2131b2o38b3o42bo$2172b2o42bo$2217bobo$2117bo
66b3o$2116b3o17b3o44bo2bo48bo$2116bob2o15bo2bo47bo47b3o$2117b3o18bo47b
o47bob2o$2117b3o18bo44bobo49b3o$2117b2o16bobo97b2o2$2191bo$2176b3o11b
3o28bo$2176bo2bo9b2obo27b3o17b3o$2176bo12b3o28bob2o15bo2bo$2176bo3bo9b
2o29b3o18bo$2176bo44b3o18bo$2177bobo41b2o16bobo$2115b3o$2115bo2bo$
2115bo$2115bo$2116bobo2$2134bo$2133b3o40bo$2133bob2o38b3o41b3o$2134b3o
37b2obo41bo2bo$1693bobo438b2o38b3o42bo$1693b2o480b2o42bo$1694bo525bobo
$2120bo66b3o$1707bo411b3o17b3o44bo2bo48bo$1706bo412bob2o15bo2bo47bo47b
3o$1706b3o411b3o18bo47bo47bob2o$2120b3o18bo44bobo49b3o$2120b2o16bobo
97b2o2$2194bo$2179b3o11b3o28bo$2179bo2bo9b2obo27b3o17b3o$2179bo12b3o
28bob2o15bo2bo$2179bo3bo9b2o29b3o18bo$2179bo44b3o18bo$2180bobo41b2o16b
obo$2118b3o$2118bo2bo$2118bo$2118bo$2119bobo2$2137bo$2136b3o40bo$2136b
ob2o38b3o$2137b3o37b2obo$2137b2o38b3o$2178b2o2$2123bo66b3o$2122b3o17b
3o44bo2bo$2122bob2o15bo2bo47bo$2123b3o18bo47bo$2123b3o18bo44bobo$2123b
2o16bobo2$2197bo$2182b3o11b3o$2182bo2bo9b2obo$2182bo12b3o$2182bo3bo9b
2o$2182bo$2183bobo$2121b3o$1674bobo444bo2bo$1674b2o445bo$1675bo445bo$
2122bobo$1688bo$1687bo452bo$1687b3o449b3o40bo$2139bob2o38b3o$2140b3o
37b2obo$2140b2o38b3o$2181b2o$1935bo$1934bo191bo66b3o$1934b3o188b3o17b
3o44bo2bo$2125bob2o15bo2bo47bo$2126b3o18bo47bo$2126b3o18bo44bobo$2126b
2o16bobo2$2200bo$2185b3o11b3o$2185bo2bo9b2obo$2185bo12b3o$2185bo3bo9b
2o$2185bo$2186bobo$2124b3o$2124bo2bo$2124bo$2124bo$2125bobo2$2143bo$
2142b3o40bo$2142bob2o38b3o$2143b3o37b2obo$2143b2o38b3o$2184b2o2$2129bo
66b3o$2128b3o17b3o44bo2bo$2128bob2o15bo2bo47bo$2129b3o18bo47bo$2129b3o
18bo44bobo$2129b2o16bobo$1655bobo$1655b2o546bo$1656bo531b3o11b3o$2188b
o2bo9b2obo$1669bo518bo12b3o$1668bo519bo3bo9b2o$1668b3o517bo$2189bobo$
2127b3o$2127bo2bo$2127bo$2127bo$2128bobo2$2146bo$2145b3o40bo$2145bob2o
38b3o$2146b3o37b2obo$2146b2o38b3o$2187b2o2$2132bo66b3o$2131b3o17b3o44b
o2bo$2131bob2o15bo2bo47bo$2132b3o18bo47bo$1644b3o12b3o470b3o18bo44bobo
$1645bo16bo469b2o16bobo$1645b3o11bo2bo$1660b2o544bo$1660b2o529b3o11b3o
$1659bo2bo528bo2bo9b2obo$1659bo531bo12b3o$1661b2o528bo3bo9b2o$2191bo$
2192bobo$2130b3o$2130bo2bo$2130bo$2130bo$2131bobo2$2149bo$2148b3o$
2148bob2o$2149b3o$2149b2o3$2135bo$2134b3o17b3o$2134bob2o15bo2bo$2135b
3o18bo$2135b3o18bo$2135b2o16bobo!

The spaceship would have to be in the middle of these helices, meaning the 7 lines of x3 NE gliders shown at the top would have to be lengthened to accomodate whatever dimensions end up happening. Because the tracks get perpetually closer to the left helix, the width isn't determined by the spine width but by a combination of the spine width and ship length. It's all just numbers though.

In the event it isn't possible to build up the full ship from just 2 tracks, it is useful to note that the 3-track forerake can fit exactly one rephasing on the left two tracks. (Unfortunately not more, or it could feasibly be possible to bring a very distant track into position). Here's what that looks like if this helps. It's actually quite the remarkable squeeze.

Code: Select all

x = 124, y = 253, rule = B3/S23
99bo$99bobo$99b2o3$112bobo$112b2o$113bo16$121bobo$121b2o$122bo20$80bo$
80bobo$80b2o3$93bobo$93b2o$94bo16$102bobo$102b2o$103bo20$61bo$61bobo$
61b2o3$74bobo$74b2o$75bo16$83bobo$83b2o$84bo20$42bo$42bobo$42b2o3$55bo
bo$55b2o$56bo16$64bobo$64b2o$65bo4$29b3o$29bobo12b3o$29bo2bo12bo$30b3o
12b3o$30b3o$28bo2bo$31bo$28bo2$30bo$29bo$29b2o$36bo$35bobo6b2o$35bobo
6b2o$36bo14bo$50bobo$33bo6b3o6b2obo$31b3o13b2o2bo$35b2o6bo3b5o4bo$36bo
2bo6bo4bo3bobo$36b2o4bo3bob3o4bobo$38bo2bo5b3o2bo3bo$34b2ob2o9bo$35bo
13bo4bo$49bo4bo$53bo10$19bo$19bobo$19b2o$45bobo$45b2o$32bobo11bo$32b2o
$33bo38$o$obo$2o$26bobo$26b2o$13bobo11bo$13b2o$14bo!

Posted: **September 9th, 2016, 2:07 pm**

I wrote: It doesn't look possible to make the 3-glider track with kickbacks only though.

Actually the 3-glider track is constructible with kickbacks. In fact, with some careful threading of the needle, all 5 tracks can be made with 15 pairs of rakes and 3 blinker trails. Is this worth considering or is there a nice way to go from either 2 or 3 tracks up to 5?

