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Game theoretical modelling of a dynamically evolving network Ⅰ: General target sequences
1. | Department of Mathematics, City, University of London, Northampton Square, London EC1V 0HB, UK |
2. | School of Mathematics and Statistics, The University of Sheffield, Hounsfield Road, Sheffield, S3 7RH, UK |
Animal (and human) populations contain a finite number of individuals with social and geographical relationships which evolve over time, at least in part dependent upon the actions of members of the population. These actions are often not random, but chosen strategically. In this paper we introduce a game-theoretical model of a population where the individuals have an optimal level of social engagement, and form or break social relationships strategically to obtain the correct level. This builds on previous work where individuals tried to optimise their number of connections by forming or breaking random links; the difference being that here we introduce a truly game-theoretic version where they can choose which specific links to form/break. This is more realistic and makes a significant difference to the model, one consequence of which is that the analysis is much more complicated. We prove some general results and then consider a single example in depth.
References:
[1] |
B. Allen and M. A. Nowak,
Games on graphs, EMS Surveys in Mathematical Sciences, 1 (2014), 113-151.
doi: 10.4171/EMSS/3. |
[2] |
T. Antal, S. Redner and V. Sood, Evolutionary dynamics on degree -heterogeneous graphs, Phys Rev Lett, 96 (2006), 188014. |
[3] |
A.-L. Barabási and R. Albert,
Emergence of scaling in random networks, Science, 286 (1999), 509-512.
doi: 10.1126/science.286.5439.509. |
[4] | |
[5] |
B. Bollobás, O. Riordan, J. Spenser and G. Tusnády,
The degree sequence of a scale-free random graph process, Random Struct.Alg, 18 (2001), 279-290.
doi: 10.1002/rsa.1009. |
[6] |
M. Broom and C. Cannings,
A dynamic network population model with strategic link formation governed by individual preferences, J. Theor. Biol., 335 (2013), 160-168.
doi: 10.1016/j.jtbi.2013.06.024. |
[7] |
M. Broom and C. Cannings,
Graphic Deviation, Discrete Mathematics, 338 (2015), 701-711.
doi: 10.1016/j.disc.2014.12.011. |
[8] |
M. Broom and C. Cannings, Games on dynamically evolving networks: Game theoretical modelling of a dynamically evolving network Ⅱ: special target sequences, In preparation. |
[9] |
M. Broom and J. Rychtář,
An analysis of the fixation probability of a mutant on special classes of non-directed graphs, Proc R Soc A, 464 (2008), 2609-2627.
doi: 10.1098/rspa.2008.0058. |
[10] |
C. Cannings,
The latent roots of certain markov chans arising in genetics: A new approach Ⅱ. Further haploid models, Adv.Appl.Prob., 7 (1975), 264-282.
doi: 10.1017/S0001867800045985. |
[11] |
C. Capitanio,
Sociability and response to video playback in adult male rhesus monkeys (macac mulatta), Primates, 43 (2002), 169-177.
|
[12] |
M. Cavaliere, S. Sedwards, C. E. Tarnita, M. A. Nowak and A. Csikász-Nagy,
Prosperity is associated with instability in dynamical networks, J. Theor. Biol., 299 (2012), 126-138.
doi: 10.1016/j.jtbi.2011.09.005. |
[13] |
R. C. Connor, M. R. Helthaus and L. M. Barre,
Superalliances of bottlenose dolphins, Nature, 397 (1999), 571-572.
|
[14] |
P. I. M. Dunbar,
Neocortex size as a constraint on group size in primates, J.Human Evoluion, 22 (1992), 468-493.
|
[15] |
C. S. Elton, Animal Ecology, Sidgwick & Jackson, London, 1927. |
[16] |
R. A. Fisher, The Genetical Theory of Natural Selection, Clarendon Press, Oxford, 1999. |
[17] |
F. Fu, C. Hauert, M. A. Nowak and L. Wang, Reputation-based partner choice promotes cooperation in social networks, Phys. Rev. E, 78 (2008), 026117. |
[18] |
S. L. Hakimi,
On the realizability of a set of integers as degrees of the vertices of a graph, SIAM J. Appl.Math., 10 (1960), 496-506.
doi: 10.1137/0110037. |
[19] |
W. Hamilton, The genetical evolution of social behaviour, Ⅰ, Journal of Theoretical Biology, 7 (1964a), 16pp. |
[20] |
W. Hamilton, The genetical evolution of social behaviour, Ⅱ, Journal of Theoretical Biology, 7 (1964b), 52pp. |
[21] |
W. D. Hamilton,
Extraordinary sex ratios, Science, 156 (1967), 477-488.
|
[22] |
W. Hässelbarth,
Die Verzweightheit von Graphen, Comm. in Math. and Computer Chem. (MATCH), 16 (1984), 3-17.
|
[23] |
V. Havel,
A remark on the existence of finite graphs, Časopis Pěst. Mat., 80 (1955), 477-480.
|
[24] |
R. A. Hill and R. I. M. Dunbar,
Social network size in humans, Human Nature, 1 (2003), 53-72.
|
[25] |
J. Hofbauer and K. Sigmund,
The Theory of Evolution and Dynamical Systems, Cambridge University Press, 1988. |
[26] |
J. Hofbauer and K. Sigmund,
Evolutionary Games and Population Dynamics, Cambridge University Press, 1998.
doi: 10.1017/CBO9781139173179. |
[27] |
M. Kimura,
"Stepping stone" model of population, Ann. Rep. Nat. Ist. Genet. Mishima, 3 (1953), 63-65.
|
[28] |
E. Lieberman, C. Hauert and M. A. Nowak,
Evolutionary dynamics on graphs, Nature, 433 (2005), 312-316.
|
[29] |
J. Maynard Smith and G. R. Price,
The logic of animal conflict, Nature, 246 (1973), 15-18.
|
[30] |
J. Maynard Smith, Evolution and the Theory of Games, Cambridge University Press, 1982. |
[31] |
B. D. McKay and N. C. Wormald,
Uniform generation of random regular graphs of moderate degree, J. Algorithms, 11 (1990), 52-67.
doi: 10.1016/0196-6774(90)90029-E. |
[32] |
R. Merris and T. Roby, The lattice of threshold graphs,
J. Inequal. Pure and Appl. Math., 6 (2005), Article 2, 21pp. |
[33] |
P. A. P. Moran,
The theory of some genetical effects of population subdivision, Aust. J. biol. Sci., 12 (1959), 109-116.
|
[34] |
R. Noë, Biological markets: Partner choice as the driving force behind the evolution of cooperation. In: Economics in Nature. Social Dilemmas, Mate Choice and Biological Markets, (Ed. by Noë, R., van Hooff, J. A. R. A. M. and Hammerstein, P. ), (2001), 93-118. Cambridge: Cambridge University Press. |
[35] |
R. Noë and P. Hammerstein,
Biological markets: Supply and demand determine the effect of partner choice in cooperation, Mutualism and Mating Behav.Ecol.Sociobio, 35 (1994), 1-11.
|
[36] |
J. M. Pacheco, A. Traulsen and M. A. Nowak,
Active linking in evolutionary games, J.Theor. Biol., 243 (2006), 437-443.
doi: 10.1016/j.jtbi.2006.06.027. |
[37] |
J. M. Pacheco, A. Traulsen and M. A. Nowak, Coevolution of strategy and structure in complex networks with dynamical linking, Phys. Rev. Lett., 97 (2006), 258103. |
[38] |
J. Pepper, J. Mitani and D. Watts,
General gregariousness and specific social preferences among wild chimpanzees, Int. J. Primatol., 20 (1999), 613-632.
|
[39] |
M. Perc and A. Szolnoki,
Coevolutionarygames -a mini review, BioSystems, 99 (2010), 109-125.
