7711 Heptadecatonic PC Sets

This (rather large) page concerns the 7711 distinct Pitch Class Sets associated with 17 note (typically equal temperament) divisions of the octave. As a theoretical system, this goes back to the thirteenth century.

Although before equal temperament was developed, the abstraction of pitch class does not demand that each such class must be realised as an actual frequency based upon fractional powers of two (i.e. in general for 20/N, 21/N, 22/N, 23/N, … 2(N-3)/N, 2(N-2)/N, 2(N-1)/N) multipled by some base frequency such as 261.2Hz or 440Hz, but only that the pitch class numbers label some pitch within an octave 'close enough' to such actualisations. (Were such demands enforced, one would be unable to model, say, Pythagorean or other rationally based tonalities, or indeed anything much before the 20th century with such tools - a plainly ridiculous restriction).

Notationwise, a 17 pitch tonality can actually be written without any microtonal extras (such as sagittal notation) if one simply regards sharps and flats as different (i.e. not enharmonic) tones, i.e. A, A#, B♭, B, C, C#, D♭, D, D#, E♭, E, F, F#, G♭, G, G#, A♭. Thus for purely performance reasons - usually out of scope for PC Set theory, which does not concern itself with actual notation - it may be of some practical interest.

As usual, PC sets are notated as interval paths rather than as explicit sets. This is because such representations are more compact. Set braces/brackets and commas are eliminated, and a sequence of single character digits (1-9 and A-Z), the same length as the size of the set, can be used to unambiguously represent the pitch class set (at least until Z's representation of the number 35).

The paths will represent the prime-form preferred by Forteans everywhere, in that the largest interval jumps pack to the right.

To convert these paths into sets is pretty painless. Simply replace each 'digit' by a string of the length signified by that digit, where the replacing string comprises all zeros except for the last, which will be a 1 (obviously this means that 1 will be replaced by 1 - and remember that A means 10, B means 11, … M means 22, etc). Thus 2 → 01, 3 → 001, … 9 → 000000001, etc. Once that has been done, move the final 1 (there must be one) to the beginning. The bitstring so created (starting on the left for pitch class 0) will indicate the pitch classes in the set with a 0 for absence and a 1 for presence.

The sets have no cyclic or rotational symmetries other than the identity because 17 is a prime number. The only possible symmetries are flips over one of the 17 vertices and which perforce swap the remaining 8 pairs of vertices (i.e. permutation cycle index a1a28).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0

For example, here we show one of the seven orientable heptagons from the symmetric 7-set associated with the interval vector <2,2,2,3,3,4,3,2> (path-)normalised as 1322315, i.e. 11001010100110000 → {0,1,4,6,8,11,12}.

As should be evident, the particular PC set shown is not in its normal orientation but has been rotated (by 9 vertices clockwise, or 3 of its edges) to path 3151322 - i.e. the (non-prime-form) set {0,3,4,9,10,13,15}.

Vertices have been labelled with the pitch class numbers for convenience.

The permutation (15)(14 16)(13 0)(12 1)(11 2)(10 3)(9 4)(8 5)(7 6) flips the heptagon but leaves it looking exactly the same - hence the a1 (vertex 15 'swaps' with itself) and the 8 pairs a28 of vertex swaps, e.g. 14 with 16, … 10 with 3, etc.

Interval vectors - as originally constructed from autocorrelation or frequency distributions of interval classes between pitch class pairs in a set - aren't particularly intuitive as musical objects. They resemble a list of random numbers. Upon examination, certain patterns may emerge. Such as each number having to be below the cardinality of the set. And the very observant may perceive that all of the numbers invariably sum to a 'triangular' number of the form n(n+1)/2 for some n (this property being a direct consequence of the counting operations involved).

It therefore seems unlikely that anyone might wish to look up a PC set 'by interval vector', as it were (despite the perilousness of such claims always being subject to accusations of failure of imagination). Not every partition of a triangular number into V chunks (where V = ⌊N/2⌋ is the number of interval classes available to PC Set tonalities of size N) is a legitimate object. (Can you prove this?)

However, this is not to say that information about the intervals between the pitch classes in the sets are not without some value. Musicians - or perhaps music fans - seem to find 'fifths' (or 'fourths') pleasing, for example. It thus may be that some object involving interval classes found within a PC set could be useful in this regard. We direct readers to this discussion.

Since there is no particular value provided by sorting the sets in order of increasing interval vector, each table is subdivided into three blocks. Interval vector sort order is then used as a secondary level sort within each block - justified only by Fortean tradition.

  • The first block (coloured bluish) lists (most of) the invertible, or symmetric, sets of pitch classes which - musically - may be melodically inverted without leaving the set. Of course each such set must use its particular 'flip vertex' for such inversions otherwise it will move to another 'mode' of the set.
  • The second block (coloured greenish) lists those sets with a common interval vector uniting a single symmetric PC set and a pair of mutually non-symmetric sets, each of which inverts into its partner. I.e the pairs are the same shape, and thus congruent, and reflect (through their flip vertex) into each other. Naturally the symmetric singleton is a different shape. In 17 PC-tonality, these triplets don't show up outside PC sets of cardinality 6 to 11.
  • The third and final block (coloured pinkish) is the biggest and contain pairs (very occasionally two pairs) of mutually invertible PC sets, all sharing the same interval vector. As for the triplets, the double pairs don't show up until there are at least 6 pitch classes in the set, and disappear again when there are more than 11.

