x = 2050, y = 857
1963b3o3b3o$1962bo3bobo3bo$1962bo3bobo3bo$1962bo3bobo3bo$1963b3o3b3o$
1937bo3b3o5b3o3bo23bo3b3o5b3o3bo$1934boob5oboo3boob5oboo17boob5oboo3b
oob5oboo$1932boboobo5bobobobo5boboobo8boo3boboobo5bobobobo5boboobo$
1931bo3bobo3b5ob5o3bobo3bo6bobbobo3bobo3b5ob5o3bobo3bo$1935b3o5boo3boo
5b3o11boo6b3o5boo3boo5b3o$1932bobbob3o13b3obobbo13bobbob3o13b3obobbo$
1934bo23bo17bo23bo19$1986bo7bo$1934boo5boo5boo5boo23booboboboo3boobobo
boo$1932bo3bo3bobbo3bobbo3bo3bo18b3obob3o9b3obob3o$1932bo3bobob3o5b3ob
obo3bo18bo3bobo5bobo5bobo3bo$1932bo5boobb3ob3obboo5bo22boo6bobo6boo$
1932boob3o15b3oboo19boo9bobo9boo$1932bo25bo19booboo15booboo$1933bo3bo
15bo3bo24bo15bo$1934bobbo15bobbo259$124boo5boo$125boo3boo$122bobbobobo
bobbo$122bo11bo$122bobbobobobobbo$97bo5boo5boo5bo7boo3boo7bo5boo5boo5b
o$95bobbooboobbo3bobbooboobbo6boo3boo4bobbooboobbo3bobbooboobbo$93b3o
4bobo3bobo3bobo4b3o3b3o7b3o4bobo3bobo3bobo4b3o$93boobbobb3oboo3boob3o
bbobboo4b3o6boobbobb3oboo3boob3obbobboo$93b3obb3o4bo3bo4b3obb3obbobbo
7b3obb3o4bo3bo4b3obb3o$94bobobbo15bobbobo4boo9bobobbo15bobbobo$95bo23b
o17bo23bo$126bo$125boo$125bobo16$146boo5boo$96bo3b3o5b3o3bo23b4obobobo
5bobobob4o$93boob5oboo3boob5oboo19b3oboboboobo3boboobobob3o$91boboobo
5bobobobo5boboobo17bo3bobo13bobo3bo$90bo3bobo3b5ob5o3bobo3bo17bob3o5b
ooboo5b3obo$94b3o5boo3boo5b3o21boo21boo$91bobbob3o13b3obobbo18b5o15b5o
$93bo23bo23boo15boo14$139bo3b3o5b3o3bo$136boob5oboo3boob5oboo$134boboo
bo5bobobobo5boboobo$133bo3bobo3b5ob5o3bobo3bo$137b3o5boo3boo5b3o$134bo
bbob3o13b3obobbo$136bo23bo25$95boo5boo5boo5boo$93bo3bo3bobbo3bobbo3bo
3bo$93bo3bobob3o5b3obobo3bo$93bo5boobb3ob3obboo5bo$93boob3o15b3oboo$
93bo25bo18bo3b3o5b3o3bo$94bo3bo15bo3bo16boob5oboo3boob5oboo$95bobbo15b
obbo15boboobo5bobobobo5boboobo$132bo3bobo3b5ob5o3bobo3bo$136b3o5boo3b
oo5b3o$133bobbob3o13b3obobbo$135bo23bo$108bo$106booboboboo$109b3obob3o
$79bo5boo5boo5bo5bo5bobo3bo$77bobbooboobbo3bobbooboobbo3bo6boo$75b3o4b
obo3bobo3bobo4b3obo9boo$75boobbobb3oboo3boob3obbobboo8booboo$75b3obb3o
4bo3bo4b3obb3o8bo$76bobobbo15bobbobo$77bo23bo4$158bo3b3o5b3o3bo$155boo
b5oboo3boob5oboo$153boboobo5bobobobo5boboobo$152bo3bobo3b5ob5o3bobo3bo
$156b3o5boo3boo5b3o$101boo5boo5boo5boo29bobbob3o13b3obobbo$99bo3bo3bo
bbo3bobbo3bo3bo29bo23bo$99bo3bobob3o5b3obobo3bo$99bo5boobb3ob3obboo5bo
