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-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22

Pseudomanifold Triangulations on 10 Vertices

Complex: 10_a_b_c_d_0_e_0_f_0_g

  • a= number of vertex links homeomorphic to the sphere
  • b= number of vertex links homeomorphic to the real projective plane
  • c= number of vertex links homeomorphic to the torus
  • d= number of vertex links homeomorphic to the Klein bottle
  • e= number of vertex links homeomorphic to the genus three nonorientable surface
  • f= number of vertex links homeomorphic to the genus four nonorientable surface
  • g= number of vertex links homeomorphic to the genus five nonorientable surface

χ - Euler characteristic of all the complexes on 10 vertices with the given vertex links.

Triangulations - The number of triangulations with the given vertex links on 10 vertices. Clicking on the link gives all of the triangulations.

minG2 - The minimum g2 over all triangulations with the given vertex links on 10 vertices. Clicking the link gives a list of the complexes which realize the minimum g2.

H1, H2, H3 - Integer homology groups of all of the triangulations with the given vertex links on 10 vertices. The homology group is trivial if blank. For H2 the shorthand n,[2] stands for the direct sum of Z/2Z and the abelian group of rank n.

Γ - A letter in this column indicates that the value of minG2 is the minimum of g2 over all triangulations of a three-dimensional normal pseudomanifold with the given singular vertices. The letter indicates the proof as follows:

  • a - For any vertex v of Δ, g2(Δ) ≥ g2 (link v).
  • b - If n is the number of singular vertices, then g2 ≥ 2 χ - <mfrac> n-3 3</mfrac>

# Complex χ Triangulations minG2 H1 H2 H3 Γ beta gamma delta epsilon
  10_0_0_0_0_0_0_0_10 20 5 15   19,[2]            
  10_0_0_0_0_0_0_0_6_0_4 22 1 15   21,[2]   a        
  10_0_0_0_0_0_2_0_8 19 2 15   18,[2]            
  10_0_0_0_0_0_3_0_6_0_1 19 2 15   18,[2]   a        
  10_0_0_0_0_0_4_0_6 18 9 15   17,[2]            
  10_0_0_0_0_0_6_0_4 17 14 15   16,[2]            
  10_0_0_0_0_0_8_0_2 16 9 15   15,[2]            
  10_0_0_0_0_0_10_0_0 15 1 15   14,[2]            
  10_0_0_0_1_0_4_0_5 17 3 15   16,[2]            
  10_0_0_0_1_0_5_0_3_0_1 17 1 15   16,[2]   a        
  10_0_0_0_1_0_6_0_3 16 29 15   15,[2]            
  10_0_0_0_1_0_7_0_1_0_1 16 1 15   15,[2]   a        
  10_0_0_0_1_0_8_0_1 15 24 15   14,[2]            
  10_0_0_0_2_0_2_0_6 17 2 15   16,[2]            
  10_0_0_0_2_0_4_0_4 16 45 14   15,[2]            
  10_0_0_0_2_0_6_0_2 15 90 14   14,[2]            
  10_0_0_0_2_0_8_0_0 14 63 14   13,[2]            
  10_0_0_0_3_0_2_0_5 16 3 15   15,[2]            
  10_0_0_0_3_0_3_0_3_0_1 16 1 15   15,[2]   a        
  10_0_0_0_3_0_4_0_3 15 89 14   14,[2]            
  10_0_0_0_3_0_5_0_1_0_1 15 1 15   14,[2]   a        
  10_0_0_0_3_0_6_0_1 14 210 14   13,[2]            
  10_0_0_0_4_0_2_0_4 15 15 14   14,[2]            
  10_0_0_0_4_0_3_0_2_0_1 15 3 15   14,[2]   a        
  10_0_0_0_4_0_4_0_2 14 232 14   13,[2]            
  10_0_0_0_4_0_5_0_0_0_1 14 5 15   13,[2]   a        
  10_0_0_0_4_0_6_0_0 13 343 14   12,[2]            
  10_0_0_0_5_0_2_0_3 14 59 14   13,[2]            
  10_0_0_0_5_0_3_0_1_0_1 14 5 15   13,[2]   a        
  10_0_0_0_5_0_4_0_1 13 443 14   12,[2]            
  10_0_0_0_6_0_0_0_4 14 2 15   13,[2]            
  10_0_0_0_6_0_2_0_2 13 125 13   12,[2]            
  10_0_0_0_6_0_3_0_0_0_1 13 7 15   12,[2]   a        
  10_0_0_0_6_0_4_0_0 12 675 12   11,[2]            
  10_0_0_0_7_0_0_0_3 13 13 14   12,[2]            
  10_0_0_0_7_0_1_0_1_0_1 13 4 15   12,[2]   a        
  10_0_0_0_7_0_2_0_1 12 243 14   11,[2]            
  10_0_0_0_8_0_0_0_2 12 8 15   11,[2]            
  10_0_0_0_8_0_2_0_0 11 876 13   10,[2]            
  10_0_0_0_9_0_0_0_1 11 38 14   10,[2]            
  10_0_0_0_10_0_0_0_0 10 43 14   9,[2]   a        
  10_0_0_1_0_0_2_0_7 18 1 15   17,[2]            
  10_0_0_1_0_0_4_0_5 17 6 15   16,[2]            
  10_0_0_1_0_0_6_0_3 16 27 15   15,[2]            
  10_0_0_1_0_0_8_0_1 15 13 15   14,[2]            
  10_0_0_1_1_0_2_0_6 17 1 15   16,[2]            
  10_0_0_1_1_0_3_0_4_0_1 17 2 15   16,[2]   a        
  10_0_0_1_1_0_4_0_4 16 52 14   15,[2]            
  10_0_0_1_1_0_5_0_2_0_1 16 2 15   15,[2]   a        
  10_0_0_1_1_0_6_0_2 15 115 14   14,[2]            
  10_0_0_1_1_0_8_0_0 14 47 15   13,[2]            
  10_0_0_1_2_0_0_0_7 17 1 15   16,[2]            
  10_0_0_1_2_0_2_0_5 16 18 15   15,[2]            
  10_0_0_1_2_0_4_0_3 15 159 14   14,[2]            
  10_0_0_1_2_0_5_0_1_0_1 15 2 15   14,[2]   a        
  10_0_0_1_2_0_6_0_1 14 361 14   13,[2]            
  10_0_0_1_3_0_2_0_4 15 43 15   14,[2]            
  10_0_0_1_3_0_3_0_2_0_1 15 5 15   14,[2]   a        
  10_0_0_1_3_0_4_0_2 14 372 14   13,[2]            
  10_0_0_1_3_0_5_0_0_0_1 14 7 15   13,[2]   a        
  10_0_0_1_3_0_6_0_0 13 639 14   12,[2]            
  10_0_0_1_4_0_0_0_5 15 2 15   14,[2]            
  10_0_0_1_4_0_1_0_3_0_1 15 1 15   14,[2]   a        
  10_0_0_1_4_0_2_0_3 14 120 14   13,[2]            
  10_0_0_1_4_0_3_0_1_0_1 14 10 15   13,[2]   a        
  10_0_0_1_4_0_4_0_1 13 1105 14   12,[2]            
  10_0_0_1_5_0_0_0_4 14 2 15   13,[2]            
  10_0_0_1_5_0_1_0_2_0_1 14 2 15   13,[2]   a        