cardinality 1 and 16 PC Sets - symmetric
# = 1# = 16 
ivecpathivecpathsym
<0,0,0,0,0,0,0,0>H<F,F,F,F,F,F,F,F>1111111111111112
8 cardinality 2 and 15 PC Sets - all symmetric
# = 2# = 15 
ivecpathivecpathsym
<0,0,0,0,0,0,0,1>89<D,D,D,D,D,D,D,E>111111121111112
<0,0,0,0,0,0,1,0>7A<D,D,D,D,D,D,E,D>111111112111112
<0,0,0,0,0,1,0,0>6B<D,D,D,D,D,E,D,D>111111111211112
<0,0,0,0,1,0,0,0>5C<D,D,D,D,E,D,D,D>111111111121112
<0,0,0,1,0,0,0,0>4D<D,D,D,E,D,D,D,D>111111111112112
<0,0,1,0,0,0,0,0>3E<D,D,E,D,D,D,D,D>111111111111212
<0,1,0,0,0,0,0,0>2F<D,E,D,D,D,D,D,D>111111111111122
<1,0,0,0,0,0,0,0>1G<E,D,D,D,D,D,D,D>111111111111113
40 cardinality 3 and 14 PC Sets - 8 symmetric, 16 asymmetric pairs
# = 3# = 14 
ivecpathivecpathsym
<0,0,0,0,1,2,0,0>566<B,B,B,B,C,D,B,B>11112111121112
<0,0,0,0,2,0,1,0>557<B,B,B,B,D,B,C,B>11111211121112
<0,0,0,2,0,0,0,1>449<B,B,B,D,B,B,B,C>11111112112112
<0,0,1,0,0,0,2,0>377<B,B,C,B,B,B,D,B>11111211111212
<0,0,2,0,0,1,0,0>33B<B,B,D,B,B,C,B,B>11111111121212
<0,2,0,1,0,0,0,0>22D<B,D,B,C,B,B,B,B>11111111111222
<1,0,0,0,0,0,0,2>188<C,B,B,B,B,B,B,D>11111121111113
<2,1,0,0,0,0,0,0>11F<D,C,B,B,B,B,B,B>11111111111114
<0,0,0,1,0,1,1,0>467<B,B,B,C,B,C,C,B>11112111112112
64711111211112112
<0,0,0,1,1,0,0,1>458<B,B,B,C,C,B,B,C>11121111112112
54811111121112112
<0,0,1,0,0,1,0,1>368<B,B,C,B,B,C,B,C>11112111111212
63811111121111212
<0,0,1,0,1,0,0,1>359<B,B,C,B,C,B,B,C>11121111111212
53911111112111212
<0,0,1,1,0,0,1,0>34A<B,B,C,C,B,B,C,B>11211111111212
43A11111111211212
<0,1,0,0,0,0,1,1>278<B,C,B,B,B,B,C,C>11111211111122
72811111121111122
<0,1,0,0,0,1,0,1>269<B,C,B,B,B,C,B,C>11112111111122
62911111112111122
<0,1,0,0,1,0,1,0>25A<B,C,B,B,C,B,C,B>11121111111122
52A11111111211122
<0,1,0,1,0,1,0,0>24B<B,C,B,C,B,C,B,B>11211111111122
42B11111111121122
<0,1,1,0,1,0,0,0>23C<B,C,C,B,C,B,B,B>12111111111122
32C11111111112122
<1,0,0,0,0,0,1,1>179<C,B,B,B,B,B,C,C>11111211111113
71911111112111113
<1,0,0,0,0,1,1,0>16A<C,B,B,B,B,C,C,B>11112111111113
61A11111111211113
<1,0,0,0,1,1,0,0>15B<C,B,B,B,C,C,B,B>11121111111113
51B11111111121113
<1,0,0,1,1,0,0,0>14C<C,B,B,C,C,B,B,B>11211111111113
41C11111111112113
<1,0,1,1,0,0,0,0>13D<C,B,C,C,B,B,B,B>12111111111113
31D11111111111213
<1,1,1,0,0,0,0,0>12E<C,C,C,B,B,B,B,B>21111111111113
21E11111111111123
140 cardinality 4 and 13 PC Sets - 28 symmetric, 56 asymmetric pairs
# = 4# = 13 
ivecpathivecpathsym
<0,0,0,3,1,0,0,2>4445<9,9,9,C,A,9,9,B>1112112112112
<0,0,1,1,2,0,0,2>3545<9,9,A,A,B,9,9,B>1112112111212
<0,0,1,2,0,1,2,0>4346<9,9,A,B,9,A,B,9>1121111211212
<0,0,2,0,1,1,0,2>3536<9,9,B,9,A,A,9,B>1111212111212
<0,0,2,1,0,0,3,0>3437<9,9,B,A,9,9,C,9>1111121211212
<0,0,3,0,0,2,0,1>3338<9,9,C,9,9,B,9,A>1111112121212
<0,1,0,0,3,0,2,0>2555<9,A,9,9,C,9,B,9>1112111211122
<0,1,0,2,0,2,1,0>4247<9,A,9,B,9,B,A,9>1121111121122
<0,1,1,0,0,2,0,2>2636<9,A,A,9,9,B,9,B>1111212111122
<0,1,2,0,2,0,0,1>3239<9,A,B,9,B,9,9,A>1211111112122
<0,2,0,0,0,1,1,2>2627<9,B,9,9,9,A,A,B>1111122111122
<0,2,0,0,1,0,2,1>2528<9,B,9,9,A,9,B,A>1111112211122
<0,2,0,1,0,2,0,1>2429<9,B,9,A,9,B,9,A>1111111221122
<0,2,1,0,2,0,1,0>232A<9,B,A,9,B,9,A,9>1111111122122
<0,3,0,2,0,1,0,0>222B<9,C,9,B,9,A,9,9>1111111112222
<1,0,0,0,2,3,0,0>5156<A,9,9,9,B,C,9,9>1112111121113
<1,0,0,1,0,2,2,0>1646<A,9,9,A,9,B,B,9>1111211211113
<1,0,0,2,2,0,0,1>4148<A,9,9,B,B,9,9,A>1121111112113
<1,0,2,2,0,0,1,0>313A<A,9,B,B,9,9,A,9>1211111111213
<1,1,0,0,0,0,2,2>1727<A,A,9,9,9,9,B,B>1111122111113
<1,2,2,0,1,0,0,0>212C<A,B,B,9,A,9,9,9>2111111111123
<2,0,0,0,0,0,1,3>1718<B,9,9,9,9,9,A,C>1111113111113
<2,0,0,0,0,1,2,1>1619<B,9,9,9,9,A,B,A>1111111311113
<2,0,0,0,1,2,1,0>151A<B,9,9,9,A,B,A,9>1111111131113
<2,0,0,1,2,1,0,0>141B<B,9,9,A,B,A,9,9>1111111113113
<2,0,1,2,1,0,0,0>131C<B,9,A,B,A,9,9,9>1111111111313
<2,1,2,1,0,0,0,0>121D<B,A,B,A,9,9,9,9>1111111111133
<3,2,1,0,0,0,0,0>111E<C,B,A,9,9,9,9,9>1111111111115
<0,0,1,1,2,0,1,1>3455<9,9,A,A,B,9,A,A>1121112111212
43551112111211212
<0,0,1,2,0,1,1,1>3446<9,9,A,B,9,A,A,A>1121121111212
44361111211211212
<0,0,2,0,1,2,0,1>3356<9,9,B,9,A,B,9,A>1112111121212
53361111211121212
<0,0,2,1,0,1,2,0>3347<9,9,B,A,9,A,B,9>1121111121212
43371111121121212
<0,1,0,1,1,1,1,1>2546<9,A,9,A,A,A,A,A>1112112111122
45261111211211122
<0,1,0,1,1,2,0,1>2456<9,A,9,A,A,B,9,A>1121112111122
54261111211121122
<0,1,0,1,1,2,1,0>4256<9,A,9,A,A,B,A,9>1112111121122
52461121111211122
<0,1,0,2,0,1,1,1>2447<9,A,9,B,9,A,A,A>1121121111122
44271111121121122
<0,1,1,0,1,0,2,1>2537<9,A,A,9,A,9,B,A>1112121111122
35271111121211122
<0,1,1,0,1,2,0,1>2366<9,A,A,9,A,B,9,A>1211112111122
32661111211112122
<0,1,1,0,2,0,1,1>2357<9,A,A,9,B,9,A,A>1211121111122
53271111121112122
<0,1,1,0,2,0,2,0>3257<9,A,A,9,B,9,B,9>1112111112122
52371211111211122
<0,1,1,1,0,1,1,1>2438<9,A,A,A,9,A,A,A>1121211111122
34281111112121122
<0,1,1,1,1,0,1,1>2348<9,A,A,A,A,9,A,A>1211211111122
43281111112112122
<0,1,1,1,1,1,0,1>3248<9,A,A,A,A,A,9,A>1121111112122
42381211111121122
<0,1,2,0,1,1,0,1>2339<9,A,B,9,A,A,9,A>1212111111122
33291111111212122
<0,2,0,1,0,1,1,1>2267<9,B,9,A,9,A,A,A>1111211111222
62271111121111222
<0,2,0,1,1,0,1,1>2258<9,B,9,A,A,9,A,A>1112111111222
52281111112111222
<0,2,0,2,0,1,0,1>2249<9,B,9,B,9,A,9,A>1121111111222
42291111111211222
<0,2,1,1,1,0,1,0>223A<9,B,A,A,A,9,A,9>1211111111222
322A1111111121222
<1,0,0,0,2,2,1,0>1556<A,9,9,9,B,B,A,9>1112111211113
55161111211121113
<1,0,0,1,1,1,1,1>1547<A,9,9,A,A,A,A,A>1112112111113
45171111121121113
<1,0,0,1,1,2,1,0>1466<A,9,9,A,A,B,A,9>1121111211113
41661111211112113
<1,0,0,1,2,0,1,1>1457<A,9,9,A,B,9,A,A>1121112111113
54171111121112113
<1,0,0,1,2,1,1,0>4157<A,9,9,A,B,A,A,9>1112111112113
51471121111121113
<1,0,0,2,1,0,0,2>1448<A,9,9,B,A,9,9,B>1121121111113
44181111112112113
<1,0,1,0,0,1,2,1>1637<A,9,A,9,9,A,B,A>1111212111113
36171111121211113
<1,0,1,0,1,1,0,2>1538<A,9,A,9,A,A,9,B>1112121111113
35181111112121113
<1,0,1,1,0,1,1,1>1367<A,9,A,A,9,A,A,A>1211112111113
63171111121111213
<1,0,1,1,0,1,2,0>3167<A,9,A,A,9,A,B,9>1111211111213
61371211111211113
<1,0,1,1,1,0,0,2>1358<A,9,A,A,A,9,9,B>1211121111113
53181111112111213
<1,0,1,1,1,0,1,1>1439<A,9,A,A,A,9,A,A>1121211111113
34191111111212113
<1,0,1,1,1,1,0,1>3158<A,9,A,A,A,A,9,A>1112111111213
51381211111121113
<1,0,1,2,0,0,1,1>1349<A,9,A,B,9,9,A,A>1211211111113
43191111111211213
<1,0,1,2,1,0,0,1>3149<A,9,A,B,A,9,9,A>1121111111213
41391211111112113
<1,0,2,1,0,1,1,0>133A<A,9,B,A,9,A,A,9>1212111111113
331A1111111121213
<1,1,0,0,0,1,1,2>1628<A,A,9,9,9,A,A,B>1111221111113
26181111112211113
<1,1,0,0,1,1,1,1>1529<A,A,9,9,A,A,A,A>1112211111113
25191111111221113
<1,1,0,1,1,1,1,0>142A<A,A,9,A,A,A,A,9>1122111111113
241A1111111122113
<1,1,1,0,0,0,2,1>1277<A,A,A,9,9,9,B,A>2111112111113
21771111121111123
<1,1,1,0,0,1,0,2>1268<A,A,A,9,9,A,9,B>2111121111113
62181111112111123
<1,1,1,0,0,1,1,1>2168<A,A,A,9,9,A,A,A>1111211111123
61282111111211113
<1,1,1,0,1,0,1,1>1259<A,A,A,9,A,9,A,A>2111211111113
52191111111211123
<1,1,1,0,1,1,0,1>2159<A,A,A,9,A,A,9,A>1112111111123
51292111111121113
<1,1,1,1,0,1,1,0>124A<A,A,A,A,9,A,A,9>2112111111113
421A1111111121123
<1,1,1,1,1,0,1,0>214A<A,A,A,A,A,9,A,9>1121111111123
412A2111111112113
<1,1,1,1,1,1,0,0>132B<A,A,A,A,A,A,9,9>1221111111113
231B1111111112213
<1,1,2,0,1,1,0,0>123B<A,A,B,9,A,A,9,9>2121111111113
321B1111111112123
<1,1,2,1,0,1,0,0>213B<A,A,B,A,9,A,9,9>1211111111123
312B2111111111213
<1,2,1,1,1,0,0,0>122C<A,B,A,A,A,9,9,9>2211111111113
221C1111111111223
<2,1,0,0,0,0,1,2>1178<B,A,9,9,9,9,A,B>1111121111114
71181111112111114
<2,1,0,0,0,1,1,1>1169<B,A,9,9,9,A,A,A>1111211111114
61191111111211114
<2,1,0,0,1,1,1,0>115A<B,A,9,9,A,A,A,9>1112111111114
511A1111111121114
<2,1,0,1,1,1,0,0>114B<B,A,9,A,A,A,9,9>1121111111114
411B1111111112114
<2,1,1,1,1,0,0,0>113C<B,A,A,A,A,9,9,9>1211111111114
311C1111111111214
<2,2,1,1,0,0,0,0>112D<B,B,A,A,9,9,9,9>2111111111114
211D1111111111124
364 cardinality 5 and 12 PC Sets - 28 symmetric, 168 asymmetric pairs
# = 5# = 12 
ivecpathivecpathsym
<0,0,3,2,0,1,4,0>33434<7,7,A,9,7,8,B,7>112121121212
<0,0,3,2,0,2,2,1>33344<7,7,A,9,7,9,9,8>112112121212
<0,0,4,0,1,3,0,2>33335<7,7,B,7,8,A,7,9>111212121212
<0,2,0,2,1,2,2,1>24425<7,9,7,9,8,9,9,8>111221121122
<0,2,0,3,1,2,0,2>42245<7,9,7,A,8,9,7,9>112111211222
<0,2,1,0,4,0,3,0>23255<7,9,8,7,B,7,A,7>111211122122
<0,2,1,1,2,0,2,2>22535<7,9,8,8,9,7,9,9>111212111222
<0,2,2,0,2,1,1,2>23327<7,9,9,7,9,8,8,9>111112212122
<0,2,2,1,2,0,3,0>32237<7,9,9,8,9,7,A,7>121111121222
<0,4,0,3,0,2,0,1>22229<7,B,7,A,7,9,7,8>111111122222
<1,0,0,4,2,0,0,3>14444<8,7,7,B,9,7,7,A>112112112113
<1,0,2,0,2,3,0,2>15335<8,7,9,7,9,A,7,9>111212121113
<1,0,2,2,2,0,1,2>31355<8,7,9,9,9,7,8,9>121112111213
<1,2,0,1,0,2,2,2>16226<8,9,7,8,7,9,9,9>111122211113
<1,2,2,0,1,2,0,2>21266<8,9,9,7,8,9,7,9>211112111123