Code: Select all

x = 3996, y = 5563, rule = B3/S23
2322b3o7$39bo$39b2o$38bobo8$2591b3o17$90bo2769b3o$90b2o$89bobo25$141bo
$141b2o$140bobo18$2319b3o7$192bo$192b2o$191bobo8$2588b3o17$243bo2613b
3o$243b2o$242bobo25$294bo$294b2o$293bobo18$2316b3o7$345bo$345b2o$344bo
bo8$2585b3o4$16b2o$15bobo$17bo11$396bo2457b3o$396b2o$395bobo12$67b2o$
66bobo$68bo11$447bo$447b2o$446bobo12$118b2o$117bobo$119bo4$2313b3o7$
498bo$498b2o$497bobo8$2582b3o4$169b2o$168bobo$170bo11$549bo2301b3o$
549b2o$548bobo12$220b2o$219bobo$221bo11$600bo$600b2o$599bobo12$271b2o$
270bobo$bo270bo$b2o$obo2$2310b3o7$651bo$651b2o$650bobo8$2579b3o4$322b
2o$321bobo$52bo270bo$52b2o$51bobo9$702bo2145b3o$702b2o$701bobo12$373b
2o$372bobo$103bo270bo$103b2o$102bobo5$3948b2o$3948bobo$3948bo2$753bo$
753b2o$752bobo12$424b2o$423bobo$154bo270bo$154b2o$153bobo2$2307b3o3$
3891b2o$3891bobo$3891bo2$804bo$804b2o$803bobo8$2576b3o4$475b2o$474bobo
$205bo270bo$205b2o$204bobo5$3834b2o$3834bobo$3834bo2$855bo1989b3o$855b
2o$854bobo12$526b2o$525bobo$256bo270bo$256b2o$255bobo5$3777b2o$3777bob
o$3777bo2$906bo$906b2o$905bobo8$3960b2o$3959b2o$3961bo2$577b2o$576bobo
$307bo270bo$307b2o$306bobo2$2304b3o3$3720b2o$3720bobo$3720bo2$957bo$
957b2o$956bobo8$2573b3o1327b2o$3902b2o$3904bo2$628b2o$627bobo$358bo
270bo$358b2o$357bobo5$3663b2o$3663bobo$3663bo2$1008bo1833b3o$1008b2o$
1007bobo8$3846b2o$3845b2o$3847bo2$679b2o$678bobo$409bo270bo$409b2o$
408bobo5$3606b2o$3606bobo$3606bo2$1059bo$1059b2o$1058bobo8$3789b2o$
3788b2o$3790bo2$730b2o$729bobo$460bo270bo$460b2o$459bobo2$2301b3o3$
3549b2o$3549bobo$3549bo2$1110bo$1110b2o$1109bobo8$2570b3o1159b2o$3731b
2o$3733bo220b2o$3954bobo$781b2o3171bo$780bobo$511bo270bo$511b2o$510bob
o5$3492b2o$3492bobo$3492bo2$1161bo1677b3o$1161b2o$1160bobo8$3675b2o$
3674b2o$3676bo220b2o$3897bobo$832b2o3063bo$831bobo$562bo270bo$562b2o$
561bobo5$3435b2o$3435bobo$3435bo2$1212bo$1212b2o$1211bobo8$3618b2o$
3617b2o$3619bo220b2o$3840bobo$883b2o2955bo$882bobo$613bo270bo$613b2o$
612bobo2$2298b3o3$3378b2o$3378bobo$3378bo2$1263bo$1263b2o$1262bobo8$
2567b3o991b2o$3560b2o$3562bo220b2o$3783bobo$934b2o2847bo$933bobo$664bo
270bo$664b2o$663bobo5$3321b2o$3321bobo$3321bo2$1314bo1521b3o$1314b2o$
1313bobo8$3504b2o$3503b2o$3505bo220b2o$3726bobo$985b2o2739bo$984bobo$
715bo270bo$715b2o$714bobo5$3264b2o$3264bobo$3264bo2$1365bo$1365b2o$11b
o1352bobo$11b2o$10bobo6$3447b2o$3446b2o$3448bo220b2o$3669bobo$1036b2o
2631bo$1035bobo$766bo270bo$766b2o$765bobo2$2295b3o3$3207b2o$3207bobo$
3207bo2$1416bo$1416b2o$62bo1352bobo$62b2o$61bobo6$2564b3o823b2o$3389b
2o$3391bo220b2o$3612bobo$1087b2o2523bo$1086bobo$817bo270bo$817b2o$816b
obo5$3150b2o$3150bobo$3150bo2$1467bo1365b3o$1467b2o$113bo1352bobo$113b
2o$112bobo6$3333b2o$3332b2o$3334bo220b2o$3555bobo$1138b2o2415bo$1137bo
bo$868bo270bo$868b2o$867bobo5$3093b2o$3093bobo$3093bo2$1518bo$1518b2o$
164bo1352bobo$164b2o$163bobo6$3276b2o$3275b2o$3277bo220b2o$3498bobo$
1189b2o2307bo$1188bobo$919bo270bo$919b2o$918bobo2$2292b3o3$3036b2o$
3036bobo$3036bo2$1569bo$1569b2o$215bo1352bobo$215b2o$214bobo6$2561b3o
655b2o$3218b2o$3220bo220b2o$3441bobo$1240b2o2199bo$1239bobo$970bo270bo
$970b2o$969bobo5$2979b2o$2979bobo$2979bo987b2o$3967bobo$1620bo1209b3o
1134bo$1620b2o$266bo1352bobo$266b2o$265bobo6$3162b2o$3161b2o$3163bo
220b2o$3384bobo$1291b2o2091bo$1290bobo$1021bo270bo$1021b2o$1020bobo5$
2922b2o$2922bobo$2922bo987b2o$3910bobo$1671bo2238bo$1671b2o$317bo1352b
obo$317b2o$316bobo6$3105b2o$3104b2o$3106bo220b2o$3327bobo$1342b2o1983b
o$1341bobo$1072bo270bo$1072b2o$1071bobo2$2289b3o3$2865b2o$2865bobo$
2865bo987b2o$3853bobo$1722bo2130bo$1722b2o$368bo1352bobo$368b2o$367bob
o6$2558b3o487b2o$3047b2o$3049bo220b2o$3270bobo$1393b2o1875bo$1392bobo$
39b2o1082bo270bo$38bobo1082b2o$40bo1081bobo5$2808b2o$2808bobo$2808bo
987b2o$3796bobo$1773bo1053b3o966bo$1773b2o$419bo1352bobo$419b2o$418bob
o6$2991b2o$2990b2o$2992bo220b2o764b2o$3213bobo762b2o$1444b2o1767bo766b
o$1443bobo$90b2o1082bo270bo$89bobo1082b2o$91bo1081bobo5$2751b2o$2751bo
bo$2751bo987b2o$3739bobo$1824bo1914bo$1824b2o$470bo1352bobo$470b2o$
469bobo6$2934b2o$2933b2o$2935bo220b2o764b2o$3156bobo762b2o$1495b2o
1659bo766bo$1494bobo$141b2o1082bo270bo$140bobo1082b2o$142bo1081bobo2$
2286b3o3$2694b2o$2694bobo$2694bo987b2o$3682bobo$1875bo1806bo$1875b2o$
521bo1352bobo$521b2o$520bobo6$2555b3o319b2o$2876b2o$2878bo220b2o764b2o
$3099bobo762b2o$1546b2o1551bo766bo$1545bobo$192b2o1082bo270bo$191bobo
1082b2o$193bo1081bobo5$2637b2o$2637bobo$2637bo987b2o$3625bobo$1926bo
897b3o798bo$1926b2o$572bo1352bobo$572b2o$571bobo6$2820b2o$2819b2o$
2821bo220b2o764b2o$3042bobo762b2o$1597b2o1443bo766bo$1596bobo$243b2o
1082bo270bo$242bobo1082b2o$244bo1081bobo5$2580b2o$2580bobo$2580bo987b
2o$3568bobo$1977bo1590bo$1977b2o$623bo1352bobo$623b2o$622bobo6$2763b2o
$2762b2o$2764bo220b2o764b2o$2985bobo762b2o$1648b2o1335bo766bo220b2o$
1647bobo2323bobo$294b2o1082bo270bo2323bo$293bobo1082b2o$24bo270bo1081b
obo$24b2o$23bobo2257b3o3$2523b2o$2523bobo$2523bo987b2o$3511bobo$2028bo
1482bo$2028b2o$674bo1352bobo$674b2o$673bobo6$2552b3o151b2o$2705b2o$
2707bo220b2o764b2o$2928bobo762b2o$1699b2o1227bo766bo220b2o$1698bobo
2215bobo$345b2o1082bo270bo2215bo$344bobo1082b2o$75bo270bo1081bobo$75b
2o$74bobo3$2466b2o$2466bobo$2466bo987b2o$3454bobo$2079bo741b3o630bo$
2079b2o$725bo1352bobo$725b2o$724bobo6$2649b2o$2648b2o$2650bo220b2o764b
2o$2871bobo762b2o$1750b2o1119bo766bo220b2o$1749bobo2107bobo$396b2o
1082bo270bo2107bo$395bobo1082b2o$126bo270bo1081bobo$126b2o$125bobo3$
2409b2o$2409bobo$2409bo987b2o$3397bobo$2130bo1266bo$2130b2o$776bo1352b
obo$776b2o$775bobo6$2592b2o$2591b2o$2593bo220b2o764b2o$2814bobo762b2o$
1801b2o1011bo766bo220b2o$1800bobo1999bobo$447b2o1082bo270bo1999bo$446b
obo1082b2o$177bo270bo1081bobo$177b2o$176bobo2101b3o3$2352b2o$2352bobo$
2352bo987b2o$3340bobo$2181bo1158bo$2181b2o$827bo1352bobo$827b2o$826bob
o6$2535b2o12b3o$2534b2o$2536bo220b2o764b2o$2757bobo762b2o$1852b2o903bo
766bo220b2o$1851bobo1891bobo$498b2o1082bo270bo1891bo$497bobo1082b2o$
228bo270bo1081bobo$228b2o$227bobo3$2295b2o$2295bobo$2295bo987b2o$3283b
obo$2232bo585b3o462bo$2232b2o$878bo1352bobo$878b2o$877bobo6$2478b2o$
2477b2o$2479bo220b2o764b2o$2700bobo762b2o$1903b2o795bo766bo220b2o$
1902bobo1783bobo$549b2o1082bo270bo1783bo$548bobo1082b2o$279bo270bo
1081bobo$279b2o$278bobo5$3226b2o$3226bobo$3226bo2$929bo$929b2o$928bobo
6$2421b2o$2420b2o$2422bo220b2o764b2o$2643bobo762b2o$1954b2o687bo766bo
220b2o$1953bobo1675bobo$600b2o1082bo270bo1675bo$599bobo1082b2o$330bo
270bo1081bobo$330b2o$329bobo1945b3o5$3169b2o$3169bobo$3169bo2$980bo$
980b2o$979bobo6$2364b2o180b3o$2363b2o$2365bo220b2o764b2o$2586bobo762b
2o$2005b2o579bo766bo220b2o$2004bobo1567bobo$651b2o1082bo270bo232bobo
1332bo$650bobo1082b2o502b2o$381bo270bo1081bobo503bo$381b2o$380bobo5$
3112b2o$3112bobo$2815b3o294bo2$1031bo$1031b2o$1030bobo6$2307b2o$2306b
2o$2308bo220b2o764b2o$2529bobo762b2o$2056b2o471bo766bo220b2o$2055bobo
1459bobo$702b2o1082bo270bo1459bo$701bobo1082b2o$432bo270bo1081bobo$
432b2o$431bobo5$3055b2o$3055bobo$3055bo2$1082bo$1082b2o$1081bobo6$
2250b2o$2249b2o$2251bo220b2o764b2o$2472bobo762b2o$2107b2o363bo766bo
220b2o$2106bobo1351bobo$753b2o1082bo270bo1351bo$752bobo1082b2o$483bo
270bo1081bobo$483b2o$482bobo1789b3o5$2998b2o$2998bobo$2998bo987b2o$
3986bobo$1133bo2852bo$1133b2o$1132bobo6$2193b2o348b3o$2192b2o$2194bo
220b2o764b2o$2415bobo762b2o$2158b2o255bo766bo220b2o$2157bobo1243bobo$
804b2o1082bo270bo1243bo$803bobo1082b2o$534bo270bo1081bobo$534b2o$533bo
bo5$2941b2o$2941bobo$2812b3o126bo987b2o$3929bobo$1184bo2744bo$1184b2o$
1183bobo8$2358b2o764b2o$2358bobo762b2o$2358bo766bo220b2o$3346bobo$855b
2o1082bo1406bo$854bobo1082b2o$585bo270bo1081bobo$585b2o$584bobo5$2884b
2o$2884bobo$2884bo987b2o$3872bobo$1235bo2636bo$1235b2o$1234bobo8$2301b
2o764b2o$2301bobo762b2o$2301bo766bo220b2o$3289bobo$906b2o1082bo191bobo
1104bo$905bobo1082b2o190b2o$636bo270bo1081bobo191bo$636b2o$635bobo
1633b3o5$2827b2o$2827bobo$2827bo987b2o$3815bobo$1286bo2528bo$1286b2o$
1285bobo6$2540b3o2$2244b2o764b2o$2244bobo762b2o$2244bo766bo220b2o$
3232bobo$957b2o1082bo1190bo$956bobo1082b2o$687bo270bo1081bobo$687b2o$
686bobo5$2770b2o$2770bobo$2770bo38b3o946b2o$3758bobo$1337bo2420bo$
1337b2o$1336bobo798bo$2137bobo$2137b2o6$2187b2o764b2o$2187bobo762b2o$
2187bo766bo220b2o764b2o$3175bobo762b2o$1008b2o1082bo1082bo766bo$1007bo
bo1082b2o$738bo270bo1081bobo$738b2o$737bobo5$2713b2o$2713bobo$2713bo
987b2o$3701bobo$1388bo2312bo$1388b2o$34bo1352bobo$34b2o$33bobo6$2896b
2o$2895b2o$2897bo220b2o764b2o$3118bobo762b2o$1059b2o2057bo766bo$1058bo
bo$789bo270bo$789b2o$788bobo1477b3o5$2656b2o$2656bobo$2131bobo522bo
987b2o$2131b2o1511bobo$1439bo692bo1511bo$1439b2o$85bo1352bobo$85b2o$
84bobo4$2537b3o2$2839b2o$2838b2o$2840bo220b2o764b2o$3061bobo762b2o$
1110b2o1949bo766bo$1109bobo$840bo270bo$840b2o$839bobo5$2599b2o$2599bob
o$2599bo206b3o778b2o$3587bobo$1490bo2096bo$1490b2o$136bo1352bobo$136b
2o$135bobo6$2782b2o$2781b2o$2783bo220b2o764b2o$3004bobo762b2o$1161b2o
962bobo876bo766bo220b2o$1160bobo962b2o1865bobo$891bo270bo963bo1865bo$
891b2o$890bobo5$2542b2o$2542bobo$2542bo987b2o$3530bobo$1541bo1988bo$
1541b2o$187bo1352bobo$187b2o$186bobo6$2725b2o$2724b2o$2726bo220b2o764b
2o$2947bobo762b2o$1212b2o1733bo766bo220b2o$1211bobo2721bobo$942bo270bo
2721bo$942b2o$941bobo1321b3o5$2485b2o$2485bobo$2485bo987b2o$3473bobo$
1592bo1880bo$1592b2o$238bo1352bobo486bo$238b2o1840bobo$237bobo1840b2o
4$2534b3o2$2668b2o$2667b2o$2669bo220b2o764b2o$2890bobo762b2o$1263b2o
1625bo766bo220b2o$1262bobo2613bobo$993bo270bo2613bo$993b2o$992bobo5$
2428b2o$2428bobo$2428bo374b3o610b2o$3416bobo$1643bo1772bo$1643b2o$289b
o1352bobo$289b2o$288bobo6$2611b2o$2610b2o$2612bo220b2o764b2o$2833bobo
762b2o$1314b2o1517bo766bo220b2o$1313bobo2505bobo$1044bo270bo2505bo$
1044b2o$1043bobo5$2371b2o$2371bobo$2074bobo294bo987b2o$2074b2o1283bobo
$1694bo380bo1283bo$1694b2o$340bo1352bobo$340b2o$339bobo6$2554b2o$2553b
2o$2555bo220b2o764b2o$2776bobo762b2o$1365b2o1409bo766bo220b2o$1364bobo
2397bobo$11b2o1082bo270bo2397bo$10bobo1082b2o$12bo1081bobo1165b3o5$
2314b2o$2314bobo$2314bo987b2o$3302bobo$1745bo1556bo$1745b2o$391bo1352b
obo$391b2o$390bobo4$2531b3o2$2497b2o$2496b2o$2498bo220b2o764b2o$2719bo
bo762b2o$1416b2o650bobo648bo766bo220b2o$1415bobo650b2o1637bobo$62b2o
1082bo270bo651bo1637bo$61bobo1082b2o$63bo1081bobo5$2257b2o$2257bobo$
2257bo542b3o442b2o$3245bobo$1796bo1448bo$1796b2o$442bo1352bobo$442b2o$
441bobo6$2440b2o$2439b2o$2441bo220b2o764b2o$2662bobo762b2o$1467b2o
1193bo766bo220b2o$1466bobo2181bobo$113b2o1082bo270bo2181bo$112bobo
1082b2o$114bo1081bobo5$2200b2o$2200bobo$2200bo987b2o$3188bobo$1847bo
1340bo$1847b2o$493bo1352bobo174bo$493b2o1528bobo$492bobo1528b2o6$2383b
2o$2382b2o$2384bo220b2o764b2o$2605bobo762b2o$1518b2o1085bo766bo220b2o$
1517bobo2073bobo$164b2o1082bo270bo2073bo$163bobo1082b2o$165bo1081bobo
1009b3o5$2143b2o$2143bobo$2143bo987b2o$3131bobo$1898bo1232bo$1898b2o$
544bo1352bobo$544b2o$543bobo4$2528b3o2$2326b2o$2325b2o$2327bo220b2o
764b2o$2548bobo762b2o$1569b2o977bo766bo220b2o$1568bobo1965bobo$215b2o
1082bo270bo1965bo$214bobo1082b2o$216bo1081bobo5$2086b2o$2086bobo$2017b
obo66bo710b3o274b2o$2017b2o1055bobo$1949bo68bo1055bo$1949b2o$595bo
1352bobo$595b2o$594bobo6$2269b2o$2268b2o$2270bo220b2o764b2o$2491bobo
762b2o$1620b2o869bo766bo220b2o$1619bobo1857bobo$266b2o1082bo270bo1857b
o$265bobo1082b2o$267bo1081bobo5$2029b2o$2029bobo$2029bo987b2o$3017bobo
$2000bo1016bo$2000b2o$646bo1352bobo$646b2o$645bobo6$2212b2o$2211b2o$
2213bo220b2o764b2o$2434bobo762b2o$1671b2o338bobo420bo766bo220b2o$1670b
obo338b2o1409bobo$317b2o1082bo270bo339bo1409bo$316bobo1082b2o$47bo270b
o1081bobo853b3o$47b2o$46bobo5$2960b2o$2960bobo$2960bo2$697bo$697b2o$
696bobo4$2525b3o2$2155b2o$2154b2o$2156bo220b2o764b2o$2377bobo762b2o$
1722b2o653bo766bo220b2o$1721bobo1641bobo$368b2o1082bo270bo1641bo$367bo
bo1082b2o$98bo270bo1081bobo$98b2o$97bobo5$2794b3o106b2o$2903bobo$2903b
o2$748bo1217bo$748b2o1216bobo$747bobo1216b2o6$2098b2o$2097b2o$2099bo
220b2o764b2o$2320bobo762b2o$1773b2o545bo766bo220b2o$1772bobo1533bobo$
419b2o1082bo270bo1533bo$418bobo1082b2o$149bo270bo1081bobo$149b2o$148bo
bo5$2846b2o$2846bobo$2846bo2$799bo$799b2o$798bobo6$2041b2o$2040b2o$
2042bo220b2o764b2o$2263bobo762b2o$1824b2o437bo766bo220b2o$1823bobo
1425bobo$470b2o1082bo270bo1425bo$469bobo1082b2o$200bo270bo1081bobo697b
3o$200b2o$199bobo3$1973bobo$1973b2o$1960bobo11bo814b2o$1960b2o827bobo$
1961bo827bo2$850bo$850b2o$849bobo4$2522b3o2$1984b2o$1983b2o$1985bo220b
2o764b2o$2206bobo762b2o$1875b2o329bo766bo220b2o$1874bobo1317bobo$521b
2o1082bo270bo1317bo$520bobo1082b2o$251bo270bo1081bobo$251b2o$250bobo5$
2732b2o57b3o$2732bobo$2732bo2$901bo$901b2o$900bobo6$1927b2o$1926b2o$
1928bo220b2o764b2o$2149bobo762b2o$1926b2o26bobo192bo766bo220b2o$1925bo
bo26b2o1181bobo$572b2o1082bo270bo27bo1181bo$571bobo1082b2o$302bo270bo
1081bobo$302b2o$301bobo5$2675b2o$2675bobo$2675bo2$952bo$952b2o$951bobo
8$2092b2o764b2o$2092bobo762b2o$2092bo766bo220b2o$3080bobo$623b2o1082bo
1372bo$622bobo1082b2o$353bo270bo1081bobo541b3o$353b2o$352bobo5$2618b2o
$2618bobo$2618bo2$1003bo905bo$1003b2o904bobo$1002bobo904b2o4$2519b3o4$
2035b2o764b2o$2035bobo762b2o$2035bo766bo220b2o$3023bobo$674b2o1082bo
1264bo$673bobo1082b2o$404bo270bo1081bobo$404b2o$403bobo5$2561b2o225b3o
$2561bobo$2561bo2$1054bo$1054b2o$1053bobo8$1978b2o764b2o$1978bobo762b
2o$1978bo766bo220b2o$2966bobo$725b2o1082bo1156bo$724bobo1082b2o$455bo
270bo1081bobo$455b2o$454bobo3$1916bobo$1916b2o$1903bobo11bo586b2o$
1903b2o599bobo$1904bo599bo2$1105bo$1105b2o$1104bobo8$1921b2o764b2o$
1921bobo762b2o$1921bo766bo220b2o$2909bobo$776b2o1082bo1048bo$775bobo
1082b2o$506bo270bo1081bobo385b3o$506b2o$505bobo5$2447b2o$2447bobo$
2447bo2$1156bo$1156b2o$1155bobo4$2516b3o3$1871bo$1871bobo756b2o$1871b
2o756b2o$1897bobo731bo220b2o$1897b2o953bobo$827b2o1069bo953bo$826bobo$
557bo270bo$557b2o$556bobo5$2390b2o393b3o$2390bobo$2390bo2$1207bo$1207b
2o$1206bobo8$2573b2o$2572b2o$2574bo220b2o$2795bobo$878b2o1915bo$877bob
o$608bo270bo$608b2o$607bobo5$2333b2o$2333bobo$2333bo2$1258bo593bo$
1258b2o592bobo$1257bobo592b2o3$1865bobo$1865b2o$1866bo3$2516b2o$2515b
2o$2517bo220b2o$2738bobo$929b2o1807bo$928bobo$659bo270bo1313b3o$659b2o
$658bobo5$2276b2o$2276bobo$2276bo2$1309bo$1309b2o$1308bobo4$2513b3o4$
2459b2o$2458b2o$2460bo220b2o$2681bobo$980b2o1699bo$979bobo$710bo270bo$
710b2o$709bobo3$1859bobo$1859b2o$1846bobo11bo358b2o561b3o$1846b2o371bo
bo$1847bo371bo2$1360bo$1360b2o$1359bobo8$2402b2o$2401b2o$2403bo220b2o$
2624bobo$1031b2o1591bo$1030bobo$761bo270bo$761b2o$760bobo5$2162b2o$
2162bobo$2162bo2$1411bo$1411b2o$1410bobo7$1814bo$1814bobo528b2o$1814b
2o528b2o$1840bobo503bo220b2o$1840b2o725bobo$1082b2o757bo725bo$1081bobo
$812bo270bo1157b3o$812b2o$811bobo5$2105b2o$2105bobo$2105bo2$1462bo$
1462b2o$1461bobo4$2510b3o4$2288b2o$2287b2o$2289bo220b2o$2510bobo$1133b
2o1375bo$1132bobo$863bo270bo$863b2o$862bobo5$2048b2o729b3o$2048bobo$
2048bo2$1513bo281bo$1513b2o280bobo$1512bobo280b2o3$1808bobo$1808b2o$
1809bo3$2231b2o$2230b2o$2232bo220b2o$2453bobo$1184b2o1267bo$1183bobo$
914bo270bo$914b2o$913bobo2$18bo$18b2o$17bobo$1991b2o$1991bobo$1991bo2$
1564bo$1564b2o$1563bobo8$2174b2o$2173b2o$2175bo220b2o$2396bobo$1235b2o
1159bo$1234bobo$965bo270bo1001b3o$965b2o$964bobo2$69bo$69b2o1731bobo$
68bobo1731b2o$1789bobo11bo130b2o$1789b2o143bobo$1790bo143bo2$1615bo$
1615b2o$1614bobo4$2507b3o4$2117b2o$2116b2o$2118bo220b2o$2339bobo$1286b
2o1051bo$1285bobo$1016bo270bo$1016b2o$1015bobo2$120bo$120b2o$119bobo$
1877b2o897b3o$1877bobo$1877bo2$1666bo$1666b2o$1665bobo7$1757bo$1757bob
o300b2o$1757b2o300b2o$1783bobo275bo220b2o$1783b2o497bobo$1337b2o445bo
497bo$1336bobo$1067bo270bo$1067b2o$1066bobo2$171bo$171b2o$170bobo$
1820b2o$1820bobo$1820bo2$1717bo$1717b2o$1716bobo8$2003b2o$2002b2o$
2004bo220b2o$2225bobo$1388b2o835bo$1387bobo$1118bo270bo845b3o$1118b2o$
1117bobo2$222bo$222b2o$221bobo5$1738bo$1738bobo$1738b2o$1764bobo$1764b
2o$1751bobo11bo$1751b2o751b3o$1752bo3$1946b2o$1945b2o$1947bo220b2o$
2168bobo$1439b2o727bo$1438bobo$1169bo270bo$1169b2o$1168bobo2$273bo$
273b2o$272bobo$2773b3o14$1889b2o$1888b2o$1890bo220b2o$2111bobo$1490b2o
619bo$1489bobo$1220bo270bo$1220b2o$1219bobo$13bo$13b2o309bo$12bobo309b
2o1419bobo$323bobo1419b2o$1732bobo11bo$1732b2o$1733bo12$1832b2o$1831b
2o$1833bo220b2o$2054bobo$1541b2o511bo$1540bobo$1271bo270bo689b3o$1271b
2o$1270bobo$64bo$64b2o309bo$63bobo309b2o$374bobo11$2501b3o3$1700bo$
1700bobo72b2o$1700b2o72b2o$1726bobo47bo220b2o$1726b2o269bobo$1592b2o
133bo269bo$1591bobo$1322bo270bo$1322b2o$1321bobo$115bo$115b2o309bo$
114bobo309b2o$425bobo$2770b3o14$1718b2o$1717b2o$1719bo220b2o$1940bobo$
1643b2o295bo$1642bobo$1373bo270bo$1373b2o$1372bobo$166bo$166b2o309bo$
165bobo309b2o$476bobo5$1681bo$1681bobo$1681b2o$1707bobo$1707b2o$1694bo
bo11bo$1694b2o$1695bo5$1883b2o$1883bobo$1883bo2$1424bo804b3o$1424b2o$
1423bobo$217bo$217b2o309bo$216bobo309b2o$527bobo11$2498b3o6$1826b2o$
1826bobo$1826bo2$1475bo$1475b2o$1474bobo185bo$268bo1393bobo$268b2o309b
o1082b2o$267bobo309b2o1107bobo$578bobo1107b2o$1675bobo11bo1077b3o$
1675b2o$1676bo14$1769b2o$1769bobo$1769bo2$1526bo$1526b2o$1525bobo$319b
o$319b2o309bo$318bobo309b2o$629bobo14$1643bo$1643bobo$1643b2o$1669bobo
40b2o$1669b2o41bobo$1670bo41bo2$1577bo648b3o$1577b2o$1576bobo$370bo$
370b2o309bo$369bobo309b2o$680bobo11$2495b3o6$1655b2o$1655bobo$1655bo2$
1628bo$1628b2o$1627bobo$421bo$421b2o309bo$420bobo309b2o$731bobo$2764b
3o4$1624bo$1624bobo$1624b2o$1650bobo$1650b2o$1637bobo11bo$1637b2o$
1638bo12$472bo$472b2o309bo$471bobo309b2o$782bobo21$2223b3o2$1605bo$
523bo1081bobo$523b2o309bo770b2o$522bobo309b2o795bobo$833bobo795b2o$
1618bobo11bo$1618b2o$1619bo8$2492b3o13$574bo$574b2o309bo$573bobo309b2o
$884bobo$2761b3o13$1586bo$1586bobo$1586b2o$1612bobo$1612b2o$1599bobo
11bo$1599b2o$1600bo3$625bo$625b2o309bo$624bobo309b2o$935bobo21$2220b3o
3$676bo$676b2o309bo$675bobo309b2o$986bobo5$1567bo$1567bobo$1567b2o$
1593bobo$1593b2o$1580bobo11bo$1580b2o907b3o$1581bo12$727bo$727b2o309bo
$726bobo309b2o$1037bobo$2758b3o22$1548bo$778bo769bobo$778b2o309bo458b
2o$777bobo309b2o483bobo$1088bobo483b2o$1561bobo11bo$1561b2o$1562bo18$
2217b3o3$829bo$829b2o309bo$828bobo309b2o$1139bobo11$2486b3o3$1529bo$
1529bobo$1529b2o$1555bobo$1555b2o$1542bobo11bo$1542b2o$1543bo3$880bo$
880b2o309bo$879bobo309b2o$1190bobo$2755b3o23$931bo$931b2o309bo$930bobo
309b2o$1241bobo5$1510bo$1510bobo$1510b2o$1536bobo$1536b2o$1523bobo11bo
$1523b2o$1524bo9$2214b3o3$982bo$982b2o309bo$981bobo309b2o$1292bobo11$
2483b3o12$1491bo$1033bo457bobo$1033b2o309bo146b2o$1032bobo309b2o171bob
o$1343bobo171b2o$1504bobo11bo1233b3o$1504b2o$1505bo21$1084bo$1084b2o
309bo$1083bobo309b2o$1394bobo14$1472bo$1472bobo$1472b2o$1498bobo$1498b
2o$1485bobo11bo$1485b2o$1486bo724b3o3$1135bo$1135b2o309bo$1134bobo309b
2o$1445bobo11$2480b3o13$1186bo$1186b2o309bo$1185bobo309b2o$1496bobo$
2749b3o4$1453bo$1453bobo$1453b2o$1479bobo$1479b2o$1466bobo11bo$1466b2o
$1467bo12$1237bo$1237b2o309bo$1236bobo309b2o$1547bobo21$2208b3o2$1434b
o$1288bo145bobo$1288b2o144b2o163bo$1287bobo170bobo136b2o$1460b2o136bob
o$1447bobo11bo$1447b2o$1448bo8$2477b3o13$1339bo$1339b2o309bo$1338bobo
309b2o$36bo1612bobo$36b2o2708b3o$35bobo12$1415bo$1415bobo$1415b2o$
1441bobo$1441b2o$1428bobo11bo$1428b2o$1429bo3$1390bo$1390b2o309bo$
1389bobo309b2o$87bo1612bobo$87b2o$86bobo19$2205b3o1747b2o$3955bobo$
3955bo$1441bo$1441b2o309bo$1440bobo309b2o$138bo1612bobo$138b2o$137bobo
3$1396bo$1396bobo$1396b2o$1422bobo$1422b2o$1409bobo11bo$1409b2o1063b3o
$1410bo9$3898b2o$3898bobo$3898bo$1492bo$1492b2o309bo$1491bobo309b2o$
189bo1612bobo$189b2o2552b3o$188bobo19$3841b2o$3841bobo$1377bo2463bo$
1377bobo163bo$1377b2o164b2o309bo$1403bobo136bobo309b2o$240bo1162b2o
448bobo$240b2o1148bobo11bo$239bobo1148b2o$1391bo18$2202b3o1579b2o$
3784bobo$3784bo$1594bo$1594b2o309bo$1593bobo309b2o$291bo1612bobo$291b
2o3677bo$290bobo3676b2o$3969bobo8$2471b3o3$1358bo$1358bobo$1358b2o$
1384bobo$1384b2o$1371bobo11bo$1371b2o$1372bo2354b2o$3727bobo$3727bo$
1645bo$1645b2o309bo$31bo1612bobo309b2o$31b2o309bo1612bobo$30bobo309b2o
2396b3o1170bo$341bobo3568b2o$3912bobo18$3670b2o$3670bobo$3670bo$1696bo
$1696b2o309bo$82bo1612bobo309b2o$82b2o309bo1612bobo$81bobo309b2o3461bo
$392bobo3460b2o$3855bobo2$1339bo$1339bobo$1339b2o$1365bobo$1365b2o$
1352bobo11bo$1352b2o$1353bo9$2199b3o1411b2o$3613bobo$3613bo$1747bo$
1747b2o309bo$133bo1612bobo309b2o$133b2o309bo1612bobo$132bobo309b2o
3353bo$443bobo3352b2o$3798bobo8$2468b3o10$3556b2o$3556bobo$1320bo2235b
o$1320bobo475bo$1320b2o476b2o309bo$184bo1161bobo448bobo309b2o$184b2o
309bo850b2o760bobo$183bobo309b2o836bobo11bo1389b3o1002bo$494bobo836b2o
2406b2o$1334bo2406bobo18$3499b2o$3499bobo$3499bo$1849bo$1849b2o309bo$
235bo1612bobo309b2o$235b2o309bo1612bobo$234bobo309b2o3137bo$545bobo
3136b2o$3684bobo11$1301bo$1301bobo$1301b2o$1327bobo$1327b2o$1314bobo
11bo$1314b2o$1315bo880b3o1243b2o$3442bobo$3442bo$1900bo$1900b2o309bo$
286bo1612bobo309b2o$286b2o309bo1612bobo$285bobo309b2o3029bo$596bobo
3028b2o$3627bobo8$2465b3o10$3385b2o$3385bobo$3385bo$1951bo$1951b2o309b
o$337bo1612bobo309b2o$337b2o309bo1612bobo$336bobo309b2o2084b3o834bo$
647bobo2920b2o$3570bobo2$1282bo$1282bobo$1282b2o$1308bobo$1308b2o$
1295bobo11bo$1295b2o$1296bo9$3328b2o$3328bobo$3328bo$2002bo$2002b2o
309bo$388bo1612bobo309b2o$388b2o309bo1612bobo$387bobo309b2o2813bo$698b
obo2812b2o$3513bobo18$2193b3o1075b2o$3271bobo$1263bo2007bo$1263bobo
787bo$1263b2o788b2o309bo$439bo849bobo760bobo309b2o$439b2o309bo538b2o
1072bobo$438bobo309b2o524bobo11bo2166bo$749bobo524b2o2178b2o$1277bo
2178bobo8$2462b3o10$3214b2o$3214bobo$3214bo$2104bo$2104b2o309bo$490bo
1612bobo309b2o$490b2o309bo1612bobo$489bobo309b2o1928b3o666bo$800bobo
2596b2o$3399bobo11$1244bo$1244bobo$1244b2o$1270bobo$1270b2o$1257bobo
11bo$1257b2o$1258bo1898b2o$3157bobo$3157bo$2155bo$2155b2o309bo$541bo
1612bobo309b2o$541b2o309bo1612bobo$540bobo309b2o2489bo$851bobo2488b2o$
3342bobo18$2190b3o907b2o$3100bobo$3100bo$2206bo$2206b2o309bo$592bo
1612bobo309b2o$592b2o309bo1612bobo$591bobo309b2o2381bo$902bobo2380b2o$
3285bobo2$1225bo$1225bobo$1225b2o$1251bobo$1251b2o$1238bobo11bo$1238b
2o1219b3o$1239bo9$3043b2o$3043bobo$3043bo$2257bo$2257b2o309bo$643bo
1612bobo309b2o$643b2o309bo1612bobo$642bobo309b2o1772b3o498bo$953bobo
2272b2o$3228bobo18$2986b2o$2986bobo$1206bo1779bo$1206bobo1099bo$1206b
2o1100b2o309bo$694bo537bobo1072bobo309b2o$694b2o309bo226b2o1384bobo$
693bobo309b2o212bobo11bo1938bo$1004bobo212b2o1950b2o$1220bo1950bobo18$
2187b3o739b2o$2929bobo$2929bo$2359bo$2359b2o309bo$745bo1612bobo309b2o$
745b2o309bo1612bobo$744bobo309b2o2057bo$1055bobo2056b2o$3114bobo8$
2456b3o3$1187bo$1187bobo$1187b2o$1213bobo$1213b2o$1200bobo11bo$1200b2o
$1201bo1670b2o$2872bobo$2872bo$2410bo$2410b2o309bo$796bo1612bobo309b2o
$796b2o309bo1612bobo$795bobo309b2o1616b3o330bo$1106bobo1948b2o$3057bob
o18$2815b2o$2815bobo$2815bo1177b2o$2461bo1531bobo$2461b2o309bo1220bo$
847bo1612bobo309b2o$847b2o309bo1612bobo$846bobo309b2o1841bo$1157bobo
1840b2o$3000bobo2$1168bo$1168bobo$1168b2o$1194bobo$1194b2o$1181bobo11b
o$1181b2o$1182bo9$2184b3o2$3936b2o$2512bo1423bobo$2512b2o1422bo$898bo
1612bobo$898b2o309bo$897bobo309b2o1733bo$1208bobo1732b2o$2943bobo8$
2453b3o12$1149bo2729b2o$1149bobo1411bo1315bobo$1149b2o1412b2o1314bo$
949bo225bobo1384bobo$949b2o224b2o83bo$948bobo211bobo11bo83b2o1460b3o
162bo$1162b2o95bobo1624b2o$1163bo1722bobo20$3822b2o$2614bo1207bobo$
2614b2o1206bo$1000bo1612bobo$1000b2o309bo$999bobo309b2o1517bo$1310bobo
1516b2o$2829bobo4$2759bobo$2759b2o$2760bo5$1130bo$1130bobo$1130b2o$
1156bobo$1156b2o$1143bobo11bo$1143b2o$1144bo1036b3o2$3765b2o$2665bo
1099bobo$2665b2o1098bo$1051bo1612bobo$1051b2o309bo$1050bobo309b2o1409b
o$1361bobo1408b2o$2772bobo1176bo$3950b2o$3950bobo6$2450b3o12$3708b2o$
2716bo991bobo$2716b2o990bo$1102bo1612bobo$1102b2o309bo$1101bobo309b2o
1304bo$1412bobo1303b3o$2717b2ob2o1172bo$2718b3o1172b2o$1111bo1607bo
1173bobo$1111bobo$1111b2o$1137bobo$1137b2o$1124bobo11bo$1124b2o$1125bo
11$3651b2o$3651bobo$3651bo$1153bo$1153b2o309bo$1152bobo309b2o$1463bobo
$3837bo$3836b2o$3836bobo16$2178b3o2$1092bo2501b2o$1092bobo2499bobo$
1092b2o2500bo$1118bobo83bo$1118b2o84b2o309bo$1105bobo11bo83bobo309b2o$
1105b2o407bobo$1106bo2673bo$3779b2o$3779bobo6$2447b3o12$3537b2o$3537bo
bo$3537bo$1255bo$1255b2o309bo$1254bobo309b2o$1565bobo$3723bo$3722b2o$
3722bobo2$2702bobo$2702b2o$2703bo5$1073bo$1073bobo$1073b2o$1099bobo$
1099b2o$1086bobo11bo$1086b2o$1087bo2$3480b2o$3480bobo$3480bo$1306bo$
1306b2o309bo$1305bobo309b2o$3bo1612bobo$3b2o3661bo$2bobo3660b2o$3665bo
bo15$2670bo$2175b3o492bobo$2670b2o$3423b2o$3423bobo$3423bo$1357bo$
1357b2o309bo$1356bobo309b2o$54bo1612bobo$54b2o3553bo$53bobo3552b2o$
1054bo2553bobo$1054bobo$1054b2o$1080bobo$1080b2o$1067bobo11bo$1067b2o
1375b3o$1068bo11$3366b2o$3366bobo$3366bo$1408bo$1408b2o309bo$1407bobo
309b2o$105bo1612bobo$105b2o3445bo$104bobo3444b2o$3551bobo18$1035bo
2273b2o$1035bobo2271bobo$1035b2o2272bo$1061bobo395bo$1061b2o396b2o309b
o$1048bobo11bo395bobo309b2o$156bo891b2o719bobo$156b2o891bo2445bo$155bo
bo3336b2o$3494bobo16$2172b3o2$3252b2o$3252bobo$3252bo$1510bo$1510b2o
309bo$1509bobo309b2o$207bo1612bobo$207b2o3229bo$206bobo3228b2o$3437bob
o2$2645bobo$2645b2o$2646bo2$2441b3o3$1016bo$1016bobo$1016b2o$1042bobo$
1042b2o$1029bobo11bo$1029b2o$1030bo2$3195b2o$3195bobo$3195bo$1561bo$
1561b2o309bo$1560bobo309b2o$258bo1612bobo$258b2o3121bo$257bobo3120b2o$
3380bobo15$2613bo$2613bobo$2613b2o$3138b2o$3138bobo$3138bo$1612bo$
1612b2o309bo$1611bobo309b2o$309bo1612bobo$309b2o3013bo$308bobo3012b2o$
997bo2325bobo$997bobo$997b2o$1023bobo$1023b2o$1010bobo11bo$1010b2o$
1011bo9$2169b3o2$3081b2o$3081bobo$3081bo$1663bo$1663b2o309bo$49bo1612b
obo309b2o$49b2o309bo1612bobo$48bobo309b2o2905bo$359bobo2904b2o$3266bob
o6$2438b3o12$978bo2045b2o$978bobo2043bobo$978b2o2044bo$1004bobo707bo$
1004b2o708b2o309bo$100bo890bobo11bo707bobo309b2o$100b2o309bo579b2o
1031bobo$99bobo309b2o579bo2217bo$410bobo2796b2o$3209bobo18$2967b2o$
2967bobo$2967bo$1765bo$1765b2o309bo$151bo1612bobo309b2o$151b2o309bo
1612bobo$150bobo309b2o2689bo$461bobo2688b2o$3152bobo2$2588bobo$2588b2o
$2589bo5$959bo$959bobo$959b2o$985bobo$985b2o$972bobo11bo$972b2o$973bo
1192b3o2$2910b2o$2910bobo$2910bo$1816bo$1816b2o309bo$202bo1612bobo309b
2o$202b2o309bo1612bobo$201bobo309b2o2581bo$512bobo2580b2o$3095bobo6$
2435b3o9$2556bo$2556bobo$2556b2o$2853b2o$2853bobo$2853bo$1867bo$1867b
2o309bo$253bo1612bobo309b2o$253b2o309bo1612bobo$252bobo309b2o2473bo$
563bobo2472b2o$940bo2097bobo$940bobo$940b2o$966bobo$966b2o$953bobo11bo
$953b2o$954bo11$2796b2o$2796bobo$2796bo1177b2o$1918bo2055bobo$1918b2o
309bo1744bo$304bo1612bobo309b2o$304b2o309bo1612bobo$303bobo309b2o2365b
o$614bobo2364b2o$2981bobo16$2163b3o2$921bo1817b2o$921bobo1815bobo$921b
2o1816bo1177b2o$947bobo1019bo1947bobo$947b2o1020b2o309bo1636bo$355bo
578bobo11bo1019bobo309b2o$355b2o309bo267b2o1343bobo$354bobo309b2o267bo
1989bo$665bobo2256b2o$2924bobo6$2432b3o12$2682b2o$2682bobo$2682bo1177b
2o$2020bo1839bobo$2020b2o309bo1528bo$406bo1612bobo309b2o$406b2o309bo
1612bobo$405bobo309b2o2149bo$716bobo2148b2o$2867bobo2$2531bobo$2531b2o
$2532bo5$902bo$902bobo$902b2o$928bobo$928b2o$915bobo11bo$915b2o$916bo
2$2625b2o$2625bobo$2625bo1177b2o$2071bo1731bobo$2071b2o309bo1420bo$
457bo1612bobo309b2o$457b2o309bo1612bobo$456bobo309b2o2041bo$767bobo
2040b2o$2810bobo1176bo$3988b2o$3988bobo13$2499bo$2160b3o336bobo$2499b
2o$2568b2o$2568bobo$2568bo1177b2o$2122bo1623bobo$2122b2o309bo1312bo$
508bo1612bobo309b2o$508b2o309bo1612bobo$507bobo309b2o1933bo$818bobo
1932b2o$883bo1869bobo1176bo$883bobo3045b2o$883b2o3046bobo$909bobo$909b
2o$896bobo11bo$896b2o1531b3o$897bo11$2511b2o$2511bobo$2511bo1177b2o$
2173bo1515bobo$2173b2o309bo1204bo$559bo1612bobo309b2o$559b2o309bo1612b
obo$558bobo309b2o1825bo$869bobo1824b2o$2696bobo1176bo$3874b2o$3874bobo
16$864bo$864bobo$864b2o2766b2o$890bobo1331bo1407bobo$890b2o1332b2o
1406bo$610bo266bobo11bo1331bobo$610b2o265b2o42bo$609bobo266bo42b2o
1717bo$920bobo1716b2o$2639bobo1176bo$3817b2o$3817bobo14$2157b3o4$3575b
2o$2275bo1299bobo$2275b2o1298bo$661bo1612bobo$661b2o309bo$660bobo309b
2o1609bo$971bobo1608b2o$2582bobo1176bo$3760b2o$2474bobo1283bobo$2474b
2o$2475bo2$2426b3o3$845bo$845bobo$845b2o$871bobo$871b2o$858bobo11bo$
858b2o$859bo4$3518b2o$2326bo1191bobo$2326b2o1190bo$712bo1612bobo$712b
2o309bo$711bobo309b2o1501bo$1022bobo1500b2o$2525bobo1176bo$3703b2o$
3703bobo13$2442bo$2442bobo$2442b2o3$2455bobo1003b2o$2377bo77b2o1004bob
o$2377b2o77bo1004bo$763bo1612bobo$763b2o309bo$762bobo309b2o1393bo$
1073bobo1392b2o$826bo1641bobo1176bo$826bobo2817b2o$826b2o2818bobo$852b
obo$852b2o$839bobo11bo$839b2o$840bo9$2154b3o4$3404b2o$3404bobo$3404bo$
814bo$814b2o309bo$813bobo309b2o$1124bobo$3590bo$2421b3o1165b2o$3589bob
o$2420bobobo$2419b2o3bo$2420bo$2421bo3bo$2422b3o11$807bo$807bobo$807b
2o2538b2o$833bobo2511bobo$833b2o2512bo$820bobo11bo30bo$820b2o43b2o309b
o$821bo42bobo309b2o$1175bobo$3533bo$3532b2o$3532bobo18$3290b2o$3290bob
o$3290bo$916bo$916b2o309bo$915bobo309b2o$1226bobo$3476bo$3475b2o$2417b
obo1055bobo$2417b2o$2418bo5$788bo$788bobo$788b2o$814bobo$814b2o$801bob
o11bo$801b2o$802bo1348b3o4$3233b2o$3233bobo$3233bo$967bo$967b2o309bo$
966bobo309b2o$1277bobo$3419bo$3418b2o$3418bobo13$2385bo$2385bobo$2385b
2o3$2398bobo775b2o$2398b2o776bobo$2399bo776bo$1018bo$1018b2o309bo$
1017bobo309b2o$1328bobo$769bo2592bo$769bobo2589b2o$769b2o2590bobo$795b
obo$795b2o$782bobo11bo$782b2o$783bo13$3119b2o$3119bobo$3119bo$1069bo$
1069b2o309bo$1068bobo309b2o$1379bobo$3305bo$3304b2o$3304bobo4$2366bo$
2366bobo$2366b2o8$2148b3o2$750bo$750bobo$750b2o2310b2o$776bobo2283bobo
$776b2o2284bo$763bobo11bo342bo$763b2o355b2o309bo$764bo354bobo309b2o$
1430bobo$3248bo$3247b2o$3247bobo18$3005b2o$3005bobo$3005bo$1171bo$
1171b2o309bo$1170bobo309b2o$1481bobo$3191bo$3190b2o$2360bobo827bobo$
2360b2o$2361bo5$731bo$731bobo$731b2o$757bobo$757b2o$744bobo11bo$744b2o
$745bo4$2948b2o$2948bobo$2948bo$1222bo$1222b2o309bo$1221bobo309b2o$
1532bobo$3134bo$3133b2o$3133bobo13$2328bo$2145b3o180bobo$2328b2o3$
2341bobo547b2o$2341b2o548bobo$2342bo548bo$1273bo$1273b2o309bo$1272bobo
309b2o$1583bobo$712bo2364bo$712bobo2361b2o$712b2o2362bobo$738bobo$738b
2o$725bobo11bo$725b2o$726bo13$2834b2o$2834bobo$2834bo$1324bo$1324b2o
309bo$1323bobo309b2o$1634bobo$3020bo$3019b2o$3019bobo4$2309bo$2309bobo
$2309b2o10$693bo$693bobo$693b2o2082b2o$719bobo2055bobo$719b2o2056bo$
706bobo11bo654bo$706b2o667b2o309bo$707bo666bobo309b2o$1685bobo$2963bo$
2962b2o$2962bobo14$2142b3o4$2720b2o$2720bobo$2720bo$1426bo$1426b2o309b
o$1425bobo309b2o$1736bobo$2906bo$2905b2o$2303bobo599bobo$2303b2o$2304b
o5$674bo$674bobo$674b2o$700bobo$700b2o$687bobo11bo$687b2o$688bo4$2663b
2o$2663bobo$2663bo$1477bo$1477b2o309bo$1476bobo309b2o$1787bobo$2849bo$
2848b2o$2848bobo13$2271bo$2271bobo$2271b2o3$2284bobo319b2o$2284b2o320b
obo$2285bo320bo$1528bo$1528b2o309bo$1527bobo309b2o$1838bobo$655bo2136b
o$655bobo2133b2o$655b2o2134bobo$681bobo$681b2o$668bobo11bo$668b2o$669b
o9$2139b3o4$2549b2o$2549bobo$2549bo$1579bo$1579b2o309bo$1578bobo309b2o
$1889bobo$2735bo$2734b2o$2734bobo4$2252bo$2252bobo$2252b2o10$636bo$
636bobo$636b2o1854b2o$662bobo1827bobo$662b2o1828bo$649bobo11bo966bo$
649b2o979b2o309bo$650bo978bobo309b2o$1940bobo$2678bo$2677b2o$2677bobo
18$2435b2o$2435bobo$2435bo$1681bo$1681b2o309bo$1680bobo309b2o$1991bobo
$2621bo$2620b2o$2246bobo371bobo$2246b2o$2247bo5$617bo$617bobo$617b2o$
643bobo$643b2o$630bobo11bo$630b2o$631bo1504b3o4$2378b2o$2378bobo$2378b
o$1732bo$1732b2o309bo$1731bobo309b2o$2042bobo$2564bo$2563b2o$2563bobo
13$2214bo$2214bobo$2214b2o3$2227bobo91b2o$2227b2o92bobo$2228bo92bo$
1783bo$1783b2o309bo$1782bobo309b2o$2093bobo$598bo1908bo$598bobo1905b2o
$598b2o1906bobo$624bobo$624b2o$611bobo11bo$611b2o$612bo13$2264b2o$
2264bobo$2264bo$1834bo$1834b2o309bo$1833bobo309b2o$2144bobo$2450bo$
2449b2o$2449bobo4$2195bo$2195bobo$2195b2o8$2133b3o2$579bo$579bobo$579b
2o1626b2o$605bobo1599bobo$605b2o1600bo$592bobo11bo1278bo$592b2o1291b2o
309bo$593bo1290bobo309b2o$2195bobo$2393bo$2392b2o$2392bobo21$1936bo$
1936b2o$1935bobo2$2336bo$2335b2o$2189bobo143bobo$2189b2o$2190bo5$560bo
$560bobo$560b2o$586bobo$586b2o$573bobo11bo$573b2o$574bo7$1987bo$1987b
2o$1986bobo2$2279bo$2278b2o$2278bobo13$2157bo$2130b3o24bobo$2157b2o3$
2170bobo$2170b2o$2171bo$2038bo$2038b2o$2037bobo2$541bo1680bo$541bobo
1677b2o$541b2o1678bobo$567bobo$567b2o$554bobo11bo$554b2o$555bo16$2089b
o$2089b2o$2088bobo2$2165bo$2164b2o$2164bobo4$2138bo$2138bobo$2138b2o3$
2151bobo$2151b2o$2152bo5$522bo$522bobo$522b2o$548bobo$548b2o$535bobo
11bo$535b2o$536bo26$2119bo$2119bobo$2119b2o3$2132bobo$2132b2o$2133bo5$
503bo$503bobo$503b2o$529bobo$529b2o$516bobo11bo$516b2o$517bo26$2100bo$
2100bobo$2100b2o3$2113bobo$2113b2o$2114bo5$484bo$484bobo$484b2o$510bob
o$510b2o$497bobo11bo$497b2o$498bo26$2081bo$2081bobo$2081b2o3$2094bobo$
2094b2o$2095bo5$465bo$465bobo$465b2o$491bobo$491b2o$478bobo11bo$478b2o
$479bo26$2062bo$2062bobo$2062b2o3$2075bobo$2075b2o$2076bo5$446bo$446bo
bo$446b2o$472bobo$472b2o$459bobo11bo$459b2o$460bo26$2043bo$2043bobo$
2043b2o3$2056bobo$2056b2o$2057bo5$427bo$427bobo$427b2o$453bobo$453b2o$
440bobo11bo$440b2o$441bo26$2024bo$2024bobo$2024b2o3$2037bobo$2037b2o$
2038bo5$408bo$408bobo$408b2o$434bobo$434b2o$421bobo11bo$421b2o$422bo
26$2005bo$2005bobo$2005b2o3$2018bobo$2018b2o$2019bo5$389bo$389bobo$
389b2o$415bobo$415b2o$402bobo11bo$402b2o$403bo!