|
[40] |
H. Richter, Dynamic landscape models of coevolutionary games, 2016, arXiv: 1611.09149v1 [q-bio.PE] |
[41] |
E. Ruch and I. Gutman,
The branching extent of graphs, J. Combin. Inform. Systems Sci., 4 (1979), 285-295.
|
[42] |
A. M. Sibbald and R. J. Hooper,
Sociability and willingness of individual sheep to move away from their companions in order to graze, Applied Animal Behaviour, 86 (2004), 51-62.
|
[43] |
B. Skyrms and R. Pemantle,
A dynamic modeloof social network formation, Proc. Naatl. Acad. Sci. USA, 97 (2000), 9340-9346.
|
[44] |
R. Southwell and C. Cannings,
Some models of reproducing graphs: Ⅰ pure reproduction, Applied Mathematics, 1 (2010), 137-145.
|
[45] |
R. Southwell and C. Cannings,
Some models of reproducing graphs: Ⅱ age capped, Reproduction Applied Mathematics, 1 (2010), 251-259.
|
[46] |
R. Southwell and C. Cannings,
Some models of reproducing graphs: Ⅲ game based reproduction, Applied Mathematics, 1 (2010), 335-343.
|
[47] |
G. Szabo and G. Fath,
Evolutionary games on graphs, Phys. Rep., 446 (2007), 97-216.
doi: 10.1016/j.physrep.2007.04.004. |
[48] |
C. Taylor, D. Fudenberg, A. Sasaki and M. A. Nowak,
Evolutionary game dynamics in finite populations, Bulletin of Mathematical Biology, 66 (2004), 1621-1644.
doi: 10.1016/j.bulm.2004.03.004. |
[49] |
B. Voelkl and C. Kasper,
Social structure of primate interaction networks facilitates the emergence of cooperation, Biology Letters, 5 (2009), 462-464.
|
[50] |
B. Voelkl and R. Noë,
The influence of social structure on the propagation of social information in artificial primate groups: A graph-based simulation approach, Journal of Theoretical Biology, 252 (2008), 77-86.
|
[51] |
J. Wiszniewski, C. Brown and L. M. Moller,
Complex patterns of male alliance formation in dolphin social networks, Journal of Mammalogy, 93 (2012), 239-250.
|
[52] |
S. Wright,
Evolution in Mendelian populations, Genetics, 16 (1931), 97-159.
|
[53] |
S. Wright,
Breeding structure of populations in relation to speciation, Am. Naturalist, 74 (1940), 232-248.
|
show all references
References:
[1] |
B. Allen and M. A. Nowak,
Games on graphs, EMS Surveys in Mathematical Sciences, 1 (2014), 113-151.
doi: 10.4171/EMSS/3. |
[2] |
T. Antal, S. Redner and V. Sood, Evolutionary dynamics on degree -heterogeneous graphs, Phys Rev Lett, 96 (2006), 188014. |
[3] |
A.-L. Barabási and R. Albert,
Emergence of scaling in random networks, Science, 286 (1999), 509-512.
doi: 10.1126/science.286.5439.509. |
[4] | |
[5] |
B. Bollobás, O. Riordan, J. Spenser and G. Tusnády,
The degree sequence of a scale-free random graph process, Random Struct.Alg, 18 (2001), 279-290.
doi: 10.1002/rsa.1009. |
[6] |
M. Broom and C. Cannings,
A dynamic network population model with strategic link formation governed by individual preferences, J. Theor. Biol., 335 (2013), 160-168.
doi: 10.1016/j.jtbi.2013.06.024. |
[7] |
M. Broom and C. Cannings,
Graphic Deviation, Discrete Mathematics, 338 (2015), 701-711.
doi: 10.1016/j.disc.2014.12.011. |
[8] |
M. Broom and C. Cannings, Games on dynamically evolving networks: Game theoretical modelling of a dynamically evolving network Ⅱ: special target sequences, In preparation. |
[9] |
M. Broom and J. Rychtář,
An analysis of the fixation probability of a mutant on special classes of non-directed graphs, Proc R Soc A, 464 (2008), 2609-2627.
doi: 10.1098/rspa.2008.0058. |
[10] |
C. Cannings,
The latent roots of certain markov chans arising in genetics: A new approach Ⅱ. Further haploid models, Adv.Appl.Prob., 7 (1975), 264-282.
doi: 10.1017/S0001867800045985. |
[11] |
C. Capitanio,
Sociability and response to video playback in adult male rhesus monkeys (macac mulatta), Primates, 43 (2002), 169-177.
|
[12] |
M. Cavaliere, S. Sedwards, C. E. Tarnita, M. A. Nowak and A. Csikász-Nagy,
Prosperity is associated with instability in dynamical networks, J. Theor. Biol., 299 (2012), 126-138.
doi: 10.1016/j.jtbi.2011.09.005. |
[13] |
R. C. Connor, M. R. Helthaus and L. M. Barre,
Superalliances of bottlenose dolphins, Nature, 397 (1999), 571-572.
|
[14] |
P. I. M. Dunbar,
Neocortex size as a constraint on group size in primates, J.Human Evoluion, 22 (1992), 468-493.
|
[15] |
C. S. Elton, Animal Ecology, Sidgwick & Jackson, London, 1927. |
[16] |
R. A. Fisher, The Genetical Theory of Natural Selection, Clarendon Press, Oxford, 1999. |
[17] |
F. Fu, C. Hauert, M. A. Nowak and L. Wang, Reputation-based partner choice promotes cooperation in social networks, Phys. Rev. E, 78 (2008), 026117. |
[18] |
S. L. Hakimi,
On the realizability of a set of integers as degrees of the vertices of a graph, SIAM J. Appl.Math., 10 (1960), 496-506.
doi: 10.1137/0110037. |
[19] |
W. Hamilton, The genetical evolution of social behaviour, Ⅰ, Journal of Theoretical Biology, 7 (1964a), 16pp. |
[20] |
W. Hamilton, The genetical evolution of social behaviour, Ⅱ, Journal of Theoretical Biology, 7 (1964b), 52pp. |
[21] |
W. D. Hamilton,
Extraordinary sex ratios, Science, 156 (1967), 477-488.
|
[22] |
W. Hässelbarth,
Die Verzweightheit von Graphen, Comm. in Math. and Computer Chem. (MATCH), 16 (1984), 3-17.
|
[23] |
V. Havel,
A remark on the existence of finite graphs, Časopis Pěst. Mat., 80 (1955), 477-480.
|
[24] |
R. A. Hill and R. I. M. Dunbar,
Social network size in humans, Human Nature, 1 (2003), 53-72.
|
[25] |
J. Hofbauer and K. Sigmund,
The Theory of Evolution and Dynamical Systems, Cambridge University Press, 1988. |
[26] |
J. Hofbauer and K. Sigmund,
Evolutionary Games and Population Dynamics, Cambridge University Press, 1998.
doi: 10.1017/CBO9781139173179. |
[27] |
M. Kimura,
"Stepping stone" model of population, Ann. Rep. Nat. Ist. Genet. Mishima, 3 (1953), 63-65.
|
[28] |
E. Lieberman, C. Hauert and M. A. Nowak,
Evolutionary dynamics on graphs, Nature, 433 (2005), 312-316.
|
[29] |
J. Maynard Smith and G. R. Price,
The logic of animal conflict, Nature, 246 (1973), 15-18.
|
[30] |
J. Maynard Smith, Evolution and the Theory of Games, Cambridge University Press, 1982. |
[31] |
B. D. McKay and N. C. Wormald,
Uniform generation of random regular graphs of moderate degree, J. Algorithms, 11 (1990), 52-67.
doi: 10.1016/0196-6774(90)90029-E. |
[32] |
R. Merris and T. Roby, The lattice of threshold graphs,
J. Inequal. Pure and Appl. Math., 6 (2005), Article 2, 21pp. |
[33] |
P. A. P. Moran,
The theory of some genetical effects of population subdivision, Aust. J. biol. Sci., 12 (1959), 109-116.