<2,0,0,0,3,4,1,0>15155<9,7,7,7,A,B,8,7>111211131113
<2,0,0,2,2,0,1,3>14417<9,7,7,9,9,7,8,A>111113112113
<2,0,1,2,1,2,2,0>13166<9,7,8,9,8,9,9,7>111121111313
<2,0,2,2,0,1,2,1>13319<9,7,9,9,7,8,9,8>111111131213
<2,1,0,0,3,2,2,0>11555<9,8,7,7,A,9,9,7>111211121114
<2,1,0,2,2,2,1,0>41147<9,8,7,9,9,9,8,7>112111112114
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<2,1,2,2,2,0,0,1>31139<9,8,9,9,9,7,7,8>121111111214
<2,2,2,1,2,1,0,0>1221B<9,9,9,8,9,8,7,7>111111111323
<2,3,2,2,0,1,0,0>2112B<9,A,9,9,7,8,7,7>211111111124
<3,1,0,0,0,0,2,4>11717<A,8,7,7,7,7,9,B>111113111114
<3,2,1,0,0,0,2,2>11177<A,9,8,7,7,7,9,9>111112111115
<4,3,2,1,0,0,0,0>1111D<B,A,9,8,7,7,7,7>111111111116
<0,1,1,3,0,2,2,1>24344<7,8,8,A,7,9,9,8>112121121122
34244112112121122
<0,1,1,3,1,1,1,2>23444<7,8,8,A,8,8,8,9>121121121122
32444112112112122
<0,1,2,1,1,2,2,1>24335<7,8,9,8,8,9,9,8>112121211122
33425111212121122
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34325111212112122
<0,1,2,1,2,1,1,2>32435<7,8,9,8,9,8,8,9>112121112122
34235121112121122
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43325111211212122
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42335121211121122
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43235121112112122
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33326111121212122
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33236121111212122
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42425111211221122
<0,2,0,3,1,1,1,2>22445<7,9,7,A,8,8,8,9>112112111222
44225111211211222
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32525111221112122
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24326111122112122
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32426112211112122
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42326111121122122
<0,2,1,1,3,0,2,1>22355<7,9,8,8,A,7,9,8>121112111222
32255111211121222
<0,2,1,2,0,2,1,2>22436<7,9,8,9,7,9,8,9>112121111222
34226111121211222
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43226111121121222
<0,2,1,2,1,2,1,1>32246<7,9,8,9,8,9,8,8>112111121222
42236121111211222
<0,2,2,0,3,0,2,1>23237<7,9,9,7,A,7,9,8>121111122122
32327111112122122
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33227111112121222
<0,3,0,1,1,1,2,2>22526<7,A,7,8,8,8,9,9>111221111222
25226111122111222
<0,3,0,2,0,2,1,2>22427<7,A,7,9,7,9,8,9>112211111222
24227111112211222
<0,3,0,2,1,2,1,1>22256<7,A,7,9,8,9,8,8>111211112222
52226111121112222
<0,3,0,3,0,2,1,1>22247<7,A,7,A,7,9,8,8>112111112222
42227111112112222
<0,3,1,1,2,0,2,1>22328<7,A,8,8,9,7,9,8>122111111222
23228111111221222
<0,3,1,2,1,1,1,1>22238<7,A,8,9,8,8,8,8>121111112222
32228111111212222
<1,0,1,2,2,1,1,2>14435<8,7,8,9,9,8,8,9>112112121113
34415111212112113
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43415111211212113
<1,0,1,2,3,0,1,2>34145<8,7,8,9,A,7,8,9>112111212113
41435112121112113
<1,0,1,3,1,1,1,2>13445<8,7,8,A,8,8,8,9>121121121113
44315111211211213
<1,0,1,3,2,0,0,3>31445<8,7,8,A,9,7,7,A>112112111213
44135121112112113
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43145112111211213
<1,0,2,1,1,2,2,1>14336<8,7,9,8,8,9,9,8>112121211113
33416111121212113
<1,0,2,1,2,1,0,3>13535<8,7,9,8,9,8,7,A>121112121113
31535111212111213
<1,0,2,1,2,2,1,1>13355<8,7,9,8,9,9,8,8>121211121113
33155111211121213
<1,0,2,2,0,1,3,1>13436<8,7,9,9,7,8,A,8>121121211113
34316111121211213
<1,0,2,2,0,2,3,0>13346<8,7,9,9,7,9,A,7>121211211113
43316111121121213
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34136121111212113
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41336121211112113
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43136121111211213
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33317111112121213
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33137121111121213
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15425111211221113
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41525111221112113
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24155111211122113
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24416111122112113
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42416111121122113
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41426112211112113
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23516111122121113
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32516111121221113
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25316111122111213
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31526111221111213
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23417111112212113
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21545111211211123
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32417111112122113
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42155111211121123
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52316111121112213
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51326122111121113
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41255211121112113
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24317111112211213
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44216111121121123
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44126211112112113
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31427112211111213
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42317111112112213
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42146112111121123
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41327122111112113
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35216111121211123
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35126211112121113
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53216111121112123
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51236212111121113
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34217111112121123
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34127211111212113
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23318111111221213
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43217111112112123
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53126211112111213
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52136121111211123
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32318111111212213
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41237212111112113
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43127211111211213
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42137121111121123
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31328122111111213
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33218111111212123
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33128211111121213
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32138121111112123
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22517111112221113
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22418111111222113
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21626111122111123
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25217111112211123
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25127211111221113
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24218111111221123
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24128211111122113
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22166111121111223
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52217111112111223
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51227221111121113
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42218111111211223
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22319111111122213
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41228221111112113
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52127211111211123
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23219111111122123
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42128211111121123
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23129211111112213
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32219111111121223
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31229221111111213
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32129211111112123
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2221A111111112223
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2212A211111111223
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15416111131112113
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41516111311112113
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51416111121113113
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41417111112113113