Posted: **September 9th, 2016, 7:22 pm**

That's a nice construction! I think that would cost around 150 *WSS to fanout from a single stream, making this helix about twice as complicated as that of the original caterpillar. I'm hoping to avoid breaking the "largest interesting construction" record, I don't know if I'm alone in this.

I would instead hope to find universality with only 2 tracks, at least to help build a 5-track cluster that can churn out recipes more quickly. It hasn't shown that much promise though, certainly a "nice way" is elusive, so the above is a good fallback to have.

The debris from a single climber is so active, I would be surprised if there wasn't some pair affording universal construction, even if it isn't a subset of the 5-track cluster. It might be good to run some more gencols searches for that. Original searches were only interested in clean paired reactions, or Nico's search that found a clean forerake on 3 that has proven very valuable. (Nico's might not have been a systematized search so much as joining two of the pairs and getting lucky, I really don't know..). Regardless, there are probably a good number of messy rakes on 2 tracks that can be manipulated into a dirty constructor. If the 150 *WSS helix is the mark to beat, and a 2-track construction was shown below to take around 60 *WSS if you include the helix, then we probably have a couple 100K vertical cells to play around with in going from 2->5.

Who knows, maybe there is a 2-track cluster that is as convenient to make our target constellations with as the 5-track cluster has been. I'm imagining all 2-track options being dirty though, so it's more likely it will build a 5-track constructor plus debris, and then the 5 will clean the debris and start the real work.

The relevant search would have one climber fixed on a track and enumerate the possible second track locations. For each location, it would count the number of ways for the second climber to interact with the first such that the tracks both survive. The track separations with the most options would be the most promising. Of course, following climber pairs can spark the debris to give new reactions, since the repeat distance is usually low enough to allow it. Basically, the space of possibilities seems so huge I can't imagine it holding nothing which could be salvaged into a constructor.

Posted: **September 14th, 2016, 12:14 am**

I've found a number of forerakes on track pairs, but none of them are clean. This unlikely pair is the cleanest so far, a forerake with only two pieces of debris. The same pair provides 4 dirty rephasing reactions by stalling the left climber 36, 44, 56 or 64 generations. 5 unique options is good, but there'll be too much junk in the way unless we have something cleaner.

Code: Select all

x = 146, y = 344, rule = B3/S23
137bobo$137b2o$138bo4$143bo$143bobo$143b2o37$118bobo$118b2o$119bo4$
124bo$124bobo$124b2o37$99bobo$99b2o$100bo4$105bo$105bobo$105b2o37$80bo
bo$80b2o$81bo4$86bo$86bobo$86b2o37$61bobo$61b2o$62bo4$67bo$67bobo$67b
2o37$42bobo$42b2o$43bo4$48bo$48bobo$48b2o37$23bobo$23b2o$24bo4$29bo$
29bobo$29b2o37$4bobo$4b2o$5bo4$10b2o$10b2o$10bobo$11b2o2b2o$17bo$10bo
2b2obo$10bo$3b3o5bo4bo$3bo2bo6bo2b2o$2bo3bo7bob2o$2b3o2bo7b2o$3b4o3$ob
o14b2o$2o15b2o$bo4$6bo$6bobo$6b2o!

Posted: **September 14th, 2016, 6:44 pm**

Another option. This pair became more promising the more I investigated it. The tracks are simple, no vertical or phase offset, just 19 cells horizontally. If the climbers are in the same phase or if the left climber is 4 generations delayed, the debris is a TL+blinker constellation. If the right climber is 4 generations delayed, the debris is a longboat + NE glider. All other options destroy either the right track or the right climber, so we only have these 3. I'll refer to them as A, B, and C, from left to right.

Code: Select all

x = 380, y = 168, rule = B3/S23
70bobo16bobo122bobo16bobo122bobo16bobo$70b2o17b2o123b2o17b2o123b2o17b
2o$71bo18bo124bo18bo124bo18bo43$51bobo16bobo122bobo16bobo122bobo16bobo
$51b2o17b2o123b2o17b2o123b2o17b2o$52bo18bo124bo18bo124bo18bo43$32bobo
16bobo122bobo16bobo122bobo16bobo$32b2o17b2o123b2o17b2o123b2o17b2o$33bo
18bo124bo18bo124bo18bo43$13bobo16bobo122bobo16bobo122bobo16bobo$13b2o
17b2o123b2o17b2o123b2o17b2o$14bo18bo124bo18bo124bo18bo23$21b3o122b3o
16b3o122b3o$22bo124bo18bo124bo$b3o18b3o122b3o16b3o122b3o14b3o$o3bo302b
o3bo2$5bo306bo$5o302b5o$bo306bo!

Some neat constructions that may hint at universality:
C, C with high spacing has no interference, the second forerake passes through the longboats.