|
[34] |
R. Noë, Biological markets: Partner choice as the driving force behind the evolution of cooperation. In: Economics in Nature. Social Dilemmas, Mate Choice and Biological Markets, (Ed. by Noë, R., van Hooff, J. A. R. A. M. and Hammerstein, P. ), (2001), 93-118. Cambridge: Cambridge University Press. |
[35] |
R. Noë and P. Hammerstein,
Biological markets: Supply and demand determine the effect of partner choice in cooperation, Mutualism and Mating Behav.Ecol.Sociobio, 35 (1994), 1-11.
|
[36] |
J. M. Pacheco, A. Traulsen and M. A. Nowak,
Active linking in evolutionary games, J.Theor. Biol., 243 (2006), 437-443.
doi: 10.1016/j.jtbi.2006.06.027. |
[37] |
J. M. Pacheco, A. Traulsen and M. A. Nowak, Coevolution of strategy and structure in complex networks with dynamical linking, Phys. Rev. Lett., 97 (2006), 258103. |
[38] |
J. Pepper, J. Mitani and D. Watts,
General gregariousness and specific social preferences among wild chimpanzees, Int. J. Primatol., 20 (1999), 613-632.
|
[39] |
M. Perc and A. Szolnoki,
Coevolutionarygames -a mini review, BioSystems, 99 (2010), 109-125.
|
[40] |
H. Richter, Dynamic landscape models of coevolutionary games, 2016, arXiv: 1611.09149v1 [q-bio.PE] |
[41] |
E. Ruch and I. Gutman,
The branching extent of graphs, J. Combin. Inform. Systems Sci., 4 (1979), 285-295.
|
[42] |
A. M. Sibbald and R. J. Hooper,
Sociability and willingness of individual sheep to move away from their companions in order to graze, Applied Animal Behaviour, 86 (2004), 51-62.
|
[43] |
B. Skyrms and R. Pemantle,
A dynamic modeloof social network formation, Proc. Naatl. Acad. Sci. USA, 97 (2000), 9340-9346.
|
[44] |
R. Southwell and C. Cannings,
Some models of reproducing graphs: Ⅰ pure reproduction, Applied Mathematics, 1 (2010), 137-145.
|
[45] |
R. Southwell and C. Cannings,
Some models of reproducing graphs: Ⅱ age capped, Reproduction Applied Mathematics, 1 (2010), 251-259.
|
[46] |
R. Southwell and C. Cannings,
Some models of reproducing graphs: Ⅲ game based reproduction, Applied Mathematics, 1 (2010), 335-343.
|
[47] |
G. Szabo and G. Fath,
Evolutionary games on graphs, Phys. Rep., 446 (2007), 97-216.
doi: 10.1016/j.physrep.2007.04.004. |
[48] |
C. Taylor, D. Fudenberg, A. Sasaki and M. A. Nowak,
Evolutionary game dynamics in finite populations, Bulletin of Mathematical Biology, 66 (2004), 1621-1644.
doi: 10.1016/j.bulm.2004.03.004. |
[49] |
B. Voelkl and C. Kasper,
Social structure of primate interaction networks facilitates the emergence of cooperation, Biology Letters, 5 (2009), 462-464.
|
[50] |
B. Voelkl and R. Noë,
The influence of social structure on the propagation of social information in artificial primate groups: A graph-based simulation approach, Journal of Theoretical Biology, 252 (2008), 77-86.
|
[51] |
J. Wiszniewski, C. Brown and L. M. Moller,
Complex patterns of male alliance formation in dolphin social networks, Journal of Mammalogy, 93 (2012), 239-250.
|
[52] |
S. Wright,
Evolution in Mendelian populations, Genetics, 16 (1931), 97-159.
|
[53] |
S. Wright,
Breeding structure of populations in relation to speciation, Am. Naturalist, 74 (1940), 232-248.
|


Target | Sets | Min. score | Number of states |
2 2 2 | d d d | 0 | 1 |
2 2 1 | b b c | 1 | 3 |
2 2 0 | b b c | 2 | 4 |
2 1 1 | d d d | 0 | 1 |
2 1 0 | b d c | 1 | 2 |
1 1 1 | a a a | 1 | 6 |
3 3 3 3 | d d d d | 0 | 1 |
3 3 3 2 | b b b c | 1 | 4 |
3 3 3 1 | b b b c | 2 | 7 |
3 3 3 0 | b b b c | 3 | 8 |
3 3 2 2 | d d d d | 0 | 1 |
3 3 2 1 | b b d c | 1 | 3 |
3 3 2 0 | b b d c | 2 | 4 |
3 3 1 1 | b b c c | 2 | 9 |
3 3 1 0 | b b c c | 3 | 12 |
3 3 0 0 | b b c c | 4 | 16 |
3 2 2 2 | b a a a | 1 | 9 |
3 2 2 1 | d d d d | 0 | 1 |
3 2 2 0 | b d d c | 1 | 2 |
3 2 1 1 | b b c c | 1 | 5 |
3 2 1 0 | b b c c | 2 | 8 |
3 1 1 1 | d d d d | 0 | 1 |
2 2 2 2 | d d d d | 0 | 1 |
2 2 2 1 | a a a a | 1 | 13 |
2 2 1 1 | d d d d | 0 | 1 |
Target | Sets | Min. score | Number of states |
2 2 2 | d d d | 0 | 1 |
2 2 1 | b b c | 1 | 3 |
2 2 0 | b b c | 2 | 4 |
2 1 1 | d d d | 0 | 1 |
2 1 0 | b d c | 1 | 2 |
1 1 1 | a a a | 1 | 6 |
3 3 3 3 | d d d d | 0 | 1 |
3 3 3 2 | b b b c | 1 | 4 |
3 3 3 1 | b b b c | 2 | 7 |
3 3 3 0 | b b b c | 3 | 8 |
3 3 2 2 | d d d d | 0 | 1 |
3 3 2 1 | b b d c | 1 | 3 |
3 3 2 0 | b b d c | 2 | 4 |
3 3 1 1 | b b c c | 2 | 9 |
3 3 1 0 | b b c c | 3 | 12 |
3 3 0 0 | b b c c | 4 | 16 |
3 2 2 2 | b a a a | 1 | 9 |
3 2 2 1 | d d d d | 0 | 1 |
3 2 2 0 | b d d c | 1 | 2 |
3 2 1 1 | b b c c | 1 | 5 |
3 2 1 0 | b b c c | 2 | 8 |
3 1 1 1 | d d d d | 0 | 1 |
2 2 2 2 | d d d d | 0 | 1 |
2 2 2 1 | a a a a | 1 | 13 |
2 2 1 1 | d d d d | 0 | 1 |
vector | codes | of | matrices | |||||
(2, 3, 1, 4, 0, 0, 0, 0) | 0 | 8 | 16 | 24 | 32 | 40 | 48 | 56 |
(0, 0, 0, 0, 4, 1, 3, 2) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
(0, 0, 0, 0, 4, 3, 1, 2) | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
(2, 1, 3, 4, 0, 0, 0, 0) | 4 | 12 | 20 | 28 | 36 | 44 | 52 | 60 |
(3, 3, 0, 3, 1, 1, 3, 2) | 17 | |||||||