  10_0_0_1_5_0_2_0_2 13 280 14   12,[2]            
  10_0_0_1_5_0_3_0_0_0_1 13 11 15   12,[2]   a        
  10_0_0_1_5_0_4_0_0 12 1836 13   11,[2]            
  10_0_0_1_6_0_0_0_3 13 12 15   12,[2]            
  10_0_0_1_6_0_1_0_1_0_1 13 1 15   12,[2]            
  10_0_0_1_6_0_2_0_1 12 895 14   11,[2]            
  10_0_0_1_7_0_0_0_2 12 20 14   11,[2]            
  10_0_0_1_7_0_1_0_0_0_1 12 1 15   11,[2]   a        
  10_0_0_1_7_0_2_0_0 11 1411 14   10,[2]            
  10_0_0_1_8_0_0_0_1 11 63 14   10,[2]            
  10_0_0_1_9_0_0_0_0 10 67 14   9,[2]            
  10_0_0_2_0_0_0_0_8 18 5 14   17,[2]            
  10_0_0_2_0_0_2_0_6 17 3 15   16,[2]            
  10_0_0_2_0_0_4_0_4 16 26 14   15,[2]            
  10_0_0_2_0_0_6_0_2 15 44 14   14,[2]            
  10_0_0_2_0_0_8_0_0 14 24 14   13,[2]            
  10_0_0_2_1_0_2_0_5 16 16 15   15,[2]            
  10_0_0_2_1_0_4_0_3 15 73 15   14,[2]            
  10_0_0_2_1_0_6_0_1 14 194 14   13,[2]            
  10_0_0_2_2_0_0_0_6 16 1 15   15,[2]            
  10_0_0_2_2_0_2_0_4 15 48 14   14,[2]            
  10_0_0_2_2_0_3_0_2_0_1 15 1 15   14,[2]   a        
  10_0_0_2_2_0_4_0_2 14 437 14   13,[2]            
  10_0_0_2_2_0_5_0_0_0_1 14 2 15   13,[2]   a        
  10_0_0_2_2_0_6_0_0 13 443 14   12,[2]            
  10_0_0_2_3_0_2_0_3 14 137 14   13,[2]            
  10_0_0_2_3_0_3_0_1_0_1 14 8 15   13,[2]   a        
  10_0_0_2_3_0_4_0_1 13 1372 14   12,[2]            
  10_0_0_2_4_0_0_0_4 14 4 15   13,[2]            
  10_0_0_2_4_0_1_0_2_0_1 14 1 15   13,[2]   a        
  10_0_0_2_4_0_2_0_2 13 414 14   12,[2]            
  10_0_0_2_4_0_3_0_0_0_1 13 5 15   12,[2]   a        
  10_0_0_2_4_0_4_0_0 12 2826 13   11,[2]            
  10_0_0_2_5_0_0_0_3 13 24 14   12,[2]            
  10_0_0_2_5_0_1_0_1_0_1 13 1 15   12,[2]   a        
  10_0_0_2_5_0_2_0_1 12 1470 13   11,[2]            
  10_0_0_2_6_0_0_0_2 12 64 14   11,[2]            
  10_0_0_2_6_0_2_0_0 11 3091 13   10,[2]            
  10_0_0_2_7_0_0_0_1 11 149 14   10,[2]            
  10_0_0_2_8_0_0_0_0 10 657 13   9,[2]            
  10_0_0_3_0_0_0_0_7 17 1 15   16,[2]            
  10_0_0_3_0_0_2_0_5 16 10 14   15,[2]            
  10_0_0_3_0_0_4_0_3 15 19 15   14,[2]            
  10_0_0_3_0_0_6_0_1 14 35 14   13,[2]            
  10_0_0_3_1_0_0_0_6 16 1 15   15,[2]            
  10_0_0_3_1_0_2_0_4 15 22 14   14,[2]            
  10_0_0_3_1_0_4_0_2 14 176 14   13,[2]            
  10_0_0_3_1_0_6_0_0 13 187 14   12,[2]            
  10_0_0_3_2_0_2_0_3 14 114 14   13,[2]            
  10_0_0_3_2_0_3_0_1_0_1 14 1 15   13,[2]   a        
  10_0_0_3_2_0_4_0_1 13 1021 14   12,[2]            
  10_0_0_3_3_0_0_0_4 14 5 15   13,[2]            
  10_0_0_3_3_0_2_0_2 13 406 13   12,[2]            
  10_0_0_3_3_0_3_0_0_0_1 13 10 15   12,[2]   a        
  10_0_0_3_3_0_4_0_0 12 2284 13   11,[2]            
  10_0_0_3_4_0_0_0_3 13 66 13   12,[2]            
  10_0_0_3_4_0_1_0_1_0_1 13 4 15   12,[2]   a        
  10_0_0_3_4_0_2_0_1 12 1881 13   11,[2]            
  10_0_0_3_5_0_0_0_2 12 33 14   11,[2]            
  10_0_0_3_5_0_1_0_0_0_1 12 4 15   11,[2]   a        
  10_0_0_3_5_0_2_0_0 11 4052 13   10,[2]            
  10_0_0_3_6_0_0_0_1 11 267 14   10,[2]            
  10_0_0_3_7_0_0_0_0 10 525 13   9,[2]            
  10_0_0_4_0_0_0_0_6 16 7 13   15,[2]            
  10_0_0_4_0_0_2_0_4 15 3 15   14,[2]            
  10_0_0_4_0_0_4_0_2 14 76 14   13,[2]            
  10_0_0_4_0_0_5_0_0_0_1 14 2 15   13,[2]   a        
  10_0_0_4_0_0_6_0_0 13 58 13   12,[2]            
  10_0_0_4_1_0_2_0_3 14 34 14   13,[2]            
  10_0_0_4_1_0_3_0_1_0_1 14 2 15   13,[2]   a        
  10_0_0_4_1_0_4_0_1 13 340 14   12,[2]            
  10_0_0_4_2_0_0_0_4 14 4 15   13,[2]            
  10_0_0_4_2_0_2_0_2 13 122 14   12,[2]            
  10_0_0_4_2_0_3_0_0_0_1 13 2 15   12,[2]   a        
  10_0_0_4_2_0_4_0_0 12 1223 13   11,[2]            
  10_0_0_4_3_0_0_0_3 13 16 14   12,[2]            
  10_0_0_4_3_0_1_0_1_0_1 13 3 15   12,[2]   a        
  10_0_0_4_3_0_2_0_1 12 935 13   11,[2]            
  10_0_0_4_4_0_0_0_2 12 130 12   11,[2]   a        
  10_0_0_4_4_0_1_0_0_0_1 12 5 15   11,[2]   a        
  10_0_0_4_4_0_2_0_0 11 2717 13   10,[2]            
  10_0_0_4_5_0_0_0_1 11 211 14   10,[2]            
  10_0_0_4_6_0_0_0_0 10 720 13   9,[2]            
  10_0_0_5_0_0_0_0_5 15 1 15   14,[2]            
  10_0_0_5_0_0_2_0_3 14 16 14   13,[2]            
  10_0_0_5_0_0_3_0_1_0_1 14 1 15   13,[2]   a        
  10_0_0_5_0_0_4_0_1 13 67 14   12,[2]            
  10_0_0_5_1_0_2_0_2 13 36 14   12,[2]            
  10_0_0_5_1_0_3_0_0_0_1 13 3 15   12,[2]   a        
  10_0_0_5_1_0_4_0_0 12 215 14   11,[2]            
  10_0_0_5_2_0_2_0_1 12 231 14   11,[2]            
  10_0_0_5_3_0_0_0_2 12 8 14   11,[2]            
  10_0_0_5_3_0_1_0_0_0_1 12 1 15   11,[2]   a        
  10_0_0_5_3_0_2_0_0 11 1061 14   10,[2]            
  10_0_0_5_4_0_0_0_1 11 65 14   10,[2]            
  10_0_0_5_5_0_0_0_0 10 218 14   9,[2]            
  10_0_0_6_0_0_0_0_4 14 11 14   13,[2]            
  10_0_0_6_0_0_2_0_2 13 9 14   12,[2]            
  10_0_0_6_0_0_4_0_0 12 48 14   11,[2]            
  10_0_0_6_1_0_2_0_1 12 67 14   11,[2]            
  10_0_0_6_2_0_0_0_2 12 1 15   11,[2]            
  10_0_0_6_2_0_2_0_0 11 445 14   10,[2]            