Code: Select all

x = 125, y = 268, rule = B3/S23
104bo18bo$103bo18bo$103b3o16b3o43$85bo18bo$84bo18bo$84b3o16b3o43$66bo
18bo$65bo18bo$65b3o16b3o43$47bo18bo$46bo18bo$46b3o16b3o43$28bo18bo$27b
o18bo$27b3o16b3o4$29b3o$28bo2bo$27bo4bo15bo$29bo17b3o$46bo2bo$30b2o13b
3o2b2o$29bobo14bo2b3o$29bobo15b2o2b2o$50b3o$35bo11b4obo$33bo13b2o2b2o$
33b2o15b2o3$24bo18bo$23bo18bo$23b3o16b3o43$5bo18bo$4bo18bo$4b3o16b3o4$
6b3o$5bo2bo$4bo4bo15bo$6bo17b3o$23bo2bo$7b2o13b3o2b2o$6bobo14bo2b3o$6b
obo15b2o2b2o$27b3o$12bo11b4obo$10bo13b2o2b2o$10b2o15b2o3$bo18bo$o18bo$
3o16b3o!

C, C, C with high spacing causes the third rake to cleanly delete the longboat left by the first. This means an infinite chain of well-spaced Cs will consist of two forerakes and no other debris.

Code: Select all

x = 284, y = 532, rule = B3/S23
192bo18bo$191bo18bo$191b3o16b3o43$173bo18bo$172bo18bo$172b3o16b3o43$
154bo18bo$153bo18bo$153b3o16b3o4$155b3o$154bo2bo$153bo4bo15bo$155bo17b
3o$172bo2bo$156b2o13b3o2b2o$155bobo14bo2b3o$155bobo15b2o2b2o$176b3o$
161bo11b4obo$159bo13b2o2b2o$159b2o15b2o3$150bo18bo$149bo18bo$149b3o16b
3o9$181bo$180bobo$181bobo$145bo36bobo$144bo36bo3bo$146bo33bo4bo$144b3o
33bo3bo$146bobo22bo8bo2b2o$146b2ob2o20bo9b3o$145bo5bo19bo10bo$146bo3bo
$147b3o$148bo21$179b3o$131bo18bo16bo7b2ob2o2bo$130bo18bo16bo5b2obobo4b
o$130b3o16b3o15b2o3b2obo$168bo3bo8bo$173bo7bo$172bo5bob2o$132b3o38bobo
2bobo$131bo2bo39bo4b2o$130bo4bo15bo26bobo15b3o$132bo17b3o25b2o18bo$
149bo2bo44bo$133b2o13b3o2b2o$132bobo14bo2b3o$132bobo15b2o2b2o$153b3o$
138bo11b4obo$136bo13b2o2b2o$136b2o15b2o58b3o$215bo$214bo$127bo18bo$
126bo18bo$126b3o16b3o4$230b3o$232bo$231bo3$158bo$157bobo18bo$158bobo
16bobo$122bo36bobo16bobo$121bo36bo3bo16b2o66b3o$123bo33bo4bo86bo$121b
3o33bo3bo86bo$123bobo22bo8bo2b2o$123b2ob2o20bo9b3o$122bo5bo19bo10bo$
123bo3bo$124b3o$125bo$264b3o$266bo$265bo7$281b3o$283bo$282bo4$177bo$
176bobo$177bobo$178b2o2$156b3o$108bo18bo16bo7b2ob2o2bo$107bo18bo16bo5b
2obobo4bo$107b3o16b3o15b2o3b2obo$145bo3bo8bo$150bo7bo$149bo5bob2o$109b
3o38bobo2bobo$108bo2bo39bo4b2o$107bo4bo15bo26bobo15b3o$109bo17b3o25b2o
18bo$126bo2bo44bo$110b2o13b3o2b2o$109bobo14bo2b3o$109bobo15b2o2b2o$
130b3o$115bo11b4obo$113bo13b2o2b2o$113b2o15b2o58b3o$192bo$191bo$104bo
18bo$103bo18bo53bo$103b3o16b3o50bobo$176bobo$177b2o2$207b3o$209bo$208b
o3$135bo$134bobo18bo$135bobo16bobo$99bo36bobo16bobo$98bo36bo3bo16b2o
66b3o$100bo33bo4bo86bo$98b3o33bo3bo86bo$100bobo22bo8bo2b2o$100b2ob2o
20bo9b3o$99bo5bo19bo10bo$100bo3bo$101b3o$102bo$241b3o$243bo$242bo2$
175bo$174bobo$175bobo$176b2o2$258b3o$260bo$259bo4$154bo$153bobo$154bob
o$155b2o2$133b3o$85bo18bo16bo7b2ob2o2bo$84bo18bo16bo5b2obobo4bo$84b3o
16b3o15b2o3b2obo$122bo3bo8bo$127bo7bo$126bo5bob2o$86b3o38bobo2bobo$85b
o2bo39bo4b2o$84bo4bo15bo26bobo15b3o$86bo17b3o25b2o18bo$103bo2bo44bo22b
o$87b2o13b3o2b2o64bobo$86bobo14bo2b3o65bobo$86bobo15b2o2b2o65b2o$107b
3o$92bo11b4obo$90bo13b2o2b2o$90b2o15b2o58b3o$169bo$168bo$81bo18bo$80bo
18bo53bo$80b3o16b3o50bobo$153bobo$154b2o7$112bo$111bobo18bo$112bobo16b
obo$76bo36bobo16bobo$75bo36bo3bo16b2o$77bo33bo4bo$75b3o33bo3bo$77bobo
22bo8bo2b2o$77b2ob2o20bo9b3o$76bo5bo19bo10bo$77bo3bo$78b3o$79bo5$152bo
$151bobo$152bobo$153b2o8$131bo$130bobo$131bobo$132b2o2$110b3o$62bo18bo
16bo7b2ob2o2bo$61bo18bo16bo5b2obobo4bo$61b3o16b3o15b2o3b2obo$99bo3bo8b
o$104bo7bo$103bo5bob2o$63b3o38bobo2bobo$62bo2bo39bo4b2o$61bo4bo15bo26b
obo15b3o$63bo17b3o25b2o18bo$80bo2bo44bo22bo$64b2o13b3o2b2o64bobo$63bob
o14bo2b3o65bobo$63bobo15b2o2b2o65b2o$84b3o$69bo11b4obo$67bo13b2o2b2o$
67b2o15b2o58b3o$146bo$145bo$58bo18bo$57bo18bo53bo$57b3o16b3o50bobo$
130bobo$131b2o7$89bo$88bobo18bo$89bobo16bobo$53bo36bobo16bobo$52bo36bo
3bo16b2o$54bo33bo4bo$52b3o33bo3bo$54bobo22bo8bo2b2o$54b2ob2o20bo9b3o$
53bo5bo19bo10bo$54bo3bo$55b3o$56bo5$129bo$128bobo$129bobo$130b2o8$108b
o$107bobo$108bobo$109b2o2$87b3o$39bo18bo16bo7b2ob2o2bo$38bo18bo16bo5b
2obobo4bo$38b3o16b3o15b2o3b2obo$76bo3bo8bo$81bo7bo$80bo5bob2o$81bobo2b
obo$82bo4b2o$86bobo15b3o$86b2o18bo$105bo22bo$127bobo$128bobo$129b2o4$
121b3o$123bo$122bo2$107bo$106bobo$107bobo$108b2o8$86bo$85bobo$86bobo$
87b2o10$20bo18bo$19bo18bo$19b3o16b3o$106bo$105bobo$106bobo$107b2o8$85b
o$84bobo$85bobo$86b2o13$105bo$104bobo$105bobo$106b2o8$84bo$83bobo$84bo
bo$85b2o$bo18bo$o18bo$3o16b3o10$104bo$103bobo$104bobo$105b2o8$83bo$82b
obo$83bobo$84b2o!

C, C with a lower spacing can cause sparks to interfere, preventing the longboats and second rake from forming. The debris is instead a boat+blinker+block constellation.

Code: Select all

x = 190, y = 269, rule = B3/S23
105bo18bo$103b2o17b2o$104b2o17b2o43$86bo18bo$84b2o17b2o$85b2o17b2o43$
67bo18bo$65b2o17b2o$66b2o17b2o43$48bo18bo$46b2o17b2o$47b2o17b2o10$46b
3o$45bo2bo$45bo4bo$44b2ob2obo13b3o$44b2obo2bo12bo2bo$46b4o13b2o2bo$47b
3o16b2o2$44bo18bo$42b2o17b2o$43b2o17b2o12$73b2o$72bo$71bo2bo$35bo4bob
2o27bo$34bo2bo2bo4b2o25bob4o$35bo2bo6b2o7bo18bob3o$36bo4bo12bo$38bo2bo
19b3o$39b2o12$29bo$28b3o$27bo2b2o$27bo3bo15bo$29bobo14b3o$45bo2b2o$26b
2ob2o14b3o$28bo2$73b2o$35bo10bo26b2o$34b3o8bobo16b2o$33b5o7bobo15b2o2b
3obo$32bo5bo14bo6b2obo3b3ob2o$31b2o2bo2b2o12b3o5bo9bo2bo$30b3obobob3o
10b5o5bo10bo$31b2o2bo2b2o10b2o3b2o5bobo$32bo5bo12b5o6bob2o$33b5o14b3o
9bo3bobo$34bo2bo15bo14bo2bo$37bo30bo2bo$34bo2bo32bo$35b2o16b2o$53b2o
30b2o$86b2o$85bo6$21bo18bo$19b2o17b2o62b2o$20b2o17b2o62b2o$102bo3$49bo
$48b3o$46b2obobo15bo$46b3o17bob2ob2o$45b4o3bo14b4o2bo45b2o$44bo2b2obo
20b2o47b2o$43b3ob3o69bo$36b2o9bo5b2o$36b2o15b2o5$136b2o$137b2o$136bo7$
153b2o$46b2o106b2o$46b2o105bo6$41bo$41bo128b2o$41bo129b2o$170bo3$50bo$
49bobo$49b2o$2bo18bo$2o17b2o166b2o$b2o17b2o166b2o$187bo!

C, A and C, B with proper spacing can prevent the TL + blinker from forming, leaving just the debris from C.

Code: Select all

x = 133, y = 314, rule = B3/S23
112bo18bo$111bo18bo$111b3o16b3o43$93bo18bo$92bo18bo$92b3o16b3o43$74bo
18bo$73bo18bo$73b3o16b3o43$55bo18bo$54bo18bo$54b3o16b3o43$36bo18bo$35b
o18bo$35b3o16b3o17$28bo$26b6o$26b2o2b2o13b3o$48bo$30bo14bo2bo$26b2o2bo
15b2o$26b2o3bo14b2o$30bo14bo2bo$28bobo14bo$29bo17b2o7$28bo$28bo16b2o$
28b2o15b2o$27bobo$26bo2bo7b3o$25bo4bo5bo3bo5b3o$25bo2b3o10bo3bobo8bo$
25b2o5bo8bo3bo9b3o$27b3o10b2o3b3o2bo2bo4bo$30bo2bo2b4o9bo6bobo$32bo5bo
11bo5b2o$33b2o16b3o19$13bo18bo$12bo18bo$12b3o16b3o24b2o$48bobo7b2o$48b
2o$49bo$46bo8b2o$46bo8b2o$46bo$51b3o$50bo3bo$13bo18bo16bo5bo$12b3o16b
3o21bo$11bo2b2o14bo2b2o15b2o3bo$11bob2o15bob2o18b2o$13b2ob2o14b2ob2o$
10bo5bo12bo5bo$11bo4bo13bo4bo$12bo2bo15bo2bo$14bo18bo$9bo18bo37b3o$8bo
18bo40bo$8b3o16b3o37bo7$83b3o$85bo$84bo2$37b3obo$35bo5bo$35b2obo2bo$
34b2o2bo$7bo25b6o$3o2bobo2b3o17b3ob4o16bo45b3o$b3o7b2o17b2o3b2o16bobo
46bo$3bo50bobo44bo$5bobo47b2o$5b2o5$117b3o$119bo$118bo16$53bo$52bobo$
53bobo$54b2o!

The above means a C, A, C, A, C, A .. chain will have one forerake and no other debris. C, A, C, A ... C, A, C, C, C, C ... will place two forerakes with a variable separation and no other debris. However, the C chain does not permit any new forerakes without some debris.

B, A with as tight of spacing as possible (tight enough that A, A or B, B or A, B won't work) can initiate a block-pull seqeunce, leaving an additional block and two blinkers. Subsequent B or A pairs with the correct spacing can continue the block pull to an arbitrary number of rephasings with no additional debris. C can be inserted into the block pull to turn it into a blinker pull with the same property and spacing. A or B can turn the blinker pull back into a block pull. I haven't found any clean termination for either, so the total cost here is 4 pieces of debris, for arbitrarily many rephasings.

Code: Select all

x = 218, y = 619, rule = B3/S23
197bo18bo$196bo18bo$196b3o16b3o43$178bo18bo$177bo18bo$177b3o16b3o43$
159bo18bo$158bo18bo$158b3o16b3o43$140bo18bo$139bo18bo$139b3o16b3o12$
135bo$134bo$136bo$134b3o$136bobo$136b2ob2o$135bo5bo$136bo3bo$137b3o$
130bo7bo10bo$129bobo16bobo$128bo3bo14bo3bo$129bo2bo15bo2bo$129bo2bo15b
o2bo$130bobo16bobo9$129b2o17b2o$129b2o17b2o$136bo18bo$135bob2o15bob2o$
132b3o16b3o$131b5o14b5o$130bo2bo2b3o2bo7bo2bo2b3o2bo$130bobo4bo2bobo6b
obo4bo2bobo$131bo3b2o3bobo7bo3b2o3bobo$136bo4bo13bo4bo$133b3o16b3o$
133b2o17b2o15$137b3o$137bo2bo$117b2o17bo2b2o16b3o$116bo2bo15bo2bo$117b
ob2o15b2o17bo5bo$117bo37bo5bo$118bobo21bo12bo5bo$117bo2b2o$123bo19b2o
12b3o$123bo18bobo$144b2o$122b2o19bo$122b2o$123bo33bo$157bo$144b2o11bo$
124b2o18b2o$124b2o5$113bo18bo$112bo18bo$112b3o16b3o4$157b2o$157b2o5$
155b3o$139b2o$139b2o4$156bo$156bo$156bo3$122bo$121bobo$102bo17bo3bo$
102bo18bo2bo$101bobo17bo2bo$122bobo$103b2o2$103b2o2$156b2o$156b2o3$
121b2o$101b2o18b2o$101b2o25bo25b3o$108bo18bob2o7b2o$107bobo14b3o11b2o$
107bobo13b5o$105bo2bo13bo2bo2b3o2bo$104b4o5bo8bobo4bo2bobo$103bo4bo3bo
bo8bo3b2o3bobo20bo$103bobob2o3bobo13bo4bo21bo$104b2o2b2o3bo11b3o27bo$
108bo16b2o$106bob4o$106b5o$108b2o9$155b2o$155b2o4$90bo18bo$89bo18bo44b
3o$89b3o16b3o4$123b2o$123b2o29bo$110bo43bo$109b3o42bo$108bo2bo$90bo16b
3o2b2o$89b3o16bo2b3o$88bo2b2o16b2o2b2o$88bob2o20b3o$90b2ob2o14b4obo$
87bo5bo15b2o2b2o$88bo4bo18b2o$89bo2bo$91bo$86bo18bo$85bo18bo$85b3o16b
3o47b2o$154b2o5$152b3o6$153bo$153bo$153bo$84bo23b2o$77b3o2bobo2b3o18b
2o$78b3o7b2o$80bo$82bobo$82b2o7$153b2o$153b2o$72b3o$72bo2bo$74b2o$90b
3o$70bo2bo16bo2bo57b3o$71b2o16bo3bo$74b2o14bo2b2o$73b3o16bo$74bo15b2o$
71bo2bo14b3o$72b2o15b3o60bo$152bo$78bobo71bo$77bobobo14b3o8b2o$95bo3bo
7b2o$75bo7bo11bo3bo$84bo8b2o5b2o$75b3o6bo7bo4bo4bo$75b2o8bo6bo3bobo3bo
$75b2o2bo4bo7bo4bo4bo$76bob3o2b2o8b2o5b2o$76b2ob4o12b6o$78b2o15b2o2b2o
$79bo18b3o$97bobo$97b2o53b2o$152b2o5$150b3o3$63bo18bo$62bo18bo$62b3o
16b3o$151bo$151bo$151bo6$91bo$91bo$91bo4$60b2o$60bob2o14bo72b2o$62b2o
14b2o71b2o$60b2o18bo$58b2o18b2o$77bobo$58bobo17bo$59bo16bobo70b3o$74bo
$74bobo4$150bo$150bo$150bo2$74b2o$73bo2bo$68b3obo3b2o$68bo4b2o9b3o$51b
2o18bo13bob2obo$50b3o2b2o11b2obo13b3obobo$51bobob2o2b2o5bo17bo2b3obo$
52b2obo3b2o6b2o4bo2b3o5b2o4bo$54b2o12bob2o3bob2o6bo$73bob2o$74bo$150b
2o$150b2o5$148b3o6$149bo$149bo$149bo4$41b3o$41bo2bo$40bo2b2o14b2o$39bo
2bo15bo2bo$40b2o17bob2o$59bo$46bo13bobo12bo$59bo2b2o11bo$47b2o16bo9bo$
46bobo16bo83b2o$48b2o99b2o$47bo16b2o$64b2o$65bo2$48b2o97b3o$48b2o16b2o
$66b2o4$148bo$36bo18bo92bo$35bo18bo93bo$35b3o16b3o12$148b2o$60bo87b2o$
60bo$60bo3$146b3o5$44bo$44bo102bo$43bobo101bo$24bo122bo$22b2ob2o18b2o$
22b2ob2o$23bob3o17b2o$22b3o6$43b2o$23b2o18b2o$23b2o25bo$30bo18bobo95b
2o$29bobo17bobo7bo87b2o$29bobo15bo2bo8bo$30bo15b4o5bo3bo$45bo4bo3bobo$
26b3o5b2o9bobob2o3bobo$26bob2o5b2o9b2o2b2o3bo89b3o$26bob2o20bo$29bo18b
ob4o$30b3o15b5o$28bo4bo16b2o$32bo$28bo117bo$29bo116bo$146bo10$13bo18bo
$12bo18bo$12b3o16b3o$146b2o$146b2o3$45b2o$45b2o$144b3o2$32bo$31b3o$30b
o2b2o$12bo17bob2o$11b3o18b2ob2o108bo$10bo2b2o14bo5bo109bo$10b3obo15bo
4bo109bo$13b2o16bo2bo$33bo$9bo18bo$8bo18bo$8b3o16b3o8$145b2o$145b2o5$
143b3o$b2o3bo$o5b2o22b2o$bobo2bo3b2o18b2o$bobob2o3b2o$2b2ob2o$4bo139bo
$144bo$144bo13$144b2o$144b2o5$142b3o6$143bo$143bo$143bo13$143b2o$143b
2o5$141b3o6$142bo$142bo$142bo!

My thought is perhaps some combination of the above will allow all debris to occupy a small footprint (ideally, exactly the size of the longboat's shadow) with respect to NE and SW rakes. Then the NE rakes could continually pass through the debris arising from continued operation and construct frozen tracks using whatever lanes remain available. The frozen tracks, by virtue of being SW gliders, also pass through the debris. Ultimately, a full cluster comes through, and once the cluster is all the way through the debris field, climbers running on it clean up the mess. That would successfully implement 2->5 without any helix help, saving us as many as 100 helix *WSS constructions down the line.

The longboat's shadow allows only 5 of the initial 13 even lanes to pass through to construction. I don't know if that is enough for universality. Can slow gliders constrained to a shooting range of lanes congruent mod 26 to 0, 2, 4, 6, or 8 produce frozen tracks?

Additional holes in the above - we can use C, A, C, A... to get a rake, and then place the longboat in the shadow of prior longboats. The issue comes from rephasing to get the next rake where it needs to be. So far, all arbitrary rephasings have some piece of debris dependent on when the rephasing ends, meaning there is debris tied to the rake. However, I haven't looked into ways to destroy the block + 2blinker constellation from beginning a block pull, and perhaps there is a solution in there that allows disentangling rephasing debris from the following rake.

There's probably something I am missing that either invalidates all of this or makes it easier than anticipated. But I definitely feel this is the most promising track pair thus far for starting off the ship, if the ship does start from only a pair.

Posted: **September 15th, 2016, 8:36 am**

What about doing construction with the NW rake you mentioned a while ago? As with SE rakes you can change lane just by delaying the climbers and once you have constructed a universal set of tracks on the left you can then start to clear away all of the debris from below. Something like this (but I think the 3 gliders tracks on the left are in an incorrect phase). It would need more spaceships in the helices in order to construct an initial slow salvo target but I think the idea is viable.