$99boob3o15b3oboo$99bo25bo$100bo3bo15bo3bo$101bobbo15bobbo$$121bo7bo$
115booboboboo3booboboboo$112b3obob3o9b3obob3o26bo3b3o5b3o3bo$112bo3bob
o5bobo5bobo3bo23boob5oboo3boob5oboo$116boo6bobo6boo25boboobo5bobobobo
5boboobo$113boo9bobo9boo21bo3bobo3b5ob5o3bobo3bo$113booboo15booboo25b
3o5boo3boo5b3o$117bo15bo26bobbob3o13b3obobbo$162bo23bo7$129bo7bo$123b
ooboboboo3booboboboo$120b3obob3o9b3obob3o$120bo3bobo5bobo5bobo3bo$124b
oo6bobo6boo$121boo9bobo9boo$121booboo15booboo20bo5boo5boo5bo1820bo5bo$
125bo15bo22bobbooboobbo3bobbooboobbo1817b3o3b3o$162b3o4bobo3bobo3bobo
4b3o$162boobbobb3oboo3boob3obbobboo$162b3obb3o4bo3bo4b3obb3o$163bobobb
o15bobbobo1788boo5boo5boo5boo19boo5boo5boo5boo$164bo23bo1787bo3bo3bobb
o3bobbo3bo3bo15bo3bo3bobbo3bobbo3bo3bo$1976bo3bobob3o5b3obobo3bo3b3o9b
o3bobob3o5b3obobo3bo$1976bo5boobb3ob3obboo5bo4bo10bo5boobb3ob3obboo5bo
$1976boob3o15b3oboo15boob3o15b3oboo$1976bo25bo15bo25bo$1977bo3bo15bo3b
o17bo3bo15bo3bo$174boo1802bobbo15bobbo19bobbo15bobbo$166b4obobobo$165b
3oboboboobo$165bo3bobo12bo3b3o5b3o3bo$166bob3o5boo3boob5oboo3boob5oboo
$166boo11boboobo5bobobobo5boboobo$166b5o11bobo3b5ob5o3bobo3bo$169boo
11b3o5boo3boo5b3o$179bobbob3o13b3obobbo$181bo23bo3$111bo7bo$105boobobo
boo3booboboboo$102b3obob3o9b3obob3o$102bo3bobo5bobo5bobo3bo$106boo6bob
o6boo$103boo9bobo9boo$103booboo15booboo32bo5boo5boo5bo$107bo15bo34bobb
ooboobbo3bobbooboobbo$156b3o4bobo3bobo3bobo4b3o$156boobbobb3oboo3boob
3obbobboo$156b3obb3o4bo3bo4b3obb3o$157bobobbo15bobbobo$158bo23bo3$153b
oo5boo$104bo7bo32b4obobobo5bobobob4o$98booboboboo3booboboboo25b3obobob
oobo3boboobobob3o$95b3obob3o9b3obob3o22bo3bobo13bobo3bo$95bo3bobo5bobo
5bobo3bo23bob3o5booboo5b3obo$99boo6bobo6boo27boo21boo$96boo9bobo9boo
24b5o15b5o$96booboo15booboo27boo15boo$100bo15bo1911bo7bo$2022boobobob
oo3booboboboo$2019b3obob3o9b3obob3o$2019bo3bobo5bobo5bobo3bo$2023boo6b
obo6boo$2020boo9bobo9boo$2020booboo15booboo$145boo5boo1870bo15bo$137b
4obobobo5bobobob4o$136b3oboboboobo3boboobobob3o$136bo3bobo13bobo3bo$
137bob3o5booboo5b3obo$137boo21boo$97bo3b3o5b3o3bo21b5o15b5o1863boo5boo
5boo5boo$94boob5oboo3boob5oboo21boo15boo1864bo3bo3bobbo3bobbo3bo3bo$
92boboobo5bobobobo5boboobo1902bo3bobob3o5b3obobo3bo$91bo3bobo3b5ob5o3b
obo3bo1901bo5boobb3ob3obboo5bo$95b3o5boo3boo5b3o1905boob3o15b3oboo$92b
obbob3o13b3obobbo1902bo25bo$94bo23bo1905bo3bo15bo3bo$2025bobbo15bobbo
