## Counting

This page presents, with a few statistical notes, the 4115 PC Sets for a 16 note division of the octave. Enjoy.

Interval Vector component reordering line.i2c { stroke-width:2; stroke:#203; } text.TETip { font-family:'Lucida Sans Typewriter'; font-size:8; stroke-width:0; fill:black; } circle.ivec { fill:#C69; } circle.cons { fill:#69C; } rect.ivec { fill:#A47; } rect.cons { fill:#47A; } interval vector 16TET index permutation: (71)(53) consonancy 7 2 5 4 3 6 1 8 For 16TET, as for 12TET, the interval vector is relatively easily transformed into the more useful consonancy. All even slots (2, 4, 6 and 8) remain as they are. Slots 1 and 7 are exchanged, as are slots 3 and 5. Thus a quick search for high values of the seventh slot of the interval vector (the second slot already counting pitch classes in secondary dominant relationships) is often sufficient to pick out sets rich in dominants and secondary dominants (if that's your taste).

Sets are organised mostly in order of increasing Forte Interval vector (which in this case has 8 components), excepting that the symmetric sets (blue = those equal to their own inverses) have been floated to the top. The (rare - and only of the hemi-cyclic 'yin-yang' type turning up only amongst cardinalities 6 and 10) green colouring applies to sets with purely cyclic (i.e. no inversional) symmetries. Thus, if you wish to hunt by interval vector (which seems unlikely, but we don't have any idea which properties of a set may excite you), bear in mind that each cardinality division is blocked up first by such symmetry considerations.

Each set is shown in prime interval path form, with - à la Forte - the largest gaps between pitch classes at the end. The interval path, or interval string, representation is preferred as it confers many advantages:

1. It provides a structurally precise, and unique (within rotations), set identifier - sans any cultural and historical baggage
2. The length of the path (in characters) is the (k) size of the set
3. Its k rotations (tail-head character shifts) exactly describe all k 'modes' of the k-set
4. The sum of the characters in the path is the (n) size of the PC 'universe'
5. Inversions of sets are simply the (renormalised) reverse of the path
6. It's easy to tell at a glance what the prime form would be (highest skips at end)
7. It's easy to tell if a set is symmetric by mentally reversing the path and spotting (in)equality
8. It's easy to see - for asymmetric sets - which of two inversions for normal form is 'best'

If you absolutely must see the path as the traditional, visually uninformative, unapprehendable brace-enclosed comma-separated list of pitch classes, there's a javascript tool to unwrap the path for you (and also show any related inverse and complementary/dual sets).

1 16-setsymmetries
ivecpathrotaflip
<GGGGGGG8>1111111111111111a168a28+8a12a27
1 1-set & 15-setsymmetries
ivecpathivecpathrotaflip
<00000000>G<EEEEEEE7>111111111111112a12a27
8 2-sets & 14-setssymmetries
ivecpathivecpathrotaflip
<00000001>88<CCCCCCC7>11111121111112a822a12a27
<00000010>79<CCCCCCD6>11111112111112a28
<00000100>6A<CCCCCDC6>11111111211112a12a27
<00001000>5B<CCCCDCC6>11111111121112a28
<00010000>4C<CCCDCCC6>11111111112112a12a27
<00100000>3D<CCDCCCC6>11111111111212a28
<01000000>2E<CDCCCCC6>11111111111122a12a27
<10000000>1F<DCCCCCC6>11111111111113a28
35 3-sets & 13-sets (21 distinct ivecs each)symmetries
ivecpathivecpathrotaflip
<00002100>556<AAAACBA5>1111211121112a12a27
<00010200>466<AAABACA5>1111211112112a12a27
<00020001>448<AAACAAA6>1111112112112a12a27
