// Vertical lines and vertical asymptotes:
Curve_analyser INPUT "this: P[2(0,P[2(0,4)(1,-12)(2,5)])(1,P[2(1,6)(2,-3)])(2,P[2(1,-2)(2,1)])]"

// Covertical points
Curve_analyser INPUT "P[6(0,P[6(0,34186452217925)(1,-47333108912824)(2,8590127185697)(3,5899658904286)(4,32145408)(5,17432576)(6,16973824)])(1,P[5(0,-7748549723572)(1,10952549708016)(2,-2445480937892)(3,-1083231084104)(4,19103744)(5,29949952)])(2,P[4(0,1061963133616)(1,-839531790032)(2,23101440)(3,12386304)(4,27492352)])(3,P[3(0,-31237868032)(1,24452318720)(2,26607616)(3,26804224)])(4,P[2(0,9830400)(1,7602176)(2,23461888)])(5,P[1(1,31293440)])(6,P[0(0,4096000)])]"

// Same with some content
Curve_analyser INPUT "P[6(0,P[10(0,239305165525475)(1,-433891119043543)(2,-105547852922974)(3,544084567642102)(4,-168636318668897)(5,-121992740815323)(6,34879008294620)(7,11799206430140)(8,-36175872)(9,85786624)(10,33947648)])(1,P[9(0,-54239848065004)(1,99913497126828)(2,19760931822856)(3,-122064771317912)(4,42619705096452)(5,24317888697724)(6,-8140916911648)(7,-2166674406544)(8,128057344)(9,59899904)])(2,P[8(0,7433741935312)(1,-9062611931072)(2,-7038911122368)(3,10741692910944)(4,-394721728272)(5,-1679188229536)(6,-164069376)(7,107249664)(8,54984704)])(3,P[7(0,-218665076224)(1,264879835136)(2,207970109440)(3,-313676665856)(4,10561338880)(5,48743222272)(6,133627904)(7,53608448)])(4,P[6(0,68812800)(1,23724032)(2,52953088)(3,-109314048)(4,-168689664)(5,85590016)(6,46923776)])(5,P[5(1,219054080)(2,-93880320)(3,-281640960)(4,93880320)(5,62586880)])(6,P[4(0,28672000)(1,-12288000)(2,-36864000)(3,12288000)(4,8192000)])]"

hmm smth realy heavy...
P[34(0,P[34(0,12952101536523102192492711540000000)(1,-84147098480789650665250232160000000)(2,-69088664533801811202671946450000000)(3,-12990598879942044092505125010000000)(4,27052642714728288021127698670000000)(5,26683266093731013401148721880000000)(6,5372171464167151111739335793000000)(7,-8934425711222817088377016721000000)(8,-8465742196405103553796952613000000)(9,-1737345552069859077855633714000000)(10,2393898184518898797964635987000000)(11,2234406641615936885853597509000000)(12,479873852041504440602579852100000)(13,-547557654615450328195988452500000)(14,-514849404082170848294946339800000)(15,-115417366169449334489378073500000)(16,113234224818672992436814644400000)(17,107962164812116405549461548900000)(18,25135425283858380820959007860000)(19,-21694664362506393046334314800000)(20,-21025627462526285456489755280000)(21,-5057323915115735386146156273000)(22,3901460484323335482987702100000)(23,3846534854318572165730297444000)(24,950752053910955172204451437900)(25,-665241246757279897517641949200)(26,-666960287213849591322741077200)(27,-168596633306616989111809611900)(28,108415065221291211390422093200)(29,110420084629074642463546936400)(30,28431730759059073988652406240)(31,-16992776198434916741021022360)(32,-17557477656685153453414375500)(33,-4588689239444215584479993393)(34,2574250362779616822482848012)])(2,P[0(0,-123917486647761741318703576800000000)])(4,P[0(0,79246903881551255661144190100000000)])(6,P[0(0,2186663392639010037975810829000000)])(8,P[0(0,-30912413603643981961132659450000000)])(10,P[0(0,22784177877224038711887972820000000)])(12,P[0(0,-8699274014787859551101246025000000)])(14,P[0(0,836940561843498171726587625200000)])(16,P[0(0,1367060050733175030564444040000000)])(18,P[0(0,-1171114486352462799313004128000000)])(20,P[0(0,567955949125204086770735562700000)])(22,P[0(0,-181911283701056707932126214300000)])(24,P[0(0,25732945948997554536421517900000)])(26,P[0(0,13209567106923403694087544950000)])(28,P[0(0,-13184322903675827636908029720000)])(30,P[0(0,6798109015505303221533146500000)])(32,P[0(0,-2528588426392935931038968129000)])(34,P[0(0,669962430844565364862639688900)])]

Maldenbrot's curve: 0 segments ?

