-- 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 free abelian group of rank n.

Γ - Γ is the minimum of g2 over all triangulations of a three-dimensional normal pseudomanifold with the given singular vertices. A letter in this column indicates that minG2=Γ and the proof is indicated below. A superscript ' indicates that Γ=minG2-1 and 11 vertices are needed to realize Γ.

  • a - For any subcomplex Δ' of Δ, g2(Δ) ≥ g2 (Δ'). Usually v is a vertex and Δ'=st(v), so g2(Δ) ≥ g2 (st v) = g2 (link v).
  • b - If n is the number of singular vertices, then g2 ≥ 2 χ - ( n-3 choose 3). If n-3 < 3, then the binomial coefficient is interepreted as zero.
  • c - If Δ has 8 singular vertices and m of them are Klein bottles, then g2 ≥ 2 χ - 10 + (m/3)
  • d - If Δ has 8 singular vertices and any of them are real projective planes, then g2 ≥ 2 χ - 7
  • e - If Δ has 8 singular vertices including 3 projective planes and 2 Klein bottles, then g2 ≥ 2 χ - 5

f-vector - A nonempty entry indicates that all possible f-vectors for complexes with the given singular vertices is known.

Except where otherwise noted, the f-vectors are characterized through h- and g-vectors by, h0=1, h4=1-χ, h3 - h1 = 2 χ, h1 ≥ f0-4, and Γ ≤ g2 ≤ (g1 +1 choose 2), where f0 is the minimum number of vertices required for a complex with the given singularities.

  • The first entry is the minimum number of vertices possible for the given singularities
  • 10 indicates that the possible f-vectors for PL-homeomorphic complexes for every complex in the group are the same and equal all possible f-vectors for that particular group of singularities
  • 10, # indicates that the possible f-vectors of complexes PL-homeomorphic to complex # equals all possible f-vectors for that group of singularities.
  • 10, #, β There is no complex with g-vector (5, Γ) for these singularities.
  • 9, # indicates that the possible f-vectors of complexes PL-homeomorphic to complex # at http://www.math.cornell.edu/~takhmejanov/pseudoManifolds.html with the same singularities equals all possible f-vectors for that group of singularities.
  • 9, #1, α There is no complex with g-vector (4,6) for these singularities.
  • 8, N# indicates that the possible f-vectors of complexes PL-homeomorphic to complex N# in "Three-Dimensional Pseudomanifolds on Eight Vertices", B. Datta and N. Nilakantan, Indian J. of Mathematics and Mathematical Sciences, 2008, equals all possible f-vectors for that group of singularities.
  • 7, The one-vertex suspension of the six-vertex triangulation of the real projective plane can be used to prove that the f-vectors of the suspension of the real projective plane has the same f-vectors as all complexes with exactly two singular vertices each with link homeomorphic to the real projective plane.
  • 5, f-vectors of three-manifolds equal all possible f-vectors of S3.

- * indicates that all complexes in this row are known to be PL-homeomorphic.

# Complex χ TriangulationsSorted ascending minG2 H1 H2 H3 Γ f-vector delta epsilon
  10_0_0_0_0_0_0_0_6_0_4 22 1 15   21,[2]   a 10 *    
  10_0_0_0_0_0_10_0_0 15 1 15   14,[2]       *    
  10_0_0_0_1_0_5_0_3_0_1 17 1 15   16,[2]   a 10 *    
  10_0_0_0_1_0_7_0_1_0_1 16 1 15   15,[2]   a 10 *    
  10_0_0_0_3_0_3_0_3_0_1 16 1 15   15,[2]   a 10 *    
  10_0_0_0_3_0_5_0_1_0_1 15 1 15   14,[2]   a 10 *    
  10_0_0_1_0_0_2_0_7 18 1 15   17,[2]       *    
  10_0_0_1_1_0_2_0_6 17 1 15   16,[2]       *    
  10_0_0_1_2_0_0_0_7 17 1 15   16,[2]       *    
  10_0_0_1_4_0_1_0_3_0_1 15 1 15   14,[2]   a 10 *    
  10_0_0_1_6_0_1_0_1_0_1 13 1 15   12,[2]   a 10 *    
  10_0_0_1_7_0_1_0_0_0_1 12 1 15   11,[2]   a 10 *    
  10_0_0_2_2_0_0_0_6 16 1 15   15,[2]       *    
  10_0_0_2_2_0_3_0_2_0_1 15 1 15   14,[2]   a 10 *    
  10_0_0_2_4_0_1_0_2_0_1 14 1 15   13,[2]   a 10 *    
  10_0_0_2_5_0_1_0_1_0_1 13 1 15   12,[2]   a 10 *    
  10_0_0_3_0_0_0_0_7 17 1 15   16,[2]       *    
  10_0_0_3_1_0_0_0_6 16 1 15   15,[2]       *    
  10_0_0_3_2_0_3_0_1_0_1 14 1 15   13,[2]   a 10 *    
  10_0_0_5_0_0_0_0_5 15 1 15   14,[2]       *    
  10_0_0_5_0_0_3_0_1_0_1 14 1 15   13,[2]   a 10 *    
  10_0_0_5_3_0_1_0_0_0_1 12 1 15   11,[2]   a 10 *    
  10_0_0_6_2_0_0_0_2 12 1 15   11,[2]       *    
  10_0_0_7_1_0_0_0_2 12 1 15   11,[2]       *    
  10_0_1_0_0_0_9_0_0 14 1 15   13,[2]       *    
  10_0_1_0_7_0_0_0_1_0_1 12 1 15   11,[2]   a 10 *    
  10_0_1_1_0_0_3_0_5 16 1 15   15,[2]       *    
  10_0_1_1_0_0_6_0_1_0_1 15 1 15   14,[2]   a 10 *    
  10_0_1_1_1_0_4_0_2_0_1 15 1 15   14,[2]   a 10 *    
  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 *    
  10_0_1_2_5_0_0_0_1_0_1 12 1 15   11,[2]   a 10

   
  10_0_1_3_0_0_4_0_1_0_1 14 1 15   13,[2]   a 10 *    
  10_0_1_3_1_0_4_0_0_0_1 13 1 15   12,[2]       *    