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31616111131111213
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15317111113111213
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31517111311111213
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14318111111311213
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31418113111111213
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51317111112111313
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41318111111211313
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31319111111121313
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45116111121121114
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54116111121112114
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51146112111121114
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44117111112112114
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16217111113111123
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21617111131111123
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15218111111311123
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21518111311111123
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34118111111212114
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14219111111131123
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31166111121111214
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53117111112111214
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21419113111111123
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51137121111121114
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43118111111211214
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41138121111112114
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61217111112111133
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51218111111211133
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33119111111121214
<2,1,2,1,1,2,1,0>1231A<9,8,9,8,8,9,8,7>111111113213
1321A111111113123
<2,1,2,2,1,0,1,1>12149<9,8,9,9,8,7,8,8>112111111133
41219111111121133
<2,1,2,2,1,1,1,0>1312A<9,8,9,9,8,8,8,7>211111111313
2131A131111111123
<2,1,3,2,0,1,1,0>1213A<9,8,A,9,7,8,8,7>121111111133
3121A111111112133
<2,2,0,0,0,1,2,3>11627<9,9,7,7,7,8,9,A>111122111114
26117111112211114
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25118111111221114
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24119111111122114
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62117111112111124
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61127211111211114
<2,2,1,1,1,0,1,2>11258<9,9,8,8,8,7,8,9>211121111114
52118111111211124
<2,2,1,1,1,1,1,1>21158<9,9,8,8,8,8,8,8>111211111124
51128211111121114
<2,2,1,1,2,1,1,0>1132A<9,9,8,8,9,8,8,7>122111111114
2311A111111112214
<2,2,1,2,0,1,1,1>11249<9,9,8,9,7,8,8,8>211211111114
42119111111121124
<2,2,1,2,1,1,0,1>21149<9,9,8,9,8,8,7,8>112111111124
41129211111112114
<2,2,2,1,1,1,1,0>1123A<9,9,9,8,8,8,8,7>212111111114
3211A111111112124
<2,2,2,2,1,0,1,0>2113A<9,9,9,9,8,7,8,7>121111111124
3112A211111111214
<2,2,3,1,1,1,0,0>1212B<9,9,A,8,8,8,7,7>211111111133
2121B111111111233
<2,3,1,2,1,1,0,0>1122B<9,A,8,9,8,8,7,7>221111111114
2211B111111111224
<3,1,0,0,0,1,2,3>11618<A,8,7,7,7,8,9,A>111131111114
16118111111311114
<3,1,0,0,1,2,2,1>11519<A,8,7,7,8,9,9,8>111311111114
15119111111131114
<3,1,0,1,2,2,1,0>1141A<A,8,7,8,9,9,8,7>113111111114
1411A111111113114
<3,1,1,2,2,1,0,0>1131B<A,8,8,9,9,8,7,7>131111111114
1311B111111111314
<3,2,1,0,0,1,1,2>11168<A,9,8,7,7,8,8,9>111121111115
61118111111211115
<3,2,1,0,1,1,1,1>11159<A,9,8,7,8,8,8,8>111211111115
51119111111121115
<3,2,1,1,1,1,1,0>1114A<A,9,8,8,8,8,8,7>112111111115
4111A111111112115
<3,2,2,1,1,1,0,0>1113B<A,9,9,8,8,8,7,7>121111111115
3111B111111111215
<3,2,2,2,1,0,0,0>1121C<A,9,9,9,8,7,7,7>311111111114
1211C111111111134
<3,3,2,1,1,0,0,0>1112C<A,A,9,8,8,7,7,7>211111111115
2111C111111111125
728 cardinality 6 and 11 PC Sets - 48 symmetric, 8 ambivalent triples,
8 pairs of asymmetric pairs, 312 asymmetric pairs
# = 6# = 11 
ivecpathivecpathsym
<0,1,5,0,2,4,0,3>233333<5,6,A,5,7,9,5,8>12121212122
<0,2,3,1,2,4,0,3>233324<5,7,8,6,7,9,5,8>11221212122
<0,2,3,1,4,0,3,2>323234<5,7,8,6,9,5,8,7>12112122122
<0,3,1,2,2,4,1,2>232424<5,8,6,7,7,9,6,7>11221122122
<0,3,1,4,0,3,2,2>222434<5,8,6,9,5,8,7,7>11212112222
<0,3,2,0,5,0,4,1>232325<5,8,7,5,A,5,9,6>11122122122
<0,3,2,2,3,1,2,2>322235<5,8,7,7,8,6,7,7>12111212222
<0,4,0,3,1,2,2,3>224225<5,9,5,8,6,7,7,8>11122211222
<0,4,1,2,2,1,3,2>223226<5,9,6,7,7,6,8,7>11112221222
<0,5,0,4,0,3,1,2>222227<5,A,5,9,5,8,6,7>11111222222
<1,0,4,3,0,2,5,0>331334<6,5,9,8,5,7,A,5>12121121213
<1,1,2,2,4,0,2,3>143234<6,6,7,7,9,5,7,8>11212212113
<1,1,2,4,0,2,3,2>243134<6,6,7,9,5,7,8,7>12112211213
<1,2,0,3,2,4,2,1>142424<6,7,5,8,7,9,7,6>11221122113
<1,2,4,0,3,3,0,2>321236<6,7,9,5,8,8,5,7>21211112123
<1,3,0,2,2,3,2,2>152225<6,8,5,7,7,8,7,7>11122221113
<1,3,2,0,3,0,4,2>212525<6,8,7,5,8,5,9,7>21112211123
<1,4,2,2,3,0,2,1>221228<6,9,7,7,8,5,7,6>22111111223
<2,0,1,3,4,1,2,2>141434<7,5,6,8,9,6,7,7>11212113113
<2,0,1,5,3,0,0,4>131444<7,5,6,A,8,5,5,9>11211211313
<2,0,2,3,1,2,3,2>134315<7,5,7,8,6,7,8,7>11131211213
<2,0,2,3,3,1,0,4>314135<7,5,7,8,8,6,5,9>11312111213
<2,0,3,2,0,3,4,1>133316<7,5,8,7,5,8,9,6>11113121213
<2,0,3,4,1,1,2,2>313136<7,5,8,9,6,6,7,7>12111121313
<2,1,0,2,3,4,3,0>142415<7,6,5,7,8,9,8,5>11131122113
<2,1,2,3,3,0,2,2>412145<7,6,7,8,8,5,7,7>11211121133
<2,1,3,1,2,2,0,4>121535<7,6,8,6,7,7,5,9>11121211133
<2,1,4,3,0,2,3,0>312137<7,6,9,8,5,7,8,5>12111112133
<2,2,2,0,1,1,4,3>125216<7,7,7,5,6,6,9,8>11113211123
<2,2,2,0,1,3,1,4>215126<7,7,7,5,6,8,6,9>11132111123
<2,2,2,1,0,2,3,3>124217<7,7,7,6,5,7,8,8>11111321123
<2,2,3,0,2,2,1,3>123218<7,7,8,5,7,7,6,8>11111132123
<2,3,4,1,2,2,0,1>212129<7,8,9,6,7,7,5,6>21111111233
<3,0,0,1,4,5,2,0>141515<8,5,5,6,9,A,7,5>11131113113
<3,0,0,2,4,3,2,1>141416<8,5,5,7,9,8,7,6>11113113113
<3,0,2,4,2,0,1,3>131318<8,5,7,9,7,5,6,8>11111131313
<3,1,2,1,0,2,4,2>121616<8,6,7,6,5,7,9,7>11113111133
<3,2,1,2,2,3,2,0>411146<8,7,6,7,7,8,7,5>11211112115
<3,2,3,2,2,2,0,1>311138<8,7,8,7,7,7,5,6>12111111215
<3,2,4,2,1,2,1,0>12121A<8,7,9,7,6,7,6,5>11111111333
<3,3,1,0,0,2,2,4>111626<8,8,6,5,5,7,7,9>11112211115
<3,4,3,2,2,0,1,0>21112A<8,9,8,7,7,5,6,5>21111111125
<4,2,0,0,0,1,3,5>116117<9,7,5,5,5,6,8,A>11111411114
<4,2,0,0,1,2,3,3>115118<9,7,5,5,6,7,8,8>11111141114
<4,2,0,1,2,3,2,1>114119<9,7,5,6,7,8,7,6>11111114114
<4,2,1,2,3,2,1,0>11311A<9,7,6,7,8,7,6,5>11111111414
<4,3,2,3,2,1,0,0>11211B<9,8,7,8,7,6,5,5>11111111144
<5,4,3,2,1,0,0,0>11111C<A,9,8,7,6,5,5,5>11111111117
<1,2,2,2,2,3,1,2>213245<6,7,7,7,7,8,6,7>12211211123
23132612211112213
42312521112112213
<1,2,2,3,1,2,2,2>212444<6,7,7,8,6,7,7,7>21121121123
22313612111122213
31322612221111213
<2,1,1,2,3,2,2,2>124145<7,6,6,7,8,7,7,7>11211132113
13152511122111313
41421511121131123
<2,1,2,2,2,2,1,3>132317<7,6,7,7,7,7,6,8>11111312213
21413611312111123
31412611321111213
<2,2,2,1,2,1,3,2>142127<7,7,7,6,7,6,8,7>21111131123
21241721131111123
21412711321111123
<2,2,3,2,1,2,2,1>121247<7,7,8,7,6,7,7,6>21121111133
21312813211111123
42121711111211233
<2,3,2,2,2,1,2,1>122219<7,8,7,7,7,6,7,6>11111113223
21132812211111124
23112821111112214
<3,2,1,1,2,2,2,2>111545<8,7,6,6,7,7,7,7>11121121115
11412811321111114
21411811111123114
<0,2,3,1,3,2,1,3>233234<5,7,8,6,8,7,6,8>12112212122
32332411212212122
<0,2,3,1,3,2,2,2>232334<5,7,8,6,8,7,7,7>12121122122
33232411212122122
<0,2,3,2,1,3,2,2>223334<5,7,8,7,6,8,7,7>12121211222
33322411212121222
<0,2,3,2,2,1,4,1>322334<5,7,8,7,7,6,9,6>12121121222
33223412112121222
<0,3,1,3,1,3,1,3>224234<5,8,6,8,6,8,6,8>11221211222
22432411212211222
<0,3,1,3,1,3,2,2>242234<5,8,6,8,6,8,7,7>12112211222
32242411221121222
<0,3,1,3,2,2,2,2>223244<5,8,6,8,7,7,7,7>12211211222
23224411211221222
<0,3,1,4,1,2,2,2>222344<5,8,6,9,6,7,7,7>12112112222
32224411211212222
<0,3,2,1,3,1,3,2>223325<5,8,7,6,8,6,8,7>12122111222
23322511122121222
<0,3,2,1,4,0,3,2>223235<5,8,7,6,9,5,8,7>12212111222
32322511121221222
<0,3,2,1,4,0,4,1>232235<5,8,7,6,9,5,9,6>12111221222
32232512211121222
<0,3,2,2,2,2,2,2>222335<5,8,7,7,7,7,7,7>12121112222
33222511121212222
<0,4,0,3,1,3,2,2>222425<5,9,5,8,6,8,7,7>11221112222
24222511122112222
<0,4,0,4,1,3,1,2>222245<5,9,5,9,6,8,6,7>11211122222
42222511121122222
<0,4,1,2,2,2,2,2>222326<5,9,6,7,7,7,7,7>12211112222
23222611112212222
<0,4,1,3,1,3,1,2>222236<5,9,6,8,6,8,6,7>12111122222
32222611112122222
<1,0,4,2,1,3,2,2>133334<6,5,9,7,6,8,7,7>12121212113
33331411212121213
<1,0,4,3,0,2,4,1>313334<6,5,9,8,5,7,9,6>12121211213
33313412112121213
<1,1,2,2,3,2,2,2>142334<6,6,7,7,8,7,7,7>11221212113
14332411212122113