P[16(0,P[16(0,97)(1,378)(2,1041)(3,2020)(4,3220)(5,4200)(6,4700)(7,4488)(8,3730)(9,2670)(10,1656)(11,872)(12,388)(13,140)(14,40)(15,8)(16,1)])(1,P[12(0,238)(1,700)(2,1608)(3,2480)(4,3192)(5,3232)(6,2784)(7,1936)(8,1132)(9,520)(10,192)(11,48)(12,8)])(2,P[12(0,593)(1,1506)(2,3244)(3,4616)(4,5620)(5,5376)(6,4464)(7,3000)(8,1722)(9,780)(10,288)(11,72)(12,12)])(3,P[12(0,1058)(1,2164)(2,4232)(3,5232)(4,5720)(5,4816)(6,3648)(7,2224)(8,1204)(9,520)(10,192)(11,48)(12,8)])(4,P[12(0,1642)(1,2720)(2,4916)(3,5336)(4,5276)(5,3860)(6,2616)(7,1376)(8,668)(9,260)(10,96)(11,24)(12,4)])(5,P[8(0,2132)(1,2760)(2,4576)(3,4208)(4,3640)(5,2112)(6,1152)(7,384)(8,96)])(6,P[8(0,2424)(1,2472)(2,3856)(3,3128)(4,2524)(5,1320)(6,720)(7,240)(8,60)])(7,P[8(0,2368)(1,1824)(2,2656)(3,1808)(4,1288)(5,528)(6,288)(7,96)(8,24)])(8,P[8(0,2030)(1,1158)(2,1600)(3,920)(4,556)(5,132)(6,72)(7,24)(8,6)])(9,P[4(0,1516)(1,600)(2,800)(3,400)(4,200)])(10,P[4(0,994)(1,252)(2,336)(3,168)(4,84)])(11,P[4(0,564)(1,72)(2,96)(3,48)(4,24)])(12,P[4(0,276)(1,12)(2,16)(3,8)(4,4)])(13,P[0(0,112)])(14,P[0(0,36)])(15,P[0(0,8)])(16,P[0(0,1)])]

partial derivative
P[24(0,P[25(9,47185920)(11,-226492416)(13,443154432)(15,-465567744)(17,289345536)(19,-109608960)(21,24848384)(23,-3096576)(25,163072)])(2,P[23(7,25165824)(9,-310640640)(11,1023148032)(13,-1552760832)(15,1285029888)(17,-615776256)(19,170393600)(21,-25242624)(23,1548288)])(4,P[21(5,4325376)(7,-135266304)(9,858808320)(11,-2031943680)(13,2348322816)(15,-1470431232)(17,508515840)(19,-91176960)(21,6606336)])(6,P[19(3,262144)(5,-23150592)(7,322174976)(9,-1319116800)(11,2271166464)(13,-1939338240)(15,863797248)(17,-191683584)(19,16691200)])(8,P[17(1,4096)(3,-1474560)(5,54183936)(7,-442417152)(9,1243618560)(11,-1535238144)(13,916328448)(15,-258932736)(17,27682560)])(10,P[15(1,-24576)(3,3588096)(5,-72566784)(7,381837312)(9,-741288960)(11,626098176)(13,-233920512)(15,31555584)])(12,P[13(1,63488)(3,-4939776)(5,60879360)(7,-211648512)(9,273792000)(11,-142442496)(13,25138176)])(14,P[11(1,-92160)(3,4214784)(5,-32762880)(7,73482240)(9,-57415680)(11,13934592)])(16,P[9(1,82176)(3,-2285568)(5,11040768)(7,-14598144)(9,5241600)])(18,P[7(1,-46080)(3,770048)(5,-2128896)(7,1269760)])(20,P[5(1,15872)(3,-147456)(5,179712)])(22,P[3(1,-3072)(3,12288)])(24,P[1(1,256)])]

cubic parabola:
P[1(1,P[0(0,1)])(0,P[3(3,-1)])]


an apple curve:
P[7(0,P[7(2,4)(3,-4)(4,-1)(5,-3)(7,1)])(1,P[5(2,-12)(3,4)(4,3)(5,-1)])(2,P[5(0,1)(1,-1)(2,10)(3,1)(4,-3)(5,2)])(3,P[4(0,-3)(1,1)(2,2)(3,-2)(4,1)])(4,P[3(0,2)(1,1)(2,-6)(3,1)])(5,P[2(0,2)(1,-1)(2,2)])(6,P[0(0,-3)])(7,P[0(0,1)])]

P[4(0,P[4(2,-4)(4,1)])(2,P[2(0,-1)(2,2)])(4,P[1(0,1)])]

P[3(0,P[3(0,-1)(1,1)(3,1)])(1,P[2(0,3)(1,-1)])(2,P[1(0,-3)])(3,P[1(0,1)])]

y - x^2 = 0
P[1(1,P[0(0,-1)])(0,P[2(2,1)])] 

y - (x - 0.25)^2 = 0
P[1(1,P[0(0,-16)])(0,P[2(2,16)(1,-8)(0,1)])]