  10_0_0_6_3_0_0_0_1 11 90 14   10,[2]            
  10_0_0_6_4_0_0_0_0 10 453 13   9,[2]            
  10_0_0_7_0_0_0_0_3 13 12 13   12,[2]            
  10_0_0_7_0_0_2_0_1 12 3 15   11,[2]            
  10_0_0_7_1_0_0_0_2 12 1 15   11,[2]            
  10_0_0_7_1_0_2_0_0 11 10 15   10,[2]            
  10_0_0_7_2_0_0_0_1 11 2 15   10,[2]            
  10_0_0_7_3_0_0_0_0 10 2 15   9,[2]            
  10_0_0_10_0_0_0_0_0 10 55 13   10,[] Z          
  10_0_1_0_0_0_7_0_2 15 3 15   14,[2]            
  10_0_1_0_0_0_9_0_0 14 1 15   13,[2]            
  10_0_1_0_1_0_5_0_3 15 13 15   14,[2]            
  10_0_1_0_1_0_6_0_1_0_1 15 2 15   14,[2]   a        
  10_0_1_0_1_0_7_0_1 14 48 14   13,[2]            
  10_0_1_0_2_0_3_0_4 15 8 15   14,[2]            
  10_0_1_0_2_0_5_0_2 14 109 14   13,[2]            
  10_0_1_0_2_0_6_0_0_0_1 14 8 15   13,[2]   a        
  10_0_1_0_2_0_7_0_0 13 151 14   12,[2]            
  10_0_1_0_3_0_1_0_5 15 2 15   14,[2]            
  10_0_1_0_3_0_3_0_3 14 76 14   13,[2]            
  10_0_1_0_3_0_4_0_1_0_1 14 6 15   13,[2]   a        
  10_0_1_0_3_0_5_0_1 13 584 14   12,[2]            
  10_0_1_0_4_0_1_0_4 14 7 15   13,[2]            
  10_0_1_0_4_0_2_0_2_0_1 14 3 15   13,[2]   a        
  10_0_1_0_4_0_3_0_2 13 356 14   12,[2]            
  10_0_1_0_4_0_4_0_0_0_1 13 19 15   12,[2]   a        
  10_0_1_0_4_0_5_0_0 12 1147 13   11,[2]            
  10_0_1_0_5_0_1_0_3 13 40 14   12,[2]            
  10_0_1_0_5_0_2_0_1_0_1 13 7 15   12,[2]   a        
  10_0_1_0_5_0_3_0_1 12 1411 14   11,[2]            
  10_0_1_0_6_0_0_0_2_0_1 13 2 15   12,[2]   a        
  10_0_1_0_6_0_1_0_2 12 104 14   11,[2]            
  10_0_1_0_6_0_2_0_0_0_1 12 4 15   11,[2]   a        
  10_0_1_0_6_0_3_0_0 11 4114 13   10,[2]            
  10_0_1_0_7_0_0_0_1_0_1 12 1 15   11,[2]   a        
  10_0_1_0_7_0_1_0_1 11 736 14   10,[2]            
  10_0_1_0_8_0_0_0_0_0_1 11 10 15   10,[2]   a        
  10_0_1_0_8_0_1_0_0 10 1001 13   9,[2]            
  10_0_1_1_0_0_3_0_5 16 1 15   15,[2]            
  10_0_1_1_0_0_5_0_3 15 10 14   14,[2]            
  10_0_1_1_0_0_6_0_1_0_1 15 1 15   14,[2]   a        
  10_0_1_1_0_0_7_0_1 14 43 14   13,[2]            
  10_0_1_1_1_0_3_0_4 15 18 15   14,[2]            
  10_0_1_1_1_0_4_0_2_0_1 15 1 15   14,[2]   a        
  10_0_1_1_1_0_5_0_2 14 163 14   13,[2]            
  10_0_1_1_1_0_7_0_0 13 159 14   12,[2]            
  10_0_1_1_2_0_1_0_5 15 3 15   14,[2]            
  10_0_1_1_2_0_3_0_3 14 151 14   13,[2]            
  10_0_1_1_2_0_4_0_1_0_1 14 8 15   13,[2]   a        
  10_0_1_1_2_0_5_0_1 13 1046 13   12,[2]            
  10_0_1_1_3_0_1_0_4 14 18 15   13,[2]            
  10_0_1_1_3_0_2_0_2_0_1 14 2 15   13,[2]   a        
  10_0_1_1_3_0_3_0_2 13 872 14   12,[2]            
  10_0_1_1_3_0_4_0_0_0_1 13 13 15   12,[2]   a        
  10_0_1_1_3_0_5_0_0 12 2673 13   11,[2]            
  10_0_1_1_4_0_1_0_3 13 124 14   12,[2]            
  10_0_1_1_4_0_2_0_1_0_1 13 17 15   12,[2]   a        
  10_0_1_1_4_0_3_0_1 12 3791 13   11,[2]            
  10_0_1_1_5_0_0_0_2_0_1 13 3 15   12,[2]   a        
  10_0_1_1_5_0_1_0_2 12 415 14   11,[2]            
  10_0_1_1_5_0_2_0_0_0_1 12 13 15   11,[2]   a        
  10_0_1_1_5_0_3_0_0 11 7576 13   10,[2]            
  10_0_1_1_6_0_1_0_1 11 1268 14   10,[2]            
  10_0_1_1_7_0_0_0_0_0_1 11 2 15   10,[2]   a        
  10_0_1_1_7_0_1_0_0 10 3824 12   9,[2]            
  10_0_1_2_0_0_3_0_4 15 4 15   14,[2]            
  10_0_1_2_0_0_5_0_2 14 73 14   13,[2]            
  10_0_1_2_0_0_7_0_0 13 44 14   12,[2]            
  10_0_1_2_1_0_1_0_5 15 1 15   14,[2]            
  10_0_1_2_1_0_2_0_3_0_1 15 1 15   14,[2]   a        
  10_0_1_2_1_0_3_0_3 14 140 14   13,[2]            
  10_0_1_2_1_0_4_0_1_0_1 14 6 15   13,[2]   a        
  10_0_1_2_1_0_5_0_1 13 620 13   12,[2]            
  10_0_1_2_2_0_1_0_4 14 28 15   13,[2]            
  10_0_1_2_2_0_2_0_2_0_1 14 3 15   13,[2]   a        
  10_0_1_2_2_0_3_0_2 13 753 13   12,[2]            
  10_0_1_2_2_0_4_0_0_0_1 13 10 15   12,[2]   a        
  10_0_1_2_2_0_5_0_0 12 2619 13   11,[2]            
  10_0_1_2_3_0_1_0_3 13 131 14   12,[2]            
  10_0_1_2_3_0_2_0_1_0_1 13 12 15   12,[2]   a        
  10_0_1_2_3_0_3_0_1 12 4802 13   11,[2]            
  10_0_1_2_4_0_0_0_2_0_1 13 3 15   12,[2]   a        
  10_0_1_2_4_0_1_0_2 12 638 14   11,[2]            
  10_0_1_2_4_0_2_0_0_0_1 12 15 15   11,[2]   a        
  10_0_1_2_4_0_3_0_0 11 12360 13   10,[2]            
  10_0_1_2_5_0_0_0_1_0_1 12 1 15   11,[2]   a        
  10_0_1_2_5_0_1_0_1 11 2910 13   10,[2]            
  10_0_1_2_6_0_0_0_0_0_1 11 5 15   10,[2]   a        
  10_0_1_2_6_0_1_0_0 10 10053 12   9,[2]            
  10_0_1_3_0_0_3_0_3 14 30 15   13,[2]            
  10_0_1_3_0_0_4_0_1_0_1 14 1 15   13,[2]   a        
  10_0_1_3_0_0_5_0_1 13 138 14   12,[2]            
  10_0_1_3_1_0_1_0_4 14 17 14   13,[2]            
  10_0_1_3_1_0_2_0_2_0_1 14 2 15   13,[2]   a        
  10_0_1_3_1_0_3_0_2 13 442 13   12,[2]            
  10_0_1_3_1_0_4_0_0_0_1 13 1 15   12,[2]            
  10_0_1_3_1_0_5_0_0 12 1286 13   11,[2]            
  10_0_1_3_2_0_1_0_3 13 93 14   12,[2]            
  10_0_1_3_2_0_2_0_1_0_1 13 5 15   12,[2]   a        
  10_0_1_3_2_0_3_0_1 12 3991 13   11,[2]            