  10_0_1_4_2_0_0_0_2_0_1 13 1 15   12,[2]   a 10 *    
  10_0_2_0_0_0_6_0_2 14 1 15   13,[2]       *    
  10_0_2_0_2_0_3_0_2_0_1 14 1 15   13,[2]   a 10 *    
  10_0_2_0_3_0_0_0_5 14 1 15   13,[2]       *    
  10_0_2_1_0_0_2_0_5 15 1 15   14,[2]       *    
  10_0_2_2_0_0_3_0_2_0_1 14 1 15   13,[2]   a 10 *    
  10_0_2_2_1_0_0_0_5 14 1 15   13,[2]       *    
  10_0_2_2_2_0_1_0_2_0_1 13 1 15   12,[2]   a 10 *    
  10_0_2_3_1_0_0_0_4 13 1 15   12,[2]       *    
  10_0_2_4_0_0_0_0_4 13 1 15   12,[2]       *    
  10_0_3_0_0_0_6_0_0_0_1 13 1 15   12,[2]   a 10 *    
  10_0_3_0_1_0_4_0_1_0_1 13 1 15   12,[2]   a 10 *    
  10_0_3_1_1_0_1_0_4 13 1 15   12,[2]       *    
  10_0_4_2_0_0_0_0_4 12 1 15   11,[2]       *    
  10_0_4_2_0_0_3_0_0_0_1 11 1 15   10,[2]   a 10 *    
  10_0_4_2_1_0_1_0_1_0_1 11 1 15   10,[2]   a 10 *    
  10_0_4_2_2_0_1_0_0_0_1 10 1 15   9,[2]   a 10 *    
  10_0_4_3_0_0_1_0_1_0_1 11 1 15   10,[2]   a 10 *    
  10_0_5_0_2_0_0_0_2_0_1 11 1 15   10,[2]   a 10 *    
  10_0_5_0_4_0_0_0_0_0_1 9 1 15   8,[2]   a 10 *    
  10_0_5_1_1_0_2_0_0_0_1 10 1 15   9,[2]   a 10 *    
  10_0_5_2_2_0_0_0_0_0_1 9 1 15   8,[2]   a 10 *    
  10_0_6_1_0_0_1_0_1_0_1 10 1 15   9,[2]   a 10 *    
  10_0_6_1_1_0_1_0_0_0_1 9 1 15   8,[2]   a 10 *    
  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 *    
  10_1_0_0_2_0_4_0_3 14 1 15   13,[2]       *    
  10_1_0_0_4_0_2_0_3 13 1 15   12,[2]       *    
  10_1_0_0_6_0_1_0_1_0_1 12 1 15   11,[2]   a 10 *    
  10_1_0_1_1_0_4_0_3 14 1 15   13,[2]       *    
  10_1_0_1_3_0_3_0_1_0_1 13 1 15   12,[2]   a 10 *    
  10_1_0_2_0_0_4_0_3 14 1 15   13,[2]       *    
  10_1_0_2_2_0_3_0_1_0_1 13 1 15   12,[2]   a 10 *    
  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 *    
  10_1_0_3_1_0_3_0_1_0_1 13 1 15   12,[2]   a 10 *    
  10_1_0_4_0_0_2_0_3 13 1 15   12,[2]       *    
  10_1_0_4_1_0_3_0_0_0_1 12 1 15   11,[2]   a 10 *    
  10_1_0_4_2_0_0_0_3 12 1 15   11,[2]       *    
  10_1_0_5_2_0_1_0_0_0_1 11 1 15   10,[2]   a 10 *    
  10_1_1_1_1_0_4_0_1_0_1 13 1 15   12,[2]   a 10 *    
  10_1_1_1_2_0_1_0_4 13 1 15   12,[2]       *    
  10_1_1_2_4_0_0_0_1_0_1 11 1 15   10,[2]   a 10 *    
  10_1_1_3_0_0_1_0_4 13 1 15   12,[2]       *    
  10_1_1_3_1_0_2_0_1_0_1 12 1 15   11,[2]   a 10 *    
  10_1_1_4_0_0_2_0_1_0_1 12 1 15   11,[2]   a 10 *    
  10_1_2_3_0_0_3_0_0_0_1 11 1 15   10,[2]   a 10 *    
  10_1_3_0_0_0_3_0_3 12 1 15   11,[2]       *    
  10_1_3_1_3_0_0_0_1_0_1 10 1 15   9,[2]   a 10 *    
  10_1_3_2_1_0_0_0_2_0_1 11 1 15   10,[2]   a 10 *    
  10_1_3_3_1_0_0_0_1_0_1 10 1 15   9,[2]   a 10 *    
  10_1_4_0_0_0_2_0_3 11 1 15   10,[2]       *    
  10_1_4_2_0_0_0_0_3 10 1 15   9,[2]       *    
  10_1_5_0_0_0_1_0_3 10 1 15   9,[2]       *    
  10_1_5_0_0_0_2_0_1_0_1 10 1 15   9,[2]   a 10 *    
  10_2_0_0_0_0_8_0_0 12 1 14   11,[2]   b   *    
  10_2_0_1_4_0_1_0_1_0_1 11 1 15   10,[2]   a 10 *    
  10_2_0_2_2_0_3_0_0_0_1 11 1 15   10,[2]   a 10 *    
  10_2_0_2_3_0_0_0_3 11 1 15   10,[2]       *    
  10_2_0_2_3_0_1_0_1_0_1 11 1 15   10,[2]   a 10 *    
  10_2_1_0_3_0_1_0_3 11 1 15   10,[2]   d 10 *    
  10_2_1_1_1_0_4_0_0_0_1 11 1 15   10,[2]   a,d 10 *    
  10_2_1_4_2_0_0_0_0_0_1 9 1 15   8,[2]   a 10 *    
  10_2_2_0_1_0_2_0_3 11 1 15   10,[2]   d 10 *    
  10_2_2_1_1_0_3_0_0_0_1 10 1 15   9,[2]   a 10 *    
  10_2_2_1_2_0_1_0_1_0_1 10 1 15   9,[2]   a 10 *    
  10_2_2_2_0_0_3_0_0_0_1 10 1 15   9,[2]   a 10 *    
  10_2_2_3_0_0_1_0_1_0_1 10 1 15   9,[2]   a 10 *    
  10_2_3_1_2_0_0_0_1_0_1 9 1 15   8,[2]   a 10 *    
  10_2_3_2_0_0_2_0_0_0_1 9 1 15   8,[2]   a 10 *    
  10_2_4_0_0_0_3_0_0_0_1 9 1 15   8,[2]   a 10 *    
  10_2_4_1_0_0_0_0_3 9 1 15   8,[2]       *    
  10_2_5_0_1_0_0_0_1_0_1 8 1 15   7,[2]   a 10 *    
  10_3_0_5_1_0_0_0_1 8 1 15   7,[2]       *    
  10_3_1_5_0_0_1_0_0 7 1 15   6,[2]       *    
  10_3_2_0_2_0_0_0_3 9 1 15   8,[2]       *    
  10_3_2_1_1_0_0_0_3 9 1 15   8,[2]       *    
  10_4_0_2_2_0_0_0_2 8 1 15   7,[2]   b 10 *    
  10_4_2_1_1_0_1_0_0_0_1 7 1 15   6,[2]   a 10 *    
  10_4_3_0_0_0_2_0_0_0_1 7 1 15   6,[2]   a 10 *    
  10_7_0_2_0_0_0_0_1 4 1 15   3,[2]       *    
  10_0_0_0_0_0_2_0_8 19 2 15   18,[2]     10      
  10_0_0_0_0_0_3_0_6_0_1 19 2 15   18,[2]   a 10      
  10_0_0_0_2_0_2_0_6 17 2 15   16,[2]            
  10_0_0_0_6_0_0_0_4 14 2 15   13,[2]            
  10_0_0_1_1_0_3_0_4_0_1 17 2 15   16,[2]   a 10      
  10_0_0_1_1_0_5_0_2_0_1 16 2 15   15,[2]   a 10      
  10_0_0_1_2_0_5_0_1_0_1 15 2 15   14,[2]   a 10      
  10_0_0_1_4_0_0_0_5 15 2 15   14,[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      
  10_0_0_2_2_0_5_0_0_0_1 14 2 15   13,[2]   a 10      
  10_0_0_4_0_0_5_0_0_0_1 14 2 15   13,[2]   a 10      