Code: Select all

x = 621, y = 1287, rule = B3/S23
605bobo$605b2o$606bo2$619bo$618bo$618b3o39$586bobo$586b2o$587bo2$600bo
$599bo$599b3o39$567bobo$567b2o$568bo2$581bo$580bo$580b3o39$548bobo$
548b2o$549bo2$562bo$561bo$561b3o39$529bobo$529b2o$530bo2$543bo$542bo$
542b3o39$510bobo$510b2o$511bo2$524bo$523bo$523b3o39$491bobo$491b2o$
492bo2$505bo$504bo$504b3o3$124b2o$124b2o3$118b2o$118b2o22$123b2o$123b
2o3$117b2o$117b2o2$163bo$161b3o$160bo311bobo$160b2o310b2o$473bo2$486bo
$485bo$485b3o6$167bo$166bobo$166b2o4$122b2o47b2o$122b2o47b2o3$116b2o$
116b2o2$162bo$160b3o$159bo$159b2o11$166bo$165bobo$165b2o3$193bo$121b2o
47b2o20bobo258bobo$121b2o47b2o20b2o259b2o$454bo2$115b2o350bo$115b2o
349bo$466b3o$161bo$159b3o$158bo$158b2o11$165bo$164bobo$164b2o3$192bo$
120b2o47b2o20bobo$120b2o47b2o20b2o3$114b2o$114b2o2$160bo$158b3o$157bo$
157b2o8$434bobo$434b2o$435bo$164bo$163bobo282bo$163b2o282bo$447b3o2$
191bo$119b2o47b2o20bobo$119b2o47b2o20b2o2$236bo$113b2o120bobo$113b2o
120bo2bo$236b2o$159bo$157b3o76b2o$156bo78bobo$156b2o77b2o11$163bo$162b
obo$162b2o3$190bo$118b2o47b2o20bobo$118b2o47b2o20b2o2$235bo$112b2o120b
obo$112b2o120bo2bo$235b2o$158bo$156b3o76b2o$155bo78bobo178bobo$155b2o
77b2o179b2o$416bo2$429bo$428bo$428b3o6$162bo$161bobo$161b2o3$189bo$
117b2o47b2o20bobo$117b2o47b2o20b2o2$234bo$111b2o120bobo$111b2o120bo2bo
$234b2o$157bo$155b3o76b2o$154bo78bobo$154b2o77b2o11$161bo$160bobo$160b
2o3$188bo$116b2o47b2o20bobo206bobo$116b2o47b2o20b2o207b2o$397bo$233bo$
110b2o120bobo175bo$110b2o120bo2bo173bo$233b2o174b3o$156bo$154b3o76b2o$
153bo78bobo$153b2o77b2o11$160bo$159bobo$159b2o3$187bo$115b2o47b2o20bob
o$115b2o47b2o20b2o2$232bo$109b2o120bobo$109b2o120bo2bo$232b2o$155bo$
153b3o76b2o$152bo78bobo$152b2o77b2o8$377bobo$377b2o$378bo$159bo$158bob
o230bo$158b2o230bo$390b3o2$186bo$114b2o47b2o20bobo$114b2o47b2o20b2o2$
231bo$108b2o120bobo$108b2o120bo2bo$231b2o$154bo$152b3o76b2o$151bo78bob
o$151b2o77b2o11$158bo$157bobo$157b2o3$185bo$113b2o47b2o20bobo$113b2o
47b2o20b2o2$230bo$107b2o120bobo$107b2o120bo2bo$230b2o$153bo$151b3o76b
2o$150bo78bobo126bobo$150b2o77b2o127b2o$359bo2$372bo$371bo$371b3o6$
157bo$156bobo$156b2o3$184bo$112b2o47b2o20bobo$112b2o47b2o20b2o2$229bo$
106b2o120bobo$106b2o120bo2bo$229b2o$152bo$150b3o76b2o$149bo78bobo$149b
2o77b2o11$156bo$155bobo$155b2o3$183bo$111b2o47b2o20bobo154bobo$111b2o
47b2o20b2o155b2o$340bo$228bo$105b2o120bobo123bo$105b2o120bo2bo121bo$
228b2o122b3o$151bo$149b3o76b2o$148bo78bobo$148b2o77b2o11$155bo$154bobo
$154b2o189bo$343b6o$343b2o2b2o$182bo$110b2o47b2o20bobo163bo$110b2o47b
2o20b2o160b2o2bo$343b2o3bo$227bo119bo$104b2o120bobo116bobo$104b2o120bo
2bo116bo$227b2o$150bo$148b3o76b2o$147bo78bobo$147b2o77b2o2$345bo$345bo
$323bo21b2o$322b3o19bobo$321b2o2bo17bo2bo7b3o$321b5o16bo4bo5bo3bo$320b
o2b2o17bo2b3o10bo$321b2o19b2o5bo8bo$344b3o10b2o$154bo192bo2bo2b4o$153b
obo172bo20bo5bo$153b2o173b2o20b2o2$329b2o$181bo147bo$109b2o47b2o20bobo
$109b2o47b2o20b2o2$226bo102b2o$103b2o120bobo101b2o$103b2o120bo2bo$226b
2o$149bo$147b3o76b2o$146bo78bobo$146b2o77b2o$316bobo$316b2o$317bo2$
330bo$329bo27b2o$329b3o25b2o$334b3o9bobo$346b2o$347bo5bobo$153bo196b2o
$152bobo200bo$152b2o194b2o$348b2o2bob2o$349bo4b2o$180bo167b2o3b3o$108b
2o47b2o20bobo167bo3bo$108b2o47b2o20b2o169b3o$350b3o$225bo$102b2o120bob
o$102b2o120bo2bo$225b2o$148bo$146b3o76b2o114b2o$145bo78bobo114bobo$
145b2o77b2o115bo6$356b2o$322b2o32b2o$322bobo8b3o$322bo$358bo$152bo194b
2o9bo$151bobo193b2o9bo$151b2o$354b3o3b3o2$179bo123b2o45b2o6bo$107b2o
47b2o20bobo122bobo44b2o6bo$107b2o47b2o20b2o123bo54bo$297bobo$224bo72b
2o$101b2o120bobo72bo$101b2o120bo2bo$224b2o85bo$147bo162bo$145b3o76b2o
58b2o24b3o$144bo78bobo58bobo$144b2o77b2o59bo6$355b2o$265b2o88b2o$265bo
bo64b3o$265bo$357bo$151bo194b2o9bo$150bobo193b2o9bo$150b2o$353b3o3b3o
2$178bo67b2o101b2o6bo$106b2o47b2o20bobo66bobo100b2o6bo$106b2o47b2o20b
2o67bo110bo2$223bo$100b2o120bobo$100b2o120bo2bo$223b2o$146bo$144b3o76b
2o2b2o$143bo78bobo2bobo$143b2o77b2o3bo4$205bo$204b2o$204bobo147b2o$
354b2o$331b3o2$278bobo75bo$150bo127b2o65b2o9bo$149bobo127bo65b2o9bo$
149b2o35bo$185b2o105bo59b3o3b3o$185bobo103bo$177bo113b3o54b2o6bo$105b
2o47b2o20bobo169b2o6bo$105b2o47b2o20b2o178bo3$99b2o$99b2o66bo$166b2o$
145bo20bobo$143b3o$142bo$142b2o76bobo$220b2o$221bo4$353b2o$353b2o$330b
3o2$355bo$344b2o9bo$145bo198b2o9bo$146b2o$147bo2bo200b3o3b3o$148b2o$
148bo27bo170b2o6bo$104b2o47b2o20bobo169b2o6bo$104b2o41bo5b2o20b2o178bo
$148bo2$98b2o$98b2o2$144bo$142b3o$141bo$141b2o$138bo120bobo$137b2o120b
2o$137bobo120bo2$273bo$272bo79b2o$272b3o77b2o$329b3o2$119bo234bo$118b
2o223b2o9bo$118bobo222b2o9bo2$350b3o3b3o2$175bo170b2o6bo$102bobo69bobo
169b2o6bo$174b2o25bobo150bo$104bo96b2o$101bo100bo$103bo$101b3o2$143bo$
141b3o$140bo$140b2o13bobo$156b2o$156bo4$351b2o$351b2o$328b3o2$353bo$
342b2o9bo$342b2o9bo2$349b3o3b3o2$174bo170b2o6bo$173bobo169b2o6bo$173b
2o178bo$240bobo$240b2o$241bo2$254bo$142bo110bo$140b3o110b3o$139bo$139b
2o6$350b2o$350b2o$327b3o$182bobo$171bo10b2o168bo$119bo49b6o8bo157b2o9b
o$120bo48b2o2b2o166b2o9bo$118b3o$170bo177b3o3b3o2$344b2o6bo$344b2o6bo$
352bo6$141bo$139b3o$138bo$138b2o6$349b2o$349b2o$326b3o2$221bobo127bo$
221b2o117b2o9bo$222bo117b2o9bo2$235bo111b3o3b3o$234bo$234b3o106b2o6bo$
343b2o6bo$351bo6$137bobo$137bo$137bo$138bobo22bobo$163b2o$150bobo11bo$
150b2o$151bo2$348b2o$348b2o$325b3o2$350bo$339b2o9bo$339b2o9bo2$346b3o
3b3o2$342b2o6bo$342b2o6bo$350bo10$202bobo$202b2o$203bo2$216bo$215bo
131b2o$215b3o129b2o$324b3o2$349bo$338b2o9bo$338b2o9bo2$345b3o3b3o$118b
o$118bobo220b2o6bo$118b2o221b2o6bo$144bobo202bo$144b2o$131bobo11bo$
131b2o$132bo6$144b3o$144bo2bo$143bo3bo$148bo$115b2o27b3ob2o$115bobo12b
3o15bo197b2o$117bo12bo2bo9bo3b2o197b2o$115bobo11bo3bo13bo175b3o$114bo
14b3o2bo$114bobo13b4o214bo$114bo25bobo194b2o9bo$113bo26b2o195b2o9bo$
127bobo11bo$127b2o215b3o3b3o$128bo$340b2o6bo$340b2o6bo$348bo$183bobo$
183b2o$184bo$113b2o$152bo44bo$139b3o9b3o42bo$108b2o29bo3b3o50b3o$107b
5o10bo28b2ob2o$106b3o13bo2bob2o2bo7bo2bo5bo5b2o$107b2o2bo2b2o8b2o3bo2b
2o5bo2bo3bo2bob2ob2o$108b3o3b2o8b2o6bo9b2o3b2o2b2obo$125b7o6b3o2bo2bo
6bo$129b2o7b2o2bo$138b3o$345b2o$345b2o$322b3o2$147bo199bo$147b2o187b2o
9bo$146bobo187b2o9bo2$343b3o3b3o2$339b2o6bo$339b2o6bo$347bo$164bo$164b
2o$163bobo5$95bo$95bobo$95b2o84bo$121bobo57b2o$121b2o57bobo$108bobo11b
o$108b2o$109bo234b2o$344b2o$321b3o2$164bobo31bo147bo$164b2o32b2o135b2o
9bo$165bo31bobo135b2o9bo2$178bo163b3o3b3o$177bo$177b3o158b2o6bo$338b2o
6bo$346bo$215bo$215b2o$214bobo12$343b2o$343b2o$320b3o2$345bo$334b2o9bo
$334b2o9bo2$341b3o3b3o2$337b2o6bo$76bo260b2o6bo$76bobo266bo$76b2o$102b
obo$102b2o$89bobo11bo$89b2o$90bo4$145bobo$145b2o$146bo2$159bo$158bo
183b2o$158b3o181b2o$319b3o2$344bo$333b2o9bo$333b2o9bo2$340b3o3b3o2$
336b2o6bo$336b2o6bo$344bo15$341b2o$341b2o$57bo260b3o$57bobo$57b2o284bo
$83bobo246b2o9bo$83b2o247b2o9bo$70bobo11bo$70b2o267b3o3b3o$71bo$335b2o
6bo$335b2o6bo$343bo$126bobo$126b2o$127bo2$140bo$139bo$139b3o8$340b2o$
340b2o$317b3o2$342bo$331b2o9bo$331b2o9bo2$338b3o3b3o2$334b2o6bo$334b2o
6bo$342bo8$38bo$38bobo$38b2o$64bobo$64b2o$51bobo11bo$51b2o$52bo4$107bo
bo$107b2o$108bo2$121bo$120bo$120b3o28$19bo$19bobo$19b2o$45bobo$45b2o$
32bobo11bo$32b2o$33bo4$88bobo$88b2o$89bo2$102bo$101bo$101b3o28$o$obo$
2o$26bobo$26b2o$13bobo11bo$13b2o$14bo4$69bobo$69b2o$70bo2$83bo$82bo$
82b3o!

Posted: **September 15th, 2016, 1:10 pm**

NW and SE constructions have the potential to be much nicer because the lane can be changed without the need for rephasings. A large number of track pairs provide NW rakes, even a singleton climber. I guess I had just thrown NW rakes away for being on the "wrong" side, and hadn't found a viable SE option.

Now that I see your construction above, it being on the "wrong" side doesn't seem problematic at all, really. It actually looks ideal! No need to worry about debris shadows, full monochromatic/monoparity construction options. A ton of debris to eventually clean, but it's doable. The helix could provide the x1 glider tracks for a single climber, and one additional x1 NE stream, which the climber's NW rake collides with for an initial target. It must be well spaced enough to allow the full construction effort to take place before things collide. This is actually cheaper than making a track pair. Since NW constructions have no need for a rephasing, and the debris is always on the opposite side of the climber, this seems fully capable of executing a 1->5.

I'm kind of curious at this point whether a singleton should try to build seeds for the entire left helix. I don't know how quickly it can pull off constructions, and the period tripling mechanism would have to be rethought. The additional debris would probably be too costly to clean, so my gut feeling is its job should still only be 1->5.

Posted: **September 16th, 2016, 8:01 pm**

What is the most effective way to lay a x1 target stream far to the left of a singleton trail? We could create a glider trail using 3 sets of x3 kickbacks, or a block trail with another collection of x3 collisions, but those both mean the same cost as if we were building two trails. That is quite a few helix ships, and I feel like better can be done.

We get to use as many x1 NW rakes as we want from the climber. There are no NW G + N LWSS reactions that rebound a glider to the NE or SE and are repeatable. LWSS reactions that drop still lives are out for this side of the trail, since the helix will plow right into them. No matter what, if we are using a NW rake we need a NE, SE or SW x1 signal to crash into.

We could potentially work this front end at x2 instead of x3, using only the rakes from the climber and a handful of x2 ships to get ourselves started. It would consist of some reaction to convert some number of x1 NW streams colliding with a N *WSS salvo into an x2 NE stream, done twice to get x1 targets. Some gliders would have to be heisenburned somewhere to actually get it to work, since the climber can only provide x1 NW rakes but x1 N LWSS aren't usable. I think it could definitely require fewer helix ships to do things this way at least.

Here's a crappy mockup:

: 92r4rbv.png (37.66 KiB) Viewed 1263 times

Posted: **September 17th, 2016, 12:18 pm**

biggiemac wrote: We could potentially work this front end at x2 instead of x3, using only the rakes from the climber and a handful of x2 ships to get ourselves started.

Interesting idea. When I was trying to come up with an example pattern I ran into problems with the second x1 NW stream colliding with the target site already constructed by the first NW stream. I came up with a workaround as below. Hopefully there exist simple *WSS salvos that can turn our phase-and-color-restricted NW gliders into the desired NE gliders but I have not got around to searching for them yet.

Code: Select all

x = 574, y = 314, rule = B3/S23
561b3o$561bo$b2o559bo$obo$2bo5$542b3o$542bo$543bo7$523b3o$523bo$35b2o
487bo$34bobo$36bo5$504b3o$504bo$505bo7$485b3o$485bo$69b2o415bo$68bobo$
70bo5$466b3o$466bo$467bo7$447b3o$447bo$103b2o343bo$102bobo$104bo5$428b
3o$428bo$429bo7$409b3o$409bo$137b2o271bo$136bobo$138bo5$390b3o$390bo$
391bo7$371b3o$371bo$171b2o199bo$170bobo$172bo5$352b3o$352bo$353bo7$
333b3o$333bo$205b2o127bo$204bobo$206bo4$571b3o$314b3o254bo$314bo257bo$
315bo5$4b2o$5b2o545b3o$4bo290b3o254bo$295bo257bo$239b2o55bo$238bobo$
240bo4$533b3o$276b3o254bo$276bo257bo$277bo5$38b2o$39b2o473b3o$38bo475b
o$515bo4$264bo$264bo$264bo$495b3o$238b3o254bo$238bo257bo$239bo5$72b2o$
73b2o401b3o$72bo403bo$477bo7$457b3o$200b3o254bo$200bo257bo$201bo5$106b
2o$107b2o329b3o$106bo331bo$439bo7$419b3o$162b3o254bo$162bo257bo$163bo
5$140b2o$141b2o257b3o$140bo259bo$401bo4$262bo$262bo$262bo$381b3o$124b
3o254bo$124bo257bo$125bo5$174b2o$175b2o185b3o$174bo187bo$363bo7$343b3o
$86b3o254bo$86bo257bo$87bo5$208b2o$209b2o113b3o$208bo115bo$325bo7$305b
3o$48b3o254bo$48bo257bo$49bo5$242b2o$243b2o41b3o$242bo43bo$287bo4$260b
o$260bo$260bo$267b3o$267bo$268bo21$260b2o$259bo2bo$259bo2bo$260b2o24$
259b2o$258bo2bo$258bo2bo$259b2o!

EDIT: Silly me. The two glider collision giving a blinker is transparent to one of the input lanes, therefore the following is a simpler alternative:

Code: Select all

x = 293, y = 109, rule = B3/S23
12b2o$11bobo$13bo$281b3o$281bo$282bo7$262b3o$262bo$263bo4$46b2o$45bobo
$47bo$243b3o$243bo$244bo7$224b3o$224bo$225bo4$80b2o$b2o76bobo$obo78bo$
2bo202b3o$205bo84b3o$206bo83bo$291bo6$186b3o$186bo84b3o$187bo83bo$272b
o3$114b2o$35b2o76bobo$34bobo78bo$36bo130b3o$167bo84b3o$168bo83bo$253bo
6$148b3o$148bo84b3o$149bo83bo$234bo4$69b2o$68bobo$70bo$214b3o$214bo$
215bo$141bo$141bo$141bo4$195b3o$195bo$196bo4$103b2o$102bobo$104bo$176b
3o$176bo$177bo7$157b3o$157bo$158bo$140bo$140bo$140bo!

Posted: **September 17th, 2016, 7:00 pm**

Some repeatable 2 *WSS salvos that rebound a glider.

Code: Select all

x = 1893, y = 92, rule = B3/S23
80b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o
98b2o108b2o98b2o98b2o98b2o$80bobo97bobo97bobo97bobo97bobo97bobo97bobo
97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo107bobo97bobo97bobo97b
obo$80bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo109bo
99bo99bo99bo16$42b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o
98b2o98b2o98b2o98b2o108b2o98b2o98b2o98b2o$42bobo97bobo97bobo97bobo97bo
bo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo107bobo
97bobo97bobo97bobo$42bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99b
o99bo99bo109bo99bo99bo99bo12$899bo$898b3o$897b2obo$897b3o$4b2o98b2o91b
3o4b2o98b2o98b2o98b2o98b2o98b2o98b2o92b2o4b2o98b2o98b2o98b2o98b2o94bo
3b2o108b2o98b2o98b2o98b2o$4bobo97bobo89bo2bo4bobo91b3o3bobo97bobo97bob
o91bo5bobo92bo4bobo97bobo97bobo91b3o3bobo97bobo97bobo97bobo92b3o2bobo
107bobo97bobo97bobo97bobo$4bo95bo3bo94bo4bo92bo2bo3bo99bo99bo92b3o4bo
93b3o3bo99bo99bo93bo2bo2bo99bo93b3o3bo99bo94bob2obo105bo3bo99bo99bo99b
o$99b3o93bo3bo100bo196b3o96b2obo97b2obo99b3o195bo199bo2bo198b3o106b3o$
bo6b3o88bob2o96bo96bo3bo106bo88bo2bo6bo89b3o7bo90b3o100bo2bo97b3o94bo
3bo97b3o95bo107bo93b2o107bob2o6bo91b3o197b3o$3o4bo2bo89b3o93bobo101bo
105b3o90bo5b3o89b2o6b3o89b3o100bo100bo2bo93bo101bo2bo94bo3bo102b3o202b
3o5b3o89bo2bo101b3o92bo2bo$ob2o6bo89b3o102bo91bobo99bo5b2obo90bo4b2obo
96b2obo90b2o100bo3bo96bo97bobo98bo97bo106bob2o97bo103b2o5b2obo92bo100b
o2bo95bo$b3o2bo3bo89b2o102b3o191b3o4b3o88bobo5b3o97b3o193bo100bo3bo
194bo3bo94bobo104b3o96b3o109b3o93bo103bo95bo$b3o2bo3bo193bob2o189b2obo
4b3o96b3o97b3o194bobo97bo198bo205b2o97bob2o108b3o90bobo104bo92bobo$b2o
7bo194b3o92b3o94b3o6b2o97b2o98b2o295bobo92b3o101bobo302b3o108b3o194bob
o$7bobo96b3o96b2o92bo2bo94b3o596bo2bo198bo207b2o110b2o$106bo2bo192bo
95b2o300b3o296bo197b3o$106bo195bo397bo2bo95b3o197bo196b2obo414bo199bo$
106bo3bo188bobo398bo98bo2bo193bobo98b3o96b3o104b3o307b3o197b3o$106bo
593bo98bo101bo194bo2bo97b2o103bo2bo306b2obo196b2obo$107bobo591bobo95bo
100b3o196bo205bo306b3o104bo92b3o$800bobo96b2obo196bo201bo3bo307b2o103b
3o91b3o$899b3o194bobo206bo412bob2o90b3o$199b3o26bo671b2o400bobo97bo
316b3o91b2o$38b3o157bo2bo26b2o70b3o297bo100bo298b3o25b2o371b3o315b2o$
40bo61bo98bo25bobo69bo2bo296b3o98b3o297bo2bo23bobo170b3o25bo172bob2o
107bo36b2o$39bo61b3o93bo3bo100bo127b2o67b3o96b2obo32b2o63b2obo99b3o
195bo28bo170bo2bo24b2o172b3o106b3o36b2o$3bo6b3o88bob2o96bo96bo3bo106bo
21b2o65bo2bo6bo89b3o7bo26b2o62b3o100bo2bo97b3o94bo3bo97b3o95bo26bobo
78bo93b2o107bob2o6bo27bo63b3o22b2o173b3o22b2o$2b3o4bo2bo89b3o93bobo
101bo31b3o71b3o19bo70bo5b3o27bo61b2o6b3o24bo64b3o100bo100bo2bo30bo62bo
101bo2bo94bo3bo102b3o26bo175b3o5b3o89bo2bo21bobo77b3o92bo2bo21bobo$2bo
b2o6bo89b3o29b2o71bo91bobo34bo64bo5b2obo90bo4b2obo27b2o67b2obo90b2o28b
o71bo3bo96bo33b2o62bobo98bo97bo106bob2o25b2o70bo103b2o5b2obo92bo23bo
76bo2bo95bo23bo$3b3o2bo3bo89b2o31b2o69b3o126bo64b3o4b3o88bobo5b3o27bob
o67b3o121b2o70bo100bo3bo28bobo163bo3bo23b3o68bobo104b3o24bobo69b3o23b
2o84b3o93bo103bo95bo$3b3o2bo3bo121bo71bob2o189b2obo4b3o96b3o97b3o120bo
bo71bobo27b2o68bo198bo29bo175b2o97bob2o23b2o83b3o90bobo104bo92bobo$3b
2o7bo194b3o92b3o94b3o6b2o97b2o98b2o223bobo69bobo92b3o101bobo25bo276b3o
22bo85b3o194bobo$9bobo96b3o96b2o92bo2bo94b3o432bo163bo2bo198bo207b2o
110b2o225b2o$108bo2bo192bo95b2o300b3o296bo197b3o546b2o$108bo195bo397bo
2bo95b3o197bo196b2obo414bo130bo68bo$108bo3bo188bobo398bo98bo2bo193bobo
98b3o96b3o104b3o307b3o197b3o$108bo593bo98bo101bo194bo2bo97b2o103bo2bo
306b2obo196b2obo$109bobo591bobo95bo100b3o196bo205bo306b3o104bo92b3o$
802bobo96b2obo196bo201bo3bo307b2o103b3o91b3o$901b3o194bobo206bo412bob
2o90b3o$201b3o698b2o400bobo97bo316b3o91b2o$200bo2bo98b3o297bo100bo298b
3o398b3o315b2o$104bo98bo97bo2bo296b3o98b3o297bo2bo196b3o198bob2o107bo$
103b3o93bo3bo100bo196b3o96b2obo97b2obo99b3o195bo199bo2bo198b3o106b3o$
5bo6b3o88bob2o96bo96bo3bo106bo88bo2bo6bo89b3o7bo90b3o100bo2bo97b3o94bo
3bo97b3o95bo107bo93b2o107bob2o6bo91b3o197b3o$4b3o4bo2bo89b3o93bobo101b
o105b3o90bo5b3o89b2o6b3o89b3o100bo100bo2bo93bo101bo2bo94bo3bo102b3o
202b3o5b3o89bo2bo101b3o92bo2bo$4bob2o6bo89b3o102bo91bobo99bo5b2obo90bo
4b2obo96b2obo90b2o100bo3bo96bo97bobo98bo97bo106bob2o97bo103b2o5b2obo
92bo100bo2bo95bo$5b3o2bo3bo89b2o102b3o191b3o4b3o88bobo5b3o97b3o193bo
100bo3bo194bo3bo94bobo104b3o96b3o109b3o93bo103bo95bo$5b3o2bo3bo193bob
2o189b2obo4b3o96b3o97b3o194bobo97bo198bo205b2o97bob2o108b3o90bobo104bo
92bobo$5b2o7bo194b3o92b3o94b3o6b2o97b2o98b2o295bobo92b3o101bobo302b3o
108b3o194bobo$11bobo96b3o96b2o92bo2bo94b3o596bo2bo198bo207b2o110b2o$
110bo2bo192bo95b2o300b3o296bo197b3o$110bo195bo397bo2bo95b3o197bo196b2o
bo414bo199bo$110bo3bo188bobo398bo98bo2bo193bobo98b3o96b3o104b3o307b3o
197b3o$110bo593bo98bo296bo2bo97b2o103bo2bo306b2obo196b2obo$111bobo591b
obo95bo299bo205bo306b3o104bo92b3o$804bobo296bo201bo3bo307b2o103b3o91b
3o$1100bobo206bo412bob2o90b3o$1306bobo414b3o91b2o$1723b2o!