  10_0_1_3_3_0_0_0_2_0_1 13 3 15   12,[2]   a        
  10_0_1_3_3_0_1_0_2 12 582 14   11,[2]            
  10_0_1_3_3_0_2_0_0_0_1 12 14 15   11,[2]   a        
  10_0_1_3_3_0_3_0_0 11 11580 12   10,[2]            
  10_0_1_3_4_0_1_0_1 11 4425 13   10,[2]            
  10_0_1_3_5_0_1_0_0 10 10635 12   9,[2]            
  10_0_1_4_0_0_1_0_4 14 6 15   13,[2]            
  10_0_1_4_0_0_3_0_2 13 78 14   12,[2]            
  10_0_1_4_0_0_5_0_0 12 134 14   11,[2]            
  10_0_1_4_1_0_1_0_3 13 9 15   12,[2]            
  10_0_1_4_1_0_2_0_1_0_1 13 2 15   12,[2]   a        
  10_0_1_4_1_0_3_0_1 12 794 13   11,[2]            
  10_0_1_4_2_0_0_0_2_0_1 13 1 15   12,[2]   a        
  10_0_1_4_2_0_1_0_2 12 388 13   11,[2]            
  10_0_1_4_2_0_2_0_0_0_1 12 12 15   11,[2]   a        
  10_0_1_4_2_0_3_0_0 11 5420 12   10,[2]            
  10_0_1_4_3_0_1_0_1 11 3079 12   10,[2]   a        
  10_0_1_4_4_0_0_0_0_0_1 11 31 15   10,[2]   a        
  10_0_1_4_4_0_1_0_0 10 8083 12   9,[2]            
  10_0_1_5_0_0_1_0_3 13 3 15   12,[2]            
  10_0_1_5_0_0_3_0_1 12 48 14   11,[2]            
  10_0_1_5_1_0_1_0_2 12 28 14   11,[2]            
  10_0_1_5_1_0_3_0_0 11 1556 13   10,[2]            
  10_0_1_5_2_0_1_0_1 11 1051 13   10,[2]            
  10_0_1_5_3_0_0_0_0_0_1 11 7 15   10,[2]   a        
  10_0_1_5_3_0_1_0_0 10 3308 12   9,[2]            
  10_0_1_6_0_0_3_0_0 11 382 13   10,[2]            
  10_0_1_6_1_0_1_0_1 11 640 13   10,[2]            
  10_0_1_6_2_0_1_0_0 10 2227 12   9,[2]            
  10_0_1_7_1_0_1_0_0 10 85 14   9,[2]            
  10_0_2_0_0_0_6_0_2 14 1 15   13,[2]            
  10_0_2_0_0_0_8_0_0 13 5 15   12,[2]            
  10_0_2_0_1_0_4_0_3 14 7 15   13,[2]            
  10_0_2_0_1_0_6_0_1 13 56 14   12,[2]            
  10_0_2_0_2_0_2_0_4 14 3 15   13,[2]            
  10_0_2_0_2_0_3_0_2_0_1 14 1 15   13,[2]   a        
  10_0_2_0_2_0_4_0_2 13 156 14   12,[2]            
  10_0_2_0_2_0_5_0_0_0_1 13 2 15   12,[2]   a        
  10_0_2_0_2_0_6_0_0 12 397 14   11,[2]            
  10_0_2_0_3_0_0_0_5 14 1 15   13,[2]            
  10_0_2_0_3_0_2_0_3 13 55 14   12,[2]            
  10_0_2_0_3_0_3_0_1_0_1 13 5 15   12,[2]   a        
  10_0_2_0_3_0_4_0_1 12 1282 13   11,[2]            
  10_0_2_0_4_0_2_0_2 12 415 14   11,[2]            
  10_0_2_0_4_0_3_0_0_0_1 12 21 15   11,[2]   a        
  10_0_2_0_4_0_4_0_0 11 4182 13   10,[2]            
  10_0_2_0_5_0_0_0_3 12 16 14   11,[2]            
  10_0_2_0_5_0_1_0_1_0_1 12 4 15   11,[2]   a        
  10_0_2_0_5_0_2_0_1 11 2720 13   10,[2]            
  10_0_2_0_6_0_0_0_2 11 117 14   10,[2]            
  10_0_2_0_6_0_1_0_0_0_1 11 26 15   10,[2]   a        
  10_0_2_0_6_0_2_0_0 10 8500 12   9,[2]            
  10_0_2_0_7_0_0_0_1 10 682 13   9,[2]            
  10_0_2_0_8_0_0_0_0 9 1949 12   8,[2]            
  10_0_2_1_0_0_2_0_5 15 1 15   14,[2]            
  10_0_2_1_0_0_4_0_3 14 8 15   13,[2]            
  10_0_2_1_0_0_6_0_1 13 25 15   12,[2]            
  10_0_2_1_1_0_2_0_4 14 5 15   13,[2]            
  10_0_2_1_1_0_4_0_2 13 183 14   12,[2]            
  10_0_2_1_1_0_5_0_0_0_1 13 3 15   12,[2]   a        
  10_0_2_1_1_0_6_0_0 12 446 13   11,[2]            
  10_0_2_1_2_0_2_0_3 13 158 14   12,[2]            
  10_0_2_1_2_0_3_0_1_0_1 13 12 15   12,[2]   a        
  10_0_2_1_2_0_4_0_1 12 2092 13   11,[2]            
  10_0_2_1_3_0_0_0_4 13 2 15   12,[2]            
  10_0_2_1_3_0_1_0_2_0_1 13 2 15   12,[2]   a        
  10_0_2_1_3_0_2_0_2 12 1004 14   11,[2]            
  10_0_2_1_3_0_3_0_0_0_1 12 19 15   11,[2]   a        
  10_0_2_1_3_0_4_0_0 11 7075 12   10,[2]            
  10_0_2_1_4_0_0_0_3 12 62 14   11,[2]            
  10_0_2_1_4_0_1_0_1_0_1 12 6 15   11,[2]   a        
  10_0_2_1_4_0_2_0_1 11 4395 13   10,[2]            
  10_0_2_1_5_0_0_0_2 11 148 14   10,[2]            
  10_0_2_1_5_0_1_0_0_0_1 11 5 15   10,[2]   a        
  10_0_2_1_5_0_2_0_0 10 15795 13   9,[2]            
  10_0_2_1_6_0_0_0_1 10 1023 13   9,[2]            
  10_0_2_1_7_0_0_0_0 9 5320 12   8,[2]            
  10_0_2_2_0_0_2_0_4 14 11 14   13,[2]            
  10_0_2_2_0_0_3_0_2_0_1 14 1 15   13,[2]   a        
  10_0_2_2_0_0_4_0_2 13 101 13   12,[2]            
  10_0_2_2_0_0_6_0_0 12 366 11   11,[2]            
  10_0_2_2_1_0_0_0_5 14 1 15   13,[2]            
  10_0_2_2_1_0_2_0_3 13 92 14   12,[2]            
  10_0_2_2_1_0_3_0_1_0_1 13 4 15   12,[2]   a        
  10_0_2_2_1_0_4_0_1 12 1487 13   11,[2]            
  10_0_2_2_2_0_0_0_4 13 2 15   12,[2]            
  10_0_2_2_2_0_1_0_2_0_1 13 1 15   12,[2]   a        
  10_0_2_2_2_0_2_0_2 12 960 13   11,[2]            
  10_0_2_2_2_0_3_0_0_0_1 12 15 15   11,[2]   a        
  10_0_2_2_2_0_4_0_0 11 6878 13   10,[2]            
  10_0_2_2_3_0_0_0_3 12 63 14   11,[2]            
  10_0_2_2_3_0_1_0_1_0_1 12 12 15   11,[2]   a        
  10_0_2_2_3_0_2_0_1 11 7268 13   10,[2]            
  10_0_2_2_4_0_0_0_2 11 176 14   10,[2]            
  10_0_2_2_4_0_1_0_0_0_1 11 19 15   10,[2]   a        
  10_0_2_2_4_0_2_0_0 10 24347 12   9,[2]            
  10_0_2_2_5_0_0_0_1 10 2250 13   9,[2]            
  10_0_2_2_6_0_0_0_0 9 15996 11   8,[2]            
  10_0_2_3_0_0_2_0_3 13 7 15   12,[2]            
  10_0_2_3_0_0_4_0_1 12 640 12   11,[2]   a        
  10_0_2_3_1_0_0_0_4 13 1 15   12,[2]            
  10_0_2_3_1_0_2_0_2 12 570 13   11,[2]            