  10_0_0_4_1_0_3_0_1_0_1 14 2 15   13,[2]   a 10      
  10_0_0_4_2_0_3_0_0_0_1 13 2 15   12,[2]   a 10      
  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_1_0_1_0_6_0_1_0_1 15 2 15   14,[2]   a 10      
  10_0_1_0_3_0_1_0_5 15 2 15   14,[2]            
  10_0_1_0_6_0_0_0_2_0_1 13 2 15   12,[2]   a 10      
  10_0_1_1_3_0_2_0_2_0_1 14 2 15   13,[2]   a 10      
  10_0_1_1_7_0_0_0_0_0_1 11 2 15   10,[2]   a 10      
  10_0_1_3_1_0_2_0_2_0_1 14 2 15   13,[2]   a 10      
  10_0_1_4_1_0_2_0_1_0_1 13 2 15   12,[2]   a 10      
  10_0_2_0_2_0_5_0_0_0_1 13 2 15   12,[2]   a 10      
  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      
  10_0_2_2_2_0_0_0_4 13 2 15   12,[2]            
  10_0_2_4_0_0_3_0_0_0_1 12 2 15   11,[2]   a 10      
  10_0_2_5_1_0_1_0_0_0_1 11 2 15   10,[2]   a 10      
  10_0_3_3_0_0_2_0_1_0_1 12 2 15   11,[2]   a 10      
  10_0_3_4_0_0_2_0_0_0_1 11 2 15   10,[2]   a 10      
  10_0_3_6_0_0_0_0_0_0_1 10 2 15   9,[2]   a 10      
  10_0_5_0_3_0_0_0_1_0_1 10 2 15   9,[2]   a 10      
  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      
  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_6_0_0_0_3 12 2 15   11,[2]            
  10_1_0_1_0_0_6_0_2 14 2 15   13,[2]            
  10_1_0_1_4_0_3_0_0_0_1 12 2 15   11,[2]   a 10      
  10_1_0_2_0_0_6_0_1 13 2 15   12,[2]            
  10_1_0_2_4_0_1_0_1_0_1 12 2 15   11,[2]   a 10      
  10_1_0_4_2_0_1_0_1_0_1 12 2 15   11,[2]   a 10      
  10_1_1_0_3_0_4_0_0_0_1 12 2 15   11,[2]   a 10      
  10_1_1_1_1_0_3_0_3 13 2 15   12,[2]            
  10_1_1_1_2_0_4_0_0_0_1 12 2 15   11,[2]   a 10      
  10_1_1_1_3_0_2_0_1_0_1 12 2 15   11,[2]   a 10      
  10_1_1_1_5_0_0_0_1_0_1 11 2 15   10,[2]   a 10      
  10_1_1_2_1_0_1_0_4 13 2 15   12,[2]            
  10_1_1_5_2_0_0_0_0_0_1 10 2 15   9,[2]   a 10      
  10_1_2_0_0_0_6_0_1 12 2 15   11,[2]            
  10_1_3_4_1_0_0_0_0_0_1 9 2 15   8,[2]   a 10      
  10_1_5_3_0_0_0_0_0_0_1 8 2 15   7,[2]   a 10      
  10_2_0_0_2_0_6_0_0 11 2 14   10,[2]       *    
  10_2_0_0_3_0_4_0_1 11 2 15   10,[2]            
  10_2_0_0_6_0_0_0_0_0_2 11 2 15   10,[2]   a 10      
  10_2_0_0_6_0_1_0_0_0_1 10 2 15   9,[2]   a 10      
  10_2_1_1_2_0_1_0_3 11 2 15   10,[2]   d 10      
  10_2_1_3_2_0_0_0_1_0_1 10 2 15   9,[2]   a 10      
  10_2_2_1_2_0_0_0_3 10 2 15   9,[2]            
  10_2_2_2_1_0_1_0_1_0_1 10 2 15   9,[2]   a 10      
  10_3_0_0_5_0_0_0_2 9 2 15   8,[2]            
  10_3_0_3_2_0_1_0_0_0_1 9 2 15   8,[2]   a 10      
  10_3_1_0_3_0_2_0_0_0_1 9 2 15   8,[2]   a 10      
  10_3_1_1_2_0_2_0_0_0_1 9 2 15   8,[2]   a 10      
  10_3_1_2_1_0_2_0_0_0_1 9 2 15   8,[2]   a 10      
  10_4_0_3_1_0_0_0_2 8 2 15   7,[2]   b 10      
  10_4_0_4_1_0_0_0_1 7 2 15   6,[2]            
  10_4_1_0_0_0_5_0_0 8 2 15   7,[2]   b 10      
  10_4_2_0_0_0_2_0_2 8 2 15   7,[2]   b 10      
  10_5_0_0_3_0_0_0_2 7 2 15   6,[2]            
  10_0_0_0_1_0_4_0_5 17 3 15   16,[2]            
  10_0_0_0_3_0_2_0_5 16 3 15   15,[2]            
  10_0_0_0_4_0_3_0_2_0_1 15 3 15   14,[2]   a 10      
  10_0_0_2_0_0_2_0_6 17 3 15   16,[2]            
  10_0_0_4_0_0_2_0_4 15 3 15   14,[2]            
  10_0_0_4_3_0_1_0_1_0_1 13 3 15   12,[2]   a 10      
  10_0_0_5_1_0_3_0_0_0_1 13 3 15   12,[2]   a 10      
  10_0_0_7_0_0_2_0_1 12 3 15   11,[2]            
  10_0_1_0_0_0_7_0_2 15 3 15   14,[2]            
  10_0_1_0_4_0_2_0_2_0_1 14 3 15   13,[2]   a 10      
  10_0_1_1_2_0_1_0_5 15 3 15   14,[2]            
  10_0_1_1_5_0_0_0_2_0_1 13 3 15   12,[2]   a 10      
  10_0_1_2_2_0_2_0_2_0_1 14 3 15   13,[2]   a 10      
  10_0_1_2_4_0_0_0_2_0_1 13 3 15   12,[2]   a 10      
  10_0_1_3_3_0_0_0_2_0_1 13 3 15   12,[2]   a 10      
  10_0_1_5_0_0_1_0_3 13 3 15   12,[2]            
  10_0_2_0_2_0_2_0_4 14 3 15   13,[2]            
  10_0_2_1_1_0_5_0_0_0_1 13 3 15   12,[2]   a 10      
  10_0_3_0_2_0_1_0_4 13 3 14   12,[2]       *    
  10_0_4_1_1_0_3_0_0_0_1 11 3 15   10,[2]   a 10      
  10_0_4_3_1_0_1_0_0_0_1 10 3 15   9,[2]   a 10      
  10_0_5_0_0_0_4_0_0_0_1 11 3 15   10,[2]   a 10      
  10_0_6_0_0_0_3_0_0_0_1 10 3 15   9,[2]   a 10      
  10_0_6_0_2_0_1_0_0_0_1 9 3 15   8,[2]   a 10      
  10_0_7_0_0_0_2_0_0_0_1 9 3 15   8,[2]   a 10      
  10_1_0_0_5_0_3_0_0_0_1 12 3 15   11,[2]   a 10      
  10_1_0_1_2_0_2_0_4 14 3 15   13,[2]            
  10_1_0_3_2_0_3_0_0_0_1 12 3 15   11,[2]   a 10      
  10_1_0_3_3_0_0_0_3 12 3 15   11,[2]            
  10_1_0_4_0_0_0_0_5 14 3 15   13,[2]            
  10_1_1_0_7_0_0_0_0_0_1 10 3 15   9,[2]   a 10      
  10_1_1_2_1_0_4_0_0_0_1 12 3 15   11,[2]   a 10      
  10_1_2_1_1_0_3_0_1_0_1 12 3 15   11,[2]   a 10      
  10_1_2_2_0_0_2_0_3 12 3 15   11,[2]            
  10_1_3_0_1_0_4_0_0_0_1 11 3 15   10,[2]   a 10      