<00200100>33A<AACAABA5>1111111121212a12a27
<01000020>277<ABAAAAC5>1111121111122a12a27
<02010000>22C<ACABAAA5>1111111111222a12a27
<21000000>11E<CBAAAAA5>1111111111114a12a27
<00011010>457<AAABBAB5>1112111112112
5471111121112112
<00100110>367<AABAABB5>1111211111212
6371111121111212
<00101001>358<AABABAA6>1112111111212
5381111112111212
<00110010>349<AABBAAB5>1121111111212
4391111111211212
<01000101>268<ABAAABA6>1111211111122
6281111112111122
<01001010>259<ABAABAB5>1112111111122
5291111111211122
<01010100>24A<ABABABA5>1121111111122
42A1111111121122
<01101000>23B<ABBABAA5>1211111111122
32B1111111112122
<10000011>178<BAAAAAB6>1111121111113
7181111112111113
<10000110>169<BAAAABB5>1111211111113
6191111111211113
<10001100>15A<BAAABBA5>1112111111113
51A1111111121113
<10011000>14B<BAABBAA5>1121111111113
41B1111111112113
<10110000>13C<BABBAAA5>1211111111113
31C1111111111213
<11100000>12D<BBBAAAA5>2111111111113
21D1111111111123
116 4-sets & 12-sets (70 distinct ivecs each)symmetries
ivecpathivecpathrotaflip
<00040002>4444<888C8886>112112112112a444a12a27
<00121020>4345<889A98A4>112111211212a28
<00202002>3535<88A8A886>111212111212a822a28
<00202101>3355<88A8A985>111211121212a12a27
<00210120>3436<88A989A4>111121211212a12a27
<00300210>3337<88B88A94>111112121212a28
<01012020>2545<8989A8A4>111211211122a12a27
<01020300>4246<898A8B84>112111121122a12a27
<01202001>3238<89A8A885>121111112122a12a27
<02000202>2626<8A888A86>111122111122a822a12a27
<02001030>2527<8A8898B4>111112211122a28
<02010201>2266<8A898A85>111121111222a12a27
2428111111221122a12a27
<02102010>2329<8A98A894>111111122122a28
<03020100>222A<8B8A8984>111111112222a12a27
<10003200>1555<9888BA84>111211121113a28
<10022010>4147<988AA894>112111112113a28
<10100220>1636<98988AA4>111121211113a28
<10220010>3139<98AA8894>121111111213a28
<12201000>212B<9AA89884>211111111123a28
<20000022>1717<A88888A6>111113111113a822a28
<20000121>1618<A88889A5>111111311113a12a27
<20001210>1519<A8889A94>111111131113a28
<20012100>141A<A889A984>111111113113a12a27
<20121000>131B<A89A9884>111111111313a28
<21000021>1177<A98888A5>111112111114a12a27
<21210000>121C<A9A98884>111111111133a12a27
<32100000>111D<BA988884>111111111115a28
<00121011>3445<889A9895>112112111212
4435111211211212
<00210210>3346<88A98A94>112111121212
4336111121121212
<01012110>2455<8989A994>112111211122
4255111211121122
<01020201>2446<898A8A85>112112111122
4426111121121122
<01101111>2536<89989995>111212111122
3526111121211122
<01102101>2356<8998A985>121112111122
5326111121112122
<01102110>3256<8998A994>111211112122
5236121111211122
<01110120>2437<899989A4>112121111122
3427111112121122
<01111020>2347<899998A4>121121111122
4327111112112122
<01111110>3247<89999994>112111112122
4237121111121122
<01201101>2338<89A89985>121211111122
3328111111212122
<02011020>2257<8A8998A4>111211111222
5227111112111222
<02020101>2248<8A8A8985>112111111222
4228111111211222
<02111010>2239<8A999894>121111111222
3229111111121222
<10011210>1546<98899A94>111211211113
4516111121121113
<10012110>1456<9889A994>112111211113
5416111121112113
<10012200>4156<9889AA84>111211112113
5146112111121113
<10021011>1447<988A9895>112112111113
4417111112112113
<10101111>1537<98989995>111212111113
3517111112121113
<10110210>1366<98998A94>121111211113
3166111121111213
<10111110>3157<98999994>111211111213
5137121111121113
<10120011>1348<989A8895>121121111113
4318111111211213
<10121001>3148<989A9885>112111111213
4138121111112113
<10210110>1339<98A98994>121211111113
3319111111121213
<11000121>1627<998889A5>111122111113
2617111112211113
<11001111>1528<99889995>111221111113