<1,1,2,3,1,3,3,1>241334<6,6,7,8,6,8,8,6>12121122113
33142411221121213
<1,1,2,3,2,1,2,3>134234<6,6,7,8,7,6,7,8>12112212113
31432411212211213
<1,1,2,3,2,1,3,2>314234<6,6,7,8,7,6,8,7>11221211213
32413412112122113
<1,1,2,3,2,2,1,3>133244<6,6,7,8,7,7,6,8>12122112113
23314411211221213
<1,1,2,3,2,2,2,2>132434<6,6,7,8,7,7,7,7>12211212113
23143411212112213
<1,1,2,3,3,1,1,3>132344<6,6,7,8,8,6,6,8>12212112113
32314411211212213
<1,1,2,4,1,2,2,2>231344<6,6,7,9,6,7,7,7>12112112213
31324412211211213
<1,1,3,1,2,3,2,2>133325<6,6,8,6,7,8,7,7>12121221113
23331511122121213
<1,1,3,1,3,2,1,3>133235<6,6,8,6,8,7,6,8>12122121113
32331511121221213
<1,1,3,1,3,3,0,3>132335<6,6,8,6,8,8,5,8>12212121113
33231511121212213
<1,1,3,2,1,2,4,1>124334<6,6,8,7,6,7,9,6>21121212113
21433411212121123
<1,1,3,2,2,1,3,2>233135<6,6,8,7,7,6,8,7>12111221213
31332512122111213
<1,1,3,2,2,1,4,1>123434<6,6,8,7,7,6,9,6>21211212113
32143411212112123
<1,1,3,2,2,2,2,2>123344<6,6,8,7,7,7,7,7>21212112113
33214411211212123
<1,1,3,2,2,2,3,1>231335<6,6,8,7,7,7,8,6>12121112213
33132512211121213
<1,1,3,2,3,1,1,3>313235<6,6,8,7,8,6,6,8>12212111213
32313512111212213
<1,1,3,3,0,2,4,1>213434<6,6,8,8,5,7,9,6>12112121123
31243421121211213
<1,1,3,3,0,3,3,1>213344<6,6,8,8,5,8,8,6>12121121123
33124421121121213
<1,1,3,3,1,2,2,2>312344<6,6,8,8,6,7,7,7>21211211213
32134412112112123
<1,1,4,0,2,4,0,3>123335<6,6,9,5,7,9,5,8>21212121113
33321511121212123
<1,1,4,1,1,3,2,2>213335<6,6,9,6,6,8,7,7>12121211123
33312521112121213
<1,1,4,1,2,3,0,3>312335<6,6,9,6,7,8,5,8>21212111213
33213512111212123
<1,1,4,1,2,3,1,2>321335<6,6,9,6,7,8,6,7>12121112123
33123521211121213
<1,2,0,4,2,2,1,3>142244<6,7,5,9,7,7,6,8>11222112113
22414411211222113
<1,2,1,1,4,2,3,1>142325<6,7,6,6,9,7,8,6>11221221113
23241511122122113
<1,2,1,2,2,4,1,2>132425<6,7,6,7,7,9,6,7>12211221113
24231511122112213
<1,2,1,2,3,1,3,2>143225<6,7,6,7,8,6,8,7>11212221113
22341511122212113
<1,2,1,2,3,2,2,2>142235<6,7,6,7,8,7,7,7>11222121113
32241511121222113
<1,2,1,2,3,2,3,1>231425<6,7,6,7,8,7,8,6>11221112213
24132512211122113
<1,2,1,3,1,2,2,3>134225<6,7,6,8,6,7,7,8>12112221113
22431511122211213
<1,2,1,3,1,3,2,2>124244<6,7,6,8,6,8,7,7>21122112113
24214411211221123
<1,2,1,3,1,3,3,1>214244<6,7,6,8,6,8,8,6>11221121123
24124421121122113
<1,2,1,3,2,1,2,3>224135<6,7,6,8,7,6,7,8>12111222113
31422511222111213
<1,2,1,3,2,3,1,2>132245<6,7,6,8,7,8,6,7>12221121113
42231511121122213
<1,2,1,3,3,1,2,2>223145<6,7,6,8,8,6,7,7>11211122213
41322512221112113
<1,2,1,4,2,1,1,3>122444<6,7,6,9,7,6,6,8>22112112113
22144411211211223
<1,2,2,1,2,2,3,2>124325<6,7,7,6,7,7,8,7>21121221113
23421511122121123
<1,2,2,1,2,3,1,3>124235<6,7,7,6,7,8,6,8>21122121113
32421511121221123
<1,2,2,1,2,3,2,2>123425<6,7,7,6,7,8,7,7>21211221113
24321511122112123
<1,2,2,1,3,0,4,2>214325<6,7,7,6,8,5,9,7>11212211123
23412521112212113
<1,2,2,1,3,1,3,2>214235<6,7,7,6,8,6,8,7>11221211123
32412521112122113
<1,2,2,1,3,2,2,2>132326<6,7,7,6,8,7,7,7>12212211113
23231611112212213
<1,2,2,1,3,2,3,1>241235<6,7,7,6,8,7,8,6>21211122113
32142511221112123
<1,2,2,1,3,3,1,2>123245<6,7,7,6,8,8,6,7>21221121113
42321511121122123
<1,2,2,1,4,1,3,1>232145<6,7,7,6,9,6,8,6>11211122123
41232521221112113
<1,2,2,2,1,2,3,2>133226<6,7,7,7,6,7,8,7>12122211113
21342512112211123
22331611112221213
24312521112211213
<1,2,2,2,1,3,2,2>242135<6,7,7,7,6,8,7,7>12111221123
31242521122111213
<1,2,2,2,2,2,1,3>122435<6,7,7,7,7,7,6,8>22112121113
34221511121211223
<1,2,2,2,2,2,3,1>132236<6,7,7,7,7,7,8,6>12221211113
32231611112122213
<1,2,2,2,2,3,2,1>231245<6,7,7,7,7,8,7,6>21121112213
42132512211121123
<1,2,2,2,3,0,3,2>221435<6,7,7,7,8,5,8,7>11212111223
34122522111212113
<1,2,2,2,3,1,2,2>122345<6,7,7,7,8,6,7,7>22121121113
43221511121121223
<1,2,2,2,4,0,2,2>322145<6,7,7,7,9,5,7,7>11211121223
41223522121112113
<1,2,2,3,2,1,2,2>221345<6,7,7,8,7,6,7,7>12112111223
43122522111211213
<1,2,2,3,2,2,0,3>312245<6,7,7,8,7,7,5,8>22112111213
42213512111211223
<1,2,3,0,2,3,1,3>123326<6,7,8,5,7,8,6,8>21212211113
23321611112212123
<1,2,3,0,3,2,2,2>123236<6,7,8,5,8,7,7,7>21221211113
32321611112122123
<1,2,3,1,1,3,1,3>213326<6,7,8,6,6,8,6,8>12122111123
23312621111221213
<1,2,3,1,2,1,3,2>212435<6,7,8,6,7,6,8,7>21121211123
34212521112121123
<1,2,3,1,2,2,2,2>122336<6,7,8,6,7,7,7,7>22121211113
33221611112121223
<1,2,3,1,2,3,0,3>213236<6,7,8,6,7,8,5,8>12212111123
32312621111212213
<1,2,3,1,2,3,1,2>232136<6,7,8,6,7,8,6,7>12111122123
31232621221111213
<1,2,3,1,2,4,0,2>231236<6,7,8,6,7,9,5,7>21211112213
32132612211112123
<1,2,3,1,3,1,2,2>212345<6,7,8,6,8,6,7,7>21211211123
43212521112112123
<1,2,3,1,3,2,1,2>321245<6,7,8,6,8,7,6,7>21121112123
42123521211121123
<1,2,3,2,1,3,1,2>221336<6,7,8,7,6,8,6,7>12121111223
33122622111121213
<1,2,3,2,2,2,1,2>312236<6,7,8,7,7,7,6,7>22121111213
32213612111121223
<1,2,4,0,2,3,0,3>212336<6,7,9,5,7,8,5,8>21212111123
33212621111212123
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<2,4,1,3,1,2,1,1>112229<7,9,6,8,6,7,6,6>22211111114
22211911111112224
<2,4,2,3,1,2,0,1>211229<7,9,7,8,6,7,5,6>22111111124
22112921111111224
<3,0,1,2,2,3,3,1>131516<8,5,6,7,7,8,8,6>11131111313
15131611113111313
<3,0,1,3,3,1,1,3>131417<8,5,6,8,8,6,6,8>11311111313
14131711111311313
<3,1,0,1,3,3,3,1>115145<8,6,5,6,8,8,8,6>11131121114
11541511121131114
<3,1,0,1,3,4,2,1>151145<8,6,5,6,8,9,7,6>11211131114
41151511131112114
<3,1,0,1,4,4,2,0>114155<8,6,5,6,9,9,7,5>11311121114
14115511121113114
<3,1,0,2,2,2,2,3>114416<8,6,5,7,7,7,7,8>11211311114
14411611113112114
<3,1,0,2,3,3,2,1>114146<8,6,5,7,8,8,7,6>11311211114
41411611112113114
<3,1,0,2,3,4,2,0>141146<8,6,5,7,8,9,7,5>11211113114
41141611311112114
<3,1,1,1,1,2,3,3>115316<8,6,6,6,6,7,8,8>11121311114
13511611113121114
<3,1,1,1,1,3,3,2>115136<8,6,6,6,6,8,8,7>11131211114
31511611112131114
<3,1,1,1,2,2,2,3>113516<8,6,6,6,7,7,7,8>12111311114
15311611113111214
<3,1,1,1,2,3,3,1>151136<8,6,6,6,7,8,8,6>12111131114
31151611131111214
<3,1,1,2,1,1,2,4>114317<8,6,6,7,6,6,7,9>11213111114
13411711111312114
<3,1,1,2,2,0,2,4>113417<8,6,6,7,7,5,7,9>12113111114
14311711111311214
<3,1,1,2,2,2,2,2>114137<8,6,6,7,7,7,7,7>11312111114
31411711111213114
<3,1,1,2,3,2,2,1>141137<8,6,6,7,8,7,7,6>12111113114
31141711311111214
<3,1,1,2,3,3,1,1>113156<8,6,6,7,8,8,6,6>13111211114
51311611112111314
<3,1,1,2,3,3,2,0>131156<8,6,6,7,8,8,7,5>11121111314
51131613111121114
<3,1,1,3,3,1,1,2>113147<8,6,6,8,8,6,6,7>13112111114
41311711111211314
<3,1,1,3,3,2,1,1>131147<8,6,6,8,8,7,6,6>11211111314
41131713111112114
<3,1,2,1,1,2,2,3>121517<8,6,7,6,6,7,7,8>11131111133
15121711111311133
<3,1,2,2,1,1,2,3>113318<8,6,7,7,6,6,7,8>12131111114
13311811111131214
<3,1,2,2,2,1,1,3>121418<8,6,7,7,7,6,6,8>11311111133
14121811111131133
<3,1,2,3,2,1,1,2>113138<8,6,7,8,7,6,6,7>13121111114
31311811111121314
<3,1,2,3,3,1,0,2>131138<8,6,7,8,8,6,5,7>12111111314
31131813111111214
<3,1,3,3,1,1,2,1>121319<8,6,8,8,6,6,7,6>13111111133
13121911111113133
<3,2,1,0,0,2,3,4>116126<8,7,6,5,5,7,8,9>11113211114
11621611112311114
<3,2,1,0,1,1,3,4>115217<8,7,6,5,6,6,8,9>11123111114
12511711111321114
<3,2,1,0,1,2,3,3>115127<8,7,6,5,6,7,8,8>11132111114
21511711111231114
<3,2,1,1,0,2,3,3>161126<8,7,6,6,5,7,8,8>21111311114
21161611113111124
<3,2,1,1,1,1,2,4>112517<8,7,6,6,6,6,7,9>21113111114
15211711111311124
<3,2,1,1,1,2,2,3>114218<8,7,6,6,6,7,7,8>11231111114
12411811111132114
<3,2,1,1,1,2,3,2>151127<8,7,6,6,6,7,8,7>21111131114
21151711131111124
<3,2,1,1,3,2,2,1>111455<8,7,6,6,8,7,7,6>11211121115
41115511121112115
<3,2,1,2,1,1,2,3>112418<8,7,6,7,6,6,7,8>21131111114
14211811111131124
<3,2,1,2,1,2,2,2>111446<8,7,6,7,6,7,7,7>11211211115
44111611112112115
<3,2,1,2,2,2,1,2>141128<8,7,6,7,7,7,6,7>21111113114
21141811311111124
<3,2,2,0,1,2,2,3>111536<8,7,7,5,6,7,7,8>11121211115
35111611112121115
<3,2,2,1,1,1,3,2>111437<8,7,7,6,6,6,8,7>11212111115
34111711111212115
<3,2,2,1,2,2,1,2>111356<8,7,7,6,7,7,6,7>12111211115
53111611112111215
<3,2,2,1,2,2,2,1>113219<8,7,7,6,7,7,7,6>12311111114
12311911111113214
<3,2,2,1,2,3,1,1>311156<8,7,7,6,7,8,6,6>11121111215
51113612111121115
<3,2,2,2,1,1,2,2>111347<8,7,7,7,6,6,7,7>12112111115
43111711111211215
<3,2,2,2,1,2,2,1>112166<8,7,7,7,6,7,7,6>31111211114
11231921311111114
12116611112111134
13211911111113124
<3,2,2,2,2,1,1,2>112157<8,7,7,7,7,6,6,7>31112111114
51211711111211134
<3,2,2,2,2,1,2,1>121157<8,7,7,7,7,6,7,6>11121111134
51121731111121114
<3,2,2,2,2,2,1,1>113129<8,7,7,7,7,7,6,6>13211111114
21311911111112314
<3,2,2,2,2,2,2,0>311147<8,7,7,7,7,7,7,5>11211111215
41113712111112115
<3,2,2,3,2,0,1,2>112148<8,7,7,8,7,5,6,7>31121111114
41211811111121134
<3,2,2,3,2,1,0,2>121148<8,7,7,8,7,6,5,7>11211111134
41121831111112114
<3,2,2,3,2,1,1,1>131129<8,7,7,8,7,6,6,6>21111111314
21131913111111124