5$107boo5boo$106bobbo3bo3bo$85bo7bo13b3obobo3bo$79booboboboo3boobobob
oo5b3obboo5bo$76b3obob3o9b3obob3o9b3oboo$76bo3bobo5bobo5bobo3bo14bo$
80boo6bobo6boo13bo3bo$77boo9bobo9boo10bobbo$77booboo15booboo$81bo15bo
3$163boo5boo$155b4obobobo5bobobob4o$154b3oboboboobo3boboobobob3o$154bo
3bobo13bobo3bo$155bob3o5booboo5b3obo$155boo21boo$103bo3b3o5b3o3bo33b5o
15b5o$100boob5oboo3boob5oboo33boo15boo$98boboobo5bobobobo5boboobo$97bo
3bobo3b5ob5o3bobo3bo$101b3o5boo3boo5b3o1888bo5boo5boo5bo$98bobbob3o13b
3obobbo1883bobbooboobbo3bobbooboobbo$100bo23bo1883b3o4bobo3bobo3bobo4b
3o$2008boobbobb3oboo3boob3obbobboo$2008b3obb3o4bo3bo4b3obb3o$114boo5b
oo5boo5boo1872bobobbo15bobbobo$112bo3bo3bobbo3bobbo3bo3bo31boo5boo
1831bo23bo$112bo3bobob3o5b3obobo3bo23b4obobobo5bobobob4o$112bo5boobb3o
b3obboo5bo22b3oboboboobo3boboobobob3o$112boob3o15b3oboo22bo3bobo13bobo
3bo1817boo5boo$112bo25bo23bob3o5booboo5b3obo1810b4obobobo5bobobob4o$
113bo3bo15bo3bo24boo21boo1809b3oboboboobo3boboobobob3o$114bobbo15bobbo
25b5o15b5o1809bo3bobo13bobo3bo$165boo15boo1813bob3o5booboo5b3obo$1997b
oo21boo$1997b5o15b5o$2000boo15boo3$1992bo3b3o5b3o3bo$122boo5boo5boo5b
oo1844boob5oboo3boob5oboo$120bo3bo3bobbo3bobbo3bo3bo1840boboobo5bobobo
bo5boboobo$120bo3bobob3o5b3obobo3bo1839bo3bobo3b5ob5o3bobo3bo$120bo5b
oobb3ob3obboo5bo1796bo7bo38b3o5boo3boo5b3o$120boob3o15b3oboo1790boobob
oboo3booboboboo29bobbob3o13b3obobbo$120bo25bo25bo7bo1753b3obob3o9b3obo
b3o28bo23bo$121bo3bo15bo3bo20booboboboo3booboboboo1747bo3bobo5bobo5bob
o3bo$122bobbo15bobbo18b3obob3o9b3obob3o1748boo6bobo6boo$163bo3bobo5bob
o5bobo3bo1745boo9bobo9boo$167boo6bobo6boo1749booboo15booboo$164boo9bob
o9boo1750bo15bo$164booboo15booboo$168bo15bo3$1983boo5boo5boo5boo$1981b
o3bo3bobbo3bobbo3bo3bo$1981bo3bobob3o5b3obobo3bo$168bo5boo1805bo5boobb
3ob3obboo5bo$166bobbooboobbo1804boob3o15b3oboo$164b3o4bobo3bo11boo5boo
1783bo25bo$164boobbobb3oboo4b4obobobo5bobobob4o1776bo3bo15bo3bo$164b3o
bb3o4bo3b3oboboboobo3boboobobob3o1776bobbo15bobbo$165bobobbo9bo3bobo
13bobo3bo$166bo14bob3o5booboo5b3obo$181boo21boo$181b5o15b5o$184boo15b
oo3$104boo5boo5boo5boo1751bo5bo$102bo3bo3bobbo3bobbo3bo3bo1748bobo3bob
o$102bo3bobob3o5b3obobo3bo$102bo5boobb3ob3obboo5bo1748b3o3b3o$102boob
3o15b3oboo1855boo5boo5boo5boo$102bo25bo37bo7bo1807bo3bo3bobbo3bobbo3bo