2518111111221113
<11011110>1429<99899994>112211111113
2419111111122113
<11100111>1267<99988995>211112111113
6217111112111123
<11100120>2167<999889A4>111121111123
6127211111211113
<11101011>1258<99989895>211121111113
5218111111211123
<11101101>2158<99989985>111211111123
5128211111121113
<11110110>1249<99998994>211211111113
4219111111121123
<11111010>2149<99999894>112111111123
4129211111112113
<11111100>132A<99999984>122111111113
231A111111112213
<11201100>123A<99A89984>212111111113
321A111111112123
<11210100>213A<99A98984>121111111123
312A211111111213
<12111000>122B<9A999884>221111111113
221B111111111223
<21000111>1168<A9888995>111121111114
6118111111211114
<21001110>1159<A9889994>111211111114
5119111111121114
<21011100>114A<A9899984>112111111114
411A111111112114
<21111000>113B<A9999884>121111111114
311B111111111214
<22110000>112C<AA998884>211111111114
211C111111111124
<10111011>1357<98999895>121112111113
1438112121111113
3418111111212113
5317111112111213
273 5-sets & 11-sets (137 distinct ivecs each)symmetries
ivecpathivecpathrotaflip
<00410320>33334<66A76983>11212121212a12a27
<01220320>24334<67886983>11212121122a12a27
<01222021>32344<67888684>12112112122a12a27
<02030401>24244<68696A64>11211221122a12a27
<02040202>22444<686A6865>11211211222a12a27
<02202202>23326<68868865>11112212122a12a27
<02212120>32236<68878783>12111121222a12a27
<03012040>22525<696786A3>11122111222a12a27
<03022120>22255<69688783>11121112222a12a27
<04030201>22228<6A696864>11111122222a12a27
<20014300>14155<8667A963>11121113113a12a27
<20022121>14416<86688784>11113112113a12a27
<20220121>13318<86886784>11111131213a12a27
<21012220>11545<87678883>11121121114a12a27
<21022300>41146<87688963>11211112114a12a27
<21210220>12166<87876883>11112111133a12a27
<21222001>31138<87888664>12111111214a12a27
<22000222>11626<88666885>11112211114a12a27
<22212100>1221A<88878763>11111111323a12a27
<23220100>2112A<89886763>21111111124a12a27
<43210000>1111C<A9876663>11111111116a12a27
<01221130>23434<67887793>12112121122
3243411212112122
<01221211>23344<67887874>12121121122
3324411211212122
<01302211>23335<67968874>12121211122
3332511121212122
<01303102>32335<67969765>12121112122
3323512111212122
<02112130>23425<68778793>11122121122
2432511122112122
<02112211>24235<68778874>12111221122
3242511221112122
<02113120>23245<68779783>11211122122
4232511121122122
<02121121>22435<68787784>11212111222
3422511121211222
<02122030>22345<68788693>12112111222
4322511121121222
<02122111>32245<68788774>11211121222
4223512111211222
<02203111>23236<68869774>12111122122
3232611112122122
<02211211>22336<68877874>12121111222
3322611112121222
<03020302>22426<69686965>11221111222
2422611112211222
<03030301>22246<69696964>11211112222
4222611112112222
<03112030>22327<69778693>12211111222
2322711111221222
<03121120>22237<69787783>12111112222
3222711111212222
<10132021>14344<76798684>11212112113
3414411211212113
<10141012>13444<767A7675>12112112113
3144411211211213
<10212211>14335<76878874>11212121113
3341511121212113
<10221121>13435<76887784>12112121113
3431511121211213
<10221220>13345<76887883>12121121113
4331511121121213
<10222012>31435<76888675>11212111213
3413512111212113
<10222111>33145<76888774>11211121213
4133512121112113
<10231021>31345<76897684>12112111213
4313512111211213
<10310320>13336<76976983>12121211113
3331611112121213
<10320220>31336<76986883>12121111213
3313612111121213
<11022211>14425<77688874>11211221113
2441511122112113
<11022310>14245<77688973>11221121113
4241511121122113
<11023120>24145<77689783>11211122113
4142511221112113
<11103211>15235<77769874>11122121113