// a grid
Curve_analyser INPUT "
P[3(0,P[3(0,36)(1,-66)(2,36)(3,-6)])(1,P[3(0,-66)(1,121)(2,-66)(3,11)])(2,P[3(0,36)(1,-66)(2,36)(3,-6)])(3,P[3(0,-6)(1,11)(2,-6)(3,1)])]

Michael's curve:
P[7(0,P[6(6,8)])(1,P[3(3,-16)])(2,P[5(0,8)(5,8)])(3,P[3(2,-8)(3,-8)])(5,P[1(1,2)])(7,P[0(0,-1)])]

f*fx:
 P[12(0,P[11(11,384)])(1,P[8(8,-1152)])(2,P[10(5,1152)(10,704)])(3,P[8(2,-384)(7,-1536)(8,-576)])(4,P[9(4,960)(5,768)(9,320)])(5,P[7(1,-128)(2,-192)(6,-336)(7,-512)])(6,P[5(4,320)(5,192)])(7,P[5(0,16)(5,48)])(8,P[3(3,-64)])(9,P[4(4,-40)])(10,P[2(1,20)(2,24)])(12,P[0(0,-2)])]

P[3(0,P[4(0,-169)(1,408)(2,-704)(3,512)])(1,P[2(0,576)(1,-512)])(2,P[2(0,-576)(1,512)])]

P[9(3,P[0(0,-1)])(4,P[3(1,1)(3,-4)])(5,P[0(0,1)])(6,P[2(2,3)])(1,P[7(7,-1)])(9,P[0(0,1)])]

a star:
P[14(0,P[14(0,-1)(14,1)])(1,P[6(6,-14)])(2,P[12(12,7)])(3,P[4(4,70)])(4,P[10(10,21)])(5,P[2(2,-42)])(6,P[8(8,35)])(7,P[0(0,2)])(8,P[6(6,35)])(10,P[4(4,21)])(12,P[2(2,7)])(14,P[0(0,1)])]

lemniscate:
P[16(0,P[16(8,-2)(16,1)])(2,P[14(6,56)(14,8)])(4,P[12(4,-140)(12,28)])(6,P[10(2,56)(10,56)])(8,P[8(0,-2)(8,70)])(10,P[6(6,56)])(12,P[4(4,28)])(14,P[2(2,8)])(16,P[0(0,1)])]

P[2(0,P[2(0,-1)(2,1)])(2,P[0(0,1)])]

P[1(1,P[3(0,15)(1,-8)(2,1)])]

P[2(0,P[1(1,1)])(1,P[1(0,1)])]

P[7(0,P[0(0,1)])(1,P[1(1,1)])(2,P[2(2,1)])(3,P[3(3,1)])(4,P[4(5,1)])(5,P[5(5,1)])(6,P[6(6,1)])(7,P[7(7,1)])]

P[10(0,P[10(10,1)])(1,P[4(4,10)])(2,P[8(8,5)])(3,P[2(2,-20)])(4,P[6(6,10)])(5,P[0(0,2)])(6,P[4(4,10)])(8,P[2(2,5)])(10,P[0(0,1)])]

a face:

P[12(0,P[12(2,-100)(4,39)(6,-200)(8,78)(10,-100)(12,39)])(1,P[6(0,-200)(2,78)(4,-1000)(6,390)])(2,P[10(0,-100)(2,84)(4,1000)(6,-300)(8,-500)(10,240)])(3,P[4(0,90)(2,2000)(4,-330)])(4,P[8(0,45)(2,1000)(4,-840)(6,-1000)(8,615)])(5,P[2(0,-200)(2,-822)])(6,P[6(0,-200)(2,-372)(4,-1000)(6,840)])(7,P[0(0,90)])(8,P[4(0,90)(2,-500)(4,645)])(10,P[2(0,-100)(2,264)])(12,P[0(0,45)])]

angry face:

P[10(0,P[18(0,1708800)(1,3465600)(2,6242400)(3,11185200)(4,21309200)(5,26766400)(6,32775200)(7,45478400)(8,55708800)(9,61884000)(10,67834400)(11,63997600)(12,48149600)(13,32289600)(14,21632000)(15,12699200)(16,5269600)(17,1299600)(18,144400)])(1,P[16(0,-17896000)(1,-18772000)(2,-44061600)(3,-73394400)(4,-107568800)(5,-135043200)(6,-166587200)(7,-196425600)(8,-205771200)(9,-184672800)(10,-148807200)(11,-107534400)(12,-66043200)(13,-32289600)(14,-11812800)(15,-2880000)(16,-360000)])(2,P[16(0,70248800)(1,43175600)(2,123359200)(3,200510400)(4,236601600)(5,276224000)(6,320782400)(7,295968000)(8,241101600)(9,182149600)(10,117148800)(11,58284800)(12,23934400)(13,9083200)(14,3097600)(15,720000)(16,90000)])(3,P[12(0,-147677600)(1,-57471200)(2,-190283200)(3,-303168000)(4,-284547200)(5,-274243200)(6,-300675200)(7,-223516800)(8,-128887200)(9,-76392000)(10,-42998400)(11,-15120000)(12,-2520000)])(4,P[12(0,194042000)(1,48374000)(2,176534800)(3,275671200)(4,206976800)(5,141984000)(6,148644800)(7,93892800)(8,34831200)(9,11532000)(10,6266400)(11,2160000)(12,360000)])(5,P[8(0,-169378400)(1,-26280800)(2,-100484000)(3,-153604800)(4,-95198400)(5,-37195200)(6,-37598400)(7,-21600000)(8,-5400000)])(6,P[8(0,100084400)(1,8952800)(2,34257600)(3,51187200)(4,27577600)(5,3892800)(6,3817600)(7,2160000)(8,540000)])(7,P[4(0,-39554400)(1,-1732800)(2,-6412800)(3,-9360000)(4,-4680000)])(8,P[4(0,9971200)(1,144400)(2,504400)(3,720000)(4,360000)])(9,P[0(0,-1440000)])(10,P[0(0,90000)])]

P[2(0,P[0(0,-1)])(2,P[3(3,-1)])]

// xy-1
Curve_analyser INPUT "P[1(0,P[0(0,-1)])(1,P[1(1,1)])]"

// Random ungeneric curve of degree 5
Curve_analyser INPUT "P[5(0,P[7(0,-153757212)(1,775846709)(2,35856805)(3,251379033)(4,-616448465)(5,525473327)(6,195623468)(7,-912992897)])(1,P[6(0,60516225)(1,-1000013256)(2,673704626)(3,-777777772)(4,-737199430)(5,-913534040)(6,-480655748)])(2,P[5(0,-744673850)(1,-1053864038)(2,-997300971)(3,-383280637)(4,1036729085)(5,184825936)])(3,P[4(0,226707734)(1,-1021909364)(2,156709742)(3,-722569311)(4,-726116830)])(4,P[3(0,-903824027)(1,-624115123)(2,1001451441)(3,853642902)])(5,P[2(0,755831997)(1,170998943)(2,469185394)])]"
	
// Random curve of degree 10
Curve_analyser INPUT "P[10(0,P[10(0,983367369)(1,517241727)(2,368193629)(3,376751336)(4,-789447461)(5,-240009055)(6,-32150548)(7,1013593973)(8,817337461)(9,-1037184685)(10,136833019)])(1,P[9(0,218630258)(1,690156150)(2,315304427)(3,-28475443)(4,-350787571)(5,-325880162)(6,409406720)(7,-361642021)(8,-232307924)(9,-479495395)])(2,P[8(0,-486247128)(1,-457356948)(2,804978692)(3,272222901)(4,508895452)(5,519347661)(6,-738774581)(7,-292810866)(8,-820757896)])(3,P[7(0,349946670)(1,-861891195)(2,-960682858)(3,-658751905)(4,180593945)(5,-285947397)(6,320263058)(7,987357500)])(4,P[6(0,630026895)(1,455693515)(2,206383558)(3,676845667)(4,575601601)(5,-850090344)(6,-716034755)])(5,P[5(0,834373205)(1,419230056)(2,-405933983)(3,56843446)(4,730377570)(5,-793542719)])(6,P[4(0,-70534160)(1,-341900245)(2,-66950551)(3,587423529)(4,672553321)])(7,P[3(0,-502919169)(1,694278587)(2,498144336)(3,-861776894)])(8,P[2(0,-416307005)(1,-142677986)(2,959822365)])(9,P[1(0,364396497)(1,79593893)])(10,P[0(0,-538054163)])]"

P[1(0,P[0(0,-1)])(1,P[0(0,100000000)])]
P[1(0,P[0(0,-1)])(1,P[0(0,100000000000000000000000000)])]
P[1(0,P[0(0,-1)])(1,P[0(0,100000000000000000000000000000000000000000)])]
P[1(0,P[0(0,-1)])(1,P[0(0,1000000000000000000000000000000000000000000000000000000000000)])]
P[1(0,P[0(0,-1)])(1,P[0(0,100000000000000000000000000000000000000000000000000000000000000000000000000000000)])]
P[1(0,P[0(0,-1)])(1,P[0(0,10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)])]
P[1(0,P[0(0,-1)])(1,P[0(0,100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)])]
P[1(0,P[0(0,-1)])(1,P[0(0,1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)])]