3bo$103bo3bo15bo3bo32booboboboo3booboboboo1670bo3b3o5b3o3bo23bo3b3o5b
3o3bo70bo3bobob3o5b3obobo3bo$104bobbo15bobbo30b3obob3o9b3obob3o1664boo
b5oboo3boob5oboo10b3o4boob5oboo3boob5oboo67bo5boobb3ob3obboo5bo$157bo
3bobo5bobo5bobo3bo1662boboobo5bobobobo5boboobo13boboobo5bobobobo5boboo
bo65boob3o15b3oboo$161boo6bobo6boo1665bo3bobo3b5ob5o3bobo3bo7bobobo3bo
bo3b5ob5o3bobo3bo64bo25bo$158boo9bobo9boo1666b3o5boo3boo5b3o12bo6b3o5b
oo3boo5b3o69bo3bo15bo3bo$158booboo15booboo1663bobbob3o13b3obobbo13bobb
ob3o13b3obobbo67bobbo15bobbo$162bo15bo1669bo23bo17bo23bo$$1987boo5boo$
147bo5boo5boo5bo1811b4obobobo5bobobob4o$97boo5boo5boo5boo25bobbooboobb
o3bobbooboobbo1808b3oboboboobo3boboobobob3o$95bo3bo3bobbo3bobbo3bo3bo
21b3o4bobo3bobo3bobo4b3o1806bo3bobo13bobo3bo$95bo3bobob3o5b3obobo3bo
21boobbobb3oboo3boob3obbobboo1807bob3o5booboo5b3obo$95bo5boobb3ob3obb
oo5bo21b3obb3o4bo3bo4b3obb3o1807boo21boo$95boob3o15b3oboo22bobobbo15bo
bbobo1808b5o15b5o$95bo25bo23bo23bo1812boo15boo$96bo3bo15bo3bo$97bobbo
15bobbo7$139bo5boo5boo5bo$137bobbooboobbo3bobbooboobbo$135b3o4bobo3bob
o3bobo4b3o$135boobbobb3oboo3boob3obbobboo$135b3obb3o4bo3bo4b3obb3o$
102boo5boo25bobobbo15bobbobo$94b4obobobo5bobobob4o18bo23bo$93b3obobob
oobo3boboobobob3o$93bo3bobo13bobo3bo1865boo5boo$94bob3o5booboo5b3obo
1858b4obobobo5bobobob4o$94boo21boo1787bo7bo61b3oboboboobo3boboobobob3o
$94b5o15b5o1781booboboboo3booboboboo11bo5boo5boo5bo23bo3bobo13bobo3bo$
97boo15boo1781b3obob3o9b3obob3o6bobbooboobbo3bobbooboobbo22bob3o5boob
oo5b3obo$1897bo3bobo5bobo5bobo3bo4b3o4bobo3bobo3bobo4b3o20boo21boo$
1901boo6bobo6boo8boobbobb3oboo3boob3obbobboo20b5o15b5o$1898boo9bobo9b
oo5b3obb3o4bo3bo4b3obb3o23boo15boo$1898booboo15booboo6bobobbo15bobbobo
$1902bo15bo11bo23bo$107b3o3bo$106boob5oboo$78boo5boo5boo5boo4bobo5bob
oobo$76bo3bo3bobbo3bobbo3bo3bobb5o3bobo3bo$76bo3bobob3o5b3obobo3bo3boo
5b3o$76bo5boobb3ob3obboo5bo8b3obobbo1782boo5boo$76boob3o15b3oboo13bo
1740boo5boo27b4obobobo5bobobob4o$76bo25bo1746b4obobobo5bobobob4o18b3ob
oboboobo3boboobobob3o$77bo3bo15bo3bo1746b3oboboboobo3boboobobob3o17bo
3bobo13bobo3bo$78bobbo15bobbo1747bo3bobo13bobo3bo18bob3o5booboo5b3obo$
1849bob3o5booboo5b3obo19boo21boo$1849boo21boo19b5o15b5o18bo5boo5boo5bo
$157bo5boo5boo5bo1671b5o15b5o22boo15boo19bobbooboobbo3bobbooboobbo$
155bobbooboobbo3bobbooboobbo1672boo15boo61b3o4bobo3bobo3bobo4b3o$153b
