example rho=(1/4,1/6): G-families 2, phase-space families 3, regions 2, parts per region [3, 5] (total 8), symmetric states singular: ['h2']
example rho=(1/3,1/6): G-families 1, phase-space families 1, regions 1, parts per region [7] (total 7), symmetric states singular: ['A1', 'h1', 'h2']
example rho=(1/3,1/5): G-families 2, phase-space families 4, regions 2, parts per region [13, 21] (total 34), symmetric states singular: ['K']
example rho=(1/3,1/4): G-families 2, phase-space families 3, regions 2, parts per region [6, 7] (total 13), symmetric states singular: ['A2']
pairs: 231 (denominators <= 12)   problems: 0
histogram (families of G, families in full phase space, regions on the boundary): count
    (1, 1, 1) 26
    (1, 2, 1) 4
    (2, 3, 2) 110
    (2, 4, 2) 91
histogram (numbers of symmetric states h1,h2,A1,A2,K in the families of Phi; number on saddle connections): count
    ((2,), 3) 30
    ((2, 2), 1) 201