  10_1_4_0_2_0_1_0_1_0_1 10 3 15   9,[2]   a 10      
  10_2_0_0_5_0_1_0_1_0_1 11 3 15   10,[2]   a 10      
  10_2_0_2_4_0_1_0_0_0_1 10 3 15   9,[2]   a 10      
  10_2_0_4_0_0_3_0_0_0_1 11 3 15   10,[2]   a 10      
  10_2_1_0_2_0_3_0_2 11 3 15   10,[2]   d 10      
  10_2_1_0_5_0_0_0_1_0_1 10 3 15   9,[2]   a 10      
  10_2_1_4_1_0_0_0_1_0_1 10 3 15   9,[2]   a 10      
  10_2_2_0_3_0_0_0_3 10 3 15   9,[2]            
  10_2_2_4_0_0_0_0_2 9 3 15   8,[2]            
  10_2_5_0_0_0_2_0_0_0_1 8 3 15   7,[2]   a 10      
  10_2_7_0_0_0_0_0_0_0_1 6 3 15   5,[2]   a 10      
  10_3_0_4_0_0_2_0_1 9 3 15   8,[2]   b' 10, #1, β      
  10_3_2_1_0_0_2_0_2 9 3 15   8,[2]            
  10_3_3_3_0_0_0_0_0_0_1 7 3 15   6,[2]   a 10      
  10_4_0_0_4_0_0_0_2 8 3 15   7,[2]   b 10      
  10_4_0_1_3_0_1_0_0_0_1 8 3 15   7,[2]   a,b 10      
  10_4_0_3_0_0_2_0_1 8 3 15   7,[2]   b 10      
  10_5_1_0_1_0_1_0_2 7 3 15   6,[2]            
  10_8_0_0_0_0_0_0_0_0_2 5 3 15   4,[2]   a 10 *    
  10_0_0_0_7_0_1_0_1_0_1 13 4 15   12,[2]   a 10      
  10_0_0_2_4_0_0_0_4 14 4 15   13,[2]            
  10_0_0_3_4_0_1_0_1_0_1 13 4 15   12,[2]   a 10      
  10_0_0_3_5_0_1_0_0_0_1 12 4 15   11,[2]   a 10      
  10_0_0_4_2_0_0_0_4 14 4 15   13,[2]            
  10_0_1_0_6_0_2_0_0_0_1 12 4 15   11,[2]   a 10      
  10_0_1_2_0_0_3_0_4 15 4 15   14,[2]            
  10_0_2_0_5_0_1_0_1_0_1 12 4 15   11,[2]   a 10      
  10_0_2_2_1_0_3_0_1_0_1 13 4 15   12,[2]   a 10      
  10_0_2_3_1_0_3_0_0_0_1 12 4 15   11,[2]   a 10      
  10_0_2_6_0_0_0_0_2 11 4 15   10,[2]            
  10_0_3_1_3_0_2_0_0_0_1 11 4 15   10,[2]   a 10      
  10_0_3_3_0_0_1_0_3 12 4 15   11,[2]            
  10_0_4_3_0_0_0_0_3 11 4 13   10,[2]            
  10_0_5_1_3_0_0_0_0_0_1 9 4 15   8,[2]   a 10      
  10_1_0_2_3_0_3_0_0_0_1 12 4 15   11,[2]   a 10      
  10_1_0_2_5_0_1_0_0_0_1 11 4 15   10,[2]   a 10      
  10_1_0_3_3_0_1_0_1_0_1 12 4 15   11,[2]   a 10      
  10_1_2_1_3_0_1_0_1_0_1 11 4 15   10,[2]   a 10      
  10_1_5_0_3_0_0_0_0_0_1 8 4 15   7,[2]   a 10      
  10_2_0_0_4_0_2_0_2 11 4 15   10,[2]            
  10_2_0_3_1_0_3_0_0_0_1 11 4 15   10,[2]   a 10      
  10_2_0_4_2_0_1_0_0_0_1 10 4 15   9,[2]   a 10      
  10_2_1_2_0_0_3_0_2 11 4 15   10,[2]   d 10      
  10_2_1_2_3_0_0_0_1_0_1 10 4 15   9,[2]   a 10      
  10_2_1_4_0_0_2_0_0_0_1 10 4 15   9,[2]   a 10      
  10_2_2_0_2_0_3_0_0_0_1 10 4 15   9,[2]   a 10      
  10_2_2_0_3_0_1_0_1_0_1 10 4 15   9,[2]   a 10      
  10_2_2_2_1_0_0_0_3 10 4 15   9,[2]            
  10_3_0_2_3_0_1_0_0_0_1 9 4 15   8,[2]   a 10      
  10_3_0_5_2_0_0_0_0 7 4 14   6,[2]       *    
  10_3_1_3_0_0_1_0_2 9 4 15   8,[2]            
  10_3_1_3_2_0_0_0_0_0_1 8 4 15   7,[2]   a 10      
  10_3_3_2_0_0_0_0_1_0_1 8 4 15   7,[2]   a 10      
  10_4_0_4_0_0_2_0_0 7 4 15   6,[2]            
  10_4_4_0_0_0_1_0_0_0_1 6 4 15   5,[2]   a 10      
  10_0_0_0_0_0_0_0_10 20 5 15   19,[2]            
  10_0_0_0_4_0_5_0_0_0_1 14 5 15   13,[2]   a 10      
  10_0_0_0_5_0_3_0_1_0_1 14 5 15   13,[2]   a 10      
  10_0_0_1_3_0_3_0_2_0_1 15 5 15   14,[2]   a 10      
  10_0_0_2_0_0_0_0_8 18 5 14   17,[2]            
  10_0_0_2_4_0_3_0_0_0_1 13 5 15   12,[2]   a 10      
  10_0_0_3_3_0_0_0_4 14 5 15   13,[2]            
  10_0_0_4_4_0_1_0_0_0_1 12 5 15   11,[2]   a 10      
  10_0_1_2_6_0_0_0_0_0_1 11 5 15   10,[2]   a 10      
  10_0_1_3_2_0_2_0_1_0_1 13 5 15   12,[2]   a 10      
  10_0_2_0_0_0_8_0_0 13 5 15   12,[2]            
  10_0_2_0_3_0_3_0_1_0_1 13 5 15   12,[2]   a 10      
  10_0_2_1_1_0_2_0_4 14 5 15   13,[2]            
  10_0_2_1_5_0_1_0_0_0_1 11 5 15   10,[2]   a 10      
  10_0_3_0_2_0_4_0_0_0_1 12 5 15   11,[2]   a 10      
  10_0_3_1_1_0_4_0_0_0_1 12 5 15   11,[2]   a 10      
  10_0_3_1_5_0_0_0_0_0_1 10 5 15   9,[2]   a 10      
  10_0_3_3_2_0_0_0_1_0_1 11 5 15   10,[2]   a 10      
  10_0_3_3_3_0_0_0_0_0_1 10 5 15   9,[2]   a 10      
  10_0_3_5_1_0_0_0_0_0_1 10 5 15   9,[2]   a 10      
  10_0_4_0_3_0_1_0_1_0_1 11 5 15   10,[2]   a 10      
  10_0_5_0_2_0_2_0_0_0_1 10 5 15   9,[2]   a 10      
  10_0_5_3_1_0_0_0_0_0_1 9 5 15   8,[2]   a 10      
  10_0_6_2_0_0_0_0_2 9 5 15   8,[2]            
  10_1_1_1_0_0_5_0_2 13 5 15   12,[2]            
  10_1_1_1_6_0_0_0_0_0_1 10 5 15   9,[2]   a 10      
  10_1_1_2_2_0_2_0_1_0_1 12 5 15   11,[2]   a 10      
  10_1_2_1_2_0_3_0_0_0_1 11 5 15   10,[2]   a 10      
  10_1_4_3_0_0_1_0_0_0_1 9 5 15   8,[2]   a 10      
  10_2_0_2_0_0_6_0_0 11 5 14   10,[2]            
  10_2_0_2_1_0_2_0_3 12 5 15   11,[2]   c 10      
  10_2_0_4_2_0_0_0_0_0_2 11 5 15   10,[2]   a 10      
  10_2_1_6_0_0_1_0_0 8 5 15   7,[2]            
  10_2_2_3_0_0_0_0_3 10 5 14   9,[2]            
  10_2_3_1_1_0_2_0_0_0_1 9 5 15   8,[2]   a 10      
  10_2_3_3_1_0_0_0_0_0_1 8 5 15   7,[2]   a 10      