I didn't look at ones where the first collision was with a HWSS. Perhaps these will be enough. There are 2 options where a LWSS is just used as a heisenburp, meaning it could continue upwards. Maybe the lower half could use one of those options, and the surviving LWSS could filter out the upper half, making a total of 5 x2 *WSS streams needed to construct the x1 target trail. If not, it's going to be 6 streams, still far better than the 12+ x3 streams needed if the target is constructed via the fanouts.

Posted: **September 17th, 2016, 7:59 pm**

A problem that I have been running into is that NE gliders cannot cross x1 NW streams. Therefore something like below is the best way I can think of getting two x2 NE streams. Am I missing something?

Code: Select all

x = 761, y = 875, rule = B3/S23
354b2o$354bobo$354bo7$335b2o$335bobo$335bo7$316b2o$316bobo$316bo441b2o
$758bobo$758bo5$297b2o$297bobo$297bo441b2o$739bobo$739bo5$278b2o$278bo
bo$278bo441b2o$720bobo$720bo5$259b2o$259bobo$259bo441b2o$701bobo$701bo
5$240b2o$240bobo$240bo441b2o$682bobo$682bo5$221b2o$221bobo$221bo441b2o
$663bobo$663bo5$202b2o$202bobo$202bo441b2o$644bobo$644bo5$183b2o$183bo
bo$183bo441b2o$625bobo$625bo5$164b2o$164bobo$164bo441b2o$606bobo$606bo
5$145b2o$145bobo$145bo441b2o$587bobo$587bo5$126b2o$126bobo$126bo441b2o
$568bobo$568bo5$107b2o$107bobo$107bo441b2o$549bobo$549bo5$88b2o$88bobo
$88bo441b2o$530bobo$530bo5$69b2o$69bobo$69bo441b2o$511bobo$511bo5$50b
2o$50bobo$50bo441b2o$492bobo$492bo5$31b2o$31bobo$31bo441b2o$473bobo$
473bo7$454b2o$454bobo$454bo7$435b2o$435bobo$5b3o427bo$5bo2bo$5bo$5bo$
6bobo$14bo$13b3o$12b2obo$12b3o$13b2o3$2bo$b3o$2obo$3o$b2o2$7b3o$7bo2bo
$7bo$7bo$8bobo$16bo$15b3o$14b2obo$14b3o$15b2o3$4bo$3b3o$2b2obo$2b3o$3b
2o2$9b3o$9bo2bo$9bo$9bo$10bobo$18bo$17b3o$16b2obo$16b3o$17b2o3$6bo$5b
3o$4b2obo$4b3o$5b2o2$11b3o$11bo2bo$11bo$11bo$12bobo$20bo$19b3o$18b2obo
$18b3o$19b2o3$8bo$7b3o$6b2obo$6b3o$7b2o2$13b3o$13bo2bo$13bo$13bo$14bob
o$22bo$21b3o$20b2obo$20b3o$21b2o3$10bo$9b3o$8b2obo$8b3o$9b2o2$15b3o$
15bo2bo$15bo$15bo$16bobo$24bo$23b3o$22b2obo$22b3o$23b2o3$12bo$11b3o$
10b2obo$10b3o$11b2o2$17b3o$17bo2bo$17bo$17bo$18bobo$26bo$25b3o$24b2obo
$24b3o$25b2o3$14bo$13b3o$12b2obo$12b3o$13b2o2$19b3o$19bo2bo$19bo$19bo$
20bobo$28bo$27b3o$26b2obo$26b3o$27b2o3$16bo$15b3o$14b2obo$14b3o$15b2o
2$21b3o$21bo2bo$21bo$21bo$22bobo$30bo$29b3o$28b2obo$28b3o$29b2o3$18bo$
17b3o$16b2obo$16b3o$17b2o185$83b3o$83bo2bo$83bo$83bo$84bobo2$89b3o$89b
o2bo$89bo$89bo$90bobo8$85b3o$85bo2bo$85bo$85bo$86bobo2$91b3o$91bo2bo$
91bo$91bo$92bobo8$87b3o$87bo2bo$87bo$87bo$88bobo2$93b3o$93bo2bo$93bo$
93bo$94bobo8$89b3o$89bo2bo$89bo$89bo$90bobo2$95b3o$95bo2bo$95bo$95bo$
96bobo8$91b3o$91bo2bo$91bo$91bo$92bobo2$97b3o$97bo2bo$97bo$97bo$98bobo
8$93b3o$93bo2bo$93bo$93bo$94bobo2$99b3o$99bo2bo$99bo$99bo$100bobo96$
218b3o$217bo2bo$220bo$216bo3bo$220bo$217bobo5$217b3o$216bo2bo$219bo$
219bo$216bobo4$220b3o$219bo2bo$222bo$218bo3bo$222bo$219bobo5$219b3o$
218bo2bo$221bo$221bo$218bobo4$222b3o$221bo2bo$224bo$220bo3bo$224bo$
221bobo5$221b3o$220bo2bo$223bo$223bo$220bobo4$224b3o$223bo2bo$226bo$
222bo3bo$226bo$223bobo5$223b3o$222bo2bo$225bo$225bo$222bobo4$226b3o$
225bo2bo$228bo$224bo3bo$228bo$225bobo5$225b3o$224bo2bo$227bo$227bo$
224bobo4$228b3o$227bo2bo$230bo$226bo3bo$230bo$227bobo5$227b3o$226bo2bo
$229bo$229bo$226bobo4$230b3o$229bo2bo$232bo$228bo3bo$232bo$229bobo5$
229b3o$228bo2bo$231bo$231bo$228bobo4$232b3o$231bo2bo$234bo$230bo3bo$
234bo$231bobo5$231b3o$230bo2bo$233bo$233bo$230bobo4$234b3o$233bo2bo$
236bo$232bo3bo$236bo$233bobo5$233b3o$232bo2bo$235bo$235bo$232bobo!

Posted: **September 17th, 2016, 8:40 pm**

Yep, I've also been a bit bummed NW and NE streams cannot pass through each other at x1. One can do things with a zig-zag, recycling the x2 stream after it makes the first blinker.

Code: Select all

x = 288, y = 413, rule = LifeHistory
206.3A$206.A$207.A7$187.3A$187.A$188.A7$168.3A$168.A$169.A7$149.3A$
149.A$150.A7$130.3A$130.A$131.A7$111.3A$111.A$112.A7$92.3A$92.A$93.A
7$73.3A$73.A$74.A7$54.3A$54.A$55.A7$35.3A$35.A$36.A7$16.3A$16.A$17.A$
13.3A$12.A2.A$15.A$11.A3.A$15.A$12.A.A4$10.3A$10.A2.A$10.A$10.A$11.A.
A2$278.3A$278.A$279.A$15.3A$14.A2.A$17.A$.3A9.A3.A26.2A$A2.A13.A25.A.
A$3.A10.A.A28.A$3.A255.3A$A.A256.A$260.A$12.3A$12.A2.A$12.A$12.A$13.A
.A2$240.3A$240.A$241.A$17.3A$16.A2.A$19.A$3.3A9.A3.A58.2A$2.A2.A13.A
57.A.A$5.A10.A.A60.A$5.A215.3A$2.A.A216.A$222.A$14.3A$14.A2.A$14.A$
14.A$15.A.A2$202.3A$202.A$203.A$19.3A$18.A2.A$21.A$5.3A9.A3.A90.2A$4.
A2.A13.A89.A.A$7.A10.A.A92.A$7.A175.3A$4.A.A176.A$184.A$16.3A$16.A2.A
$16.A$16.A$17.A.A2$164.3A$164.A$165.A$21.3A$20.A2.A$23.A$7.3A9.A3.A$
6.A2.A13.A$9.A10.A.A122.2A$9.A135.3A.A135.3A$6.A.A138.2A.A134.A$150.A
135.A$18.3A128.A$18.A2.A126.A$18.A126.3A$18.A$19.A.A2$126.3A137.3A$
126.A139.A$127.A139.A$23.3A$22.A2.A$25.A$9.3A9.A3.A$8.A2.A13.A$11.A
10.A.A$11.A235.3A$8.A.A236.A$248.A$20.3A$20.A2.A$20.A$20.A$21.A.A2$
89.2A137.3A$89.2A137.A$229.A$25.3A58.A$24.A2.A57.A.2A.A$27.A56.A5.A$
11.3A9.A3.A62.A$10.A2.A13.A57.A.A$13.A10.A.A$13.A195.3A$10.A.A196.A$
83.3A124.A$22.3A58.A2.A$22.A2.A57.A$22.A60.A$22.A61.A.A$23.A.A2$190.
3A$190.A$88.3A100.A$27.3A57.A2.A$26.A2.A60.A55.A$29.A56.A3.A55.A$13.
3A9.A3.A60.A27.2A26.A$12.A2.A13.A57.A.A27.A.A$15.A10.A.A90.A$15.A155.
3A$12.A.A156.A$85.3A84.A$24.3A58.A2.A$24.A2.A57.A$24.A60.A$24.A61.A.A
$25.A.A2$152.3A$152.A$90.3A60.A$29.3A57.A2.A$28.A2.A60.A$31.A56.A3.A$
15.3A9.A3.A60.A$14.A2.A13.A57.A.A$17.A10.A.A$17.A$14.A.A$87.3A$26.3A
58.A2.A$26.A2.A57.A$26.A60.A$26.A61.A.A$27.A.A2$114.3A$114.A$92.3A20.
A$31.3A57.A2.A$30.A2.A60.A$33.A56.A3.A$17.3A9.A3.A60.A$16.A2.A13.A57.
A.A$19.A10.A.A$19.A$16.A.A$89.3A14.3A$28.3A58.A2.A12.A2.A$28.A2.A57.A
18.A$28.A60.A18.A$28.A61.A.A12.A.A$29.A.A4$94.3A$33.3A57.A2.A$32.A2.A
60.A$35.A56.A3.A$19.3A9.A3.A60.A$18.A2.A13.A57.A.A$21.A10.A.A$21.A$
18.A.A$91.3A14.3A$30.3A58.A2.A12.A2.A$30.A2.A57.A18.A$30.A60.A18.A$
30.A61.A.A12.A.A$31.A.A4$96.3A$35.3A57.A2.A$34.A2.A60.A$37.A56.A3.A$
21.3A9.A3.A60.A$20.A2.A13.A57.A.A$23.A10.A.A$23.A$20.A.A$93.3A14.3A$
32.3A58.A2.A12.A2.A$32.A2.A57.A18.A$32.A60.A18.A$32.A61.A.A12.A.A$33.
A.A4$98.3A$37.3A57.A2.A$36.A2.A60.A$39.A56.A3.A$23.3A9.A3.A60.A$22.A
2.A13.A57.A.A$25.A10.A.A$25.A$22.A.A$95.3A14.3A$34.3A58.A2.A12.A2.A$
34.A2.A57.A18.A$34.A60.A18.A$34.A61.A.A12.A.A$35.A.A4$100.3A$39.3A57.
A2.A$38.A2.A60.A$41.A56.A3.A$25.3A9.A3.A60.A$24.A2.A13.A57.A.A$27.A
10.A.A$27.A$24.A.A$97.3A14.3A$36.3A58.A2.A12.A2.A$36.A2.A57.A18.A$36.
A60.A18.A$36.A61.A.A12.A.A$37.A.A4$102.3A$41.3A57.A2.A$40.A2.A60.A$
43.A56.A3.A$27.3A9.A3.A60.A$26.A2.A13.A57.A.A$29.A10.A.A$29.A$26.A.A$
99.3A14.3A$38.3A58.A2.A12.A2.A$38.A2.A57.A18.A$38.A60.A18.A$38.A61.A.
A12.A.A$39.A.A4$104.3A$43.3A57.A2.A$42.A2.A60.A$45.A56.A3.A$29.3A9.A
3.A60.A$28.A2.A13.A57.A.A$31.A10.A.A$31.A$28.A.A$101.3A14.3A$40.3A58.
A2.A12.A2.A$40.A2.A57.A18.A$40.A60.A18.A$40.A61.A.A12.A.A$41.A.A4$
106.3A$45.3A57.A2.A$44.A2.A60.A$47.A56.A3.A$31.3A9.A3.A60.A$30.A2.A
13.A57.A.A$33.A10.A.A$33.A$30.A.A$103.3A14.3A$42.3A58.A2.A12.A2.A$42.
A2.A57.A18.A$42.A60.A18.A$42.A61.A.A12.A.A$43.A.A4$108.3A$47.3A57.A2.
A$46.A2.A60.A$49.A56.A3.A$33.3A9.A3.A60.A$32.A2.A13.A57.A.A$35.A10.A.
A$35.A$32.A.A$105.3A$44.3A58.A2.A$44.A2.A57.A$44.A60.A$44.A61.A.A$45.
A.A!

I'm just hoping that doesn't end up costing more space than it saves. It will probably require the dirty singleton constructor to build the x2 *WSS streams, rather than the clean one, so that they can be packed tightly enough.

This whole ship is resistant to top-down construction, since everything must be spaced at the top such that it aligns perfectly at the bottom. And when modular restrictions come into play, the chinese remainder theorem helps us out but not without giving some pretty big numbers, given that 17 and 19 are both in play. The above isn't actually possible, since the NW streams have a specific horizontal restriction. Consecutive NW rakes must have offset (-4, 2x). I am working out a version of the above pattern that respects this, and I'll add lifehistory comments designating the amount by which pieces can be shifted.

Posted: **September 17th, 2016, 9:09 pm**

That looks promising. I didn't find that reflector in my search so here is what I came up with instead. I realised that the NW rakes need to have a fixed sequence of horizontal spacing but I didn't want to hurt my head with that just yet!

Code: Select all

x = 1445, y = 1026, rule = B3/S23
354b2o$354bobo$354bo7$335b2o$335bobo$335bo7$316b2o$316bobo$316bo441b2o
$758bobo$758bo5$297b2o$297bobo1030b2o$297bo441b2o589bobo$739bobo588bo$
739bo5$278b2o$278bobo1030b2o$278bo441b2o589bobo$720bobo588bo$720bo5$
259b2o$259bobo1030b2o$259bo441b2o589bobo$701bobo588bo$701bo5$240b2o$
240bobo1030b2o$240bo441b2o589bobo$682bobo588bo$682bo5$221b2o$221bobo
1030b2o$221bo441b2o589bobo$663bobo588bo$663bo5$202b2o$202bobo1030b2o$
202bo441b2o589bobo$644bobo588bo$644bo5$183b2o$183bobo1030b2o$183bo441b
2o589bobo$625bobo588bo$625bo5$164b2o$164bobo1030b2o$164bo441b2o589bobo
$606bobo588bo$606bo5$145b2o$145bobo1030b2o$145bo441b2o589bobo$587bobo
588bo$587bo5$126b2o$126bobo1030b2o$126bo441b2o589bobo$568bobo588bo$
568bo5$107b2o$107bobo1030b2o$107bo441b2o589bobo$549bobo588bo$549bo5$
88b2o$88bobo1030b2o$88bo441b2o589bobo$530bobo588bo$530bo5$69b2o$69bobo
1030b2o$69bo441b2o589bobo$511bobo588bo$511bo5$50b2o$50bobo1030b2o$50bo
441b2o589bobo$492bobo588bo$492bo5$31b2o$31bobo1030b2o$31bo441b2o589bob
o$473bobo588bo$473bo6$1045b2o$454b2o589bobo$454bobo588bo$454bo6$1026b
2o414b2o$435b2o589bobo413bobo$435bobo588bo415bo$5b3o427bo$5bo2bo$5bo$
5bo$6bobo$14bo$13b3o991b2o414b2o$12b2obo991bobo413bobo$12b3o992bo415bo
$13b2o3$2bo$b3o$2obo$3o1401b2o$b2o1401bobo$1404bo$7b3o$7bo2bo$7bo$7bo$
8bobo$16bo$15b3o1367b2o$14b2obo1367bobo$14b3o1368bo$15b2o3$4bo$3b3o$2b
2obo$2b3o1361b2o$3b2o1361bobo$1366bo$9b3o$9bo2bo$9bo$9bo$10bobo$18bo$
17b3o1327b2o$16b2obo1327bobo$16b3o1328bo$17b2o3$6bo$5b3o$4b2obo$4b3o
1321b2o$5b2o1321bobo$1328bo$11b3o$11bo2bo$11bo$11bo$12bobo$20bo$19b3o
1287b2o$18b2obo1287bobo$18b3o1288bo$19b2o3$8bo$7b3o$6b2obo$6b3o1281b2o
$7b2o1281bobo$1290bo$13b3o$13bo2bo$13bo$13bo$14bobo$22bo$21b3o1247b2o$
20b2obo1247bobo$20b3o1248bo$21b2o3$10bo$9b3o$8b2obo$8b3o1241b2o$9b2o
1241bobo$1252bo$15b3o$15bo2bo$15bo$15bo$16bobo$24bo$23b3o1207b2o$22b2o
bo1207bobo$22b3o1208bo$23b2o3$12bo$11b3o$10b2obo$10b3o1201b2o$11b2o
1201bobo$1214bo$17b3o$17bo2bo$17bo$17bo$18bobo$26bo$25b3o1167b2o$24b2o
bo1167bobo$24b3o1168bo$25b2o3$14bo$13b3o$12b2obo$12b3o1161b2o$13b2o
1161bobo$1176bo$19b3o$19bo2bo$19bo$19bo$20bobo$28bo$27b3o1127b2o$26b2o
bo1127bobo$26b3o1128bo$27b2o3$16bo$15b3o$14b2obo$14b3o1121b2o$15b2o
1121bobo$1138bo$21b3o$21bo2bo$21bo$21bo$22bobo$30bo$29b3o1087b2o$28b2o
bo1087bobo$28b3o1088bo$29b2o3$18bo$17b3o$16b2obo$16b3o$17b2o187$82b3o$
82bo2bo$82bo$82bo$83bobo$91bo$90b3o$89b2obo$89b3o$90b2o9$84b3o$84bo2bo
$84bo$84bo$85bobo$93bo$92b3o$91b2obo$91b3o$92b2o9$86b3o$86bo2bo$86bo$
86bo$87bobo$95bo$94b3o$93b2obo$93b3o$94b2o9$88b3o$88bo2bo$88bo$88bo$
89bobo$97bo$96b3o$95b2obo$95b3o$96b2o9$90b3o$90bo2bo$90bo$90bo$91bobo$
99bo$98b3o$97b2obo$97b3o$98b2o9$92b3o$92bo2bo$92bo$92bo$93bobo$101bo$
100b3o$99b2obo$99b3o$100b2o9$94b3o$94bo2bo$94bo$94bo$95bobo$103bo$102b
3o$101b2obo$101b3o$102b2o9$96b3o$96bo2bo$96bo$96bo$97bobo$105bo$104b3o
$103b2obo$103b3o$104b2o9$98b3o$98bo2bo$98bo$98bo$99bobo$107bo$106b3o$
105b2obo$105b3o$106b2o9$100b3o$100bo2bo$100bo$100bo$101bobo$109bo$108b
3o$107b2obo$107b3o$108b2o174$218b3o$218bo2bo$218bo$218bo3bo$218bo$219b
obo5$217b3o$217bo2bo$217bo$217bo$218bobo4$220b3o$220bo2bo$220bo$220bo
3bo$220bo$221bobo5$219b3o$219bo2bo$219bo$219bo$220bobo4$222b3o$222bo2b
o$222bo$222bo3bo$222bo$223bobo5$221b3o$221bo2bo$221bo$221bo$222bobo4$
224b3o$224bo2bo$224bo$224bo3bo$224bo$225bobo5$223b3o$223bo2bo$223bo$
223bo$224bobo4$226b3o$226bo2bo$226bo$226bo3bo$226bo$227bobo5$225b3o$
225bo2bo$225bo$225bo$226bobo4$228b3o$228bo2bo$228bo$228bo3bo$228bo$
229bobo5$227b3o$227bo2bo$227bo$227bo$228bobo4$230b3o$230bo2bo$230bo$
230bo3bo$230bo$231bobo5$229b3o$229bo2bo$229bo$229bo$230bobo4$232b3o$
232bo2bo$232bo$232bo3bo$232bo$233bobo5$231b3o$231bo2bo$231bo$231bo$
232bobo4$234b3o$234bo2bo$234bo$234bo3bo$234bo$235bobo5$233b3o$233bo2bo
$233bo$233bo$234bobo!