3o4bobo3bobo3bobo4b3o1750boobbobb3oboo3boob3obbobboo$153boobbobb3oboo
3boob3obbobboo1750b3obb3o4bo3bo4b3obb3o$153b3obb3o4bo3bo4b3obb3o1751bo
bobbo15bobbobo$108boo5boo37bobobbo15bobbobo1753bo23bo$100b4obobobo5bob
obob4o30bo23bo1806boo5boo$99b3oboboboobo3boboobobob3o1852b4obobobo5bob
obob4o$99bo3bobo13bobo3bo1851b3oboboboobo3boboobobob3o$100bob3o5booboo
5b3obo1852bo3bobo13bobo3bo$100boo21boo1853bob3o5booboo5b3obo$100b5o15b
5o1853boo21boo$103boo15boo1856b5o15b5o$1981boo15boo$$116bo3b3o5b3o3bo
1804boo5boo5boo5boo15boo5boo5boo5boo$113boob5oboo3boob5oboo26bo5boo5b
oo5bo1752bo3bo3bobbo3bobbo3bo3bo11bo3bo3bobbo3bobbo3bo3bo$111boboobo5b
obobobo5boboobo22bobbooboobbo3bobbooboobbo1750bo3bobob3o5b3obobo3bo11b
o3bobob3o5b3obobo3bo$110bo3bobo3b5ob5o3bobo3bo19b3o4bobo3bobo3bobo4b3o
1703boo5boo5boo5boo22bo5boobb3ob3obboo5bo11bo5boobb3ob3obboo5bo$114b3o
5boo3boo5b3o23boobbobb3oboo3boob3obbobboo1701bo3bo3bobbo3bobbo3bo3bo
20boob3o15b3oboo11boob3o15b3oboo$111bobbob3o13b3obobbo20b3obb3o4bo3bo
4b3obb3o1701bo3bobob3o5b3obobo3bo20bo25bo11bo25bo$113bo23bo23bobobbo
15bobbobo1665bo3b3o5b3o3bo18bo5boobb3ob3obboo5bo21bo3bo15bo3bo13bo3bo
15bo3bo$162bo23bo1663boob5oboo3boob5oboo15boob3o15b3oboo22bobbo15bobbo
15bobbo15bobbo$1848boboobo5bobobobo5boboobo13bo25bo$1847bo3bobo3b5ob5o
3bobo3bo13bo3bo15bo3bo$1851b3o5boo3boo5b3o18bobbo15bobbo$1848bobbob3o
13b3obobbo$1850bo23bo3$124bo3b3o5b3o3bo$121boob5oboo3boob5oboo$119bob
oobo5bobobobo5boboobo$118bo3bobo3b5ob5o3bobo3bo$122b3o5boo3boo5b3o$
119bobbob3o13b3obobbo17boo5boo5boo5boo$121bo23bo17bo3bo3bobbo3bobbo3bo
3bo$163bo3bobob3o5b3obobo3bo$163bo5boobb3ob3obboo5bo$163boob3o15b3oboo
$163bo25bo$164bo3bo15bo3bo$165bobbo15bobbo5$174bo$168booboboboo$165b3o
bob3o$165bo3bobo5bo5bo5boo5boo5bo$169boo6bo3bobbooboobbo3bobbooboobbo$
166boo9bob3o4bobo3bobo3bobo4b3o$166booboo8boobbobb3oboo3boob3obbobboo$
170bo8b3obb3o4bo3bo4b3obb3o$180bobobbo15bobbobo$181bo23bo4$106bo3b3o5b
3o3bo$103boob5oboo3boob5oboo$101boboobo5bobobobo5boboobo$100bo3bobo3b
5ob5o3bobo3bo$104b3o5boo3boo5b3o$101bobbob3o13b3obobbo29boo5boo5boo5b
oo$103bo23bo29bo3bo3bobbo3bobbo3bo3bo$157bo3bobob3o5b3obobo3bo$157bo5b
oobb3ob3obboo5bo$157boob3o15b3oboo$157bo25bo$158bo3bo15bo3bo$159bobbo
15bobbo$$153bo7bo$147booboboboo3booboboboo$99bo3b3o5b3o3bo26b3obob3o9b
3obob3o$96boob5oboo3boob5oboo23bo3bobo5bobo5bobo3bo$94boboobo5bobobobo