  10_0_2_3_1_0_3_0_0_0_1 12 4 15   11,[2]   a        
  10_0_2_3_1_0_4_0_0 11 3245 13   10,[2]            
  10_0_2_3_2_0_0_0_3 12 48 14   11,[2]            
  10_0_2_3_2_0_2_0_1 11 5790 12   10,[2]   a        
  10_0_2_3_3_0_0_0_2 11 541 13   10,[2]            
  10_0_2_3_3_0_1_0_0_0_1 11 22 15   10,[2]   a        
  10_0_2_3_3_0_2_0_0 10 20819 12   9,[2]            
  10_0_2_3_4_0_0_0_1 10 1750 13   9,[2]            
  10_0_2_3_5_0_0_0_0 9 8223 12   8,[2]            
  10_0_2_4_0_0_0_0_4 13 1 15   12,[2]            
  10_0_2_4_0_0_2_0_2 12 177 13   11,[2]            
  10_0_2_4_0_0_3_0_0_0_1 12 2 15   11,[2]   a        
  10_0_2_4_0_0_4_0_0 11 384 13   10,[2]            
  10_0_2_4_1_0_0_0_3 12 12 14   11,[2]            
  10_0_2_4_1_0_2_0_1 11 1467 13   10,[2]            
  10_0_2_4_2_0_0_0_2 11 133 14   10,[2]            
  10_0_2_4_2_0_1_0_0_0_1 11 45 15   10,[2]   a        
  10_0_2_4_2_0_2_0_0 10 10933 12   9,[2]            
  10_0_2_4_3_0_0_0_1 10 931 13   9,[2]            
  10_0_2_4_4_0_0_0_0 9 4886 12   8,[2]            
  10_0_2_5_0_0_2_0_1 11 144 14   10,[2]            
  10_0_2_5_1_0_0_0_2 11 12 15   10,[2]            
  10_0_2_5_1_0_1_0_0_0_1 11 2 15   10,[2]   a        
  10_0_2_5_1_0_2_0_0 10 1602 13   9,[2]            
  10_0_2_5_2_0_0_0_1 10 972 12   9,[2]   a        
  10_0_2_5_3_0_0_0_0 9 3041 12   8,[2]            
  10_0_2_6_0_0_0_0_2 11 4 15   10,[2]            
  10_0_2_6_0_0_2_0_0 10 1124 12   9,[2]            
  10_0_2_6_1_0_0_0_1 10 89 14   9,[2]            
  10_0_2_6_2_0_0_0_0 9 4543 11   8,[2]            
  10_0_2_7_1_0_0_0_0 9 16 14   8,[2]            
  10_0_3_0_0_0_5_0_2 13 7 15   12,[2]            
  10_0_3_0_0_0_6_0_0_0_1 13 1 15   12,[2]   a        
  10_0_3_0_0_0_7_0_0 12 11 15   11,[2]            
  10_0_3_0_1_0_3_0_3 13 11 15   12,[2]            
  10_0_3_0_1_0_4_0_1_0_1 13 1 15   12,[2]   a        
  10_0_3_0_1_0_5_0_1 12 260 14   11,[2]            
  10_0_3_0_2_0_1_0_4 13 3 14   12,[2]            
  10_0_3_0_2_0_3_0_2 12 260 13   11,[2]            
  10_0_3_0_2_0_4_0_0_0_1 12 5 15   11,[2]   a        
  10_0_3_0_2_0_5_0_0 11 1281 12   10,[2]            
  10_0_3_0_3_0_1_0_3 12 22 15   11,[2]            
  10_0_3_0_3_0_2_0_1_0_1 12 8 15   11,[2]   a        
  10_0_3_0_3_0_3_0_1 11 2126 13   10,[2]            
  10_0_3_0_4_0_1_0_2 11 504 14   10,[2]            
  10_0_3_0_4_0_2_0_0_0_1 11 20 15   10,[2]   a        
  10_0_3_0_4_0_3_0_0 10 13243 12   9,[2]            
  10_0_3_0_5_0_1_0_1 10 3977 13   9,[2]            
  10_0_3_0_6_0_0_0_0_0_1 10 12 15   9,[2]   a        
  10_0_3_0_6_0_1_0_0 9 11659 12   8,[2]            
  10_0_3_1_0_0_3_0_3 13 13 14   12,[2]            
  10_0_3_1_0_0_5_0_1 12 82 14   11,[2]            
  10_0_3_1_1_0_1_0_4 13 1 15   12,[2]            
  10_0_3_1_1_0_3_0_2 12 293 13   11,[2]            
  10_0_3_1_1_0_4_0_0_0_1 12 5 15   11,[2]   a        
  10_0_3_1_1_0_5_0_0 11 1347 13   10,[2]            
  10_0_3_1_2_0_1_0_3 12 44 14   11,[2]            
  10_0_3_1_2_0_2_0_1_0_1 12 8 15   11,[2]   a        
  10_0_3_1_2_0_3_0_1 11 3267 13   10,[2]            
  10_0_3_1_3_0_1_0_2 11 541 13   10,[2]            
  10_0_3_1_3_0_2_0_0_0_1 11 4 15   10,[2]   a        
  10_0_3_1_3_0_3_0_0 10 14867 12   9,[2]            
  10_0_3_1_4_0_1_0_1 10 4984 13   9,[2]            
  10_0_3_1_5_0_0_0_0_0_1 10 5 15   9,[2]   a        
  10_0_3_1_5_0_1_0_0 9 31459 12   8,[2]            
  10_0_3_2_0_0_3_0_2 12 87 14   11,[2]            
  10_0_3_2_0_0_5_0_0 11 254 14   10,[2]            
  10_0_3_2_1_0_1_0_3 12 30 14   11,[2]            
  10_0_3_2_1_0_2_0_1_0_1 12 6 15   11,[2]   a        
  10_0_3_2_1_0_3_0_1 11 2191 13   10,[2]            
  10_0_3_2_2_0_1_0_2 11 1143 13   10,[2]            
  10_0_3_2_2_0_2_0_0_0_1 11 20 15   10,[2]   a        
  10_0_3_2_2_0_3_0_0 10 11384 13   9,[2]            
  10_0_3_2_3_0_1_0_1 10 5586 13   9,[2]            
  10_0_3_2_4_0_0_0_0_0_1 10 11 15   9,[2]   a        
  10_0_3_2_4_0_1_0_0 9 38699 12   8,[2]            
  10_0_3_3_0_0_1_0_3 12 4 15   11,[2]            
  10_0_3_3_0_0_2_0_1_0_1 12 2 15   11,[2]   a        
  10_0_3_3_0_0_3_0_1 11 461 13   10,[2]            
  10_0_3_3_1_0_1_0_2 11 486 14   10,[2]            
  10_0_3_3_1_0_2_0_0_0_1 11 9 15   10,[2]   a        
  10_0_3_3_1_0_3_0_0 10 8666 12   9,[2]            
  10_0_3_3_2_0_0_0_1_0_1 11 5 15   10,[2]   a        
  10_0_3_3_2_0_1_0_1 10 3260 13   9,[2]            
  10_0_3_3_3_0_0_0_0_0_1 10 5 15   9,[2]   a        
  10_0_3_3_3_0_1_0_0 9 19789 12   8,[2]            
  10_0_3_4_0_0_1_0_2 11 25 14   10,[2]            
  10_0_3_4_0_0_2_0_0_0_1 11 2 15   10,[2]   a        
  10_0_3_4_0_0_3_0_0 10 1089 13   9,[2]            
  10_0_3_4_1_0_1_0_1 10 2263 13   9,[2]            
  10_0_3_4_2_0_0_0_0_0_1 10 7 15   9,[2]   a        
  10_0_3_4_2_0_1_0_0 9 6845 12   8,[2]            
  10_0_3_5_0_0_1_0_1 10 206 13   9,[2]            
  10_0_3_5_1_0_0_0_0_0_1 10 5 15   9,[2]   a        
  10_0_3_5_1_0_1_0_0 9 2558 12   8,[2]            
  10_0_3_6_0_0_0_0_0_0_1 10 2 15   9,[2]   a        
  10_0_3_6_0_0_1_0_0 9 3483 11   8,[2]            
  10_0_4_0_0_0_4_0_2 12 16 14   11,[2]            
  10_0_4_0_0_0_6_0_0 11 146 13   10,[2]            
  10_0_4_0_1_0_2_0_3 12 12 15   11,[2]            
  10_0_4_0_1_0_4_0_1 11 443 12   10,[2]   a        