1532511121221113
<11112220>14236<77778883>11221211113
3241611112122113
<11113210>13255<77779873>12211121113
2315511121112213
<11120221>13426<77786884>12112211113
2431611112211213
<11121310>13246<77787973>12211211113
4231611112112213
<11122021>21445<77788684>11211211123
4412521112112113
<11122120>41245<77788783>21121112113
4214511211121123
<11122201>23146<77788864>11211112213
4132612211112113
<11202112>12535<77868775>21112121113
2153511121211123
<11203201>12355<77869864>21211121113
3215511121112123
<11210230>12436<77876893>21121211113
3421611112121123
<11211220>12346<77877883>21211211113
4321611112112123
<11212210>32146<77878873>11211112123
4123621211112113
<11220211>21346<77886874>12112111123
4312621111211213
<11220310>31246<77886973>21121111213
4213612111121123
<11221120>23137<77887783>12111112213
3132712211111213
<11301211>12337<77967874>21212111113
3321711111212123
<11310220>21337<77976883>12121111123
3312721111121213
<11311210>31237<77977873>21211111213
3213712111112123
<12011221>15226<78677884>11122211113
2251611112221113
<12021121>14227<78687784>11222111113
2241711111222113
<12101131>12526<78767794>21112211113
2521611112211123
<12101212>21526<78767875>11122111123
2512621111221113
<12110221>12427<78776884>21122111113
2421711111221123
<12111130>21427<78777793>11221111123
2412721111122113
<12112120>12256<78778783>22111211113
5221611112111223
<12112201>22156<78778864>11121111223
5122622111121113
<12122020>22147<78788683>11211111223
4122722111112113
<12211120>21247<78877783>21121111123
4212721111121123
<12211201>21328<78877864>12211111123
2312821111112213
<12212011>12238<78878674>22121111113
3221811111121223
<12221101>22138<78887764>12111111223
3122822111111213
<12302101>21238<78968764>21211111123
3212821111112123
<13121110>12229<79787773>22211111113
2221911111112223
<13212010>21229<79878673>22111111123
2212921111111223
<20013310>15145<86679973>11211131113
4151511131112113
<20023210>14146<86689873>11211113113
4141611112113113
<20111221>13516<86777884>11113121113
1531611113111213
<20111320>15136<86777983>12111131113
3151611131111213
<20121022>13417<86787685>11111312113
1431711111311213
<20122111>14137<86788774>12111113113
3141711311111213
<20122210>13156<86788873>11121111313
5131611112111313
<20132011>13147<86798674>11211111313
4131711111211313
<20231011>13138<86897674>12111111313
3131811111121313
<21013210>11455<87679873>11211121114
4115511121112114
<21021211>11446<87687874>11211211114
4411611112112114
<21100231>16126<87766894>21111311113
2161611113111123
<21101122>12517<87767785>11111321113
1521711111311123
<21112210>31156<87778873>11121111214
5113612111121114
<21121021>11347<87787684>12112111114
4311711111211214
<21122110>31147<87788773>11211111214
4113712111112114
<21211210>12319<87877873>11111113213
1321911111113123
<21221011>12148<87887674>11211111133
4121811111121133
<21221110>13129<87887773>21111111313
2131913111111123
<21320110>12139<87986773>12111111133
3121911111112133
<22001131>11527<88667794>11122111114
2511711111221114
<22011211>11428<88677874>11221111114
2411811111122114
<22110211>11266<88776874>21111211114
2116611112111124
<22111021>11257<88777684>21112111114
5211711111211124
<22111120>21157<88777783>11121111124
5112721111121114
<22112110>11329<88778773>12211111114
2311911111112214
<22120111>11248<88786774>21121111114
4211811111121124
<22121101>21148<88787764>11211111124
4112821111112114
<22211110>11239<88877773>21211111114
3211911111112124
<22221010>21139<88887673>12111111124
3112921111111214
<22311100>1212A<88977763>21111111133
2121A11111111233
<23121100>1122A<89787763>22111111114