5boboobo25boo6bobo6boo$93bo3bobo3b5ob5o3bobo3bo21boo9bobo9boo$97b3o5b
oo3boo5b3o25booboo15booboo$94bobbob3o13b3obobbo26bo15bo$96bo23bo7$145b
o7bo$139booboboboo3booboboboo$136b3obob3o9b3obob3o$136bo3bobo5bobo5bob
o3bo$140boo6bobo6boo$137boo9bobo9boo$96bo5boo5boo5bo20booboo15booboo$
94bobbooboobbo3bobbooboobbo22bo15bo$92b3o4bobo3bobo3bobo4b3o$92boobbo
bb3oboo3boob3obbobboo$92b3obb3o4bo3bo4b3obb3o$93bobobbo15bobbobo$94bo
23bo6$107boo$107bobobob4o$106boboobobob3o$80bo3b3o5b3o3bo12bobo3bo$77b
oob5oboo3boob5oboo3boo5b3obo$75boboobo5bobobobo5boboobo11boo$74bo3bobo
3b5ob5o3bobo11b5o$78b3o5boo3boo5b3o11boo$75bobbob3o13b3obobbo$77bo23bo
3$163bo7bo$34boo5boo114booboboboo3booboboboo$35boo3boo112b3obob3o9b3ob
ob3o$32bobbobobobobbo109bo3bobo5bobo5bobo3bo$32bo11bo113boo6bobo6boo$
32bobbobobobobbo110boo9bobo9boo$7bo5boo5boo5bo7boo3boo7bo5boo5boo5bo
32bo5boo5boo5bo32booboo15booboo$5bobbooboobbo3bobbooboobbo6boo3boo4bo
bbooboobbo3bobbooboobbo28bobbooboobbo3bobbooboobbo34bo15bo$3b3o4bobo3b
obo3bobo4b3o3b3o7b3o4bobo3bobo3bobo4b3o24b3o4bobo3bobo3bobo4b3o$3boobb
obb3oboo3boob3obbobboo4b3o6boobbobb3oboo3boob3obbobboo24boobbobb3oboo
3boob3obbobboo$3b3obb3o4bo3bo4b3obb3obbobbo7b3obb3o4bo3bo4b3obb3o24b3o
bb3o4bo3bo4b3obb3o$4bobobbo15bobbobo4boo9bobobbo15bobbobo26bobobbo15bo
bbobo$5bo23bo17bo23bo28bo23bo3$121boo5boo$113b4obobobo5bobobob4o32bo7b
o$112b3oboboboobo3boboobobob3o25booboboboo3booboboboo$112bo3bobo13bobo
3bo22b3obob3o9b3obob3o$113bob3o5booboo5b3obo23bo3bobo5bobo5bobo3bo$
113boo21boo27boo6bobo6boo$113b5o15b5o24boo9bobo9boo$116boo15boo27boob
oo15booboo$166bo15bo8$56boo5boo$6bo3b3o5b3o3bo23b4obobobo5bobobob4o$3b
oob5oboo3boob5oboo19b3oboboboobo3boboobobob3o$boboobo5bobobobo5boboobo
17bo3bobo13bobo3bo$o3bobo3b5ob5o3bobo3bo17bob3o5booboo5b3obo$4b3o5boo
3boo5b3o21boo21boo$bobbob3o13b3obobbo18b5o15b5o$3bo23bo23boo15boo97bo
3b3o5b3o3bo$164boob5oboo3boob5oboo$131boo5boo22boboobo5bobobobo5boboob
o$123b4obobobo5bobobob4o13bo3bobo3b5ob5o3bobo3bo$122b3oboboboobo3boboo
bobob3o16b3o5boo3boo5b3o$122bo3bobo13bobo3bo13bobbob3o13b3obobbo$123bo
b3o5booboo5b3obo16bo23bo$123boo21boo$123b5o15b5o$126boo15boo5$49bo3b3o
5b3o3bo$46boob5oboo3boob5oboo$44boboobo5bobobobo5boboobo$43bo3bobo3b5o
b5o3bobo3bo$47b3o5boo3boo5b3o$44bobbob3o13b3obobbo$46bo23bo27$5boo5boo