  10_3_0_1_4_0_1_0_0_0_1 9 5 15   8,[2]   a 10      
  10_4_1_2_2_0_0_0_0_0_1 7 5 15   6,[2]   a 10      
  10_5_1_0_0_0_3_0_1 7 5 15   6,[2]            
  10_0_0_1_0_0_4_0_5 17 6 15   16,[2]            
  10_0_1_0_3_0_4_0_1_0_1 14 6 15   13,[2]   a 10      
  10_0_1_2_1_0_4_0_1_0_1 14 6 15   13,[2]   a 10      
  10_0_1_4_0_0_1_0_4 14 6 15   13,[2]            
  10_0_2_1_4_0_1_0_1_0_1 12 6 15   11,[2]   a 10      
  10_0_3_2_1_0_2_0_1_0_1 12 6 15   11,[2]   a 10      
  10_0_5_0_1_0_1_0_3 11 6 15   10,[2]            
  10_0_6_0_1_0_0_0_3 10 6 15   9,[2]            
  10_0_6_1_0_0_0_0_3 10 6 15   9,[2]            
  10_1_1_0_1_0_7_0_0 12 6 15   11,[2]            
  10_1_2_1_0_0_4_0_2 12 6 15   11,[2]            
  10_1_2_5_0_0_1_0_0_0_1 10 6 15   9,[2]   a 10      
  10_1_3_0_2_0_1_0_3 11 6 15   10,[2]            
  10_1_4_1_1_0_1_0_1_0_1 10 6 15   9,[2]   a 10      
  10_1_5_0_2_0_0_0_1_0_1 9 6 15   8,[2]   a 10      
  10_1_5_2_1_0_0_0_0_0_1 8 6 15   7,[2]   a 10      
  10_1_6_0_0_0_1_0_1_0_1 9 6 15   8,[2]   a 10      
  10_2_0_3_3_0_1_0_0_0_1 10 6 15   9,[2]   a 10      
  10_2_0_6_0_0_0_0_2 10 6 13   9,[2]   a' 10,#5,β *    
  10_2_1_1_1_0_3_0_2 11 6 15   10,[2]   d 10      
  10_2_3_0_0_0_3_0_2 10 6 15   9,[2]            
  10_2_3_0_3_0_0_0_1_0_1 9 6 15   8,[2]   a 10      
  10_3_0_1_4_0_0_0_2 9 6 15   8,[2]            
  10_4_0_2_0_0_4_0_0 8 6 15   7,[2]   b 10      
  10_4_2_2_0_0_1_0_0_0_1 7 6 15   6,[2]   a 10      
  10_5_0_1_2_0_0_0_2 7 6 15   6,[2]            
  10_0_0_0_6_0_3_0_0_0_1 13 7 15   12,[2]   a 10      
  10_0_0_1_3_0_5_0_0_0_1 14 7 15   13,[2]   a 10      
  10_0_0_4_0_0_0_0_6 16 7 13   15,[2]            
  10_0_1_0_4_0_1_0_4 14 7 15   13,[2]            
  10_0_1_0_5_0_2_0_1_0_1 13 7 15   12,[2]   a 10      
  10_0_1_5_3_0_0_0_0_0_1 11 7 15   10,[2]   a 10      
  10_0_2_0_1_0_4_0_3 14 7 15   13,[2]            
  10_0_2_3_0_0_2_0_3 13 7 15   12,[2]            
  10_0_3_0_0_0_5_0_2 13 7 15   12,[2]            
  10_0_3_4_2_0_0_0_0_0_1 10 7 15   9,[2]   a 10      
  10_0_4_1_0_0_2_0_3 12 7 15   11,[2]            
  10_0_4_1_3_0_1_0_0_0_1 10 7 15   9,[2]   a 10      
  10_0_4_4_0_0_1_0_0_0_1 10 7 15   9,[2]   a 10      
  10_1_0_1_6_0_1_0_0_0_1 11 7 15   10,[2]   a 10      
  10_1_1_0_4_0_2_0_1_0_1 12 7 15   11,[2]   a 10      
  10_1_1_4_0_0_1_0_3 12 7 14   11,[2]            
  10_1_3_2_2_0_0_0_1_0_1 10 7 15   9,[2]   a 10      
  10_1_4_0_1_0_3_0_0_0_1 10 7 15   9,[2]   a 10      
  10_1_6_0_0_0_0_0_3 9 7 15   8,[2]            
  10_2_0_1_5_0_1_0_0_0_1 10 7 15   9,[2]   a 10      
  10_3_0_2_3_0_0_0_2 9 7 15   8,[2]            
  10_3_2_0_3_0_1_0_0_0_1 8 7 15   7,[2]   a 10      
  10_4_0_1_3_0_0_0_2 8 7 15   7,[2]   b 10      
  10_4_1_1_1_0_1_0_2 8 7 15   7,[2]   b 10      
  10_7_1_0_1_0_0_0_0_0_1 4 7 15   3,[2]   a 10      
  10_0_0_0_8_0_0_0_2 12 8 15   11,[2]            
  10_0_0_2_3_0_3_0_1_0_1 14 8 15   13,[2]   a 10      
  10_0_0_5_3_0_0_0_2 12 8 14   11,[2]            
  10_0_1_0_2_0_3_0_4 15 8 15   14,[2]            
  10_0_1_0_2_0_6_0_0_0_1 14 8 15   13,[2]   a 10      
  10_0_1_1_2_0_4_0_1_0_1 14 8 15   13,[2]   a 10      
  10_0_2_1_0_0_4_0_3 14 8 15   13,[2]            
  10_0_3_0_3_0_2_0_1_0_1 12 8 15   11,[2]   a 10      
  10_0_3_1_2_0_2_0_1_0_1 12 8 15   11,[2]   a 10      
  10_1_1_3_3_0_0_0_1_0_1 11 8 15   10,[2]            
  10_1_2_3_1_0_1_0_1_0_1 11 8 15   10,[2]   a 10      
  10_1_3_2_0_0_1_0_3 11 8 15   10,[2]            
  10_1_3_4_0_0_0_0_1_0_1 10 8 15   9,[2]   a 10      
  10_1_6_0_1_0_1_0_0_0_1 8 8 15   7,[2]   a 10      
  10_2_0_2_0_0_4_0_2 12 8 14   11,[2]   b 10, #7      
  10_2_0_3_2_0_0_0_3 11 8 15   10,[2]            
  10_2_1_2_1_0_1_0_3 11 8 15   10,[2]   d 10      
  10_2_5_0_2_0_0_0_0_0_1 7 8 15   6,[2]   a 10      
  10_3_0_3_2_0_0_0_2 9 8 15   8,[2]            
  10_3_3_0_3_0_0_0_0_0_1 7 8 15   6,[2]   a 10      
  10_3_5_0_0_0_0_0_1_0_1 7 8 15   6,[2]   a 10      
  10_3_5_1_0_0_0_0_0_0_1 6 8 15   5,[2]   a 10      
  10_4_1_0_2_0_1_0_2 8 8 15   7,[2]   b 10      
  10_4_2_0_2_0_1_0_0_0_1 7 8 15   6,[2]   a 10      
  10_0_0_0_0_0_4_0_6 18 9 15   17,[2]            
  10_0_0_0_0_0_8_0_2 16 9 15   15,[2]            
  10_0_0_6_0_0_2_0_2 13 9 14   12,[2]            
  10_0_1_4_1_0_1_0_3 13 9 15   12,[2]            
  10_0_3_3_1_0_2_0_0_0_1 11 9 15   10,[2]   a 10      
  10_0_4_5_0_0_0_0_1 9 9 15   8,[2]            
  10_1_0_0_7_0_1_0_0_0_1 11 9 15   10,[2]   a 10      
  10_1_0_1_5_0_0_0_3 12 9 14   11,[2]            
  10_1_1_0_4_0_1_0_3 12 9 15   11,[2]            
  10_1_1_2_0_0_3_0_3 13 9 15   12,[2]            
  10_1_3_1_4_0_0_0_0_0_1 9 9 15   8,[2]   a 10      
  10_2_0_4_1_0_1_0_1_0_1 11 9 15   10,[2]   a 10      
  10_2_2_5_0_0_0_0_1 8 9 15   7,[2]            