(4, 3, 2, 2, 2, 2, 3, 4) | 18 | |||||||
(6, 3, 0, 0, 4, 4, 9, 8) | 19 | 23 | ||||||
(6, 3, 3, 6, 2, 2, 6, 4) | 21 | |||||||
(6, 3, 6, 6, 2, 2, 3, 4) | 22 | |||||||
(1, 1, 0, 1, 1, 1, 1, 1) | 25 | |||||||
(4, 3, 2, 2, 6, 6, 3, 6) | 26 | |||||||
(2, 1, 0, 0, 4, 4, 3, 4) | 27 | 31 | ||||||
(2, 1, 1, 2, 2, 2, 2, 2) | 29 | |||||||
(2, 1, 2, 2, 2, 2, 1, 2) | 30 | |||||||
(1, 2, 0, 2, 2, 0, 2, 1) | 33 | |||||||
(2, 3, 1, 1, 3, 0, 3, 3) | 34 | |||||||
(1, 2, 0, 0, 4, 0, 4, 3) | 35 | 39 | ||||||
(1, 1, 1, 2, 2, 0, 2, 1) | 37 | |||||||
(1, 1, 1, 1, 1, 0, 1, 1) | 38 | |||||||
(1, 2, 0, 2, 2, 1, 1, 1) | 41 | |||||||
(4, 6, 2, 2, 6, 3, 3, 6) | 42 | |||||||
(1, 2, 0, 0, 4, 2, 2, 3) | 43 | 47 | ||||||
(1, 1, 1, 2, 2, 1, 1, 1) | 45 | |||||||
(2, 2, 2, 2, 2, 1, 1, 2) | 46 | |||||||
(3, 4, 0, 4, 0, 0, 2, 1) | 49 | 57 | ||||||
(8, 9, 4, 4, 0, 0, 3, 6) | 50 | 58 | ||||||
(1, 1, 0, 0, 0, 0, 1, 1) | 51 | 55 | 59 | 63 | ||||
(3, 2, 2, 4, 0, 0, 2, 1) | 53 | 61 | ||||||
(4, 3, 4, 4, 0, 0, 1, 2) | 54 | 62 |
vector | codes | of | matrices | |||||
(2, 3, 1, 4, 0, 0, 0, 0) | 0 | 8 | 16 | 24 | 32 | 40 | 48 | 56 |
(0, 0, 0, 0, 4, 1, 3, 2) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
(0, 0, 0, 0, 4, 3, 1, 2) | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
(2, 1, 3, 4, 0, 0, 0, 0) | 4 | 12 | 20 | 28 | 36 | 44 | 52 | 60 |
(3, 3, 0, 3, 1, 1, 3, 2) | 17 | |||||||
(4, 3, 2, 2, 2, 2, 3, 4) | 18 | |||||||
(6, 3, 0, 0, 4, 4, 9, 8) | 19 | 23 | ||||||
(6, 3, 3, 6, 2, 2, 6, 4) | 21 | |||||||
(6, 3, 6, 6, 2, 2, 3, 4) | 22 | |||||||
(1, 1, 0, 1, 1, 1, 1, 1) | 25 | |||||||
(4, 3, 2, 2, 6, 6, 3, 6) | 26 | |||||||
(2, 1, 0, 0, 4, 4, 3, 4) | 27 | 31 | ||||||
(2, 1, 1, 2, 2, 2, 2, 2) | 29 | |||||||
(2, 1, 2, 2, 2, 2, 1, 2) | 30 | |||||||
(1, 2, 0, 2, 2, 0, 2, 1) | 33 | |||||||
(2, 3, 1, 1, 3, 0, 3, 3) | 34 | |||||||
(1, 2, 0, 0, 4, 0, 4, 3) | 35 | 39 | ||||||
(1, 1, 1, 2, 2, 0, 2, 1) | 37 | |||||||
(1, 1, 1, 1, 1, 0, 1, 1) | 38 | |||||||
(1, 2, 0, 2, 2, 1, 1, 1) | 41 | |||||||
(4, 6, 2, 2, 6, 3, 3, 6) | 42 | |||||||
(1, 2, 0, 0, 4, 2, 2, 3) | 43 | 47 | ||||||
(1, 1, 1, 2, 2, 1, 1, 1) | 45 | |||||||
(2, 2, 2, 2, 2, 1, 1, 2) | 46 | |||||||
(3, 4, 0, 4, 0, 0, 2, 1) | 49 | 57 | ||||||
(8, 9, 4, 4, 0, 0, 3, 6) | 50 | 58 | ||||||
(1, 1, 0, 0, 0, 0, 1, 1) | 51 | 55 | 59 | 63 | ||||
(3, 2, 2, 4, 0, 0, 2, 1) | 53 | 61 | ||||||
(4, 3, 4, 4, 0, 0, 1, 2) | 54 | 62 |
index | | | | |
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index | | | | |
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code | c4 | c3 | c1 | c0 |
0L | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
0R | 0.30000 | 0.500000 | 0.000000 | 1.200000 |
1 | 0.300000 | 0.500000 | 0.000000 | 1.200000 |
2 | 0.300000 | 0.500000 | 0.000000 | 1.200000 |
3 | 0.300000 | 0.500000 | 0.000000 | 1.200000 |
4L | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
4R | 0.300000 | 0.500000 | 0.00000 | 1.200000 |
5 | 0.300000 | 0.500000 | 0.000000 | 1.200000 |
6 | 0.300000 | 0.500000 | 0.000000 | 1.200000 |
7 | 0.300000 | 0.500000 | 0.000000 | 1.200000 |
8L | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
8R | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
9 | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
10 | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
11 | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
12L | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
12R | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
13 | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
14 | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
15 | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
16 | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
17 | 0.750000 | 0.312500 | 0.375000 | 0.562500 |
18 | 0.681818 | 0.318182 | 0.318182 | 0.681818 |
19 | 0.441176 | 0.500000 | 0.264706 | 0.794118 |
20 | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
21 | 0.750000 | 0.312500 | 0.281250 | 0.656250 |
22 | 0.843750 | 0.218750 | 0.281250 | 0.656250 |
23 | 0.441176 | 0.500000 | 0.264706 | 0.794118 |
24 | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
25 | 0.714286 | 0.285714 | 0.285714 | 0.714286 |
26 | 0.656250 | 0.281250 | 0.218750 | 0.843750 |
27 | 0.500000 | 0.388889 | 0.166667 | 0.944444 |
28 | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
29 | 0.714286 | 0.285714 | 0.214286 | 0.785714 |
30 | 0.785714 | 0.214286 | 0.214286 | 0.785714 |
31 | 0.500000 | 0.388889 | 0.166667 | 0.944444 |
32 | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
33 | 0.700000 | 0.300000 | 0.300000 | 0.700000 |
34 | 0.562500 | 0.375000 | 0.312500 | 0.750000 |
35 | 0.357143 | 0.500000 | 0.214286 | 0.928571 |
36 | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
37 | 0.700000 | 0.300000 | 0.200000 | 0.800000 |
38 | 0.714286 | 0.285714 | 0.285714 | 0.714286 |
39 | 0.357143 | 0.500000 | 0.214286 | 0.928571 |
40 | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
41 | 0.800000 | 0.200000 | 0.300000 | 0.700000 |