Posted: **September 17th, 2016, 9:50 pm**

Here's the modular arithmetic all worked out for the transparent blinker trail. I'm not sure if there is a value of M where the spare glider heisenburns in the *WSS streams, I didn't bother to work out whether it was invariant.

Code: Select all

x = 1222, y = 1380, rule = LifeHistory
885.3A$885.A$886.A7$866.3A$866.A$867.A7$847.3A$847.A$848.A7$828.3A$
828.A$829.A7$809.3A$809.A$810.A7$790.3A$790.A$791.A7$771.3A$771.A$
772.A7$752.3A$752.A$753.A7$733.3A$733.A$734.A7$714.3A$714.A$715.A7$
695.3A$695.A$696.A7$676.3A$676.A$677.A7$657.3A$657.A$658.A7$638.3A$
638.A$639.A7$619.3A$619.A$620.A7$600.3A$600.A$601.A7$581.3A$581.A$
582.A7$562.3A$562.A$563.A7$543.3A$543.A$544.A7$524.3A$524.A$525.A7$
505.3A$505.A$506.A7$486.3A$486.A$487.A7$467.3A$467.A$468.A2$330.D$
329.3D$328.D.D.D$327.D2.D2.D$330.D$330.D117.3A$330.D117.A$330.D118.A$
330.D$330.D$330.D$330.D3$429.3A$429.A$430.A3$319.D6.D2.4D2.D3.D$319.D
6.D2.D2.D2.2D2.D$319.D6.D2.D2.D2.2D2.D$316.7D3.D2.4D2.D.D.D$319.D6.D
2.D2.D2.D2.2D70.3A$319.D6.D2.D2.D2.D2.2D70.A$319.D6.D2.4D2.D3.D71.A7$
391.3A$330.D60.A$330.D61.A$330.D$330.D$330.D$330.D$330.D$330.D$327.D
2.D2.D38.3A$328.D.D.D39.A$329.3D41.A$330.D6$353.3A$353.A$354.A7$334.
3A$334.A$335.A7$315.3A$315.A$316.A7$296.3A$296.A$297.A7$277.3A$277.A$
278.A7$258.3A$258.A$259.A7$239.3A$239.A$240.A7$220.3A$220.A$221.A7$
201.3A$201.A$202.A7$182.3A$182.A$183.A7$163.3A$163.A$164.A7$144.3A$
144.A$145.A7$125.3A$125.A$126.A7$106.3A$106.A$107.A7$87.3A$87.A$88.A
7$68.3A$68.A$69.A7$49.3A$49.A$50.A7$30.3A$30.A$31.A13$15.2A$14.A.A$
16.A8$15.3A$14.A2.A$17.A$.3A9.A3.A$A2.A13.A$3.A10.A.A$3.A$A.A$49.2A$
12.3A33.A.A$12.A2.A34.A$12.A$12.A$13.A.A5$17.3A$16.A2.A$19.A$3.3A9.A
3.A$2.A2.A13.A$5.A10.A.A$5.A$2.A.A$83.2A$14.3A65.A.A$14.A2.A66.A$14.A
$14.A$15.A.A5$19.3A$18.A2.A$21.A$5.3A9.A3.A$4.A2.A13.A$7.A10.A.A$7.A$
4.A.A$117.2A$16.3A97.A.A$16.A2.A98.A$16.A$16.A$17.A.A5$21.3A$20.A2.A$
23.A$7.3A9.A3.A$6.A2.A13.A$9.A10.A.A$9.A$6.A.A$151.2A$18.3A129.A.A$
18.A2.A130.A$18.A$18.A$19.A.A5$23.3A$22.A2.A$25.A969.3A$9.3A9.A3.A
969.A$8.A2.A13.A970.A$11.A10.A.A$11.A$8.A.A$185.2A$20.3A161.A.A$20.A
2.A162.A$20.A955.3A$20.A955.A$21.A.A953.A5$25.3A$24.A2.A$27.A929.3A$
11.3A9.A3.A929.A$10.A2.A13.A930.A$13.A10.A.A$13.A$10.A.A$219.2A$22.3A
193.A.A$22.A2.A194.A$22.A915.3A$22.A915.A$23.A.A913.A5$27.3A$26.A2.A$
29.A889.3A$13.3A9.A3.A889.A$12.A2.A13.A890.A$15.A10.A.A$15.A$12.A.A$
253.2A$24.3A225.A.A$24.A2.A226.A$24.A875.3A$24.A875.A$25.A.A873.A5$
29.3A$28.A2.A$31.A849.3A$15.3A9.A3.A849.A$14.A2.A13.A850.A$17.A10.A.A
$17.A$14.A.A$287.2A$26.3A257.A.A$26.A2.A258.A$26.A835.3A$26.A835.A$
27.A.A833.A5$31.3A$30.A2.A$33.A809.3A$17.3A9.A3.A809.A$16.A2.A13.A
810.A$19.A10.A.A$19.A$16.A.A$321.2A$28.3A289.A.A$28.A2.A290.A$28.A
795.3A$28.A795.A$29.A.A793.A5$33.3A$32.A2.A$35.A769.3A$19.3A9.A3.A
769.A$18.A2.A13.A770.A$21.A10.A.A$21.A$18.A.A$355.2A$30.3A321.A.A$30.
A2.A322.A$30.A755.3A$30.A755.A$31.A.A753.A5$35.3A$34.A2.A$37.A729.3A$
21.3A9.A3.A729.A$20.A2.A13.A730.A$23.A10.A.A$23.A$20.A.A$389.2A$32.3A
353.A.A$32.A2.A354.A$32.A715.3A$32.A715.A$33.A.A713.A5$37.3A$36.A2.A$
39.A689.3A$23.3A9.A3.A689.A$22.A2.A13.A690.A$25.A10.A.A$25.A$22.A.A$
423.2A$34.3A385.A.A$34.A2.A386.A$34.A675.3A$34.A675.A$35.A.A673.A4$
454.248D$39.3A412.D246.D$38.A2.A412.D246.D$41.A412.D236.3A7.D$25.3A9.
A3.A412.D236.A9.D$24.A2.A13.A412.D237.A8.D$27.A10.A.A413.D246.D$27.A
426.D246.D$24.A.A427.D86.4D2.5D2.D3.D2.4D2.3D131.D$454.D2.2A82.D7.D4.
D3.D2.D5.D2.D130.D$36.3A415.D.A.A82.D7.D5.D.D3.D5.D3.D129.D$36.A2.A
414.D3.A82.3D5.D6.D4.3D3.D3.D129.D$36.A417.D86.D7.D5.D.D3.D5.D3.D100.
3A26.D$36.A417.D86.D7.D4.D3.D2.D5.D2.D101.A28.D$37.A.A414.D86.D5.5D2.
D3.D2.4D2.3D103.A27.D$454.D246.D$454.D246.D$454.D246.D$454.D246.D$41.
3A410.D246.D$40.A2.A410.D246.D$43.A410.D198.3A45.D$27.3A9.A3.A410.D
198.A47.D$26.A2.A13.A410.D199.A46.D$29.A10.A.A411.D246.D$29.A424.D
246.D$26.A.A425.D246.D$454.D36.2A208.D$38.3A413.D35.A.A208.D$38.A2.A
412.D37.A208.D$38.A415.D179.3A64.D$38.A415.D179.A66.D$39.A.A412.D180.
A65.D$454.D246.D$454.D246.D$454.D246.D$454.D246.D$43.3A408.D246.D$42.
A2.A408.D246.D$45.A408.D160.3A83.D$29.3A9.A3.A408.D160.A85.D$28.A2.A
13.A408.D161.A84.D$31.A10.A.A409.D246.D$31.A422.D246.D$28.A.A423.D
246.D$454.D70.2A174.D$40.3A411.D69.A.A174.D$40.A2.A410.D71.A174.D$40.
A413.D141.3A102.D$40.A413.D141.A104.D$41.A.A410.D142.A103.D$454.D246.
D$454.D246.D$454.D246.D$454.D246.D$45.3A406.D246.D$44.A2.A406.D246.D$
47.A406.D122.3A121.D$31.3A9.A3.A406.D122.A123.D$30.A2.A13.A406.D123.A
122.D$33.A10.A.A407.248D$33.A$30.A.A2$42.3A$42.A2.A512.2A$42.A515.3A.
A$42.A517.2A.A$43.A.A517.A$562.A$561.A$558.3A2$47.3A$46.A2.A$49.A489.
3A$33.3A9.A3.A489.A$32.A2.A13.A490.A$35.A10.A.A$35.A$32.A.A2$44.3A$
44.A2.A$44.A$44.A$45.A.A5$49.3A$48.A2.A$51.A449.3A$35.3A9.A3.A449.A$
34.A2.A13.A450.A$37.A10.A.A$37.A$34.A.A2$46.3A$46.A2.A$46.A$46.A$47.A
.A5$51.3A$50.A2.A$53.A409.3A753.3A$37.3A9.A3.A409.A755.A$36.A2.A13.A
410.A755.A$39.A10.A.A$39.A519.A$36.A.A520.A$559.A$48.3A$48.A2.A$48.A
1151.3A$48.A1151.A$49.A.A1149.A5$53.3A$52.A2.A$55.A369.3A753.3A$39.3A
9.A3.A369.A755.A$38.A2.A13.A370.A755.A$41.A10.A.A$41.A$38.A.A2$50.3A$
50.A2.A$50.A1111.3A$50.A1111.A$51.A.A1109.A5$55.3A$54.A2.A$57.A329.3A
753.3A$41.3A9.A3.A329.A755.A$40.A2.A13.A330.A755.A$43.A10.A.A$43.A$
40.A.A2$52.3A$52.A2.A$52.A1071.3A$52.A1071.A$53.A.A1069.A5$57.3A$56.A
2.A$59.A289.3A753.3A$43.3A9.A3.A289.A755.A$42.A2.A13.A290.A755.A$45.A
10.A.A$45.A511.A$42.A.A512.A$557.A$54.3A$54.A2.A$54.A1031.3A$54.A
1031.A$55.A.A1029.A5$59.3A$58.A2.A$61.A249.3A753.3A$45.3A9.A3.A249.A
755.A$44.A2.A13.A250.A755.A$47.A10.A.A$47.A$44.A.A2$56.3A$56.A2.A$56.
A991.3A$56.A991.A$57.A.A989.A5$61.3A$60.A2.A$63.A209.3A753.3A$47.3A9.
A3.A209.A755.A$46.A2.A13.A210.A755.A$49.A10.A.A$49.A$46.A.A2$58.3A$
58.A2.A$58.A951.3A$58.A951.A$59.A.A949.A5$63.3A$62.A2.A$65.A169.3A
753.3A$49.3A9.A3.A169.A755.A$48.A2.A13.A170.A755.A$51.A10.A.A$51.A
503.A$48.A.A504.A$555.A$60.3A$60.A2.A$60.A911.3A$60.A911.A$61.A.A909.
A5$65.3A$64.A2.A$67.A885.3A$51.3A9.A3.A885.A$50.A2.A13.A886.A$53.A10.
A.A$53.A$50.A.A145.A$197.A.A$62.3A$62.A2.A131.3A$62.A131.3A737.3A$62.
A131.A2.A736.A$63.A.A128.A740.A$194.A$195.A.A3$67.3A$66.A2.A$69.A129.
3A713.3A$53.3A9.A3.A128.A2.A713.A$52.A2.A13.A131.A714.A$55.A10.A.A
128.A3.A$55.A145.A$52.A.A143.A.A$231.2A$64.3A163.A.A$64.A2.A164.A$64.
A131.3A697.3A$64.A131.A2.A696.A$65.A.A128.A700.A$196.A$197.A.A3$69.3A
$68.A2.A$71.A129.3A673.3A$55.3A9.A3.A128.A2.A673.A$54.A2.A13.A131.A
674.A$57.A10.A.A128.A3.A$57.A145.A349.A$54.A.A143.A.A350.A$265.2A286.
A$66.3A195.A.A$66.A2.A196.A$66.A131.3A657.3A$66.A131.A2.A656.A$67.A.A
128.A660.A$198.A$199.A.A3$71.3A$70.A2.A$73.A129.3A633.3A$57.3A9.A3.A
128.A2.A633.A$56.A2.A13.A131.A634.A$59.A10.A.A128.A3.A$59.A145.A$56.A
.A143.A.A$299.2A$68.3A227.A.A$68.A2.A228.A$68.A131.3A617.3A$68.A131.A
2.A616.A$69.A.A128.A620.A$200.A$201.A.A3$73.3A$72.A2.A$75.A129.3A593.
3A$59.3A9.A3.A128.A2.A593.A$58.A2.A13.A131.A594.A$61.A10.A.A128.A3.A$
61.A145.A$58.A.A143.A.A$333.2A$70.3A259.A.A$70.A2.A260.A$70.A131.3A
577.3A$70.A131.A2.A576.A$71.A.A128.A580.A$202.A$203.A.A3$75.3A$74.A2.
A$77.A129.3A553.3A$61.3A9.A3.A128.A2.A553.A$60.A2.A13.A131.A554.A$63.
A10.A.A128.A3.A$63.A145.A341.A$60.A.A143.A.A342.A$294.D11.D5.4D2.4D.
4D2.D3.D11.D21.2A182.A$72.3A218.D12.D5.D2.D2.D2.D.D2.D2.2D.2D12.D19.A
.A$72.A2.A216.D13.D5.D2.D2.D2.D.D2.D2.2D.2D13.D20.A$72.A131.3A84.10D
2.7D2.4D2.4D.4D2.D.D.D5.10D395.3A$72.A131.A2.A84.D13.D8.D2.D2.D.D2.D
2.D3.D13.D396.A$73.A.A128.A88.D12.D8.D2.D2.D.D2.D2.D3.D12.D398.A$204.
A89.D11.D5.4D2.4D.4D2.D3.D11.D$205.A.A3$77.3A$76.A2.A$79.A129.3A513.
3A$63.3A9.A3.A128.A2.A513.A$62.A2.A13.A131.A514.A$65.A10.A.A128.A3.A$
65.A145.A535.D$62.A.A143.A.A535.3D$401.2A342.D.D.D$74.3A323.A.A341.D
2.D2.D$74.A2.A324.A344.D$74.A131.3A497.3A38.D$74.A131.A2.A496.A40.D$
75.A.A128.A500.A39.D$206.A540.D$207.A.A537.D$747.D$747.D$79.3A$78.A2.
A$81.A129.3A473.3A$65.3A9.A3.A128.A2.A473.A$64.A2.A13.A131.A474.A$67.
A10.A.A128.A3.A$67.A145.A$64.A.A143.A.A520.D6.4D3.3D3.D2.D2.D3.D$435.
2A296.D6.D5.D3.D2.D2.D2.2D.2D$76.3A355.A.A296.D6.D5.D3.D2.D2.D2.2D.2D
$76.A2.A356.A293.7D4.3D2.D3.D2.4D2.D.D.D$76.A131.3A457.3A62.D9.D2.D3.
D5.D2.D3.D$76.A131.A2.A456.A64.D9.D2.D3.D5.D2.D3.D$77.A.A128.A460.A
63.D6.4D3.3D6.D2.D3.D$208.A$209.A.A3$81.3A$80.A2.A$83.A129.3A433.3A$
67.3A9.A3.A128.A2.A433.A97.D$66.A2.A13.A131.A434.A96.D$69.A10.A.A128.
A3.A531.D$69.A145.A333.A197.D$66.A.A143.A.A334.A197.D$469.2A78.A197.D
$78.3A387.A.A276.D$78.A2.A388.A276.D$78.A131.3A417.3A111.D2.D2.D$78.A
131.A2.A416.A114.D.D.D$79.A.A128.A420.A114.3D$210.A536.D$211.A.A3$83.
3A$82.A2.A$85.A129.3A393.3A$69.3A9.A3.A128.A2.A393.A$68.A2.A13.A131.A
394.A$71.A10.A.A128.A3.A$71.A145.A$68.A.A143.A.A$503.2A$80.3A419.A.A$
80.A2.A420.A$80.A131.3A377.3A$80.A131.A2.A376.A$81.A.A128.A380.A$212.
A$213.A.A3$85.3A$84.A2.A$87.A129.3A353.3A$71.3A9.A3.A128.A2.A353.A$
70.A2.A13.A131.A354.A$73.A10.A.A128.A3.A$73.A145.A$70.A.A143.A.A$537.
2A$82.3A451.A.A$82.A2.A452.A$82.A131.3A337.3A$82.A131.A2.A336.A$83.A.
A128.A340.A$214.A$215.A.A3$87.3A$86.A2.A$89.A129.3A313.3A$73.3A9.A3.A
128.A2.A313.A$72.A2.A13.A131.A314.A$75.A10.A.A128.A3.A$75.A145.A325.A
$72.A.A143.A.A326.A$547.A$84.3A$84.A2.A$84.A131.3A$84.A131.A2.A$85.A.
A128.A$216.A$217.A.A3$89.3A$88.A2.A$91.A129.3A273.3A$75.3A9.A3.A128.A
2.A273.A$74.A2.A13.A131.A274.A$77.A10.A.A128.A3.A$77.A145.A$74.A.A
143.A.A2$86.3A$86.A2.A$86.A131.3A$86.A131.A2.A$87.A.A128.A$218.A$219.
A.A324.A$546.A$546.A$91.3A$90.A2.A$93.A129.3A233.3A$77.3A9.A3.A128.A
2.A233.A$76.A2.A13.A131.A234.A$79.A10.A.A128.A3.A$79.A145.A$76.A.A
143.A.A2$88.3A$88.A2.A$88.A131.3A$88.A131.A2.A$89.A.A128.A$220.A$221.
A.A3$93.3A$92.A2.A$95.A129.3A193.3A$79.3A9.A3.A128.A2.A193.A$78.A2.A
13.A131.A194.A$81.A10.A.A128.A3.A$81.A145.A317.A$78.A.A143.A.A318.A$
545.A$90.3A$90.A2.A$90.A131.3A$90.A131.A2.A$91.A.A128.A$222.A$223.A.A
3$95.3A$94.A2.A$97.A129.3A153.3A$81.3A9.A3.A128.A2.A153.A$80.A2.A13.A
131.A154.A$83.A10.A.A128.A3.A$83.A145.A$80.A.A143.A.A2$92.3A$92.A2.A$
92.A131.3A$92.A131.A2.A$93.A.A128.A$224.A$225.A.A316.A$544.A$544.A$
97.3A$96.A2.A$99.A129.3A113.3A$83.3A9.A3.A128.A2.A113.A$82.A2.A13.A
131.A114.A$85.A10.A.A128.A3.A$85.A145.A$82.A.A143.A.A2$94.3A$94.A2.A$
94.A131.3A$94.A131.A2.A$95.A.A128.A$226.A$227.A.A3$99.3A$98.A2.A$101.
A129.3A73.3A$85.3A9.A3.A128.A2.A73.A$84.A2.A13.A131.A74.A$87.A10.A.A
128.A3.A$87.A145.A309.A$84.A.A143.A.A310.A$543.A$96.3A$96.A2.A$96.A
131.3A$96.A131.A2.A$97.A.A128.A$228.A$229.A.A3$101.3A$100.A2.A$103.A
129.3A33.3A$87.3A9.A3.A128.A2.A33.A$86.A2.A13.A131.A34.A$89.A10.A.A
128.A3.A$89.A145.A$86.A.A143.A.A2$98.3A$98.A2.A$98.A131.3A$98.A131.A
2.A$99.A.A128.A30.3A$230.A29.A2.A$231.A.A29.A278.A$263.A278.A$260.A.A
279.A$103.3A$102.A2.A$105.A129.3A$89.3A9.A3.A128.A2.A$88.A2.A13.A131.
A$91.A10.A.A128.A3.A$91.A145.A$88.A.A143.A.A2$100.3A$100.A2.A$100.A
131.3A$100.A131.A2.A$101.A.A128.A30.3A$232.A29.A2.A$233.A.A29.A$265.A
$262.A.A$105.3A$104.A2.A$107.A129.3A$91.3A9.A3.A128.A2.A$90.A2.A13.A
131.A$93.A10.A.A128.A3.A$93.A145.A301.A$90.A.A143.A.A302.A$541.A$102.
3A$102.A2.A$102.A131.3A$102.A131.A2.A$103.A.A128.A30.3A$234.A29.A2.A$
235.A.A29.A$267.A$264.A.A$107.3A$106.A2.A$109.A129.3A$93.3A9.A3.A128.
A2.A$92.A2.A13.A131.A$95.A10.A.A128.A3.A$95.A145.A$92.A.A143.A.A2$
104.3A$104.A2.A$104.A131.3A$104.A131.A2.A$105.A.A128.A30.3A$236.A29.A
2.A$237.A.A29.A270.A$269.A270.A$266.A.A271.A$109.3A$108.A2.A$111.A
129.3A$95.3A9.A3.A128.A2.A$94.A2.A13.A131.A$97.A10.A.A128.A3.A$97.A
145.A$94.A.A143.A.A2$106.3A$106.A2.A$106.A131.3A$106.A131.A2.A$107.A.
A128.A30.3A$238.A29.A2.A$239.A.A29.A$271.A$268.A.A$111.3A$110.A2.A$
113.A129.3A$97.3A9.A3.A128.A2.A$96.A2.A13.A131.A$99.A10.A.A128.A3.A$
99.A145.A293.A$96.A.A143.A.A294.A$539.A$108.3A$108.A2.A$108.A131.3A$
108.A131.A2.A$109.A.A128.A30.3A$240.A29.A2.A$241.A.A29.A$273.A$270.A.
A$113.3A$112.A2.A$115.A129.3A$99.3A9.A3.A128.A2.A$98.A2.A13.A131.A$
101.A10.A.A128.A3.A$101.A145.A$98.A.A143.A.A2$110.3A$110.A2.A$110.A
131.3A$110.A131.A2.A$111.A.A128.A$242.A$243.A.A292.A$538.A$538.A$115.
3A$114.A2.A$117.A129.3A$101.3A9.A3.A128.A2.A$100.A2.A13.A131.A$103.A
10.A.A128.A3.A$103.A145.A$100.A.A143.A.A2$112.3A$112.A2.A$112.A131.3A
$112.A131.A2.A$113.A.A128.A$244.A$245.A.A3$117.3A$116.A2.A$119.A$103.
3A9.A3.A$102.A2.A13.A$105.A10.A.A$105.A431.A$102.A.A432.A$537.A$114.
3A$114.A2.A$114.A$114.A$115.A.A5$119.3A$118.A2.A$121.A$105.3A9.A3.A$
104.A2.A13.A$107.A10.A.A$107.A$104.A.A2$116.3A$116.A2.A$116.A$116.A$
117.A.A!