  10_2_4_0_1_0_1_0_1_0_1 9 9 15   8,[2]   a 10      
  10_4_2_4_0_0_0_0_0 5 9 14   4,[2]            
  10_7_0_0_0_0_2_0_1 5 9 15   4,[2]            
  10_0_0_1_4_0_3_0_1_0_1 14 10 15   13,[2]   a 10      
  10_0_0_3_0_0_2_0_5 16 10 14   15,[2]            
  10_0_0_3_3_0_3_0_0_0_1 13 10 15   12,[2]   a 10      
  10_0_0_7_1_0_2_0_0 11 10 15   10,[2]            
  10_0_1_0_8_0_0_0_0_0_1 11 10 15   10,[2]   a 10      
  10_0_1_1_0_0_5_0_3 15 10 14   14,[2]            
  10_0_1_2_2_0_4_0_0_0_1 13 10 15   12,[2]   a 10      
  10_1_0_0_2_0_6_0_1 13 10 15   12,[2]            
  10_1_1_1_0_0_7_0_0 12 10 14   11,[2]            
  10_1_1_2_5_0_0_0_0_0_1 10 10 15   9,[2]   a 10      
  10_1_2_0_2_0_2_0_3 12 10 15   11,[2]            
  10_1_2_1_1_0_2_0_3 12 10 15   11,[2]            
  10_1_3_2_1_0_2_0_0_0_1 10 10 15   9,[2]   a 10      
  10_2_3_0_4_0_0_0_0_0_1 8 10 15   7,[2]   a 10      
  10_2_5_2_0_0_0_0_0_0_1 7 10 15   6,[2]   a 10      
  10_2_6_0_0_0_1_0_0_0_1 7 10 15   6,[2]   a 10      
  10_3_4_1_0_0_1_0_0_0_1 7 10 15   6,[2]   a 10      
  10_4_0_0_2_0_4_0_0 8 10 15   7,[2]   b 10      
  10_6_0_0_2_0_0_0_2 6 10 14   5,[2]            
  10_0_0_1_5_0_3_0_0_0_1 13 11 15   12,[2]   a 10      
  10_0_0_6_0_0_0_0_4 14 11 14   13,[2]            
  10_0_2_2_0_0_2_0_4 14 11 14   13,[2]            
  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_2_4_0_0_0_0_0_1 10 11 15   9,[2]   a 10      
  10_1_4_2_1_0_1_0_0_0_1 9 11 15   8,[2]   a 10      
  10_2_1_1_3_0_2_0_0_0_1 10 11 15   9,[2]   a 10      
  10_2_1_1_5_0_0_0_0_0_1 9 11 15   8,[2]   a 10      
  10_2_1_2_2_0_2_0_0_0_1 10 11 15   9,[2]   a 10      
  10_2_4_0_1_0_0_0_3 9 11 15   8,[2]            
  10_3_3_1_1_0_0_0_1_0_1 8 11 15   7,[2]   a 10      
  10_7_0_0_1_0_0_0_2 5 11 15   4,[2]            
  10_0_0_1_6_0_0_0_3 13 12 15   12,[2]            
  10_0_0_7_0_0_0_0_3 13 12 13   12,[2]            
  10_0_1_2_3_0_2_0_1_0_1 13 12 15   12,[2]   a 10      
  10_0_1_4_2_0_2_0_0_0_1 12 12 15   11,[2]   a 10      
  10_0_2_1_2_0_3_0_1_0_1 13 12 15   12,[2]   a 10      
  10_0_2_2_3_0_1_0_1_0_1 12 12 15   11,[2]   a 10      
  10_0_2_4_1_0_0_0_3 12 12 14   11,[2]            
  10_0_2_5_1_0_0_0_2 11 12 15   10,[2]            
  10_0_3_0_6_0_0_0_0_0_1 10 12 15   9,[2]   a 10      
  10_0_4_0_1_0_2_0_3 12 12 15   11,[2]            
  10_0_4_0_2_0_3_0_0_0_1 11 12 15   10,[2]   a 10      
  10_0_5_0_0_0_3_0_2 11 12 14   10,[2]            
  10_1_2_0_3_0_3_0_0_0_1 11 12 15   10,[2]   a 10      
  10_1_2_0_4_0_1_0_1_0_1 11 12 15   10,[2]   a 10      
  10_1_2_1_3_0_0_0_3 11 12 15   10,[2]            
  10_1_3_0_4_0_0_0_1_0_1 10 12 15   9,[2]   a 10      
  10_1_3_0_5_0_0_0_0_0_1 9 12 15   8,[2]   a 10      
  10_1_3_3_2_0_0_0_0_0_1 9 12 15   8,[2]   a 10      
  10_1_4_0_2_0_0_0_3 10 12 15   9,[2]            
  10_1_5_1_2_0_0_0_0_0_1 8 12 15   7,[2]   a 10      
  10_2_0_3_0_0_2_0_3 12 12 14   11,[2]   b 10, #4      
  10_2_5_1_1_0_0_0_0_0_1 7 12 15   6,[2]   a 10      
  10_4_5_0_0_0_0_0_0_0_1 5 12 15   3,[2]   a 10      
  10_7_0_0_1_0_1_0_0_0_1 5 12 15   4,[2]   a 10      
  10_0_0_0_7_0_0_0_3 13 13 14   12,[2]            
  10_0_0_1_0_0_8_0_1 15 13 15   14,[2]            
  10_0_1_0_1_0_5_0_3 15 13 15   14,[2]            
  10_0_1_1_3_0_4_0_0_0_1 13 13 15   12,[2]   a 10      
  10_0_1_1_5_0_2_0_0_0_1 12 13 15   11,[2]   a 10      
  10_0_3_1_0_0_3_0_3 13 13 14   12,[2]            
  10_0_10_0_0_0_0_0_0 5 13 14   4,[2]            
  10_1_0_1_1_0_6_0_1 13 13 15   12,[2]            
  10_1_1_4_3_0_0_0_0_0_1 10 13 15   9,[2]   a 10      
  10_2_0_6_1_0_0_0_1 9 13 14   8,[2]            
  10_2_1_3_1_0_2_0_0_0_1 10 13 15   9,[2]   a 10      
  10_2_2_0_0_0_6_0_0 10 13 14   9,[2]            
  10_4_1_1_0_0_3_0_1 8 13 15   7,[2]   b 10      
  10_5_0_2_1_0_0_0_2 7 13 15   6,[2]            
  10_6_1_1_1_0_0_0_0_0_1 5 13 15   4,[2]   a 10      
  10_0_0_0_0_0_6_0_4 17 14 15   16,[2]            
  10_0_1_3_3_0_2_0_0_0_1 12 14 15   11,[2]   a 10      
  10_1_0_5_0_0_2_0_2 12 14 15   11,[2]            
  10_1_2_2_2_0_1_0_1_0_1 11 14 15   10,[2]   a 10      
  10_2_0_0_6_0_0_0_2 10 14 14   9,[2]            
  10_4_0_1_1_0_4_0_0 8 14 15   7,[2]   b 10      
  10_6_0_0_0_0_4_0_0 6 14 14   5,[2]            
  10_0_0_0_4_0_2_0_4 15 15 14   14,[2]            
  10_0_1_2_4_0_2_0_0_0_1 12 15 15   11,[2]   a 10      
  10_0_2_2_2_0_3_0_0_0_1 12 15 15   11,[2]   a 10      
  10_1_0_3_4_0_1_0_0_0_1 11 15 15   10,[2]   a 10      
  10_1_1_0_6_0_0_0_1_0_1 11 15 15   10,[2]   a 10      
  10_1_2_0_1_0_4_0_2 12 15 14   11,[2]            
  10_3_1_2_3_0_0_0_0_0_1 8 15 15   7,[2]   a 10      
  10_3_3_0_1_0_2_0_0_0_1 8 15 15   7,[2]   a 10      
  10_3_5_0_1_0_0_0_0_0_1 6 15 15   5,[2]   a 10      
  10_0_0_2_1_0_2_0_5 16 16 15   15,[2]            