<3,2,3,1,1,2,1,2>111338<8,7,8,6,6,7,6,7>12121111115
33111811111121215
<3,2,3,3,1,1,1,1>112139<8,7,8,8,6,6,6,6>31211111114
31211911111112134
<3,2,3,3,2,0,1,1>121139<8,7,8,8,7,5,6,6>12111111134
31121931111111214
<3,3,1,0,1,1,3,3>111527<8,8,6,5,6,6,8,8>11122111115
25111711111221115
<3,3,1,1,1,2,2,2>111428<8,8,6,6,6,7,7,7>11221111115
24111811111122115
<3,3,2,1,1,2,1,2>111266<8,8,7,6,6,7,6,7>21111211115
21116611112111125
<3,3,2,1,2,0,2,2>111257<8,8,7,6,7,5,7,7>21112111115
52111711111211125
<3,3,2,1,2,1,2,1>211157<8,8,7,6,7,6,7,6>11121111125
51112721111121115
<3,3,2,1,2,2,1,1>111329<8,8,7,6,7,7,6,6>12211111115
23111911111112215
<3,3,2,2,1,1,1,2>111248<8,8,7,7,6,6,6,7>21121111115
42111811111121125
<3,3,2,2,2,1,1,1>211148<8,8,7,7,7,6,6,6>11211111125
41112821111112115
<3,3,2,2,2,2,1,0>11221A<8,8,7,7,7,7,6,5>23111111114
12211A11111111324
<3,3,3,1,2,1,1,1>111239<8,8,8,6,7,6,6,6>21211111115
32111911111112125
<3,3,3,2,2,1,0,1>211139<8,8,8,7,7,6,5,6>12111111125
31112921111111215
<3,3,3,2,2,1,1,0>11212A<8,8,8,7,7,6,6,5>32111111114
21211A11111111234
<3,3,3,3,1,1,1,0>12112A<8,8,8,8,6,6,6,5>21111111134
21121A31111111124
<3,4,2,2,2,1,1,0>11122A<8,9,7,7,7,6,6,5>22111111115
22111A11111111225
<4,2,1,0,0,1,3,4>111617<9,7,6,5,5,6,8,9>11113111115
16111711111311115
<4,2,1,0,1,2,2,3>111518<9,7,6,5,6,7,7,8>11131111115
15111811111131115
<4,2,1,1,2,2,2,1>111419<9,7,6,6,7,7,7,6>11311111115
14111911111113115
<4,2,2,2,2,2,1,0>11131A<9,7,7,7,7,7,6,5>13111111115
13111A11111111315
<4,3,2,1,0,1,2,2>111167<9,8,7,6,5,6,7,7>11112111116
61111711111211116
<4,3,2,1,1,1,1,2>111158<9,8,7,6,6,6,6,7>11121111116
51111811111121116
<4,3,2,2,1,1,1,1>111149<9,8,7,7,6,6,6,6>11211111116
41111911111112116
<4,3,3,2,1,1,1,0>11113A<9,8,8,7,6,6,6,5>12111111116
31111A11111111216
<4,3,3,2,2,1,0,0>11121B<9,8,8,7,7,6,5,5>31111111115
12111B11111111135
<4,4,3,2,1,1,0,0>11112B<9,9,8,7,6,6,5,5>21111111116
21111B11111111126
1144 cardinality 7 and 10 PC Sets - 48 symmetric, 8 ambivalent triples,
16 pairs of asymmetric pairs, 504 asymmetric pairs
# = 7# = 10 
ivecpathivecpathsym
<0,4,3,1,6,0,5,2>2232323<3,7,6,4,9,3,8,5>1221221222
<0,4,3,2,4,1,5,2>2232233<3,7,6,5,7,4,8,5>1212221222
<0,4,3,3,2,4,2,3>2222333<3,7,6,6,5,7,5,6>1212122222
<0,6,0,5,1,4,2,3>2222225<3,9,3,8,4,7,5,6>1112222222
<1,2,4,2,4,3,1,4>2313233<4,5,7,5,7,6,4,7>1221212213
<1,2,4,3,2,2,5,2>1332233<4,5,7,6,5,5,8,5>1212221213
<1,2,6,0,3,5,0,4>2123333<4,5,9,3,6,8,3,7>2121212123
<1,4,0,5,2,4,2,3>1422224<4,7,3,8,5,7,5,6>1122222113
<1,4,2,3,1,4,2,4>2124224<4,7,5,6,4,7,5,7>2112221123
<1,4,2,4,3,2,2,3>2212244<4,7,5,7,6,5,5,6>2211211223
<2,0,5,4,0,3,6,1>1331333<5,3,8,7,3,6,9,4>1212131213
<2,0,5,4,1,3,4,2>1313333<5,3,8,7,4,6,7,5>1212121313
<2,1,5,2,2,4,2,3>1133333<5,4,8,5,5,7,5,6>1212121214
<2,2,1,5,3,2,2,4>1314224<5,5,4,8,6,5,5,7>1122211313
<2,2,3,3,4,1,4,2>1221434<5,5,6,6,7,4,7,5>1121211323
<2,2,3,4,1,4,4,1>2131244<5,5,6,7,4,7,7,4>1321121123
<2,2,4,0,3,5,1,4>1233215<5,5,7,3,6,8,4,7>1113212123
<2,2,4,2,1,3,4,3>2133125<5,5,7,5,4,6,7,6>1213211123
<2,2,4,3,3,3,0,4>3122135<5,5,7,6,6,6,3,7>1211121323
<2,3,1,2,4,4,3,2>1142324<5,6,4,5,7,7,6,5>1122122114
<2,3,2,2,5,2,4,1>2311325<5,6,5,5,8,5,7,4>1221112214
<2,3,3,4,0,3,4,2>2112434<5,6,6,7,3,6,7,5>2112121124
<2,4,4,1,4,1,3,2>2122127<5,7,7,4,7,4,6,5>2111112323
<2,5,2,4,2,3,1,2>2211227<5,8,5,7,5,6,4,5>2211111224
<3,0,2,4,4,3,2,3>1331414<6,3,5,7,7,6,5,6>1131131213
<3,0,2,6,4,0,1,5>1313144<6,3,5,9,7,3,4,8>1121131313
<3,1,2,4,2,2,3,4>1143134<6,4,5,7,5,5,6,7>1121312114
<3,1,2,4,4,0,2,5>1431134<6,4,5,7,7,3,5,8>1211311214
<3,2,2,1,4,5,2,2>1221515<6,5,5,4,7,8,5,5>1113111323
<3,2,4,2,3,4,1,2>1212155<6,5,7,5,6,7,4,5>1112111333
<3,3,2,0,3,2,4,4>1152125<6,6,5,3,6,5,7,7>1112321114
<3,4,1,1,2,2,4,4>1115225<6,7,4,4,5,5,7,7>1112221115
<3,4,3,2,4,0,3,2>2111255<6,7,6,5,7,3,6,5>2111211125
<4,1,0,2,5,6,3,0>1411415<7,4,3,5,8,9,6,3>1131113114
<4,1,1,2,3,4,4,2>1151315<7,4,4,5,6,7,7,5>1113131114
<4,1,2,4,4,2,1,3>1311317<7,4,5,7,7,5,4,6>1311111314
<4,2,0,2,3,4,3,3>1144115<7,5,3,5,6,7,6,6>1114112114
<4,2,1,2,5,4,3,0>1131155<7,5,4,5,8,7,6,3>1112111414
<4,2,2,2,2,1,3,5>1133117<7,5,5,5,5,4,6,8>1111141214
<4,3,3,1,2,2,2,4>1111535<7,6,6,4,5,5,5,7>1112121116
<4,3,4,3,2,2,3,0>3111137<7,6,7,6,5,5,6,3>1211111216
<4,3,4,4,2,1,2,1>1211219<7,6,7,7,5,4,5,4>3111111134
<4,4,2,3,2,3,2,1>1122119<7,7,5,6,5,6,5,4>1111111424
<4,5,4,3,2,2,0,1>2111129<7,8,7,6,5,5,3,4>2111111126
<5,3,1,0,0,2,4,6>1116116<8,6,4,3,3,5,7,9>1111411115
<5,3,2,1,0,2,4,4>1111616<8,6,5,4,3,5,7,7>1111311116
<5,4,3,2,1,2,2,2>1111166<8,7,6,5,4,5,5,5>1111211117
<6,5,4,3,2,1,0,0>111111B<9,8,7,6,5,4,3,3>1111111118
<2,2,2,3,3,4,3,2>1322315<5,5,5,6,6,7,6,5>1113122213
14213241221131123
14231242113112213
<2,2,3,2,4,2,3,3>1232144<5,5,6,5,7,5,6,6>1121132123
14212342121131123
14321242113112123
<2,3,4,2,3,3,2,2>2121245<5,6,7,5,6,6,5,5>2112111233
32112352121112124
42121252111211233
<2,4,2,3,2,2,3,3>1222217<5,7,5,6,5,5,6,6>1111132223
21132261222111124
22311262111122214
<3,2,3,2,2,3,4,2>1114334<6,5,6,5,5,6,7,5>1121212115
12124162113111133
14212161111311233
<3,2,3,4,2,2,2,3>2113136<6,5,6,7,5,5,5,6>1312111124
31113441211211215
31311262111121314
<3,3,2,2,2,3,2,4>1521125<6,6,5,5,5,6,5,7>2111311124
21141261132111124
21411262111123114
<4,3,2,3,3,2,2,2>1131128<7,6,5,6,6,5,5,5>2111111414
21131181411111124
41111451121112116
<0,4,3,2,4,2,3,3>2223233<3,7,6,5,7,5,6,6>1221212222
23222331212212222
<0,5,1,4,2,3,3,3>2223224<3,8,4,7,5,6,6,6>1222112222
22322241122212222
<0,5,1,4,2,4,2,3>2222324<3,8,4,7,5,7,5,6>1221122222
23222241122122222
<0,5,1,5,1,4,2,3>2222234<3,8,4,8,4,7,5,6>1211222222
32222241121222222
<1,2,4,2,4,2,3,3>1323233<4,5,7,5,7,5,6,6>1221221213
23231331212212213
<1,2,4,3,2,3,4,2>1322333<4,5,7,6,5,6,7,5>1222121213
22313331212122213
<1,2,5,1,3,4,1,4>1233233<4,5,8,4,6,7,4,7>2121221213
21332331212212123
<1,2,5,1,3,4,2,3>1232333<4,5,8,4,6,7,5,6>2122121213
23213331212122123
<1,2,5,1,3,5,0,4>2132333<4,5,8,4,6,8,3,7>1221212123
23123332121212213
<1,2,5,2,2,4,2,3>1223333<4,5,8,5,5,7,5,6>2212121213
22133331212121223
<1,3,2,3,4,2,3,3>1323224<4,6,5,6,7,5,6,6>1221222113
22323141122212213
<1,3,2,3,4,2,4,2>1322324<4,6,5,6,7,5,7,5>1222122113
23223141122122213
<1,3,2,4,2,3,3,3>1332224<4,6,5,7,5,6,6,6>1212222113
22233141122221213
<1,3,2,4,2,4,2,3>2231324<4,6,5,7,5,7,5,6>1221122213
23132241222112213
<1,3,2,4,3,2,3,3>1322234<4,6,5,7,6,5,6,6>1222212113
32223141121222213
<1,3,2,5,1,3,3,3>2223134<4,6,5,8,4,6,6,6>1211222213
31322241222211213
<1,3,3,1,5,2,4,2>1232324<4,6,6,4,8,5,7,5>2122122113
23232141122122123
<1,3,3,2,3,3,3,3>1233224<4,6,6,5,6,6,6,6>2121222113
22332141122212123
<1,3,3,2,3,4,2,3>2132324<4,6,6,5,6,7,5,6>1221221123
23231242112212213
<1,3,3,2,3,5,1,3>2312324<4,6,6,5,6,8,4,6>2122112213
23213241221122123
<1,3,3,2,4,1,5,2>1232234<4,6,6,5,7,4,8,5>2122212113
32232141121222123
<1,3,3,2,4,2,3,3>1223324<4,6,6,5,7,5,6,6>2212122113
23322141122121223
<1,3,3,2,5,0,4,3>1223234<4,6,6,5,8,3,7,6>2212212113
32322141121221223
<1,3,3,3,1,4,3,3>2133224<4,6,6,6,4,7,6,6>1212221123
22331242112221213
<1,3,3,3,2,3,3,3>2232134<4,6,6,6,5,6,6,6>1211222123
31232242122211213
<1,3,3,3,2,3,4,2>2132234<4,6,6,6,5,6,7,5>1222121123
32231242112122213
<1,3,3,3,2,4,1,4>2213324<4,6,6,6,5,7,4,7>1212211223
23312242211221213
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<4,3,3,3,3,1,2,2>1112147<7,6,6,6,6,4,5,5>3112111115
41211171111121135
<4,3,3,3,3,2,1,2>1311128<7,6,6,6,6,5,4,5>2111111315
21113181311111125
<4,3,3,3,3,2,2,1>1211147<7,6,6,6,6,5,5,4>1121111135
41112173111112115
<4,3,3,4,3,1,1,2>1121138<7,6,6,7,6,4,4,5>1211111144
31121181111112144
<4,3,4,2,1,2,3,2>1111337<7,6,7,5,4,5,6,5>1212111116
33111171111121216
<4,3,4,3,2,2,1,2>1112138<7,6,7,6,5,5,4,5>3121111115
31211181111112135
<4,3,4,3,2,2,2,1>1121219<7,6,7,6,5,5,5,4>3311111114
12121191111111334
<4,3,4,3,3,2,0,2>1211138<7,6,7,6,6,5,3,5>1211111135
31112183111111215
<4,4,2,1,1,2,3,4>1111526<7,7,5,4,4,5,6,7>1112211116
25111161111221116
<4,4,2,2,1,2,3,3>1111427<7,7,5,5,4,5,6,6>1122111116
24111171111122116
<4,4,3,2,2,2,2,2>1111256<7,7,6,5,5,5,5,5>2111211116
11113281221111116
23111181111112216
52111161111211126
<4,4,3,2,2,3,1,2>2111156<7,7,6,5,5,6,4,5>1112111126
51111262111121116
<4,4,3,2,3,2,2,1>1112219<7,7,6,5,6,5,5,4>2311111115
12211191111111325
<4,4,3,3,1,2,2,2>1111247<7,7,6,6,4,5,5,5>2112111116
42111171111121126
<4,4,3,3,2,2,2,1>2111147<7,7,6,6,5,5,5,4>1121111126
41111272111112116
<4,4,3,4,2,2,1,1>1121129<7,7,6,7,5,5,4,4>2111111144
21121191111111244
<4,4,4,2,2,2,1,2>1111238<7,7,7,5,5,5,4,5>2121111116
32111181111112126
<4,4,4,2,3,2,1,1>1112129<7,7,7,5,6,5,4,4>3211111115
21211191111111235
<4,4,4,3,2,2,1,1>2111138<7,7,7,6,5,5,4,4>1211111126
31111282111111216
<4,4,4,3,3,1,1,1>1211129<7,7,7,6,6,4,4,4>2111111135