Edited for clarity : now NW rakes list vertical movement, NE rakes horizontal. To move a NW rake 2 cells down, delay its climber 4 generations. To move a NE rake right by 2 cells, advance the helix by 4 generations.

Posted: **September 19th, 2016, 4:35 pm**

I wrote:I'm not sure if there is a value of M where the spare glider heisenburns in the *WSS streams, I didn't bother to work out whether it was invariant.

Moving the last glider stream down 504 cells brings it 56 cells closer horizontally to the *WSS stream, since the *WSS are offset (2, 18) and (56, 504) = 28 * (2, 18). The NW x2 gliders are offset (-38, 18), meaning the horizontal separation in a snapshot is invariant mod 2 - (-38) = 40. The gcd of 40 and 56 is 8, meaning we only have 40/8 = 5 reachable separations through varying M. None of these provide a heisenburn for the glider, although if we could change the horizontal separation by 6 cells instead of 8 it would. It's a bit unfortunate, since I initially thought there were 19 reachable separations instead of 5, before I caught my error.

It's really hard to guess beforehand which primes one will encounter when working with a caterpillar design!

chris_c wrote:Here is what I came up with instead (7 *WSS with an intermediate block, one spare glider to clean)

I do like this design, especially since there is no costly extra zigzag. The *WSS streams have to continue downwards all the way until they are constructed, which could put them as far left as the helix. The rebounding glider streams would then have to make a circuit the full width of the ship front, which won't be trivial and will eat up a lot of space. My design does this circuit twice, yours only once with the cost 2 *WSS higher. Not sure which is better.

I still want it to be possible to do all the construction for these x2 streams using the singleton track, allowing the *WSS to be much further right and making the zigzags less costly. That would require some elegant x2 feedback loop. If that turns out to be reasonable, my design would probably win out. If not, I imagine we should go with yours.

Posted: **September 19th, 2016, 5:41 pm**

biggiemac wrote: It's really hard to guess beforehand which primes one will encounter when working with a caterpillar design!

Agreed! Your latest arithmetic regarding the possibility of heisenburns is particularly scary. I didn't want to go near that problem.

biggiemac wrote: I still want it to be possible to do all the construction for these x2 streams using the singleton track, allowing the *WSS to be much further right and making the zigzags less costly. That would require some elegant x2 feedback loop. If that turns out to be reasonable, my design would probably win out. If not, I imagine we should go with yours.

I hope that your version can be made to work best because it is very elegant. Here is a version with zig-zaging but only 5 LWSS. I haven't worked out the modular arithmetic for the repeated -4 offsets (sorry).

Code: Select all

x = 574, y = 626, rule = B3/S23
440b2o$440bobo$440bo7$421b2o$421bobo$421bo7$402b2o$402bobo$402bo7$383b
2o$383bobo$383bo7$364b2o$364bobo$364bo7$345b2o$345bobo$345bo7$326b2o$
326bobo$326bo7$307b2o$307bobo$307bo7$288b2o$288bobo$288bo7$269b2o$269b
obo$269bo7$250b2o$250bobo$250bo7$231b2o$231bobo$231bo7$212b2o$212bobo$
212bo7$193b2o$193bobo$193bo7$174b2o$174bobo$174bo7$155b2o$155bobo$155b
o7$136b2o$136bobo$136bo6$560b2o$117b2o441bobo$117bobo440bo$117bo6$541b
2o$98b2o441bobo$98bobo440bo$98bo6$522b2o$79b2o441bobo$79bobo440bo$79bo
6$503b2o$60b2o441bobo$60bobo440bo$60bo6$484b2o$41b2o441bobo$41bobo440b
o$41bo6$465b2o$22b2o441bobo$22bobo440bo$22bo6$446b2o$446bobo$446bo5$2b
o$b3o$2obo10b2o411b2o$3o10bobo411bobo$b2o12bo411bo2$7b3o$7bo2bo$7bo$7b
o$8bobo$16bo391b2o$15b3o390bobo$14b2obo390bo$14b3o$15b2o3$4bo$3b3o$2b
2obo42b2o339b2o$2b3o42bobo339bobo$3b2o44bo339bo2$9b3o$9bo2bo$9bo$9bo$
10bobo$18bo351b2o$17b3o350bobo$16b2obo350bo$16b3o$17b2o3$6bo$5b3o$4b2o
bo74b2o267b2o$4b3o74bobo267bobo$5b2o76bo267bo2$11b3o$11bo2bo$11bo$11bo
$12bobo$20bo311b2o$19b3o310bobo$18b2obo310bo$18b3o$19b2o3$8bo$7b3o$6b
2obo106b2o195b2o$6b3o106bobo195bobo$7b2o108bo195bo2$13b3o$13bo2bo$13bo
$13bo$14bobo$22bo271b2o$21b3o270bobo274b2o$20b2obo270bo276bobo$20b3o
548bo$21b2o3$10bo$9b3o$8b2obo138b2o123b2o$8b3o138bobo123bobo274b2o$9b
2o140bo123bo276bobo$552bo$15b3o$15bo2bo$15bo$15bo$16bobo$24bo231b2o$
23b3o230bobo274b2o$22b2obo230bo276bobo$22b3o508bo$23b2o3$12bo$11b3o$
10b2obo170b2o51b2o$10b3o170bobo51bobo274b2o$11b2o172bo51bo276bobo$514b
o$17b3o$17bo2bo$17bo$17bo$18bobo$26bo191b2o$25b3o190bobo274b2o$24b2obo
190bo276bobo$24b3o468bo$25b2o3$14bo$13b3o$12b2obo$12b3o461b2o$13b2o
461bobo$476bo$19b3o$19bo2bo$19bo$19bo$20bobo$28bo151b2o$27b3o150bobo
274b2o$26b2obo150bo26b2ob2o245bobo$26b3o178b2ob2o245bo$27b2o3$16bo$15b
3o$14b2obo$14b3o421b2o$15b2o421bobo$438bo$21b3o$21bo2bo$21bo$21bo$22bo
bo$30bo111b2o$29b3o110bobo274b2o$28b2obo110bo276bobo$28b3o388bo$29b2o
3$18bo$17b3o$16b2obo$16b3o381b2o$17b2o381bobo$400bo$23b3o$23bo2bo$23bo
$23bo$24bobo$32bo71b2o$31b3o70bobo274b2o$30b2obo70bo276bobo$30b3o348bo
$31b2o3$20bo$19b3o$18b2obo$18b3o341b2o$19b2o341bobo$362bo$25b3o$25bo2b
o$25bo$25bo$26bobo$34bo$33b3o307b2o$32b2obo36b3o130b2ob2o133bobo$32b3o
39bo130b2ob2o133bo$33b2o38bo3$22bo$21b3o$20b2obo$20b3o301b2o$21b2o301b
obo$324bo$27b3o38b3o$27bo2bo37bo2bo$27bo40bo$27bo40bo$28bobo38bobo$36b
o$35b3o36b3o228b2o$34b2obo36bo2bo28b3o196bobo$34b3o37bo33bo196bo$35b2o
37bo32bo$75bobo2$24bo$23b3o$22b2obo$22b3o261b2o$23b2o261bobo$286bo$29b
3o38b3o$29bo2bo37bo2bo$29bo40bo$29bo40bo$30bobo38bobo$38bo$37b3o36b3o
188b2o$36b2obo36bo2bo60b3o124bobo$36b3o37bo65bo124bo$37b2o37bo64bo$77b
obo2$26bo$25b3o$24b2obo$24b3o221b2o$25b2o221bobo$248bo$31b3o38b3o$31bo
2bo37bo2bo$31bo40bo$31bo40bo$32bobo38bobo$40bo$39b3o36b3o148b2o$38b2ob
o36bo2bo92b3o26b2ob2o21bobo$38b3o37bo97bo26b2ob2o21bo$39b2o37bo96bo$
79bobo2$28bo$27b3o$26b2obo$26b3o181b2o$27b2o181bobo$210bo$33b3o38b3o$
33bo2bo37bo2bo$33bo40bo$33bo40bo$34bobo38bobo$42bo$41b3o36b3o$40b2obo
36bo2bo$40b3o37bo$41b2o37bo$81bobo2$30bo172bo$29b3o170bobo$28b2obo170b
obo$28b3o172bo$29b2o$198b2o7b2o$35b3o38b3o118bo2bo5bo2bo$35bo2bo37bo2b
o118b2o7b2o$35bo40bo$35bo40bo126bo$36bobo38bobo122bobo$44bo157bobo$43b
3o36b3o118bo$42b2obo36bo2bo$42b3o37bo$43b2o37bo$83bobo2$32bo$31b3o$30b
2obo$30b3o$31b2o2$37b3o38b3o$37bo2bo37bo2bo$37bo40bo$37bo40bo123bo$38b
obo38bobo119bobo$46bo154bobo$45b3o36b3o115bo$44b2obo36bo2bo$44b3o37bo
112b2o7b2o$45b2o37bo111bo2bo5bo2bo$85bobo109b2o7b2o2$34bo167bo$33b3o
165bobo$32b2obo165bobo$32b3o167bo$33b2o2$39b3o38b3o$39bo2bo37bo2bo$39b
o40bo$39bo40bo$40bobo38bobo$48bo$47b3o36b3o$46b2obo36bo2bo$46b3o37bo$
47b2o37bo$87bobo2$36bo164bo$35b3o162bobo$34b2obo162bobo$34b3o164bo$35b
2o$196b2o7b2o$41b3o38b3o110bo2bo5bo2bo$41bo2bo37bo2bo110b2o7b2o$41bo
40bo$41bo40bo118bo$42bobo38bobo114bobo$50bo149bobo$49b3o36b3o110bo$48b
2obo36bo2bo$48b3o37bo$49b2o37bo$89bobo2$38bo$37b3o$36b2obo$36b3o$37b2o
2$43b3o38b3o$43bo2bo37bo2bo$43bo40bo$43bo40bo$44bobo38bobo$52bo$51b3o
36b3o$50b2obo36bo2bo$50b3o37bo$51b2o37bo$91bobo2$40bo$39b3o$38b2obo$
38b3o$39b2o2$45b3o38b3o$45bo2bo37bo2bo$45bo40bo$45bo40bo$46bobo38bobo$
54bo$53b3o36b3o$52b2obo36bo2bo$52b3o37bo$53b2o37bo$93bobo2$42bo$41b3o$
40b2obo$40b3o$41b2o2$47b3o38b3o$47bo2bo37bo2bo$47bo40bo$47bo40bo$48bob
o38bobo$56bo$55b3o36b3o$54b2obo36bo2bo$54b3o37bo$55b2o37bo$95bobo2$44b
o$43b3o$42b2obo$42b3o$43b2o2$49b3o38b3o$49bo2bo37bo2bo$49bo40bo$49bo
40bo$50bobo38bobo$58bo$57b3o36b3o$56b2obo36bo2bo$56b3o37bo$57b2o37bo$
97bobo2$46bo$45b3o$44b2obo$44b3o$45b2o2$51b3o38b3o$51bo2bo37bo2bo$51bo
40bo$51bo40bo$52bobo38bobo$60bo$59b3o36b3o$58b2obo36bo2bo$58b3o37bo$
59b2o37bo$99bobo!

For the record here are the other ways I found for potentially doing the same kind of trick:

Code: Select all

x = 261, y = 102, rule = B3/S23
5b2o3b2o$4bobo3bobo$6bo3bo5$186b2o$186bobo$180bo5bo$16b2o89bo72b2o60b
2o$16bobo88b2o70bobo60bobo$16bo89bobo133bo$113b2o121b3o$113bobo122bo$
113bo123bo2$194b2o$194bobo$194bo$258b2o$258bobo$258bo5$b2o$2b2o4b2o
118b2o$bo6bobo117bobo$8bo119bo8$182b2o$181bobo$183bo54b2o$190b2o47b2o
7b3o$190bobo45bo9bo$190bo58bo$122b2o$122bobo$10b2o110bo$b3o6bobo101b2o
$3bo6bo102bobo$2bo112bo15$3o$2bo6b2o101b3o$bo7bobo102bo$9bo103bo6b2o$
120bobo$120bo11$121b2o$121bobo$121bo$112b3o$114bo$113bo10$124b2o$124bo
bo$124bo2$118bo$118b2o$117bobo!

Another thing that could be annoying is that the LWSS recipe I posted a few pages back doesn't work with the 2 cell offset although the method in general (R-pent + glider + blinker) would still work at x2. I'm not sure how you propose to build the *WSS so I'm not sure if this is relevant.

Posted: **September 19th, 2016, 6:08 pm**

chris_c wrote:Here is a version with zig-zaging but only 5 LWSS.

Nice! To make the extra zig zag less costly, all the singleton needs to build is the *WSS salvo that rebounds the second glider. In your design, that is two LWSS with the same shape and color (yay). The other 3 LWSS all have different shape/color combinations from the rightmost pair, so it will require 4 distinct recipes if we want to build all 5.

I think what we should look for in these recipes is something clean that also releases a NE glider, where again a signal encodes whether the LWSS is produced or not. The NE glider is caught to make the next construction target, giving the required space.

But if this is what we are going for, we might want our first two initial targets to have some x2 component, instead of building doubling reactions from scratch. There has to be an elegant way to accomplish that. Are there reaction pairs similar to the [G + (G|bi-block) -> HF] where instead of the results being identical, one is a (workable at x1) subset of the other?

Posted: **September 19th, 2016, 7:30 pm**

biggiemac wrote:Are there reaction pairs similar to the [G + (G|bi-block) -> HF] where instead of the results being identical, one is a (workable at x1) subset of the other?

I'm not sure what you mean by "workable at x1" but all the way back when I wrote:

I wrote:When I was trying to come up with an example pattern I ran into problems with the second x1 NW stream colliding with the target site already constructed by the first NW stream

I was referring to this. Is it useful?

Code: Select all

x = 147, y = 160, rule = B3/S23
46b3o2$44bo5bo$44bo5bo$44bo5bo2$46b3o48$44b3o2$42bo5bo$42bo5bo$42bo5bo
2$44b3o33$59b2o$59bobo$59bo5$144b2o$144bobo$40b2o102bo$40bobo$40bo5$
125b2o$125bobo$21b2o102bo$21bobo$21bo5$106b2o$106bobo$2b2o102bo$2bobo$
2bo5$b3o83b2o$o2bo83bobo$3bo83bo$3bo$obo6$5bo$4b3o$4bob2o$5b3o$5b2o4$
3b3o$2bo2bo$5bo$5bo$2bobo6$7bo$6b3o$6bob2o$7b3o$7b2o!

Posted: **September 19th, 2016, 7:40 pm**

I meant something where the x2 part was well isolated from a x1 part, such that the trail can be treated as x1 for the purposes of construction. The best example would be something like this:

Code: Select all

x = 190, y = 131, rule = LifeHistory
55.A$54.A.A$54.A.A$55.A2$50.2A7.2A$49.A2.A5.A2.A$50.2A7.2A2$55.A$54.A
.A$54.A.A$55.A27$64.2D$64.2D2$2A$.2A$A2$134.2A$134.A.A$134.A6$53.A$
52.A.A60.2A$52.A.A60.A.A$53.A61.A2$48.2A7.2A$34.2A11.A2.A5.A2.A$35.2A
11.2A7.2A$34.A$53.A$52.A.A41.2A$52.A.A41.A.A$53.A42.A7$77.2A$77.A.A$
77.A26$187.2A$187.A.A$187.A7$168.2A$168.A.A$168.A7$149.2A$149.A.A$
149.A7$130.2A$130.A.A$130.A!

Except where the block in red was present after the second rake went by. That way construction can begin using the right blocks, and the left blocks can filter for fire/no fire. I found nothing starting from HF -> 2 blocks using only 2 rakes, but perhaps there is something that converges to a x1 trail with a third rake.

Is there a way after some number of construction rakes to isolate the x1 part and x2 part of the TL you posted?

Edit: Another option, except this particular example doesn't work because the left half of the blockade would stop the incoming NE glider. The glider in yellow is there to kill it off to at least show the concept I am looking for.

Code: Select all

x = 211, y = 125, rule = LifeHistory
96.A$95.A.A$95.A.A$96.A22$111.2D$111.2D6$69.E$70.E$68.3E4$155.2A$155.
A.A$155.A7$136.2A$136.A.A$136.A5$94.A$93.A.A$93.A.A21.2A$94.A22.A.A$
117.A7$98.2A$98.A.A$98.A16$.2A$A.A$2.A10$208.2A$208.A.A$208.A4$35.2A$
34.A.A$36.A$189.2A$189.A.A$189.A7$170.2A$170.A.A$170.A7$151.2A$151.A.
A$151.A!

Posted: **September 19th, 2016, 8:31 pm**

biggiemac wrote:Is there a way after some number of construction rakes to isolate the x1 part and x2 part of the TL you posted?

Seems like there would be, probably not too many rakes away, unless there are severe constraints on the rakes that I haven't been paying attention to. Which is quite likely. But would something like this work?

Code: Select all

x = 150, y = 82, rule = B3/S23
2b3o57b3o2$o5bo53bo5bo$o5bo53bo5bo$o5bo53bo5bo2$2b3o30$40b3o57b3o$40bo
59bo$41bo59bo41$87b3o57b3o$87bo59bo$88bo59bo!

Some time ago I discovered that I could explore this kind of parallel cleanup problem pretty well by pasting something like

Code: Select all

x = 67, y = 7, rule = B3/S23
2b3o57b3o2$o5bo53bo5bo$o5bo53bo5bo$o5bo53bo5bo2$2b3o!

into the Seeds of Destruction Game, and then playing around with different phases of glider pairs, pasted in with the "seed" option:

Code: Select all

x = 63, y = 3, rule = B3/S23
3o57b3o$o59bo$bo59bo!

Of course a script would find a lot more options a lot quicker, but then I wouldn't get to personally cause as many entertaining explosions...!

Posted: **September 19th, 2016, 8:43 pm**

The constraints on the rakes aren't really that bad, they just have to be monochromatic and have the same shape (p4).

The cleanup you posted doesn't accomplish what I am interested in - there has to be a surviving x1 part, ideally pretty far to the right of the x2 part. Far enough to the right that construction can be done pretending the x2 part doesn't even exist. That's why I was most interested in widely-separated patterns with blocks, like the HF block splitter or a blockade. If we use one NE stream to help replicate the right block, and let the left block(s) be, that helps start off the x2 feedback loop.

Edit: Something like this could be sufficient. (All gliders used are the right color and parity)

Code: Select all

x = 105, y = 47, rule = B3/S23
2b3o57b3o2$o5bo53bo5bo$o5bo53bo5bo$o5bo53bo5bo2$2b3o9b3o57b3o$14bo59bo
$15bo59bo16$30b3o57b3o$30bo59bo$31bo59bo8$32b3o57b3o$32bo59bo$33bo59bo
8$42b3o57b3o$42bo59bo$43bo59bo!

Posted: **September 19th, 2016, 10:18 pm**

I suppose, I've only been suggesting to have a constellation trail with something x2 on the left and everything x1 on the right because I am assuming that gives the best route to successfully making some of the x2 *WSS streams using the singleton constructor.

However, if we dream big and take dvgrn's parallel construction idea to heart, there's no reason we can't at least ask if something like the following exists:

Two slightly different constellations (like the TL and the TL missing a blinker from above), for which some monochromatic monoparity NW salvo exists giving
1) An edge-shooting LWSS or MWSS from one of the constellations with no other debris besides a NE glider
2) A NE glider only from the other constellation (not necessarily identical to that from 1, but that'd be cool)

The salvos are completely parallel, and the initial difference encodes whether it's option 1 or option 2. Given how outlandish that sounds, I feel like the best way to achieve this without tons of brute force is for the two to converge as quickly as possible, but retain some difference clear from the construction path that ultimately prevents the edgy *WSS from forming in (2). Then it's just standard construction instead of parallel.

Since the *WSS is triggered by a single NW glider, the R + blinker + G option will be hard to orchestrate. I'm trying to scrape the forums for *WSS seeds edgy enough. The "Champion" from the 31c/240 project is activated from the wrong direction. (A turner is possible but if there is a better option it'd be nice).

ConwayLife.com

(27,1)c/72 caterpillar challenge

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