P[23(0,P[3(0,36)(1,-66)(2,36)(3,-6)])(1,P[3(0,-66)(1,121)(2,-66)(3,11)])(2,P[3(0,36)(1,-66)(2,36)(3,-6)])(23,P[2(0,-6)(1,11)(2,-6)])]

// 3 vertical cusps
Curve_analyser INPUT "P[5(0,P[5(0,-632729)(1,6667802)(2,-22582612)(3,27171166)(4,-13391285)(5,398034)])(1,P[4(0,947700)(1,-9630360)(2,27674406)(3,-15680304)(4,4855599)])(2,P[3(0,968112)(1,-3986118)(2,-8291943)(3,1358640)])(3,P[2(0,2151099)(1,1443420)(2,754596)])(4,P[1(0,-2752947)(1,1436130)])(5,P[0(0,1068714)])]"

// 2 vertical cusps toghether with a vertical asymptote
Curve_analyser INPUT "P[3(0,P[4(0,1516403)(1,-2072063)(2,362677)(3,197175)(4,12912)])(1,P[3(0,-370048)(1,656460)(2,-139984)(3,-31452)])(2,P[2(0,-3668)(1,-95364)(2,10288)])(3,P[1(0,10768)(1,9232)])]"

// 2x2 covertical vertical flex points
Curve_analyser INPUT "P[6(0,P[6(0,12651894111773)(1,-9997374643979)(2,2719744)(3,8224768)(4,12419072)(5,3424256)(6,9240576)])(1,P[5(0,6758287772180)(1,-5340298837900)(2,15745024)(3,8142848)(4,180224)(5,10567680)])(2,P[4(0,1437941176784)(1,-1136010459312)(2,1703936)(3,14843904)(4,1818624)])(3,P[3(0,155008805056)(1,-122434227520)(2,3588096)(3,5914624)])(4,P[2(1,-3260888064)(2,2521967616)])(5,P[1(0,249876480)(1,-207040512)])(6,P[0(0,9519104)])]"

// 2x vertical flex point and vertical cusp covertical (bad running time) - 
Curve_analyser INPUT "P[6(0,P[6(0,-5723842310963)(1,6925613393727)(2,191867134075)(3,-1651898083863)(4,1277952)(5,1593344)(6,3895296)])(1,P[5(0,83040397608)(1,197268251348)(2,129296337192)(3,-266321073476)(4,1818624)(5,1949696)])(2,P[4(0,411446467908)(1,-325047869916)(2,565248)(3,1081344)(4,307200)])(3,P[3(0,44348533488)(1,-35031218320)(2,2883584)(3,1712128)])(4,P[2(1,-933085440)(2,721647360)])(5,P[1(0,71500800)(1,-59243520)])(6,P[0(0,2723840)])]"

// Bad running time even in randomized case (CORE:85.6, LEDA 243) - not more, about 2.5 seconds
Curve_analyser INPUT "P[10(0,P[10(0,-58839514)(1,997566287)(2,-398965577)(3,-199895037)(4,-603204463)(5,600943081)(6,271318110)(7,-882003767)(8,-164806141)(9,-1029187694)(10,826514948)])(1,P[9(0,19075966)(1,204274524)(2,-90102622)(3,903093486)(4,-394893232)(5,-277006244)(6,-911160401)(7,586392981)(8,-223783897)(9,921217842)])(2,P[8(0,-514375856)(1,755423550)(2,-794462920)(3,-762055005)(4,-702335492)(5,-759699145)(6,-702474569)(7,-1071113005)(8,-1014738416)])(3,P[7(0,-26088529)(1,-833213015)(2,830001332)(3,662243311)(4,-276405197)(5,370348247)(6,436089864)(7,-581335997)])(4,P[6(0,-834102847)(1,649166302)(2,287845396)(3,-769952670)(4,155841674)(5,947363172)(6,-645261597)])(5,P[5(0,587641549)(1,-14926519)(2,36690021)(3,566250291)(4,-938411566)(5,322058299)])(6,P[4(0,310341803)(1,-1067619071)(2,-317268399)(3,-1018907206)(4,315682396)])(7,P[3(0,-289128276)(1,-888507237)(2,78238330)(3,-358181715)])(8,P[2(0,-667728184)(1,-938204810)(2,-672284322)])(9,P[1(0,-33935435)(1,353503874)])(10,P[0(0,564672829)])]"