21112193111111125
<4,5,3,3,2,2,1,1>1111229<7,8,6,6,5,5,4,4>2211111116
22111191111111226
<5,3,1,0,1,2,4,5>1115117<8,6,4,3,4,5,7,8>1114111115
11511171111141115
<5,3,1,1,2,3,3,3>1114118<8,6,4,4,5,6,6,6>1141111115
11411181111114115
<5,3,2,1,1,2,3,4>1111517<8,6,5,4,4,5,6,7>1113111116
15111171111131116
<5,3,2,2,2,2,2,3>1111418<8,6,5,5,5,5,5,6>1131111116
14111181111113116
<5,3,2,2,3,3,2,1>1113119<8,6,5,5,6,6,5,4>1411111115
11311191111111415
<5,3,3,3,2,2,2,1>1111319<8,6,6,6,5,5,5,4>1311111116
13111191111111316
<5,4,3,2,2,1,2,2>1111157<8,7,6,5,5,4,5,5>1112111117
51111171111121117
<5,4,3,3,2,1,1,2>1111148<8,7,6,6,5,4,4,5>1121111117
41111181111112117
<5,4,3,3,3,2,1,0>111211A<8,7,6,6,6,5,4,3>4111111115
112111A1111111145
<5,4,4,3,2,1,1,1>1111139<8,7,7,6,5,4,4,4>1211111117
31111191111111217
<5,4,4,3,2,2,1,0>111121A<8,7,7,6,5,5,4,3>3111111116
121111A1111111136
<5,5,4,3,2,1,1,0>111112A<8,8,7,6,5,4,4,3>2111111117
211111A1111111127
1430 cardinality 8 and 9 PC Sets - 62 symmetric, 8 ambivalent triples,
44 pairs of asymmetric pairs, 584 asymmetric pairs
# = 8# = 9 
ivecpathivecpathsym
<0,7,1,6,2,5,3,4>22222223<1,8,2,7,3,6,4,5>122222222
<1,5,2,6,2,5,3,4>13222223<2,6,3,7,3,6,4,5>122222213
<1,5,4,2,5,3,4,4>21232223<2,6,5,3,6,4,5,5>212222123
<1,5,4,2,7,0,6,3>22122323<2,6,5,3,8,1,7,4>221221223
<1,6,2,5,3,4,4,3>22212224<2,7,3,6,4,5,5,4>222112223
<2,3,3,6,3,3,4,4>13132223<3,4,4,7,4,4,5,5>122221313
<2,3,5,2,4,6,1,5>12321323<3,4,6,3,5,7,2,6>122132123
<2,3,5,2,5,4,4,3>21312323<3,4,6,3,6,5,5,4>132122123
<2,3,5,4,2,5,4,3>12221333<3,4,6,5,3,6,5,4>121213223
<2,3,7,1,4,6,0,5>21212333<3,4,8,2,5,7,1,6>212121233
<2,4,3,3,6,1,5,4>12232214<3,5,4,4,7,2,6,5>113221223
<2,4,3,5,3,4,2,5>22131224<3,5,4,6,4,5,3,6>132211223
<2,4,5,1,4,4,3,5>21232124<3,5,6,2,5,5,4,6>211232123
<2,5,2,4,3,5,3,4>12222215<3,6,3,5,4,6,4,5>111322223
<2,5,4,2,5,1,6,3>21222125<3,6,5,3,6,2,7,4>211123223
<2,5,4,3,5,2,4,3>22121225<3,6,5,4,6,3,5,4>221112233
<3,1,4,6,4,2,3,5>13131323<4,2,5,7,5,3,4,6>122131313
<3,1,6,5,0,4,7,2>12133133<4,2,7,6,1,5,8,3>121312133
<3,2,4,3,4,5,5,2>12313214<4,3,5,4,5,6,6,3>113213123
<3,2,4,3,5,5,2,4>13212314<4,3,5,4,6,6,3,5>213113123
<3,2,4,5,2,4,5,3>21313124<4,3,5,6,3,5,6,4>131321123
<3,2,6,5,1,4,5,2>31212134<4,3,7,6,2,5,6,3>121121333
<3,3,2,4,6,3,4,3>12221414<4,4,3,5,7,4,5,4>113113223
<3,3,4,3,3,2,6,4>12142124<4,4,5,4,4,3,7,5>112321133
<3,3,4,3,4,4,4,3>14212124<4,4,5,4,5,5,5,4>211311233
<3,3,5,2,4,4,2,5>11133233<4,4,6,3,5,5,3,6>121221215
<3,4,3,3,4,6,2,3>23111324<4,5,4,4,5,7,3,4>122112215
<3,4,5,3,4,2,5,2>32111234<4,5,6,4,5,3,6,3>212112125
<3,4,6,2,3,5,1,4>21212126<4,5,7,3,4,6,2,5>211112333
<3,5,1,4,2,5,4,4>11142224<4,6,2,5,3,6,5,5>112222115
<3,6,3,4,4,3,3,2>22111226<4,7,4,5,5,4,4,3>221111225
<4,0,3,7,5,1,2,6>13131314<5,1,4,8,6,2,3,7>113131313
<4,1,3,5,5,2,2,6>12141314<5,2,4,6,6,3,3,7>113131133
<4,1,4,5,3,4,5,2>13121315<5,2,5,6,4,5,6,3>131113133
<4,2,3,5,5,2,3,4>31131134<5,3,4,6,6,3,4,5>121121414
<4,2,4,3,3,3,3,6>12141215<5,3,5,4,4,4,4,7>111331133
<4,2,5,4,1,3,6,3>12131216<5,3,6,5,2,4,7,4>111133133
<4,3,1,4,5,6,3,2>11311424<5,4,2,5,6,7,4,3>112211414
<4,3,2,2,5,4,5,3>11323115<5,4,3,3,6,5,6,4>111412214
<4,3,4,5,5,1,2,4>31121135<5,4,5,6,6,2,3,5>121112144
<4,3,6,3,2,4,3,3>12121217<5,4,7,4,3,5,4,4>111113333
<4,4,2,3,1,4,5,5>11242115<5,5,3,4,2,5,6,6>111421124
<4,4,3,2,2,3,5,5>11232116<5,5,4,3,3,4,6,6>111142124
<4,4,3,4,3,3,3,4>21131126<5,5,4,5,4,4,4,5>142111124
<4,5,2,4,2,3,3,5>11222117<5,6,3,5,3,4,4,6>111114224
<4,5,4,5,2,3,3,2>21121127<5,6,5,6,3,4,4,3>211111244
<5,2,0,3,6,7,4,1>11411414<6,3,1,4,7,8,5,2>113114114
<5,2,1,3,6,5,4,2>11141414<6,3,2,4,7,6,5,3>113113115
<5,2,2,4,4,3,3,5>11313116<6,3,3,5,5,4,4,6>111141314
<5,2,3,4,4,5,4,1>13111316<6,3,4,5,5,6,5,2>131111315
<5,3,2,3,4,5,4,2>11211515<6,4,3,4,5,6,5,3>111311144
<5,3,3,1,2,4,4,6>11151215<6,4,4,2,3,5,5,7>111331115
<5,4,3,5,3,2,2,4>11111444<6,5,4,6,4,3,3,5>112112117
<5,4,5,4,3,3,2,2>31111136<6,5,6,5,4,4,3,3>121111217
<5,4,5,4,4,2,1,3>12111218<6,5,6,5,5,3,2,4>311111135
<5,5,3,2,3,2,4,4>11111525<6,6,4,3,4,3,5,5>111221117
<5,6,5,4,3,2,2,1>21111128<6,7,6,5,4,3,3,2>211111127
<6,4,2,0,1,3,5,7>11151116<7,5,3,1,2,4,6,8>111151115
<6,4,2,1,2,3,5,5>11141117<7,5,3,2,3,4,6,6>111115115
<6,4,3,2,3,4,3,3>11131118<7,5,4,3,4,5,4,4>111111515
<6,5,4,3,4,3,2,1>11121119<7,6,5,4,5,4,3,2>111111155
<7,6,5,4,3,2,1,0>1111111A<8,7,6,5,4,3,2,1>111111119
<2,3,5,3,4,4,3,4>12132323<3,4,6,4,5,5,4,5>122122133
21312233132212123
22131233132121223
<3,3,4,4,3,4,5,2>12121424<4,4,5,5,4,5,6,3>112211333
21311234212112314
32113124132112124
<3,4,4,2,5,3,4,3>11212325<4,5,5,3,6,4,5,4>321221114
12212216111132323
23212115111221234
<3,5,3,4,2,4,3,4>12221126<4,6,4,5,3,5,4,5>211113224
21112424211221125
21122216223111124
<4,2,3,3,4,5,4,3>11313215<5,3,4,4,5,6,5,4>131231114
11333114114121214
12313115111321314
<4,3,3,5,4,3,2,4>11211434<5,4,4,6,5,4,3,5>112121144
13111244211211315
21113144131121125
<4,4,2,3,3,3,4,5>11223116<5,5,3,4,4,4,5,6>111142214
11322116111141224
21141125114211124
<5,4,4,4,3,2,3,3>11111345<6,5,5,5,4,3,4,4>121121117
11212118111111434
43111115111211217
<1,5,3,4,3,5,3,4>12322223<2,6,4,5,4,6,4,5>212222213
21322223122222123
<1,5,3,4,4,3,4,4>12232223<2,6,4,5,5,4,5,5>221222213
22132223122221223
<1,5,3,4,4,3,5,3>12223223<2,6,4,5,5,4,6,4>222122213
22213223122212223
<1,5,3,4,4,4,3,4>12222323<2,6,4,5,5,5,4,5>222212213
22221323122122223
<1,5,3,5,2,5,3,4>12222233<2,6,4,6,3,6,4,5>222221213
22222133121222223
<1,5,4,2,6,1,6,3>21223223<2,6,5,3,7,2,7,4>221222123
22123223212221223
<1,5,4,2,6,2,5,3>21222323<2,6,5,3,7,3,6,4>222122123
22212323212212223
<1,5,4,3,4,4,3,4>21222233<2,6,5,4,5,5,4,5>222212123
22221233212122223
<1,5,4,3,5,2,5,3>22122233<2,6,5,4,6,3,6,4>222121223
22212233221212223
<1,6,1,6,2,5,3,4>12222224<2,7,2,7,3,6,4,5>222222113
22222214112222223
<1,6,2,5,2,5,3,4>21222224<2,7,3,6,3,6,4,5>222221123
22222124211222223
<1,6,2,5,3,4,3,4>22122224<2,7,3,6,4,5,4,5>222211223
22221224221122223
<2,3,4,4,3,5,4,3>12313223<3,4,5,5,4,6,5,4>122213213
13213223122213123
<2,3,4,4,4,3,5,3>13123223<3,4,5,5,5,4,6,4>212221313
21313223131222123
<2,3,4,4,4,4,2,5>12231323<3,4,5,5,5,5,3,6>122132213
13221323122131223
<2,3,4,4,5,2,4,4>13122323<3,4,5,5,6,3,5,5>221221313
22131323131221223
<2,3,4,5,2,4,5,3>12223133<3,4,5,6,3,5,6,4>121322213
13222133121312223
<2,3,4,5,3,3,5,3>13122233<3,4,5,6,4,4,6,4>222121313
22213133131212223
<2,3,5,2,4,6,2,4>12312323<3,4,6,3,5,7,3,5>212213213
21321323122123123
<2,3,5,2,5,4,3,4>13212323<3,4,6,3,6,5,4,5>212213123
21231323213122123
<2,3,5,3,3,4,4,4>12232133<3,4,6,4,4,5,5,5>121322123
12322133121321223
<2,3,5,3,3,5,2,5>12231233<3,4,6,4,4,6,3,6>212132213
21322133121231223
<2,3,5,3,3,5,3,4>12312233<3,4,6,4,4,6,4,5>221213213
22132133123121223
<2,3,5,3,4,3,4,4>13221233<3,4,6,4,5,4,5,5>212131223
21223133221312123
<2,3,5,3,4,3,5,3>13212233<3,4,6,4,5,4,6,4>221213123
22123133213121223
<2,3,5,3,4,5,1,5>12213233<3,4,6,4,5,6,2,6>122121323
23122133121221323
<2,3,5,4,2,4,5,3>12132233<3,4,6,5,3,5,6,4>122212133
22312133121222133
<2,3,6,1,4,5,2,5>12321233<3,4,7,2,5,6,3,6>212132123
21232133121232123
<2,3,6,1,4,6,1,5>21231233<3,4,7,2,5,7,2,6>213212123
21321233212123123
<2,3,6,2,4,4,3,4>12123233<3,4,7,3,5,5,4,5>212212133
23212133121221233
<2,3,6,2,4,5,1,5>21213233<3,4,7,3,5,6,2,6>122121233
23121233212122133
<2,3,6,2,4,5,2,4>12212333<3,4,7,3,5,6,3,5>212121323
21221333121212323
<2,3,6,3,3,4,4,3>12122333<3,4,7,4,4,5,5,4>221212133
22121333121212233
<2,4,2,5,4,4,3,4>12222314<3,5,3,6,5,5,4,5>113222213
13222214113122223
<2,4,2,6,3,4,3,4>13122224<3,5,3,7,4,5,4,5>222211313
22221314131122223
<2,4,3,3,5,3,5,3>12223214<3,5,4,4,6,4,6,4>113222123
12322214113212223
<2,4,3,3,6,2,5,3>11322323<3,5,4,4,7,3,6,4>122212214
22311323122122214
<2,4,3,4,3,4,5,3>12223124<3,5,4,5,4,5,6,4>211322213
21322214112312223
<2,4,3,4,3,5,4,3>12312224<3,5,4,5,4,6,5,4>222113213
22213214123112223
<2,4,3,4,4,3,3,5>12231224<3,5,4,5,5,4,4,6>221132213
22132214112231223
<2,4,3,4,4,3,4,4>11322233<3,5,4,5,5,4,5,5>122221214
22231133121222214
<2,4,3,4,4,3,5,3>13222124<3,5,4,5,5,4,6,4>211312223
21222314222131123
<2,4,3,4,4,4,3,4>12213224<3,5,4,5,5,5,4,5>122211323
22312214112221323
<2,4,3,4,4,4,4,3>12221324<3,5,4,5,5,5,5,4>122113223
13212224222113123
22212314213112223
23122214112213223
<2,4,3,4,5,2,4,4>13221224<3,5,4,5,6,3,5,5>221131223
22122314221311223
<2,4,3,5,2,4,4,4>12132224<3,5,4,6,3,5,5,5>122221133
22231214112222133
<2,4,3,5,2,5,4,3>21312224<3,5,4,6,3,6,5,4>132221123
22213124132112223
<2,4,3,5,3,3,4,4>12222134<3,5,4,6,4,4,5,5>121132223
31222214112132223
<2,4,4,2,5,2,5,4>12232124<3,5,5,3,6,3,6,5>211322123
21232214112321223
<2,4,4,2,5,2,6,3>12322124<3,5,5,3,6,3,7,4>211321223
21223214112322123
<2,4,4,2,5,3,4,4>12321224<3,5,5,3,6,4,5,5>221132123