42 | 0.656250 | 0.281250 | 0.312500 | 0.750000 |
43 | 0.500000 | 0.357143 | 0.214286 | 0.928571 |
44 | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
45 | 0.800000 | 0.200000 | 0.200000 | 0.800000 |
46 | 0.785714 | 0.214286 | 0.285714 | 0.714286 |
47 | 0.500000 | 0.357143 | 0.214286 | 0.928571 |
48 | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
49 | 0.928571 | 0.214286 | 0.500000 | 0.357143 |
50 | 0.794118 | 0.264706 | 0.500000 | 0.441176 |
51 | 0.500000 | 0.500000 | 0.500000 | 0.500000 |
52 | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
53 | 0.928571 | 0.214286 | 0.357143 | 0.500000 |
54 | 0.944444 | 0.166667 | 0.388889 | 0.500000 |
55 | 0.500000 | 0.500000 | 0.500000 | 0.500000 |
56 | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
57 | 0.928571 | 0.214286 | 0.500000 | 0.357143 |
58 | 0.794118 | 0.264706 | 0.500000 | 0.441176 |
59 | 0.500000 | 0.500000 | 0.500000 | 0.500000 |
60 | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
61 | 0.928571 | 0.214286 | 0.357143 | 0.500000 |
62 | 0.944444 | 0.166667 | 0.388889 | 0.500000 |
63 | 0.500000 | 0.500000 | 0.500000 | 0.500000 |
code | c4 | c3 | c1 | c0 |
0L | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
0R | 0.30000 | 0.500000 | 0.000000 | 1.200000 |
1 | 0.300000 | 0.500000 | 0.000000 | 1.200000 |
2 | 0.300000 | 0.500000 | 0.000000 | 1.200000 |
3 | 0.300000 | 0.500000 | 0.000000 | 1.200000 |
4L | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
4R | 0.300000 | 0.500000 | 0.00000 | 1.200000 |
5 | 0.300000 | 0.500000 | 0.000000 | 1.200000 |
6 | 0.300000 | 0.500000 | 0.000000 | 1.200000 |
7 | 0.300000 | 0.500000 | 0.000000 | 1.200000 |
8L | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
8R | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
9 | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
10 | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
11 | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
12L | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
12R | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
13 | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
14 | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
15 | 0.500000 | 0.300000 | 0.000000 | 1.200000 |
16 | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
17 | 0.750000 | 0.312500 | 0.375000 | 0.562500 |
18 | 0.681818 | 0.318182 | 0.318182 | 0.681818 |
19 | 0.441176 | 0.500000 | 0.264706 | 0.794118 |
20 | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
21 | 0.750000 | 0.312500 | 0.281250 | 0.656250 |
22 | 0.843750 | 0.218750 | 0.281250 | 0.656250 |
23 | 0.441176 | 0.500000 | 0.264706 | 0.794118 |
24 | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
25 | 0.714286 | 0.285714 | 0.285714 | 0.714286 |
26 | 0.656250 | 0.281250 | 0.218750 | 0.843750 |
27 | 0.500000 | 0.388889 | 0.166667 | 0.944444 |
28 | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
29 | 0.714286 | 0.285714 | 0.214286 | 0.785714 |
30 | 0.785714 | 0.214286 | 0.214286 | 0.785714 |
31 | 0.500000 | 0.388889 | 0.166667 | 0.944444 |
32 | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
33 | 0.700000 | 0.300000 | 0.300000 | 0.700000 |
34 | 0.562500 | 0.375000 | 0.312500 | 0.750000 |
35 | 0.357143 | 0.500000 | 0.214286 | 0.928571 |
36 | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
37 | 0.700000 | 0.300000 | 0.200000 | 0.800000 |
38 | 0.714286 | 0.285714 | 0.285714 | 0.714286 |
39 | 0.357143 | 0.500000 | 0.214286 | 0.928571 |
40 | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
41 | 0.800000 | 0.200000 | 0.300000 | 0.700000 |
42 | 0.656250 | 0.281250 | 0.312500 | 0.750000 |
43 | 0.500000 | 0.357143 | 0.214286 | 0.928571 |
44 | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
45 | 0.800000 | 0.200000 | 0.200000 | 0.800000 |
46 | 0.785714 | 0.214286 | 0.285714 | 0.714286 |
47 | 0.500000 | 0.357143 | 0.214286 | 0.928571 |
48 | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
49 | 0.928571 | 0.214286 | 0.500000 | 0.357143 |
50 | 0.794118 | 0.264706 | 0.500000 | 0.441176 |
51 | 0.500000 | 0.500000 | 0.500000 | 0.500000 |
52 | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
53 | 0.928571 | 0.214286 | 0.357143 | 0.500000 |
54 | 0.944444 | 0.166667 | 0.388889 | 0.500000 |
55 | 0.500000 | 0.500000 | 0.500000 | 0.500000 |
56 | 1.200000 | 0.000000 | 0.500000 | 0.300000 |
57 | 0.928571 | 0.214286 | 0.500000 | 0.357143 |
58 | 0.794118 | 0.264706 | 0.500000 | 0.441176 |
59 | 0.500000 | 0.500000 | 0.500000 | 0.500000 |
60 | 1.200000 | 0.000000 | 0.300000 | 0.500000 |
61 | 0.928571 | 0.214286 | 0.357143 | 0.500000 |
62 | 0.944444 | 0.166667 | 0.388889 | 0.500000 |
63 | 0.500000 | 0.500000 | 0.500000 | 0.500000 |
0 | 1 | 2 | 0 | 0 | 16 | 32 | 3 | 48 | 32 | 33 | 34 | 32 | 32 | 32 | 32 | 35 | 32 |
1 | 1 | 1 | 1 | 1 | 17 | 33 | 1 | 49 | 33 | 33 | 35 | 33 | 33 | 49 | 33 | 33 | 33 |
2 | 2 | 2 | 2 | 2 | 18 | 34 | 2 | 50 | 34 | 35 | 34 | 34 | 34 | 50 | 34 | 33 | 18 |