// Some guy of degree 10 through a lot of grid points
Curve_analyser INPUT "
P[10(0,P[10(0,-1568097320217486954746038222353264026124512729824624140426456084821674570338465467115580714883216239107431783632422654199126792637300589725752422709531566351360)(1,-692563692415572318330323720402173161988316873095299189456136185500332943799067714445185021088927369538994355822090055822540308818921080515367880457083296043872)(2,253759163389114495396260637563587662071357335892714002172477255584362164269846375379865259715040361882164928513427118257776517099038249139355957960821160815480)(3,228321764539581846874415958281084770105508240539684522497896538757865464015496801378415832681329734921170115055154276152587366836814448449062771611393335215440)(4,23297564534131932947260767016711450615937572178549208236407791346513133276363676808903928649353251176275730407623435310269988351997577191345351813388188679050)(5,-6684460444656328064217464609376317635603611936196647805476345384416686419219855253002846565210053169581286716421895283845414891455830670472563596097393104246)(6,-891975470096534658237690594782632964154870189971651305507462848252818830192614064263105937219158639680516155615505952238983550670279268547342052362585300830)(7,59792773603068934091129808588368823608837077391105352241612919512734983815206605009217945942349531406006730102527346111193274630234004373042701634417238700)(8,8852949514373724385933084135236850246470310378064839540418577804292336631941178851572493811466566550104039417757057739523774429023786998544920017229065790)(9,-108756784622601867650828638243365668511233392755208032557131233861602277448163741223246147383052623177961936506536169803893047671772124680844953487107622)(10,-21562186090918943273457833810776075070768046068364536876193316913524298129985025435629921414620391197261609374816318535561371186238785499898843801557730)])(1,P[9(0,2102640749630557402251474067629846369580001087025340906470884065038008268736569710248647075029043427112646437490912159319849485801890088504431765375900293612512)(1,217753848411190167550974654772690253357857328105368483064290179476153820932588952121543097531065070493452810591276890711355038362912585182980152057152815641188)(2,-565666935869059297494011823428722473464383830001382482636486753579578696118817148191134485451450333731318422358172603443907907905120251638217221752116126556184)(3,-93216793187451456612449679034417662419824339229410488056421321014646962455208620062478647639644267191228615026745789053735513852265184456836286054734049429341)(4,15555254512881101767886771862264626347977743214927422668921205567116434332906950757984637242058720114628222084674496433000703652498871116717063005757875431980)(5,2011157326514161917986077496256796440304672022629861556161279348956662461111241224743192856754553857092391787590535004163957208931490008976141187805241552324)(6,-203233963488323140034402673031520522551629925731660104689538959661298615916030015023466287394177100105218702705002602550105190646893756078920929800452513398)(7,-13945901433907053286030315829282038145963396165011519717972052715036537290267261641668712577034698646610295800461194048673993199457157169891863531747186003)(8,873517262230827384637469817322358323937247564015146441284805517323621071503671996382475713759626517968528493338458152288950401577183697914427607742630610)(9,34519765592572180325101014364678830039214590392665752559418908437495757211832622180043839938956557488347214092289333087395427057443245631043338438355192)])(2,P[8(0,-470765054838349225376551476798338971567688056186293072300495383616789606948706789946285955617719354572064300372206993293046860538656326371787866926227176935688)(1,126009619539996070055758197041045783276266544678598823037460856005462543550171893824897377784994825214383775236645691765816200467956428325268011218787858057370)(2,52885669730993033067662473339637778382953108222291285118661896936940299582882692130950197845137216467597016712582794374863095293119654426127707596912867337692)(3,-13060380873855280394651846347550596848344808404960922093113577473113294324023012843306478123002186497472947705945018749739089552811093039299951358083965466475)(4,-2025505014367039907325695459124622139854878957610920749528708053869797040485154827835721397953560284974075731487433222992940033867377608817097648415887960309)(5,370629365334835371790422503092179949290022770029279591810682766902278111266550533134686470893169334472214098416890641847889021130749752237996273350331296639)(6,23551950642491921305481776496556946645363518065547447048595996299236919863050638920203866950074254220697554697554983528484361501072602631003193675784863437)(7,-2362496062424809192925873155090930076421305840816123839147050292683593087712761863011921957759922101487294961400238256186802122844062789820139627705186998)(8,-144213525795471482598981387246391138087452884033169462637453750440068671565393433750594613628849073654682546388241250167814394962113199904124682252781220)])(3,P[7(0,-87565503278334076207256423012344226419975414298155427352921802016638508763304885859289549753464156961580242846974171093034105838932288721113279546091412472906)(1,29394782757432240004837889368320112298532358642196074708026287929308550556096245857323153095533760323622953916985518026149392310471152507094579930418324062629)(2,15204358532645537335627171931315676352619807658933813277277720387955756371270681723561270310