2211A11111111224
<31000132>11617<97666795>11113111114
1611711111311114
<31001221>11518<97667884>11131111114
1511811111131114
<31012210>11419<97678873>11311111114
1411911111113114
<31122100>1131A<97788763>13111111114
1311A11111111314
<32100121>11167<98766784>11112111115
6111711111211115
<32101111>11158<98767774>11121111115
5111811111121115
<32111110>11149<98777773>11211111115
4111911111112115
<32211100>1113A<98877763>12111111115
3111A11111111215
<32221000>1121B<98887663>31111111114
1211B11111111134
<33211000>1112B<99877663>21111111115
2111B11111111125
<11112121>14326<77778784>11212211113
2341611112212113
2513512111221113
3152511122111213
<11121211>12445<77787874>21121121113
2413612111122113
3142611221111213
4421511121121123
<11211121>13327<77877784>12122111113
2143611212111123
2331711111221213
3412621111212113
<11212111>13237<77878774>12212111113
2135512111211123
3125521112111213
3231711111212213
<12121111>12247<78787774>22112111113
1322812221111113
2231811111122213
4221711111211223
<12202111>12328<78868774>21221111113
2125621112111123
2321811111122123
5212621111211123
<21101221>11536<87767884>11121211114
1512721111131113
2151711131111123
3511611112121114
<21111121>11437<87777784>11212111114
1241811111132113
1421811111131123
3411711111212114
<21112111>11356<87778774>12111211114
1412821111113113
2141811311111123
5311611112111214
<21211111>11338<87877774>12121111114
1215711121111133
3311811111121214
5121711111211133
504 6-sets & 10-sets (246 distinct ivecs each)symmetries
ivecpathivecpathrotaflip
<02404203>233233<46848645>1212212122a822a12a27
<02404212>232333<46848654>1212122122a28
<02412321>223333<46856763>1212121222a12a27
<03214221>232324<47658663>1122122122a12a27
<03232140>322234<47676582>1211212222a12a27
<04040403>224224<48484845>1122211222a822a12a27
<04040502>222424<48484944>1122112222a12a27
<04050402>222244<48494844>1121122222a12a27
<04123050>223225<48567492>1112221222a28
<05040402>222226<49484844>1111222222a12a27
<10520430>133333<54964872>1212121213a28
<12124230>142324<56568672>1122122113a28
<12223230>231325<56667672>1221112213a28
<12321240>212434<56765682>2112121123a28
<12404202>321235<56848644>2121112123a28
<14223030>221227<58667472>2211111223a28
<20242032>143134<64686474>1211311213a28
<20243022>131434<64687464>1121211313a28
<20321430>133315<64765872>1113121213a28
<20342022>313135<64786464>1211121313a28
<21034320>141424<65478762>1122113113a12a27
<21430320>312136<65874762>1211112133a12a27
<22202232>215125<66646674>1113211123a28
<22203222>152125<66647664>2111311123a28
<22210341>124216<66654783>1111321123a12a27
<22214301>122155<66658743>1112111323a12a27
<22302222>123217<66746664>1111132123a28
<22321230>213127<66765672>1321111123a28
<23012241>115225<67456683>1112221114a12a27
<23412201>212128<67856643>2111111233a12a27
<30025410>141415<74469852>1113113113a28
<30123420>131515<74567862>1113111313a28
<30242022>131317<74686464>1111131313a28
<32123220>411145<76567662>1121112115a28
<32202222>111535<76646664>1112121115a28
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5111262111121115
715 7-sets & 9-sets (327 distinct ivecs each)symmetries
ivecpathivecpathrotaflip
<05234160>2223223<27456381>122212222a12a27
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4111135121112116
4121116111121135

The 8-sets, being comprised of those which divide the 16 tone space exactly into two complementary parts, admit the possibility that the dual of the set is the same set, or that it is the inverse to the set (or both, in the case of symmetric sets). The first 12 sets listed are such self-inverse-duals.