3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 35 | 35 | 35 | 35 | 35 | 35 | 35 | 35 | 35 |
4 | 5 | 6 | 4 | 4 | 20 | 36 | 7 | 52 | 36 | 37 | 38 | 36 | 36 | 36 | 36 | 39 | 36 |
5 | 5 | 5 | 5 | 5 | 21 | 37 | 5 | 53 | 37 | 37 | 37 | 37 | 37 | 53 | 37 | 37 | 37 |
6 | 6 | 6 | 6 | 6 | 22 | 38 | 6 | 54 | 38 | 39 | 38 | 34 | 38 | 54 | 38 | 37 | 22 |
7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 39 | 39 | 37 | 39 | 39 | 39 | 39 | 39 | 39 |
8 | 9 | 10 | 8 | 8 | 24 | 40 | 11 | 56 | 40 | 41 | 42 | 40 | 40 | 40 | 40 | 43 | 40 |
9 | 9 | 9 | 9 | 9 | 25 | 41 | 9 | 57 | 41 | 41 | 43 | 41 | 41 | 41 | 41 | 41 | 41 |
10 | 10 | 10 | 10 | 10 | 26 | 42 | 10 | 58 | 42 | 43 | 42 | 42 | 42 | 58 | 42 | 41 | 42 |
11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 43 | 43 | 43 | 43 | 43 | 43 | 11 | 43 | 43 |
12 | 13 | 14 | 12 | 12 | 28 | 44 | 15 | 60 | 44 | 45 | 46 | 44 | 44 | 44 | 44 | 47 | 44 |
13 | 13 | 13 | 13 | 13 | 29 | 45 | 13 | 61 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 |
14 | 14 | 14 | 14 | 14 | 30 | 46 | 14 | 62 | 46 | 47 | 46 | 42 | 46 | 62 | 46 | 45 | 46 |
15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 47 | 47 | 45 | 47 | 47 | 47 | 15 | 47 | 47 |
16 | 17 | 18 | 16 | 16 | 16 | 16 | 19 | 16 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 |
17 | 17 | 19 | 17 | 17 | 17 | 49 | 18 | 33 | 49 | 49 | 49 | 49 | 49 | 49 | 49 | 49 | 49 |
18 | 19 | 18 | 18 | 18 | 18 | 50 | 18 | 18 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |
19 | 19 | 19 | 19 | 19 | 19 | 19 | 19 | 19 | 51 | 51 | 51 | 51 | 51 | 51 | 51 | 51 | 51 |
20 | 21 | 22 | 20 | 20 | 20 | 20 | 23 | 20 | 52 | 52 | 52 | 52 | 52 | 52 | 52 | 52 | 52 |
21 | 21 | 23 | 21 | 21 | 21 | 53 | 21 | 37 | 53 | 52 | 53 | 53 | 53 | 53 | 53 | 53 | 53 |
22 | 23 | 22 | 18 | 22 | 22 | 54 | 22 | 22 | 54 | 54 | 52 | 50 | 54 | 54 | 54 | 53 | 54 |
23 | 23 | 23 | 23 | 23 | 23 | 23 | 23 | 23 | 55 | 54 | 53 | 55 | 55 | 55 | 55 | 52 | 55 |
24 | 25 | 26 | 24 | 24 | 24 | 24 | 27 | 24 | 56 | 56 | 56 | 56 | 56 | 56 | 56 | 56 | 56 |
25 | 25 | 27 | 25 | 17 | 25 | 57 | 26 | 41 | 57 | 57 | 57 | 57 | 57 | 41 | 57 | 57 | 57 |
26 | 27 | 26 | 26 | 18 | 26 | 58 | 26 | 26 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 |
27 | 27 | 27 | 27 | 19 | 11 | 27 | 27 | 43 | 59 | 59 | 59 | 59 | 59 | 43 | 27 | 59 | 11 |
28 | 29 | 30 | 28 | 28 | 28 | 28 | 31 | 28 | 60 | 60 | 60 | 60 | 60 | 60 | 60 | 60 | 60 |
29 | 29 | 31 | 29 | 21 | 29 | 61 | 29 | 45 | 61 | 60 | 61 | 61 | 61 | 45 | 61 | 61 | 61 |
30 | 31 | 30 | 26 | 22 | 30 | 62 | 30 | 30 | 62 | 62 | 60 | 58 | 62 | 62 | 62 | 61 | 62 |
31 | 31 | 31 | 31 | 23 | 15 | 31 | 31 | 47 | 63 | 62 | 61 | 63 | 63 | 47 | 31 | 60 | 15 |
0 | 1 | 2 | 0 | 0 | 16 | 32 | 3 | 48 | 32 | 33 | 34 | 32 | 32 | 32 | 32 | 35 | 32 |
1 | 1 | 1 | 1 | 1 | 17 | 33 | 1 | 49 | 33 | 33 | 35 | 33 | 33 | 49 | 33 | 33 | 33 |
2 | 2 | 2 | 2 | 2 | 18 | 34 | 2 | 50 | 34 | 35 | 34 | 34 | 34 | 50 | 34 | 33 | 18 |
3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 35 | 35 | 35 | 35 | 35 | 35 | 35 | 35 | 35 |
4 | 5 | 6 | 4 | 4 | 20 | 36 | 7 | 52 | 36 | 37 | 38 | 36 | 36 | 36 | 36 | 39 | 36 |
5 | 5 | 5 | 5 | 5 | 21 | 37 | 5 | 53 | 37 | 37 | 37 | 37 | 37 | 53 | 37 | 37 | 37 |
6 | 6 | 6 | 6 | 6 | 22 | 38 | 6 | 54 | 38 | 39 | 38 | 34 | 38 | 54 | 38 | 37 | 22 |
7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 39 | 39 | 37 | 39 | 39 | 39 | 39 | 39 | 39 |
8 | 9 | 10 | 8 | 8 | 24 | 40 | 11 | 56 | 40 | 41 | 42 | 40 | 40 | 40 | 40 | 43 | 40 |
9 | 9 | 9 | 9 | 9 | 25 | 41 | 9 | 57 | 41 | 41 | 43 | 41 | 41 | 41 | 41 | 41 | 41 |
10 | 10 | 10 | 10 | 10 | 26 | 42 | 10 | 58 | 42 | 43 | 42 | 42 | 42 | 58 | 42 | 41 | 42 |
11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 43 | 43 | 43 | 43 | 43 | 43 | 11 | 43 | 43 |
12 | 13 | 14 | 12 | 12 | 28 | 44 | 15 | 60 | 44 | 45 | 46 | 44 | 44 | 44 | 44 | 47 | 44 |
13 | 13 | 13 | 13 | 13 | 29 | 45 | 13 | 61 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 |
14 | 14 | 14 | 14 | 14 | 30 | 46 | 14 | 62 | 46 | 47 | 46 | 42 | 46 | 62 | 46 | 45 | 46 |
15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 47 | 47 | 45 | 47 | 47 | 47 | 15 | 47 | 47 |
16 | 17 | 18 | 16 | 16 | 16 | 16 | 19 | 16 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 |
17 | 17 | 19 | 17 | 17 | 17 | 49 | 18 | 33 | 49 | 49 | 49 | 49 | 49 | 49 | 49 | 49 | 49 |
18 | 19 | 18 | 18 | 18 | 18 | 50 | 18 | 18 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |
19 | 19 | 19 | 19 | 19 | 19 | 19 | 19 | 19 | 51 | 51 | 51 | 51 | 51 | 51 | 51 | 51 | 51 |
20 | 21 | 22 | 20 | 20 | 20 | 20 | 23 | 20 | 52 | 52 | 52 | 52 | 52 | 52 | 52 | 52 | 52 |
21 | 21 | 23 | 21 | 21 | 21 | 53 | 21 | 37 | 53 | 52 | 53 | 53 | 53 | 53 | 53 | 53 | 53 |
22 | 23 | 22 | 18 | 22 | 22 | 54 | 22 | 22 | 54 | 54 | 52 | 50 | 54 | 54 | 54 | 53 | 54 |
23 | 23 | 23 | 23 | 23 | 23 | 23 | 23 | 23 | 55 | 54 | 53 | 55 | 55 | 55 | 55 | 52 | 55 |
24 | 25 | 26 | 24 | 24 | 24 | 24 | 27 | 24 | 56 | 56 | 56 | 56 | 56 | 56 | 56 | 56 | 56 |
25 | 25 | 27 | 25 | 17 | 25 | 57 | 26 | 41 | 57 | 57 | 57 | 57 | 57 | 41 | 57 | 57 | 57 |