152922976513990269232836730459601354612491138583103942088168818476)(3,2151713347027487112549870558827574650278766901536074268308433142593886809717067642040733034964474751884938690068140985858130714359742294689928328365759994602)(4,-238610379706296145025219404472249758916703002223091051986163943308507751929353056520064528438324302081610809412036340086945981165921515075399571659553353106)(5,-43957128509012749952821814453282448646167166980167895093357498516092262420565727741245323533808847001238176930645226373387835925989084661492882503440733428)(6,1118715322129490260970448636380631301011212305996274427322441084564395270539252726145916278780149407430168476129565049346274581129898720936673129718659416)(7,230552231844437782450514940307508426737523013617837905915854159692061085671287107568742075760424894378697885729668333744373094141027270073679824900533281)])(4,P[6(0,24148648434941074533464294528368734996870684156146134427331908436365035424120099703937717573247237585020266722879728311407802075209094102018816581006548353855)(1,-9519918172738526759919821462642607130768103330265957018184147071393543331130546025560598604190291975591072748902618403664839174360373696047091310028795836758)(2,-821465697957419659335415783326221916277022305013076011838187515080477819785409525219794328517354484211404803627827856261396835422203217273847353232755462661)(3,22414386045701119268382912324005268771050161438660689205597225720349828533132489720903808933413490058750083279364546750124575453360031283063920851540338047)(4,21321340579478477379454750379079577921114509136670881599507732454461156640096039791745251348263257578595162252945064167268733331021097476343657455419773097)(5,-84267868716981092829906946993064118622817940467481178409918610343220892634729655609643124372434998691172336037036675819830735882235794834862105293350225)(6,-567504531134038429280145990712877370219975479724742492995645728841295423792103473360822051030100591769209236111894786531570155316518645733988412894995)])(5,P[5(0,-40528535297042347078166126562040356331882166204464741869770388010860374774145077822641181808348370927104084432387245934003283382260319349306095847158994612)(1,-370784127079180655064019394529750963116368486683696148387224010898110550405582685222508502396222160608817892736758709353936807121708972106580182225106423181)(2,-130710578540392822925733696600750404432780481643413979179751439495801315713005609913821551372328078776589769467402588860027245189882580008384254911079592788)(3,-2010192443370259250343828432367710385681766522923894485525931941249535893141414683217075385341615777500619436947358812448055480923522479270380299245825894)(4,1198019003802276362327892813807871202998142527856833299642309726363134376201533380422022655354028141451918556958510487782818292818590793543861897011604370)(5,-20614065142805210559379008060820541507589759736937082654846720242565139615786009667000933245768745045663957769356357216822338524646463654768514584961334)])(6,P[4(0,-344213503091664636175696672721312729718376301888536519680676216859441904885009107214709064341270783230527738962191156931634176466327780563956962993301167235)(1,171726130884907072050396172298000646786155260877163510541152587418251435882463611747234158999637206338478163567459229842859084101206588774723444594552375370)(2,2795317660222968685019728593823526303444898031337366934525983309809680373333224049024793247417540194193462197571459608780200420479009710156371274755682542)(3,-384159465188258846252697906798471372303603491715977455300017693118830563446639307366854076110117165610454986071170730290981087177827360128466668413417836)(4,-133109585817358069159817041450632561730657687779577054126928599880532129510640014409457470472342848061894793984482341558247988752460773888779932741144562)])(7,P[3(0,22419108354769003085492730829015614924474288530499184650241318116619449406780034468830143454503972052369575035938104710443647916423548243335290542868818966)(1,-5058651783178943686780886494546986773286464545811648247543599464402618558474330565579211727593503783799559382308739625154434301608080355849025876800962401)(2,199184234077514524831290089659388997957661321596817511461525119410825012688725490717178078133234782272686900280855650957792939055780218272318073197888224)(3,42729533982983353458713205261488880930429580967574170297653041864179647146789143811718862611708717049565755009885731945788498948144343298695003476013177)])(8,P[2(0,904063336089078156275415495674606886172747982363436133324615861064178857485280844098418927772318351841633602622169084511970516970783376054066450581320985)(1,-619569635999033481394165006701117928519936108181492022659838724201917144138136440655727545469015797308135525926207322427917409621532722642438513534844334)(2,17504322414485718083081249545834236097464807020976170033450776695400186772547644942722657030362143993947612800859529974893303869895104451869982312059619)])(9,P[1(0,-101900820098317198969803261869385449204137545000669636006452651993626797351635228706194337514346742674301619055866935713958318584199141985677189075047160)(1,27352552531796730046362133322519089394606013643782808497989127821984616349582585277323499157469221465801653305094950542901862452656637404050461653397989)])(10,P[0(0,1036189726764118824461952651784993244696710738492060184104273994167979573473524555530213943153905717554187004949956866937523800179638846603979398862643)])]