  10_0_4_0_2_0_2_0_2 11 257 14   10,[2]            
  10_0_4_0_2_0_3_0_0_0_1 11 12 15   10,[2]   a        
  10_0_4_0_2_0_4_0_0 10 4445 12   9,[2]            
  10_0_4_0_3_0_0_0_3 11 36 14   10,[2]            
  10_0_4_0_3_0_1_0_1_0_1 11 5 15   10,[2]   a        
  10_0_4_0_3_0_2_0_1 10 4279 13   9,[2]            
  10_0_4_0_4_0_0_0_2 10 371 14   9,[2]            
  10_0_4_0_4_0_1_0_0_0_1 10 21 15   9,[2]   a        
  10_0_4_0_4_0_2_0_0 9 22467 12   8,[2]            
  10_0_4_0_5_0_0_0_1 9 2117 12   8,[2]   a        
  10_0_4_0_6_0_0_0_0 8 5706 11   7,[2]            
  10_0_4_1_0_0_2_0_3 12 7 15   11,[2]            
  10_0_4_1_0_0_4_0_1 11 237 13   10,[2]            
  10_0_4_1_1_0_2_0_2 11 306 13   10,[2]            
  10_0_4_1_1_0_3_0_0_0_1 11 3 15   10,[2]   a        
  10_0_4_1_1_0_4_0_0 10 2170 13   9,[2]            
  10_0_4_1_2_0_0_0_3 11 19 14   10,[2]            
  10_0_4_1_2_0_2_0_1 10 4083 13   9,[2]            
  10_0_4_1_3_0_0_0_2 10 137 14   9,[2]            
  10_0_4_1_3_0_1_0_0_0_1 10 7 15   9,[2]   a        
  10_0_4_1_3_0_2_0_0 9 34775 12   8,[2]            
  10_0_4_1_4_0_0_0_1 9 2805 13   8,[2]            
  10_0_4_1_5_0_0_0_0 8 15194 11   7,[2]            
  10_0_4_2_0_0_0_0_4 12 1 15   11,[2]            
  10_0_4_2_0_0_2_0_2 11 129 14   10,[2]            
  10_0_4_2_0_0_3_0_0_0_1 11 1 15   10,[2]   a        
  10_0_4_2_0_0_4_0_0 10 1061 12   9,[2]            
  10_0_4_2_1_0_0_0_3 11 26 14   10,[2]            
  10_0_4_2_1_0_1_0_1_0_1 11 1 15   10,[2]   a        
  10_0_4_2_1_0_2_0_1 10 1304 13   9,[2]            
  10_0_4_2_2_0_0_0_2 10 344 14   9,[2]            
  10_0_4_2_2_0_1_0_0_0_1 10 1 15   9,[2]   a        
  10_0_4_2_2_0_2_0_0 9 23539 12   8,[2]            
  10_0_4_2_3_0_0_0_1 9 3527 12   8,[2]   a        
  10_0_4_2_4_0_0_0_0 8 29990 12   7,[2]            
  10_0_4_3_0_0_0_0_3 11 4 13   10,[2]            
  10_0_4_3_0_0_1_0_1_0_1 11 1 15   10,[2]   a        
  10_0_4_3_0_0_2_0_1 10 1143 12   9,[2]   a        
  10_0_4_3_1_0_0_0_2 10 45 14   9,[2]            
  10_0_4_3_1_0_1_0_0_0_1 10 3 15   9,[2]   a        
  10_0_4_3_1_0_2_0_0 9 6925 12   8,[2]            
  10_0_4_3_2_0_0_0_1 9 1253 13   8,[2]            
  10_0_4_3_3_0_0_0_0 8 25954 10   7,[2]            
  10_0_4_4_0_0_0_0_2 10 121 14   9,[2]            
  10_0_4_4_0_0_1_0_0_0_1 10 7 15   9,[2]   a        
  10_0_4_4_0_0_2_0_0 9 633 13   8,[2]            
  10_0_4_4_1_0_0_0_1 9 445 12   8,[2]   a        
  10_0_4_4_2_0_0_0_0 8 9219 12   7,[2]            
  10_0_4_5_0_0_0_0_1 9 9 15   8,[2]            
  10_0_4_5_1_0_0_0_0 8 525 13   7,[2]            
  10_0_5_0_0_0_3_0_2 11 12 14   10,[2]            
  10_0_5_0_0_0_4_0_0_0_1 11 3 15   10,[2]   a        
  10_0_5_0_0_0_5_0_0 10 227 13   9,[2]            
  10_0_5_0_1_0_1_0_3 11 6 15   10,[2]            
  10_0_5_0_1_0_3_0_1 10 714 13   9,[2]            
  10_0_5_0_2_0_0_0_2_0_1 11 1 15   10,[2]   a        
  10_0_5_0_2_0_1_0_2 10 284 13   9,[2]            
  10_0_5_0_2_0_2_0_0_0_1 10 5 15   9,[2]   a        
  10_0_5_0_2_0_3_0_0 9 9484 12   8,[2]            
  10_0_5_0_3_0_0_0_1_0_1 10 2 15   9,[2]   a        
  10_0_5_0_3_0_1_0_1 9 4739 13   8,[2]            
  10_0_5_0_4_0_0_0_0_0_1 9 1 15   8,[2]   a        
  10_0_5_0_4_0_1_0_0 8 19240 12   7,[2]            
  10_0_5_1_0_0_1_0_3 11 2 15   10,[2]            
  10_0_5_1_0_0_2_0_1_0_1 11 2 15   10,[2]   a        
  10_0_5_1_0_0_3_0_1 10 210 13   9,[2]            
  10_0_5_1_1_0_1_0_2 10 268 13   9,[2]            
  10_0_5_1_1_0_2_0_0_0_1 10 1 15   9,[2]   a        
  10_0_5_1_1_0_3_0_0 9 5870 12   8,[2]            
  10_0_5_1_2_0_1_0_1 9 4016 13   8,[2]            
  10_0_5_1_3_0_0_0_0_0_1 9 4 15   8,[2]   a        
  10_0_5_1_3_0_1_0_0 8 31917 12   7,[2]            
  10_0_5_2_0_0_1_0_2 10 32 14   9,[2]            
  10_0_5_2_0_0_3_0_0 9 2213 12   8,[2]            
  10_0_5_2_1_0_1_0_1 9 1686 13   8,[2]            
  10_0_5_2_2_0_0_0_0_0_1 9 1 15   8,[2]   a        
  10_0_5_2_2_0_1_0_0 8 29269 11   7,[2]            
  10_0_5_3_0_0_1_0_1 9 494 13   8,[2]            
  10_0_5_3_1_0_0_0_0_0_1 9 5 15   8,[2]   a        
  10_0_5_3_1_0_1_0_0 8 10551 11   7,[2]            
  10_0_5_4_0_0_1_0_0 8 974 13   7,[2]            
  10_0_6_0_0_0_2_0_2 10 45 14   9,[2]            
  10_0_6_0_0_0_3_0_0_0_1 10 3 15   9,[2]   a        
  10_0_6_0_0_0_4_0_0 9 552 12   8,[2]            
  10_0_6_0_1_0_0_0_3 10 6 15   9,[2]            
  10_0_6_0_1_0_2_0_1 9 1876 13   8,[2]            
  10_0_6_0_2_0_0_0_2 9 343 13   8,[2]            
  10_0_6_0_2_0_1_0_0_0_1 9 3 15   8,[2]   a        
  10_0_6_0_2_0_2_0_0 8 13305 12   7,[2]            
  10_0_6_0_3_0_0_0_1 8 1221 13   7,[2]            
  10_0_6_0_4_0_0_0_0 7 26805 9   6,[2]            
  10_0_6_1_0_0_0_0_3 10 6 15   9,[2]            
  10_0_6_1_0_0_1_0_1_0_1 10 1 15   9,[2]   a        
  10_0_6_1_0_0_2_0_1 9 551 13   8,[2]            
  10_0_6_1_1_0_0_0_2 9 39 14   8,[2]            
  10_0_6_1_1_0_1_0_0_0_1 9 1 15   8,[2]   a        
  10_0_6_1_1_0_2_0_0 8 9272 12   7,[2]            
  10_0_6_1_2_0_0_0_1 8 1925 12   7,[2]   a        
  10_0_6_1_3_0_0_0_0 7 14335 12   6,[2]            
  10_0_6_2_0_0_0_0_2 9 5 15   8,[2]            
  10_0_6_2_0_0_2_0_0 8 1898 12   7,[2]            
  10_0_6_2_1_0_0_0_1 8 1014 13   7,[2]            
  10_0_6_2_2_0_0_0_0 7 12718 11   6,[2]            