26 | 27 | 26 | 26 | 18 | 26 | 58 | 26 | 26 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 |
27 | 27 | 27 | 27 | 19 | 11 | 27 | 27 | 43 | 59 | 59 | 59 | 59 | 59 | 43 | 27 | 59 | 11 |
28 | 29 | 30 | 28 | 28 | 28 | 28 | 31 | 28 | 60 | 60 | 60 | 60 | 60 | 60 | 60 | 60 | 60 |
29 | 29 | 31 | 29 | 21 | 29 | 61 | 29 | 45 | 61 | 60 | 61 | 61 | 61 | 45 | 61 | 61 | 61 |
30 | 31 | 30 | 26 | 22 | 30 | 62 | 30 | 30 | 62 | 62 | 60 | 58 | 62 | 62 | 62 | 61 | 62 |
31 | 31 | 31 | 31 | 23 | 15 | 31 | 31 | 47 | 63 | 62 | 61 | 63 | 63 | 47 | 31 | 60 | 15 |
0 | 1 | 2 | 4 | 8 | 16 | 32 | 3 | 48 | 32 | 33 | 34 | 36 | 40 | 48 | 0 | 35 | 16 |
1 | 0 | 3 | 5 | 9 | 17 | 33 | 2 | 49 | 33 | 33 | 35 | 37 | 41 | 49 | 33 | 33 | 33 |
2 | 3 | 0 | 6 | 10 | 18 | 34 | 1 | 50 | 34 | 35 | 34 | 34 | 42 | 50 | 34 | 33 | 18 |
3 | 2 | 1 | 7 | 11 | 19 | 35 | 0 | 51 | 35 | 35 | 35 | 39 | 43 | 51 | 3 | 35 | 19 |
4 | 5 | 6 | 0 | 12 | 20 | 36 | 7 | 52 | 36 | 37 | 38 | 32 | 44 | 52 | 4 | 39 | 20 |
5 | 4 | 7 | 1 | 13 | 21 | 37 | 6 | 53 | 37 | 37 | 37 | 33 | 45 | 53 | 37 | 37 | 37 |
6 | 7 | 4 | 2 | 14 | 22 | 38 | 5 | 54 | 38 | 39 | 38 | 34 | 46 | 54 | 38 | 37 | 22 |
7 | 6 | 5 | 3 | 15 | 23 | 39 | 4 | 55 | 39 | 39 | 37 | 35 | 47 | 55 | 7 | 39 | 23 |
8 | 9 | 10 | 12 | 0 | 24 | 40 | 11 | 56 | 40 | 41 | 42 | 44 | 32 | 56 | 8 | 43 | 24 |
9 | 8 | 11 | 13 | 1 | 25 | 41 | 10 | 57 | 41 | 41 | 43 | 45 | 33 | 41 | 41 | 41 | 41 |
10 | 11 | 8 | 14 | 2 | 26 | 42 | 9 | 58 | 42 | 43 | 42 | 42 | 34 | 58 | 42 | 41 | 26 |
11 | 10 | 9 | 15 | 3 | 11 | 11 | 8 | 11 | 43 | 43 | 43 | 47 | 35 | 43 | 11 | 43 | 43 |
12 | 13 | 14 | 8 | 4 | 28 | 44 | 15 | 60 | 44 | 45 | 46 | 40 | 36 | 60 | 12 | 47 | 28 |
13 | 12 | 15 | 9 | 5 | 29 | 45 | 14 | 61 | 45 | 45 | 45 | 41 | 37 | 45 | 45 | 45 | 45 |
14 | 15 | 12 | 10 | 6 | 30 | 46 | 13 | 62 | 46 | 47 | 46 | 42 | 38 | 62 | 46 | 45 | 30 |
15 | 14 | 13 | 11 | 7 | 15 | 15 | 12 | 15 | 47 | 47 | 45 | 43 | 39 | 47 | 15 | 47 | 47 |
16 | 17 | 18 | 20 | 24 | 0 | 48 | 19 | 32 | 48 | 49 | 50 | 52 | 56 | 32 | 16 | 51 | 0 |
17 | 17 | 19 | 21 | 17 | 17 | 49 | 18 | 33 | 49 | 48 | 51 | 53 | 57 | 49 | 49 | 50 | 49 |
18 | 19 | 18 | 18 | 18 | 18 | 50 | 18 | 18 | 50 | 51 | 48 | 50 | 58 | 50 | 50 | 49 | 50 |
19 | 19 | 19 | 23 | 19 | 3 | 51 | 19 | 35 | 51 | 50 | 49 | 55 | 59 | 35 | 19 | 48 | 3 |
20 | 21 | 22 | 16 | 28 | 4 | 52 | 23 | 36 | 52 | 52 | 52 | 48 | 60 | 36 | 20 | 52 | 4 |
21 | 21 | 23 | 17 | 21 | 21 | 53 | 22 | 37 | 53 | 52 | 53 | 49 | 61 | 53 | 53 | 53 | 53 |
22 | 23 | 22 | 18 | 22 | 22 | 54 | 21 | 22 | 54 | 54 | 52 | 50 | 62 | 54 | 54 | 53 | 54 |
23 | 23 | 23 | 19 | 23 | 7 | 55 | 23 | 39 | 55 | 54 | 53 | 51 | 63 | 39 | 23 | 52 | 7 |
24 | 25 | 26 | 28 | 16 | 8 | 56 | 27 | 40 | 56 | 57 | 58 | 60 | 48 | 40 | 24 | 59 | 8 |
25 | 25 | 27 | 29 | 17 | 25 | 57 | 26 | 41 | 57 | 56 | 59 | 61 | 49 | 41 | 57 | 58 | 57 |
26 | 27 | 26 | 26 | 18 | 26 | 58 | 26 | 42 | 58 | 59 | 56 | 58 | 50 | 58 | 58 | 57 | 58 |
27 | 27 | 27 | 31 | 19 | 11 | 27 | 27 | 43 | 59 | 58 | 57 | 63 | 51 | 43 | 27 | 56 | 11 |
28 | 29 | 30 | 24 | 20 | 12 | 60 | 31 | 44 | 60 | 60 | 60 | 56 | 52 | 44 | 28 | 60 | 12 |
29 | 29 | 31 | 25 | 21 | 29 | 61 | 30 | 45 | 61 | 60 | 61 | 57 | 53 | 45 | 61 | 61 | 61 |
30 | 31 | 30 | 26 | 22 | 30 | 62 | 29 | 46 | 62 | 62 | 60 | 58 | 54 | 62 | 62 | 61 | 62 |
31 | 31 | 31 | 27 | 23 | 15 | 31 | 31 | 47 | 63 | 62 | 61 | 59 | 55 | 47 | 31 | 60 | 15 |
0 | 1 | 2 | 4 | 8 | 16 | 32 | 3 | 48 | 32 | 33 | 34 | 36 | 40 | 48 | 0 | 35 | 16 |
1 | 0 | 3 | 5 | 9 | 17 | 33 | 2 | 49 | 33 | 33 | 35 | 37 | 41 | 49 | 33 | 33 | 33 |
2 | 3 | 0 | 6 | 10 | 18 | 34 | 1 | 50 | 34 | 35 | 34 | 34 | 42 | 50 | 34 | 33 | 18 |
3 | 2 | 1 | 7 | 11 | 19 | 35 | 0 | 51 | 35 | 35 | 35 | 39 | 43 | 51 | 3 | 35 | 19 |
4 | 5 | 6 | 0 | 12 | 20 | 36 | 7 | 52 | 36 | 37 | 38 | 32 | 44 | 52 | 4 | 39 | 20 |
5 | 4 | 7 | 1 | 13 | 21 | 37 | 6 | 53 | 37 | 37 | 37 | 33 | 45 | 53 | 37 | 37 | 37 |
6 | 7 | 4 | 2 | 14 | 22 | 38 | 5 | 54 | 38 | 39 | 38 | 34 | 46 | 54 | 38 | 37 | 22 |
7 | 6 | 5 | 3 | 15 | 23 | 39 | 4 | 55 | 39 | 39 | 37 | 35 | 47 | 55 | 7 | 39 | 23 |
8 | 9 | 10 | 12 | 0 | 24 | 40 | 11 | 56 | 40 | 41 | 42 | 44 | 32 | 56 | 8 | 43 | 24 |
9 | 8 | 11 | 13 | 1 | 25 | 41 | 10 | 57 | 41 | 41 | 43 | 45 | 33 | 41 | 41 | 41 | 41 |
10 | 11 | 8 | 14 | 2 | 26 | 42 | 9 | 58 | 42 | 43 | 42 | 42 | 34 | 58 | 42 | 41 | 26 |
11 | 10 | 9 | 15 | 3 | 11 | 11 | 8 | 11 | 43 | 43 | 43 | 47 | 35 | 43 | 11 | 43 | 43 |
12 | 13 | 14 | 8 | 4 | 28 | 44 | 15 | 60 | 44 | 45 | 46 | 40 | 36 | 60 | 12 | 47 | 28 |
13 | 12 | 15 | 9 | 5 | 29 | 45 | 14 | 61 | 45 | 45 | 45 | 41 | 37 | 45 | 45 | 45 | 45 |
14 | 15 | 12 | 10 | 6 | 30 | 46 | 13 | 62 | 46 | 47 | 46 | 42 | 38 | 62 | 46 | 45 | 30 |
15 | 14 | 13 | 11 | 7 | 15 | 15 | 12 | 15 | 47 | 47 | 45 | 43 | 39 | 47 | 15 | 47 | 47 |
16 | 17 | 18 | 20 | 24 | 0 | 48 | 19 | 32 | 48 | 49 | 50 | 52 | 56 | 32 | 16 | 51 | 0 |
17 | 17 | 19 | 21 | 17 | 17 | 49 | 18 | 33 | 49 | 48 | 51 | 53 | 57 | 49 | 49 | 50 | 49 |