5boo5boo$3bo3bo3bobbo3bobbo3bo3bo$3bo3bobob3o5b3obobo3bo$3bo5boobb3ob
3obboo5bo18bo3b3o5b3o3bo$3boob3o15b3oboo15boob5oboo3boob5oboo$3bo25bo
13boboobo5bobobobo5boboobo$4bo3bo15bo3bo13bo3bobo3b5ob5o3bobo3bo$5bobb
o15bobbo18b3o5boo3boo5b3o$43bobbob3o13b3obobbo$45bo23bo!

A period 18060 c/5 rake which demonstrates a method of constructing
arbitrarily large period c/5 rakes and ships with (perhaps) full
coverage of all large periods which are a multiple of 30.

This consists of three parts.  The first part is the Herschel c/5 track
at the left side.  This converts a single incoming glider moving left into
two outgoing gliders moving right.  The tracks of these two gliders are
separated by 40 rows, which is the magic separation required to form my
latest still life which can be activated by spiders.  The second part is
the convoy of c/5 ships which convert the two incoming gliders into the
magical still life composed of three blocks and a ship.  (The first glider
forms the three blocks, and the second glider forms the ship.)  The
third part consists of the convoy of ships which ignite the still life
to form a glider which is used to close the loop, and an output glider.
Also required with the last part is a glider delayer convoy which is
needed to make the parity of the glider's path correct.

The ships in this convoy are all period 5 spiders or period 30 pre-pulsar
ships. So there is the possibility of obtaining periods which are any
large multiple of 30 by adjusting the parts.  (This fact is not yet
demonstrated, however.)

The adjustments are as follows.  Firstly, the whole right half of the
rake can be moved diagonally to the upper right by any number of cells,
with the generations adjusted by the extra distance the the incoming
gliders have to travel.  Doing this will raise the inpact point of the
final glider because of the extra flight time of the gliders between the
left and right halfs.  Secondly, the activation of the still life can be
delayed by any number of generations.  This will lower the impact point
of the final glider because of the extra generations that the still
life is undisturbed.  For adjustments by non-multiples of 30 generations,
the glider delayer also has to be adjusted to react properly with the
glider.

David I. Bell, September 1999