  10_0_6_3_0_0_0_0_1 8 211 12   7,[2]   a        
  10_0_6_3_1_0_0_0_0 7 7718 12   6,[2]            
  10_0_6_4_0_0_0_0_0 7 2018 9   6,[2]            
  10_0_7_0_0_0_1_0_2 9 75 14   8,[2]            
  10_0_7_0_0_0_2_0_0_0_1 9 3 15   8,[2]   a        
  10_0_7_0_0_0_3_0_0 8 911 13   7,[2]            
  10_0_7_0_1_0_1_0_1 8 1066 13   7,[2]            
  10_0_7_0_2_0_1_0_0 7 19515 11   6,[2]            
  10_0_7_1_0_0_1_0_1 8 274 13   7,[2]            
  10_0_7_1_1_0_1_0_0 7 6950 12   6,[2]            
  10_0_7_2_0_0_1_0_0 7 2001 12   6,[2]            
  10_0_8_0_0_0_0_0_2 8 1 15   7,[2]            
  10_0_8_0_0_0_1_0_0_0_1 8 1 15   7,[2]   a        
  10_0_8_0_0_0_2_0_0 7 1254 12   6,[2]            
  10_0_8_0_1_0_0_0_1 7 693 12   6,[2]   a        
  10_0_8_0_2_0_0_0_0 6 11784 12   5,[2]            
  10_0_8_1_0_0_0_0_1 7 18 14   6,[2]            
  10_0_8_1_1_0_0_0_0 6 989 12   5,[2]            
  10_0_8_2_0_0_0_0_0 6 871 11   5,[2]            
  10_0_9_0_0_0_1_0_0 6 686 12   5,[2]            
  10_0_10_0_0_0_0_0_0 5 13 14   4,[2]            
  10_1_0_0_1_0_6_0_2 14 2 15   13,[2]            
  10_1_0_0_1_0_8_0_0 13 2 15   12,[2]            
  10_1_0_0_2_0_4_0_3 14 1 15   13,[2]            
  10_1_0_0_2_0_6_0_1 13 10 15   12,[2]            
  10_1_0_0_3_0_4_0_2 13 21 14   12,[2]            
  10_1_0_0_3_0_6_0_0 12 71 14   11,[2]            
  10_1_0_0_4_0_2_0_3 13 1 15   12,[2]            
  10_1_0_0_4_0_4_0_1 12 213 13   11,[2]            
  10_1_0_0_5_0_2_0_2 12 87 14   11,[2]            
  10_1_0_0_5_0_3_0_0_0_1 12 3 15   11,[2]   a        
  10_1_0_0_5_0_4_0_0 11 970 12   10,[2]            
  10_1_0_0_6_0_0_0_3 12 2 15   11,[2]            
  10_1_0_0_6_0_1_0_1_0_1 12 1 15   11,[2]   a        
  10_1_0_0_6_0_2_0_1 11 557 13   10,[2]            
  10_1_0_0_7_0_0_0_2 11 40 14   10,[2]            
  10_1_0_0_7_0_1_0_0_0_1 11 9 15   10,[2]   a        
  10_1_0_0_7_0_2_0_0 10 1586 11   9,[2]            
  10_1_0_0_8_0_0_0_1 10 86 13   9,[2]            
  10_1_0_0_9_0_0_0_0 9 447 10   8,[2]            
  10_1_0_1_0_0_6_0_2 14 2 15   13,[2]            
  10_1_0_1_1_0_4_0_3 14 1 15   13,[2]            
  10_1_0_1_1_0_6_0_1 13 13 15   12,[2]            
  10_1_0_1_2_0_2_0_4 14 3 15   13,[2]            
  10_1_0_1_2_0_4_0_2 13 65 14   12,[2]            
  10_1_0_1_2_0_6_0_0 12 125 14   11,[2]            
  10_1_0_1_3_0_2_0_3 13 20 14   12,[2]            
  10_1_0_1_3_0_3_0_1_0_1 13 1 15   12,[2]   a        
  10_1_0_1_3_0_4_0_1 12 516 13   11,[2]            
  10_1_0_1_4_0_2_0_2 12 274 13   11,[2]            
  10_1_0_1_4_0_3_0_0_0_1 12 2 15   11,[2]   a        
  10_1_0_1_4_0_4_0_0 11 1904 12   10,[2]            
  10_1_0_1_5_0_0_0_3 12 9 14   11,[2]            
  10_1_0_1_5_0_2_0_1 11 1559 12   10,[2]   a        
  10_1_0_1_6_0_0_0_2 11 112 12   10,[2]   a        
  10_1_0_1_6_0_1_0_0_0_1 11 7 15   10,[2]   a        
  10_1_0_1_6_0_2_0_0 10 4184 12   9,[2]            
  10_1_0_1_7_0_0_0_1 10 232 13   9,[2]            
  10_1_0_1_8_0_0_0_0 9 1743 10   8,[2]            
  10_1_0_2_0_0_4_0_3 14 1 15   13,[2]            
  10_1_0_2_0_0_6_0_1 13 2 15   12,[2]            
  10_1_0_2_1_0_4_0_2 13 31 15   12,[2]            
  10_1_0_2_1_0_6_0_0 12 98 14   11,[2]            
  10_1_0_2_2_0_2_0_3 13 38 14   12,[2]            
  10_1_0_2_2_0_3_0_1_0_1 13 1 15   12,[2]   a        
  10_1_0_2_2_0_4_0_1 12 637 13   11,[2]            
  10_1_0_2_3_0_0_0_4 13 1 15   12,[2]            
  10_1_0_2_3_0_1_0_2_0_1 13 1 15   12,[2]   a        
  10_1_0_2_3_0_2_0_2 12 428 14   11,[2]            
  10_1_0_2_3_0_3_0_0_0_1 12 4 15   11,[2]   a        
  10_1_0_2_3_0_4_0_0 11 2987 12   10,[2]            
  10_1_0_2_4_0_0_0_3 12 26 14   11,[2]            
  10_1_0_2_4_0_1_0_1_0_1 12 2 15   11,[2]   a        
  10_1_0_2_4_0_2_0_1 11 3244 12   10,[2]   a        
  10_1_0_2_5_0_0_0_2 11 118 14   10,[2]            
  10_1_0_2_5_0_1_0_0_0_1 11 4 15   10,[2]   a        
  10_1_0_2_5_0_2_0_0 10 9413 11   9,[2]            
  10_1_0_2_6_0_0_0_1 10 699 13   9,[2]            
  10_1_0_2_7_0_0_0_0 9 2967 11   8,[2]            
  10_1_0_3_0_0_4_0_2 13 18 14   12,[2]            
  10_1_0_3_0_0_6_0_0 12 23 14   11,[2]            
  10_1_0_3_1_0_2_0_3 13 24 14   12,[2]            
  10_1_0_3_1_0_3_0_1_0_1 13 1 15   12,[2]   a        
  10_1_0_3_1_0_4_0_1 12 381 13   11,[2]            
  10_1_0_3_2_0_2_0_2 12 402 13   11,[2]            
  10_1_0_3_2_0_3_0_0_0_1 12 3 15   11,[2]   a        
  10_1_0_3_2_0_4_0_0 11 2424 12   10,[2]            
  10_1_0_3_3_0_0_0_3 12 3 15   11,[2]            
  10_1_0_3_3_0_1_0_1_0_1 12 4 15   11,[2]   a        
  10_1_0_3_3_0_2_0_1 11 3312 12   10,[2]   a        
  10_1_0_3_4_0_0_0_2 11 191 13   10,[2]            
  10_1_0_3_4_0_1_0_0_0_1 11 15 15   10,[2]   a        
  10_1_0_3_4_0_2_0_0 10 11726 11   9,[2]            
  10_1_0_3_5_0_0_0_1 10 776 12   9,[2]   a        
  10_1_0_3_6_0_0_0_0 9 5697 10   8,[2]            
  10_1_0_4_0_0_0_0_5 14 3 15   13,[2]            
  10_1_0_4_0_0_2_0_3 13 1 15   12,[2]            
  10_1_0_4_0_0_4_0_1 12 83 13   11,[2]            
  10_1_0_4_1_0_2_0_2 12 131 13   11,[2]            
  10_1_0_4_1_0_3_0_0_0_1 12 1 15   11,[2]   a        
  10_1_0_4_1_0_4_0_0 11 1097 12   10,[2]            
  10_1_0_4_2_0_0_0_3 12 1 15   11,[2]            