  10_0_0_4_3_0_0_0_3 13 16 14   12,[2]            
  10_0_0_5_0_0_2_0_3 14 16 14   13,[2]            
  10_0_2_0_5_0_0_0_3 12 16 14   11,[2]            
  10_0_2_7_1_0_0_0_0 9 16 14   8,[2]            
  10_0_4_0_0_0_4_0_2 12 16 14   11,[2]            
  10_1_1_4_1_0_2_0_0_0_1 11 16 15   10,[2]   a 10      
  10_1_3_1_1_0_1_0_3 11 16 15   10,[2]            
  10_2_0_3_2_0_1_0_1_0_1 11 16 15   10,[2]   a 10      
  10_2_1_2_4_0_0_0_0_0_1 9 16 15   8,[2]   a 10      
  10_2_4_2_0_0_1_0_0_0_1 8 16 15   7,[2]   a 10      
  10_3_3_1_0_0_2_0_0_0_1 8 16 15   7,[2]   a 10      
  10_5_1_1_2_0_0_0_0_0_1 6 16 15   5,[2]   a 10      
  10_0_1_1_4_0_2_0_1_0_1 13 17 15   12,[2]   a 10      
  10_0_1_3_1_0_1_0_4 14 17 14   13,[2]            
  10_1_2_2_1_0_3_0_0_0_1 11 17 15   10,[2]   a 10      
  10_1_2_6_0_0_0_0_1 9 17 14   8,[2]            
  10_1_3_3_0_0_2_0_0_0_1 10 17 15   9,[2]   a 10      
  10_1_4_1_1_0_0_0_3 10 17 14   9,[2]            
  10_1_5_0_1_0_2_0_0_0_1 9 17 15   8,[2]   a 10      
  10_3_2_0_1_0_2_0_2 9 17 15   8,[2]            
  10_4_0_2_1_0_2_0_1 8 17 15   7,[2]   b 10      
  10_4_1_1_3_0_0_0_0_0_1 7 17 15   6,[2]   a 10      
  10_0_0_1_2_0_2_0_5 16 18 15   15,[2]            
  10_0_1_1_1_0_3_0_4 15 18 15   14,[2]            
  10_0_1_1_3_0_1_0_4 14 18 15   13,[2]            
  10_0_8_1_0_0_0_0_1 7 18 14   6,[2]            
  10_1_0_3_0_0_4_0_2 13 18 14   12,[2]            
  10_2_1_3_3_0_0_0_0_0_1 9 18 15   8,[2]   a 10      
  10_2_2_3_1_0_1_0_0_0_1 9 18 15   8,[2]   a 10      
  10_6_0_1_0_0_2_0_1 6 18 14   5,[2]            
  10_0_0_3_0_0_4_0_3 15 19 15   14,[2]            
  10_0_1_0_4_0_4_0_0_0_1 13 19 15   12,[2]   a 10      
  10_0_2_1_3_0_3_0_0_0_1 12 19 15   11,[2]   a 10      
  10_0_2_2_4_0_1_0_0_0_1 11 19 15   10,[2]   a 10      
  10_0_4_1_2_0_0_0_3 11 19 14   10,[2]            
  10_1_1_3_4_0_0_0_0_0_1 10 19 15   9,[2]   a 10      
  10_1_3_2_3_0_0_0_0_0_1 9 19 15   8,[2]   a 10      
  10_3_1_0_3_0_1_0_2 9 19 15   8,[2]            
  10_3_4_0_1_0_1_0_0_0_1 7 19 15   6,[2]   a 10      
  10_0_0_1_7_0_0_0_2 12 20 14   11,[2]            
  10_0_3_0_4_0_2_0_0_0_1 11 20 15   10,[2]   a 10      
  10_0_3_2_2_0_2_0_0_0_1 11 20 15   10,[2]   a 10      
  10_1_0_1_3_0_2_0_3 13 20 14   12,[2]            
  10_3_1_1_0_0_5_0_0 9 20 14   8,[2]   b 10,#5      
  10_5_0_2_0_0_2_0_1 7 20 14   6,[2]   b 10, #7      
  10_7_1_0_0_0_0_0_1_0_1 5 20 15   4,[2]   a 10      
  10_0_2_0_4_0_3_0_0_0_1 12 21 15   11,[2]   a 10      
  10_0_4_0_4_0_1_0_0_0_1 10 21 15   9,[2]   a 10      
  10_1_0_0_3_0_4_0_2 13 21 14   12,[2]            
  10_1_1_3_1_0_1_0_3 12 21 14   11,[2]            
  10_1_1_5_0_0_1_0_2 11 21 14   10,[2]            
  10_1_4_1_2_0_1_0_0_0_1 9 21 15   8,[2]   a 10      
  10_2_1_0_4_0_2_0_0_0_1 10 21 15   9,[2]   a 10      
  10_5_1_0_3_0_0_0_0_0_1 6 21 15   5,[2]   a 10      
  10_0_0_3_1_0_2_0_4 15 22 14   14,[2]            
  10_0_2_3_3_0_1_0_0_0_1 11 22 15   10,[2]   a 10      
  10_0_3_0_3_0_1_0_3 12 22 15   11,[2]            
  10_1_2_4_1_0_1_0_0_0_1 10 22 15   9,[2]   a 10      
  10_1_2_6_1_0_0_0_0 8 22 14   7,[2]            
  10_2_3_0_2_0_2_0_0_0_1 9 22 15   8,[2]   a 10      
  10_3_2_2_1_0_1_0_0_0_1 8 22 15   7,[2]   a 10      
  10_1_0_3_0_0_6_0_0 12 23 14   11,[2]            
  10_1_2_0_4_0_0_0_3 11 23 14   10,[2]            
  10_2_2_0_4_0_1_0_0_0_1 9 23 15   8,[2]   a 10      
  10_3_1_1_2_0_1_0_2 9 23 15   8,[2]            
  10_0_0_0_1_0_8_0_1 15 24 15   14,[2]     10      
  10_0_0_2_0_0_8_0_0 14 24 14   13,[2]            
  10_0_0_2_5_0_0_0_3 13 24 14   12,[2]            
  10_1_0_3_1_0_2_0_3 13 24 14   12,[2]            
  10_6_3_0_0_0_0_0_0_0_1 4 24 15   3,[2]   a 10      
  10_0_2_1_0_0_6_0_1 13 25 15   12,[2]            
  10_0_3_4_0_0_1_0_2 11 25 14   10,[2]            
  10_3_0_2_1_0_4_0_0 9 25 14   8,[2]   b 10, #11      
  10_0_0_2_0_0_4_0_4 16 26 14   15,[2]            
  10_0_2_0_6_0_1_0_0_0_1 11 26 15   10,[2]   a 10      
  10_0_4_2_1_0_0_0_3 11 26 14   10,[2]            
  10_1_0_2_4_0_0_0_3 12 26 14   11,[2]            
  10_1_3_0_0_0_5_0_1 11 26 14   10,[2]            
  10_1_3_1_2_0_2_0_0_0_1 10 26 15   9,[2]   a 10      
  10_5_2_0_1_0_1_0_0_0_1 6 26 15   5,[2]   a 10      
  10_0_0_1_0_0_6_0_3 16 27 15   15,[2]            
  10_1_0_4_3_0_1_0_0_0_1 11 27 15   10,[2]   a 10      
  10_1_1_1_4_0_2_0_0_0_1 11 27 15   10,[2]   a 10      
  10_2_4_0_2_0_1_0_0_0_1 8 27 15   7,[2]   a 10      
  10_3_0_0_3_0_4_0_0 9 27 14   8,[2]   b 10, #14      
  10_3_1_1_4_0_0_0_0_0_1 8 27 15   7,[2]   a,b 10      
  10_0_1_2_2_0_1_0_4 14 28 15   13,[2]            
  10_0_1_5_1_0_1_0_2 12 28 14   11,[2]            
  10_2_0_1_2_0_4_0_1 11 28 14   10,[2]            
  10_3_3_2_1_0_0_0_0_0_1 7 28 15   6,[2]   a 10      
  10_4_3_2_0_0_0_0_0_0_1 6 28 15   5,[2]   a 10      