// Vertical cusps and singularities, free coefficients are chosen such that the curves go through gridpoints
// running time: 170 s on 2.August
Curve_analyser INPUT "P[8(0,P[8(0,-2354751542574437597775621634008186470593466450420025662957059143052822504137801268896556960261473335747319347045760)(1,6285639785008691521623446895893814107168956586373371442555702705882141322002741721341981662124220692623299365969360)(2,-8608704708591214273881310868410678290883421085820141740724780948955158688512833364750108230725323134192261253461324)(3,14395852203835408324392302536008949534658892862372606662329746645177947010078705223588503054432524355185394072802736)(4,4794565982514594084134399673902615135801769035155863949091071384904628526343399765913906052030110138592078278902375)(5,-32684954498814209426418389422677334001347583932234502368212252705469196199347394908002606381509860090756855547228178)(6,-4423338807990846085216023613918119682824954136049419292354491032345121535815458401634869917153419211412635267115112)(7,1509226100862279945277327126466582924317900283483319511388519985426889105070615565124907269779736983366105407035282)(8,97992667534074237613243578126381873298238437128517995006976370466255439927360871420414660936727483178080887299021)])(1,P[7(0,17028011824034512760225397040784571393581268035529959635465504121717446130117995311380974266450945373624109887025424)(1,-39548076736703065857139928063317147587530102024167142289991048242538799009503886498090618712113593877283561226879416)(2,24754004118830835161210109664979001111204281831405529750127526852910628208259776472355959170391534789582180870076836)(3,36497914949626915963055001866422432831457841193817097130785846065232714135295203322096740738943209069216327838829258)(4,-49840128492280948503250079963539084038703224785037951947396429851070531196499621127148731798729261010285355076872237)(5,-18024088426504743836647935395440240174927152459066613021504546832839962078013881299044424536289662317149897649419585)(6,3592305468232917172813322639172009484258868369648379601455266000470991657217005600114072854007564276833850347034005)(7,475444272628222941663925874897739840296670695669062291188634107793173260399140817904709784222108303517682742459475)])(2,P[6(0,-17793942400784917055338968084511084639986248275513185970277227914680806474126977619910649131699155034086721393842524)(1,366427731027603614422518977548189570501149531184897228015066931821844282017117540786271571990025749389312521539168)(2,36329416064415833058493676913956466356907916264699864669544036191000588103102320431212205699509261893344623342113120)(3,29390236211537651863664112156085628161170746473072030454872699557727450406742460572258291554771198653440720883805632)(4,-15477373044509267671180916265247114276535727785047099728256180465935019716583178370314690763001156443491152798076579)(5,780799497029034871001583870710258863688866301475858938363251305728934406491403509867891508986299664638242513271708)(6,393368291991918102843987565172648992260075789417291509271954625304186001767126291973071252809301977783375146999843)])(3,P[5(0,-13316140357663461813070991360759477348068119042803702446683786042808520083685203031441123226790727427760909067355924)(1,-2332653452890144191455460722206459649474748151753762040496002307581057817925860078353251244814283321243422562173674)(2,57783798202330990331194833328126860452326817570931366653759803381527422574874058810101910561204079715170976770612658)(3,6463408833352637105579815329156962514869188420927168678395800070948336562110986877946172646796739708338293690015314)(4,-5164684012160090223396971497584355775235466849787178864019525581091712793754683635809331772407434134165919535604971)(5,-578418494871715952091284368998430120745990342761302729234146679447925593468202067531326135505225878478833383883023)])(4,P[4(0,-10837061077449908117644447857266050334656143521221896181583480794131897486516671430305996895495577386613949380049031)(1,-8154796807321780899482549498863324353307358362192685490945461038215902320237916603906547168145572762620790095886318)(2,9404381240736212438973510805020735483911731041460330797915950885549562394108750937611506278792239508261290705025654)(3,-5487347119158620094311415961654818542667790105136133785844650871874324942797607581646624322818304933600601154034812)(4,-800512918224035331190604665459266140242187401942803410142322956781979227848678313827389826748599815170286424440679)])(5,P[3(0,-18648771994063357106251052422232395609994553381812762847028437567978511768412993447269991222785259865972389662166085)(1,-480058251564484000052659204555862950706256459629257116757326119822765800101439504483674700527082057969583233837017)(2,-376033327459721913515861209306232313177558366915282321500159922481797226915738328060261484905793903468737842222127)(3,26266105489702078715270763312368531350690843362385076360770598265542552222742229180995324908614741748085046893225)])(6,P[2(0,-1421311987865687623861359936988121612466583460424934343608466368012609871307651108449010588319252953160350582964323)(1,2137440043072109385819918809724489756102662016280160877116509318141848597860745685082504486521805691668553286668958)(2,318102647692827144153578661149068558786204194116596152713021464313217453973836122505639070605949180705598641592717)])(7,P[1(0,884711658084859873854900623405213679648841654810770590310072496169983556870171313014986786267802079918949206874005)(1,69872015498548864045834835704264716680147813247867074168605971092024000352468262573851829866441603701599031599587)])(8,P[0(0,-16220093629556375222085220231430558986638344838445575923185383368080889807749438796214667254481587318426548879622)])]"