  10_1_0_4_2_0_1_0_1_0_1 12 2 15   11,[2]   a        
  10_1_0_4_2_0_2_0_1 11 1507 12   10,[2]   a        
  10_1_0_4_3_0_0_0_2 11 61 14   10,[2]            
  10_1_0_4_3_0_1_0_0_0_1 11 27 15   10,[2]   a        
  10_1_0_4_3_0_2_0_0 10 7136 11   9,[2]            
  10_1_0_4_4_0_0_0_1 10 623 13   9,[2]            
  10_1_0_4_5_0_0_0_0 9 1005 11   8,[2]            
  10_1_0_5_0_0_2_0_2 12 14 15   11,[2]            
  10_1_0_5_0_0_4_0_0 11 525 11   10,[2]            
  10_1_0_5_1_0_2_0_1 11 629 13   10,[2]            
  10_1_0_5_2_0_0_0_2 11 32 14   10,[2]            
  10_1_0_5_2_0_1_0_0_0_1 11 1 15   10,[2]   a        
  10_1_0_5_2_0_2_0_0 10 2559 12   9,[2]            
  10_1_0_5_3_0_0_0_1 10 944 12   9,[2]   a        
  10_1_0_5_4_0_0_0_0 9 7808 10   8,[2]            
  10_1_0_6_0_0_2_0_1 11 395 13   10,[2]            
  10_1_0_6_1_0_0_0_2 11 47 14   10,[2]            
  10_1_0_6_1_0_2_0_0 10 2213 11   9,[2]            
  10_1_0_6_2_0_0_0_1 10 88 14   9,[2]            
  10_1_0_6_3_0_0_0_0 9 263 11   8,[2]            
  10_1_0_9_0_0_0_0_0 9 712 10   9,[] Z          
  10_1_1_0_1_0_7_0_0 12 6 15   11,[2]            
  10_1_1_0_2_0_5_0_1 12 58 14   11,[2]            
  10_1_1_0_3_0_3_0_2 12 97 14   11,[2]            
  10_1_1_0_3_0_4_0_0_0_1 12 2 15   11,[2]   a        
  10_1_1_0_3_0_5_0_0 11 543 13   10,[2]            
  10_1_1_0_4_0_1_0_3 12 9 15   11,[2]            
  10_1_1_0_4_0_2_0_1_0_1 12 7 15   11,[2]   a        
  10_1_1_0_4_0_3_0_1 11 985 13   10,[2]            
  10_1_1_0_5_0_1_0_2 11 336 14   10,[2]            
  10_1_1_0_5_0_2_0_0_0_1 11 32 15   10,[2]   a        
  10_1_1_0_5_0_3_0_0 10 5601 12   9,[2]            
  10_1_1_0_6_0_0_0_1_0_1 11 15 15   10,[2]   a        
  10_1_1_0_6_0_1_0_1 10 2034 13   9,[2]            
  10_1_1_0_7_0_0_0_0_0_1 10 3 15   9,[2]   a        
  10_1_1_0_7_0_1_0_0 9 5128 11   8,[2]            
  10_1_1_1_0_0_5_0_2 13 5 15   12,[2]            
  10_1_1_1_0_0_7_0_0 12 10 14   11,[2]            
  10_1_1_1_1_0_3_0_3 13 2 15   12,[2]            
  10_1_1_1_1_0_4_0_1_0_1 13 1 15   12,[2]   a        
  10_1_1_1_1_0_5_0_1 12 75 14   11,[2]            
  10_1_1_1_2_0_1_0_4 13 1 15   12,[2]            
  10_1_1_1_2_0_3_0_2 12 191 14   11,[2]            
  10_1_1_1_2_0_4_0_0_0_1 12 2 15   11,[2]   a        
  10_1_1_1_2_0_5_0_0 11 813 13   10,[2]            
  10_1_1_1_3_0_1_0_3 12 41 14   11,[2]            
  10_1_1_1_3_0_2_0_1_0_1 12 2 15   11,[2]   a        
  10_1_1_1_3_0_3_0_1 11 2451 13   10,[2]            
  10_1_1_1_4_0_1_0_2 11 534 13   10,[2]            
  10_1_1_1_4_0_2_0_0_0_1 11 27 15   10,[2]   a        
  10_1_1_1_4_0_3_0_0 10 11024 12   9,[2]            
  10_1_1_1_5_0_0_0_1_0_1 11 2 15   10,[2]   a        
  10_1_1_1_5_0_1_0_1 10 4364 12   9,[2]   a        
  10_1_1_1_6_0_0_0_0_0_1 10 5 15   9,[2]   a        
  10_1_1_1_6_0_1_0_0 9 20132 11   8,[2]            
  10_1_1_2_0_0_3_0_3 13 9 15   12,[2]            
  10_1_1_2_0_0_5_0_1 12 61 14   11,[2]            
  10_1_1_2_1_0_1_0_4 13 2 15   12,[2]            
  10_1_1_2_1_0_3_0_2 12 184 14   11,[2]            
  10_1_1_2_1_0_4_0_0_0_1 12 3 15   11,[2]   a        
  10_1_1_2_1_0_5_0_0 11 738 13   10,[2]            
  10_1_1_2_2_0_1_0_3 12 39 14   11,[2]            
  10_1_1_2_2_0_2_0_1_0_1 12 5 15   11,[2]   a        
  10_1_1_2_2_0_3_0_1 11 3252 12   10,[2]            
  10_1_1_2_3_0_1_0_2 11 1208 13   10,[2]            
  10_1_1_2_3_0_2_0_0_0_1 11 44 15   10,[2]   a        
  10_1_1_2_3_0_3_0_0 10 15110 12   9,[2]            
  10_1_1_2_4_0_0_0_1_0_1 11 1 15   10,[2]   a        
  10_1_1_2_4_0_1_0_1 10 7662 12   9,[2]            
  10_1_1_2_5_0_0_0_0_0_1 10 10 15   9,[2]   a        
  10_1_1_2_5_0_1_0_0 9 38543 10   8,[2]            
  10_1_1_3_0_0_1_0_4 13 1 15   12,[2]            
  10_1_1_3_0_0_3_0_2 12 99 13   11,[2]            
  10_1_1_3_0_0_5_0_0 11 259 13   10,[2]            
  10_1_1_3_1_0_1_0_3 12 21 14   11,[2]            
  10_1_1_3_1_0_2_0_1_0_1 12 1 15   11,[2]   a        
  10_1_1_3_1_0_3_0_1 11 1636 13   10,[2]            
  10_1_1_3_2_0_1_0_2 11 1280 13   10,[2]            
  10_1_1_3_2_0_2_0_0_0_1 11 60 15   10,[2]   a        
  10_1_1_3_2_0_3_0_0 10 13538 12   9,[2]            
  10_1_1_3_3_0_0_0_1_0_1 11 8 15   10,[2]            
  10_1_1_3_3_0_1_0_1 10 6347 12   9,[2]            
  10_1_1_3_4_0_0_0_0_0_1 10 19 15   9,[2]   a        
  10_1_1_3_4_0_1_0_0 9 21720 11   8,[2]            
  10_1_1_4_0_0_1_0_3 12 7 14   11,[2]            
  10_1_1_4_0_0_2_0_1_0_1 12 1 15   11,[2]   a        
  10_1_1_4_0_0_3_0_1 11 330 13   10,[2]            
  10_1_1_4_1_0_1_0_2 11 310 13   10,[2]            
  10_1_1_4_1_0_2_0_0_0_1 11 16 15   10,[2]   a        
  10_1_1_4_1_0_3_0_0 10 3913 12   9,[2]            
  10_1_1_4_2_0_0_0_1_0_1 11 36 15   10,[2]   a        
  10_1_1_4_2_0_1_0_1 10 5510 12   9,[2]            
  10_1_1_4_3_0_0_0_0_0_1 10 13 15   9,[2]   a        
  10_1_1_4_3_0_1_0_0 9 15013 11   8,[2]            
  10_1_1_5_0_0_1_0_2 11 21 14   10,[2]            
  10_1_1_5_0_0_3_0_0 10 1151 12   9,[2]            
  10_1_1_5_1_0_1_0_1 10 1802 12   9,[2]            
  10_1_1_5_2_0_0_0_0_0_1 10 2 15   9,[2]   a        
  10_1_1_5_2_0_1_0_0 9 13397 11   8,[2]            
  10_1_1_6_0_0_1_0_1 10 72 13   9,[2]            
  10_1_1_6_1_0_1_0_0 9 14302 9   8,[2]   a        
  10_1_1_7_0_0_1_0_0 9 41 12   8,[2]