22123214212311223
<2,4,4,2,6,2,5,3>11232323<3,5,5,3,7,3,6,4>212212214
21132323122122124
<2,4,4,2,6,3,4,3>12212324<3,5,5,3,7,4,5,4>212211323
23212214112212323
<2,4,4,3,3,4,4,4>21223124<3,5,5,4,4,5,5,5>221321123
21322124211231223
<2,4,4,3,3,5,2,5>21231224<3,5,5,4,4,6,3,6>213221123
22132124123211223
<2,4,4,3,3,5,3,4>21321224<3,5,5,4,4,6,4,5>221123123
22123124213211223
<2,4,4,3,4,2,6,3>11232233<3,5,5,4,5,3,7,4>212221214
22321133121222124
<2,4,4,3,4,3,4,4>12123224<3,5,5,4,5,4,5,5>212221133
22321214112221233
<2,4,4,3,4,3,5,3>21132233<3,5,5,4,5,4,6,4>122212124
22311233212122214
<2,4,4,3,4,5,2,4>21221324<3,5,5,4,5,6,3,5>122112323
23122124211221323
<2,4,4,3,5,2,4,4>11223233<3,5,5,4,6,3,5,5>221221214
23221133121221224
<2,4,4,3,5,2,5,3>12122324<3,5,5,4,6,3,6,4>221221133
12221234212113223
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42211115111211226
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41111225221112116
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23211116111122126
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22121117111112235
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21112217231111125
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42111125211121126
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31111226221111216
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32111126211112126
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22211117111112226
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22111127211111226
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11413115111411314
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13114115114111314
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14113115111311414
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13141115111313115
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14131115111311315
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14111315131113115
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13113116111131414
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13131116111131315
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11411144112114115
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11341115111412115
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11431115111411215
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12115115111411134
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31141115111214115
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31114115114111215
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11412116111141134
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12114116114111134
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41131115111211415
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41113115141112115
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14111144112113116
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14112116111131144
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11331116111141215
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12141116111133115
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12111515111311135
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13411115111312116
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31411115111213116
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14311115111311216
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14121116111131135
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14111135121113116
31111415113111216
31131116111121415
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14111216311113115
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31113116141111215
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11312117111114134
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12113117141111134
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41311115111211316
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41111315131112116
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13112117111113144
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13311116111131216
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12131117111113315
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31311116111121316
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13121117111113135
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31111316131111216
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13111217311111315
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11152115111241115
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21115115111411125
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11241116111142115
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21141116111124115
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21114116114111125
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11115215111231116
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12411116111132116
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11132117124111115
11231117111114215
21411116111123116
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11321117111114125
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21111515111311126
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14211116111131126
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21131117111112415
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21111416113111126
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21113117141111125
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11211155111211145
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41121116111121145
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41112116411112115
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12311117111113216
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13211117111113126
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21311117111112316
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34111115111212117
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12111155111211136
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13111127211111316
21111317131111126
41211116111121136
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41111216311112116
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41111135121112117
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31121117111112145
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31112117411111215
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12112118111111344
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33111116111121217
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12121118111111335
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31211117111112136
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31111217311111216
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24111116111122117
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11221118111111425
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23111117111112217
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12211118111111326
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21111155111211127
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42111116111121127
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21111146112111127
21121118111111245
41111126211112117
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32111117111112127
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21211118111111236
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31111127211111217
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21111218311111126
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22111118111111227
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11511116111141116
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11411117111114116
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15111116111131117
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14111117111113117
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11311118111111416
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13111118111111317
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51111116111121118
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41111117111112118
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11211119111111146
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31111118111111218
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12111119111111137
<6,6,5,4,3,2,1,1>11111129<7,7,6,5,4,3,2,2>211111118
21111119111111128

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