  10_0_0_0_1_0_6_0_3 16 29 15   15,[2]     10      
  10_1_2_3_1_0_0_0_3 11 29 13   10,[2]            
  10_5_0_1_0_0_4_0_0 7 29 14   6,[2]   b 10, #7      
  10_0_1_3_0_0_3_0_3 14 30 15   13,[2]            
  10_0_3_2_1_0_1_0_3 12 30 14   11,[2]            
  10_5_2_1_0_0_1_0_0_0_1 6 30 15   5,[2]   a 10      
  10_0_1_4_4_0_0_0_0_0_1 11 31 15   10,[2]   a 10      
  10_1_0_2_1_0_4_0_2 13 31 15   12,[2]            
  10_3_1_2_1_0_1_0_2 9 31 15   8,[2]            
  10_4_3_0_0_0_1_0_2 7 31 15   6,[2]            
  10_0_5_2_0_0_1_0_2 10 32 14   9,[2]            
  10_1_0_5_2_0_0_0_2 11 32 14   10,[2]            
  10_1_1_0_5_0_2_0_0_0_1 11 32 15   10,[2]   a 10      
  10_2_4_1_1_0_1_0_0_0_1 8 32 15   7,[2]   a 10      
  10_0_0_3_5_0_0_0_2 12 33 14   11,[2]            
  10_2_3_2_2_0_0_0_0_0_1 8 33 15   7,[2]   a 10      
  10_0_0_4_1_0_2_0_3 14 34 14   13,[2]            
  10_1_2_2_2_0_0_0_3 11 34 14   10,[2]            
  10_2_4_0_0_0_2_0_2 9 34 15   8,[2]            
  10_3_0_3_1_0_2_0_1 9 34 14   8,[2]   b 10, #10      
  10_0_0_3_0_0_6_0_1 14 35 14   13,[2]            
  10_4_0_0_3_0_2_0_1 8 35 15   7,[2]   b 10      
  10_6_0_1_1_0_0_0_2 6 35 14   5,[2]            
  10_0_0_5_1_0_2_0_2 13 36 14   12,[2]            
  10_0_4_0_3_0_0_0_3 11 36 14   10,[2]            
  10_1_1_4_2_0_0_0_1_0_1 11 36 15   10,[2]   a 10      
  10_3_2_3_0_0_0_0_2 8 36 14   7,[2]            
  10_1_2_1_4_0_1_0_0_0_1 10 37 15   9,[2]   a 10      
  10_1_4_3_0_0_0_0_2 9 37 14   8,[2]            
  10_0_0_0_9_0_0_0_1 11 38 14   10,[2]            
  10_1_0_2_2_0_2_0_3 13 38 14   12,[2]            
  10_2_2_1_3_0_1_0_0_0_1 9 38 15   8,[2]   a 10      
  10_0_6_1_1_0_0_0_2 9 39 14   8,[2]            
  10_1_1_2_2_0_1_0_3 12 39 14   11,[2]            
  10_2_1_4_0_0_1_0_2 10 39 14   9,[2]            
  10_3_0_0_4_0_2_0_1 9 39 14   8,[2]   b 10, #25      
  10_4_1_4_0_0_1_0_0 6 39 14   5,[2]            
  10_0_1_0_5_0_1_0_3 13 40 14   12,[2]            
  10_1_0_0_7_0_0_0_2 11 40 14   10,[2]            
  10_1_1_1_3_0_1_0_3 12 41 14   11,[2]            
  10_1_1_7_0_0_1_0_0 9 41 12   8,[2]            
  10_1_3_1_0_0_3_0_2 11 41 14   10,[2]            
  10_2_2_2_2_0_1_0_0_0_1 9 41 15   8,[2]   a 10      
  10_3_2_0_0_0_4_0_1 9 41 14   8,[2]   b 10, #13      
  10_1_3_0_3_0_2_0_0_0_1 10 42 15   9,[2]   a 10      
  10_5_0_1_1_0_2_0_1 7 42 14   6,[2]   b 10, #24      
  10_0_0_0_10_0_0_0_0 10 43 14   9,[2]            
  10_0_0_1_3_0_2_0_4 15 43 15   14,[2]            
  10_0_1_1_0_0_7_0_1 14 43 14   13,[2]            
  10_1_2_0_5_0_1_0_0_0_1 10 43 15   9,[2]   a 10      
  10_3_1_2_0_0_3_0_1 9 43 14   8,[2]   b 10, #7      
  10_4_1_0_1_0_3_0_1 8 43 15   7,[2]   b 10      
  10_5_3_1_0_0_0_0_0_0_1 5 43 15   4,[2]   a 10      
  10_0_0_2_0_0_6_0_2 15 44 14   14,[2]            
  10_0_1_2_0_0_7_0_0 13 44 14   12,[2]            
  10_0_3_1_2_0_1_0_3 12 44 14   11,[2]            
  10_1_1_2_3_0_2_0_0_0_1 11 44 15   10,[2]   a 10      
  10_3_1_0_1_0_5_0_0 9 44 14   8,[2]   b 10, #30      
  10_4_3_1_1_0_0_0_0_0_1 6 44 15   5,[2]   a 10      
  10_0_0_0_2_0_4_0_4 16 45 14   15,[2]            
  10_0_2_4_2_0_1_0_0_0_1 11 45 15   10,[2]   a 10      
  10_0_4_3_1_0_0_0_2 10 45 14   9,[2]            
  10_0_6_0_0_0_2_0_2 10 45 14   9,[2]            
  10_1_4_0_3_0_1_0_0_0_1 9 45 15   8,[2]   a 10      
  10_4_0_1_2_0_2_0_1 8 46 15   7,[2]   b 10      
  10_0_0_1_1_0_8_0_0 14 47 15   13,[2]            
  10_1_0_6_1_0_0_0_2 11 47 14   10,[2]            
  10_0_0_2_2_0_2_0_4 15 48 14   14,[2]            
  10_0_0_6_0_0_4_0_0 12 48 14   11,[2]            
  10_0_1_0_1_0_7_0_1 14 48 14   13,[2]            
  10_0_1_5_0_0_3_0_1 12 48 14   11,[2]            
  10_0_2_3_2_0_0_0_3 12 48 14   11,[2]            
  10_1_4_1_0_0_2_0_2 10 48 14   9,[2]            
  10_1_2_3_2_0_1_0_0_0_1 10 50 15   9,[2]   a 10      
  10_0_0_1_1_0_4_0_4 16 52 14   15,[2]            
  10_2_0_4_0_0_2_0_2 11 52 13   10,[2]            
  10_3_0_3_0_0_4_0_0 9 52 14   8,[2]   b 10, #31      
  10_6_1_0_2_0_0_0_0_0_1 5 52 15   4,[2]   a 10      
  10_2_0_1_5_0_0_0_2 10 53 14   9,[2]            
  10_2_0_2_1_0_4_0_1 11 54 14   10,[2]            
  10_0_0_10_0_0_0_0_0 10 55 13   10,[] Z          
  10_0_2_0_3_0_2_0_3 13 55 14   12,[2]            
  10_1_6_1_0_0_0_0_2 8 55 14   7,[2]            
  10_0_2_0_1_0_6_0_1 13 56 14   12,[2]            
  10_1_2_1_0_0_6_0_0 11 56 14   10,[2]            
  10_6_0_0_1_0_2_0_1 6 56 14   5,[2]            
  10_0_0_4_0_0_6_0_0 13 58 13   12,[2]            
  10_1_1_0_2_0_5_0_1 12 58 14   11,[2]            
  10_1_3_0_1_0_3_0_2 11 58 14   10,[2]            
  10_0_0_0_5_0_2_0_3 14 59 14   13,[2]            
  10_2_0_1_3_0_2_0_2 11 59 14   10,[2]            
  10_3_2_1_2_0_1_0_0_0_1 8 59 15   7,[2]   a 10