The next 29 sets listed are those symmetric 8-sets (i.e. self-inverses) which are not the same shape as their duals. These are thus 'Z-related' in Fortean terms.

Of the remaining - all non-symmetric - sets, 60 are single pairs where the inverse is also the dual. There follow 148 quartets of 8-sets (each quartet with a common interval vector) where the set's inverse is not its dual but its dual's inverse's dual. There are a final 6 quartets of similarly related 8-sets but where 3 pairs of quartets (i.e. 3 octets of 8-sets - confused yet?) share each of three interval vectors.

Because each of these 8-sets have duals which are also 8-sets, and consequently may be used to complete a 16TET tone row (after appropriate transposition from prime-form), they may be of some interest to those intrigued by Hauer's Tropes (but with the 254 tropes - rather more numerous - available to Hexadecaphonics).

810 8-sets (254 distinct ivecs)symmetries
ivecpathrotaflip
<76543210>11111119a28
<64202464>11151115a822a28
<56543230>21111127a28
<52345630>13111315a28
<52147630>11311414a28
<40484044>13131313a444a28
<36345250>22111225a28
<32741650>12121333a28
<32543650>13213123a28
<24606424>21232123a822a28
<16345270>22212223a28
<08080804>22222222a288a12a27
ivecprim
path
dual
path
rotaflip
<24444523>1221322312221323a12a27
<24445252>1322122322131223a28
<24452542>1213222312222133a12a27
<24616423>2121232321221233a12a27
<25254442>1132222312222214a12a27
<25434361>2112322321222124a12a27
<25444423>2211223322121224a12a27
<32544442>1313212321313123a28
<34426432>1113232312212215a28
<34624432>2111233321212125a28
<41464342>1311313313121314a12a27
<42444244>1133113312141214a822a12a27
<42445432>1131133312121414a28
<42542452>1113313312131215a28
<43236541>1132311411412214a12a27
<43464142>1211214431121134a12a27
<43632541>1111333312121216a12a27
<44242543>1142112421141124a12a27
<44254522>1121142411221144a12a27
<44323462>1114212411232115a28
<44344252>1421112421131125a28
<45242443>1111422411222116a12a27
<45452422>2111124421121126a12a27
<52245442>1114131411313115a28
<54443242>1111143411212117a28
<54544222>1211121731111135a28
<64212463>1111511511141116a12a27
<64323442>1111151511131117a28
<65434321>1111115511121118a12a27
<16262623>1222222322222213
<16344442>2122222322222123
<16345261>2212222322221223
<24363442>1312222322221313
<24443632>1231222322213213
<24525442>2132122322123123
<24526423>1221232321221323
<24543451>1212223322212133
<24625423>2121223322121233
<26162623>1122222422222114
<26261623>2112222422221124
<26262613>2211222422211224
<32464243>1313122322131313
<32543641>1312312321321313
<32641651>1213213312312133
<32643442>1312123321213133
<34245451>1132221412223114
<34264432>1311222422211314
<34344262>1223112421132214
<34344451>1231122422113214
<34344622>1122132423122114
<34345450>1221132412211324
<34424443>1123212421232114
<34441642>2112312421321124
<34445242>1121223432212114
<34462432>2211213431211224
<34543441>2112123432121124
<34543450>2121123421211234
<36243442>1112222522221115
<36344251>2111222522211125
<42345631>1131231413213114
<42346432>1231131413113214
<42364243>1313112421131314
<42443452>1133121412133114
<42463243>1121313431312114
<42464233>1311213431211314
<44144632>1141122422114114
<44324443>1113221512231115
<44345431>1311122522111315
<44363422>1121124421121144
<44423443>1112312521321115
<44424433>1231112521113215
<44525422>1112123532121115
<44544232>2111213531211125
<46342432>1111222622211116
<46443412>2111122622111126
<52146631>1141131413114114
<52344442>1113131513131115
<54222463>1114211511241115