18 | 19 | 18 | 18 | 18 | 18 | 50 | 18 | 18 | 50 | 51 | 48 | 50 | 58 | 50 | 50 | 49 | 50 |
19 | 19 | 19 | 23 | 19 | 3 | 51 | 19 | 35 | 51 | 50 | 49 | 55 | 59 | 35 | 19 | 48 | 3 |
20 | 21 | 22 | 16 | 28 | 4 | 52 | 23 | 36 | 52 | 52 | 52 | 48 | 60 | 36 | 20 | 52 | 4 |
21 | 21 | 23 | 17 | 21 | 21 | 53 | 22 | 37 | 53 | 52 | 53 | 49 | 61 | 53 | 53 | 53 | 53 |
22 | 23 | 22 | 18 | 22 | 22 | 54 | 21 | 22 | 54 | 54 | 52 | 50 | 62 | 54 | 54 | 53 | 54 |
23 | 23 | 23 | 19 | 23 | 7 | 55 | 23 | 39 | 55 | 54 | 53 | 51 | 63 | 39 | 23 | 52 | 7 |
24 | 25 | 26 | 28 | 16 | 8 | 56 | 27 | 40 | 56 | 57 | 58 | 60 | 48 | 40 | 24 | 59 | 8 |
25 | 25 | 27 | 29 | 17 | 25 | 57 | 26 | 41 | 57 | 56 | 59 | 61 | 49 | 41 | 57 | 58 | 57 |
26 | 27 | 26 | 26 | 18 | 26 | 58 | 26 | 42 | 58 | 59 | 56 | 58 | 50 | 58 | 58 | 57 | 58 |
27 | 27 | 27 | 31 | 19 | 11 | 27 | 27 | 43 | 59 | 58 | 57 | 63 | 51 | 43 | 27 | 56 | 11 |
28 | 29 | 30 | 24 | 20 | 12 | 60 | 31 | 44 | 60 | 60 | 60 | 56 | 52 | 44 | 28 | 60 | 12 |
29 | 29 | 31 | 25 | 21 | 29 | 61 | 30 | 45 | 61 | 60 | 61 | 57 | 53 | 45 | 61 | 61 | 61 |
30 | 31 | 30 | 26 | 22 | 30 | 62 | 29 | 46 | 62 | 62 | 60 | 58 | 54 | 62 | 62 | 61 | 62 |
31 | 31 | 31 | 27 | 23 | 15 | 31 | 31 | 47 | 63 | 62 | 61 | 59 | 55 | 47 | 31 | 60 | 15 |
Fee | New | PNEs | |||
.5 | 0 | 4 | 8 | * | * |
.3 | 12 | * | * | * | * |
.28125 | 6 | 24 | * | * | * |
.2 | 1 | 5 | 32 | 40 | * |
.181818 | 2 | 16 | * | * | * |
.161932 | 22 | 26 | * | * | * |
.151786 | 25 | 38 | * | * | * |
.150326 | 27 | 31 | 54 | 62 | * |
.142857 | 55 | 59 | 63 | * | * |
.129464 | 29 | 30 | 46 | * | * |
.110294 | 17 | 34 | * | * | * |
.1 | 9 | 13 | 36 | 44 | * |
.098214 | 21 | 42 | * | * | * |
.085714 | 14 | 28 | 33 | 37 | 41 |
.057143 | 43 | 47 | 53 | 61 | * |
.053467 | 18 | * | * | * | * |
.01875 | 10 | 20 | * | * | * |
.014286 | 39 | 57 | * | * | * |
0 | 3 | 7 | 11 | 15 | * |
19 | 23 | 35 | 45 | * | |
48 | 49 | 50 | 51 | * | |
52 | 56 | 58 | 60 | * |
Fee | New | PNEs | |||
.5 | 0 | 4 | 8 | * | * |
.3 | 12 | * | * | * | * |
.28125 | 6 | 24 | * | * | * |
.2 | 1 | 5 | 32 | 40 | * |
.181818 | 2 | 16 | * | * | * |
.161932 | 22 | 26 | * | * | * |
.151786 | 25 | 38 | * | * | * |
.150326 | 27 | 31 | 54 | 62 | * |
.142857 | 55 | 59 | 63 | * | * |
.129464 | 29 | 30 | 46 | * | * |
.110294 | 17 | 34 | * | * | * |
.1 | 9 | 13 | 36 | 44 | * |
.098214 | 21 | 42 | * | * | * |
.085714 | 14 | 28 | 33 | 37 | 41 |
.057143 | 43 | 47 | 53 | 61 | * |
.053467 | 18 | * | * | * | * |
.01875 | 10 | 20 | * | * | * |
.014286 | 39 | 57 | * | * | * |
0 | 3 | 7 | 11 | 15 | * |
19 | 23 | 35 | 45 | * | |
48 | 49 | 50 | 51 | * | |
52 | 56 | 58 | 60 | * |
| | | | | | | | | | |
* | * | * | * | | * | * | * | * | | |
.9414 | * | * | * | * | * | * | * | * | (27, 31, 54, 62) | * |
* | * | * | * | * | * | * | * | * | | * |
.9285 | * | * | * | * | * | * | * | * | * | (35, 39, 49, 57) |
* | * | * | * | * | * | * | * | * | * | |
.8437 | * | * | (22, 26) | * | * | * | * | * | * | * |
* | * | * | | * | * | * | * | * | * | * |
.8 | (45) | * | * | * | (37, 41) | * | * | * | * | * |
* | | * | * | * | | * | * | * | * | * |
.794 | * | * | * | * | * | * | * | * | * | (19, 23, 50, 58) |
.* | * | * | * | * | * | * | * | * | * | |
.785 | * | (30) | * | (29, 46) | * | * | * | * | * | * |
* | * | | * | | * | * | * | * | * | * |
.75 | * | * | * | * | * | (21, 42) | * | (17, 34) | * | * |
* | * | * | * | * | * | | * | | * | * |
.714 | * | * | * | (25, 38) | * | * | * | * | * | * |
* | * | * | * | | * | * | * | * | * | * |
.7 | * | * | * | * | (33) | * | * | * | * | * |
* | * | * | * | * | * | * | * | * | * | |
.68 | * | * | * | * | * | * | (18) | * | * | * |
* | * | * | * | * | * | * | | * | * | * |
.5 | * | * | * | * | * | * | * | * | * | (51, 55, 59, 63) |
* | * | * | * | * | * | * | * | * | * | |
| | | | | | | | | | |
* | * | * | * | | * | * | * | * | | |
.9414 | * | * | * | * | * | * | * | * | (27, 31, 54, 62) | * |
* | * | * | * | * | * | * | * | * | | * |
.9285 | * | * | * | * | * | * | * | * | * | (35, 39, 49, 57) |
* | * | * | * | * | * | * | * | * | * | |
.8437 | * | * | (22, 26) | * | * | * | * | * | * | * |
* | * | * | | * | * | * | * | * | * | * |
.8 | (45) | * | * | * | (37, 41) | * | * | * | * | * |
* | | * | * | * | | * | * | * | * | * |
.794 | * | * | * | * | * | * | * | * | * | (19, 23, 50, 58) |
.* | * | * | * | * | * | * | * | * | * | |
.785 | * | (30) | * | (29, 46) | * | * | * | * | * | * |
* | * | | * | | * | * | * | * | * | * |
.75 | * | * | * | * | * | (21, 42) | * | (17, 34) | * | * |
* | * | * | * | * | * | | * | | * | * |
.714 | * | * | * | (25, 38) | * | * | * | * | * | * |
* | * | * | * | | * | * | * | * | * | * |
.7 | * | * | * | * | (33) | * | * | * | * | * |
* | * | * | * | * | * | * | * | * | * | |
.68 | * | * | * | * | * | * | (18) | * | * | * |
* | * | * | * | * | * | * | | * | * | * |
.5 | * | * | * | * | * | * | * | * | * | (51, 55, 59, 63) |
* | * | * | * | * | * | * | * | * | * | |
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