<54224452>1141112521114115
<54345421>1112114541121115
<54345430>1121114511211145
<54422452>1111321612311116
<54443431>1311112621111316
<54542431>1111213631211116
<54543430>1211113612111136
<56443231>1111122722111117
<64222453>1111411611411116
<64443232>1111131713111117
<66543211>1111112821111118
<24444451>1322212321312223
1321222322213123
<24525433>2123122321322123
1232122322132123
<24534442>1222123321213223
1212322321222133
<24535342>1221223322121323
1212232322122133
<25344361>1222212421132223
1123222321222214
<25345261>1222122422113223
1122322322122214
<25345351>1221222422211323
1122232322212214
<25353442>1212222422221133
1122223322221214
<25435342>2122122422112323
2112232322122124
<25443532>2121222422211233
2112223322212124
<32553442>1221313313121323
1213132313122133
<32642551>1213123313212133
1212313321312133
<33355342>1222131413113223
1131322313122214
<33435532>1221321412311323
1132132312312214
<33436432>1221231421311323
1131232313212214
<33444343>1213221412231133
1132213312231214
<33444451>1221312413211323
1123132321312214
<33445333>1212231422131133
1131223313221214
<33445342>1312212421131323
1311232321221314
<33453352>1213122413221133
1122313322131214
<33454342>1312122422113133
1311223322121314
<33525433>1212321421231133
1132123312321214
<33533452>1213212412321133
1123213321231214
<33533542>1212312421321133
1123123321321214
<33533551>1231212421132133
1231123321213214
<33534532>2113123313212124
1321212421131233
<33542551>2112313321312124
1321123321213124
<33543541>1212132412211333
1122133323121214
<33544333>1212213423121133
1121323331221214
<33544342>1221213412113233
1211323312212134
<33634432>1212123421211333
1121233332121214
<33642541>2112133331212124
1211233321212134
<34254532>1131222413222114
1122231422213114
<34335352>1132212412232114
1123221421223114
<34335442>1132122412322114
1122321422123114
<34343533>1123122421322114
1122312422132114
<34353532>2131122422112314
1321122422113124
<34354252>1222113412113224
1211322412221134
<34433452>2112321421231124
1232112421132124
<34434442>1212221522311133
1113223312221215
<34435432>1122123423212114
1121232432122114
<34444351>2122113412112324
1211232421221134
<34444441>2121132412211234
1221123421211324
<34452532>2112213423121124
2112132431221124
<34454242>2212113412112234
1211223422121134
<34525333>1212212523211133
1112323321221215
<34525423>2111323312212125
1221212521113233
<34534432>1212122522111333
1112233322121215
<35243542>1122221522231114
1113222412222115
<35334352>1122212522321114
1112322421222115
<35335351>1122122523221114
1112232422122115
<35343433>2111322412221125
1222112521113224
<35344351>1121222532221114
1112223422212115
<35344522>2211132412211225
1221122522111324
<35353432>2221113412112225
1211222522211134
<35434342>2112212523211124
2111232421221125
<35444251>2112122532211124
2111223422121125
<35444341>2211123421211225
2121122522111234
<41464243>1213131413131133
1131313313131214
<42345541>1132131412313114
1131321413123114
<42354442>1131312413132114
1123131421313114
<42355432>1311312413211314
1311231421311314
<42453442>1131213413312114
1121331431213114
<42454243>1213113412113314
1211331412131134
<42464143>1312113412113134
1211313413121134
<42543541>1212131513111333
1113133313121215
<43246531>1131132412211414
1122141423113114
<43334542>1133211411412124
1123311411421214
<43335532>1131221513231114
1113231412213115
<43343353>1214112421133114
1133112421141214
<43344343>1123113412114214
1121412431132114
<43344352>1132113412114124
1121421431123114
<43344541>1122131523131114
1113132413122115
<43345441>1411212432113114
1131123421211414
<43345531>1311132412211315
1221131513111324
<43354342>2112141431131124
1412112421131134
<43424542>1132121512331114
1113321412123115
<43432552>1123121521331114
1113312412132115
<43433542>1121321531231114
1113213412312115
<43434541>1121231532131114
1113123413212115
<43443343>1331112421131215
1213112521113314
<43443352>1121312531321114
1112313421312115
<43443541>1321121531113124
1211231521311134
<43444333>1321113412113125
1211312513211134
<43445332>1311212532111314
1311123421211315
<43453342>2111313413121125
1312112521113134
<43454332>1121214433112114
1121133412121144
<43543441>1121213533121114
1112133431212115
<43544332>1212113512111334
1211133412121135
<43553332>3111213431211215
1211213531211134
<44234452>1114221411223115
1114122411322115
<44245441>1411122422113115
1131122522111414
<44333362>1123112521114214
1112412421132115
<44333452>2111412411321125
1132112521114124
<44334442>1113122513221115
1112231522131115
<44344441>1122113512111424
1112142431122115
<44345341>1121132512211144
1112214423112115
<44414443>1113212512321115
1112321521231115
<44433442>1122121623311114
1111332412122116
<44434432>1112213523121115
1112132531221115
<44435422>1221113512111325
1211132512211135
<44443441>1221121631111324
1211221623111134
<44444431>1121123521211144
1112124432112115
<44454232>2111214431121125
1211124421121135
<44533432>1121212633211114
1111233421212116
<44535322>2121113512111235
1211123521211135
<44542441>2111133412121126
1212112621111334
<44543341>2121121631111234
1211212632111134
<45333352>1112221622311115
1111322512221116
<45342532>1122112621111424
1111242421122116
<45353422>1121122622111144
1111224422112116
<45424342>1112212623211115
1111232521221116
<45434332>1112122632211115
1111223522121116
<45434341>2111132512211126
1221112621111325
<45444331>2211113512111226
1211122622111135
<45534322>2111212632111125
2111123521211126
<52246531>1131131513111414
1113141413113115
<53234452>1114311411214115
1114113411412115
<53234542>1141121531114114
1141113412114115
<53245531>1121141511311144
1113114414112115
<53323453>1114121511331115
1113311512141115
<53335432>1113113514121115
1112141531131115
<53335531>1211141511311135
1131113512111415
<53343343>1111431411213116
1111413411312116
<53344342>1211311614111134
1131121631111414
<53354332>1121131613111144
1111314413112116
<53432452>1113121613311115
1111331512131116
<53443342>1112131631311115
1111313513121116
<53444431>1311113512111316
1211131613111135
<54223453>1114112511421115
1112411521141115
<54322453>1113211612411115
1111421511231116
<54323353>1112311621411115
1111412511321116
<54333442>1113112614211115
1111241521131116
<54334432>1411112521113116
1131112621111415
<54432442>1111312613211116
1111231621311116
<54444331>1112113641211115
1111214531121116
<54444421>1211114511211136
1121113612111145
<54453232>1121121731111144
1111134412112117
<54533332>1112121733111115
1111133512121117
<55333342>1112211724111115
1111142511221117
<55433332>1111221723111116
1111132612211117
<55443331>1112112742111115
1111124521121117
<55444231>2111114511211127
1121112721111145
<55533331>1111212732111116
1111123621211117
<55543321>2111113612111127
1211112721111136
<64333342>1111311714111116
1111141611311117
<65443321>1111211841111116
1111114611211118
<65543221>1111121831111117
1111113712111118
<34353433>1121322431222114
1122213422312114
1322112421131224
2112231422131124
<43434442>1112331421213115
1131212513321114
1211321512311134
1231113412113215
<44434342>1111323412212116
1121221632311114
1221211611113234
1321112521113125