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Statistic identifier: St001617

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Collection: Lattices

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Description: The dimension of the space of valuations of a lattice.

A valuation, or modular function, on a lattice $L$ is a function $v:L\mapsto\mathbb R$ satisfying
$$
v(a\vee b) + v(a\wedge b) = v(a) + v(b).
$$

It was shown by Birkhoff [1, thm. X.2], that a lattice with a positive valuation must be modular.  This was sharpened by Fleischer and Traynor [2, thm. 1], which states that the modular functions on an arbitrary lattice are in bijection with the modular functions on its modular quotient [[Mp00196]].

Moreover, Birkhoff [1, thm. X.2] showed that the dimension of the space of modular functions equals the number of subsets of projective prime intervals.

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References: [1]   Birkhoff, G. Lattice theory [[MathSciNet:0227053]]
[2]   Fleischer, I., Traynor, T. Group-valued modular functions [[MathSciNet:0654397]]

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Code:
def projective_prime_intervals(L):
    assert L.is_modular()
    I = [tuple(r) for r in L.cover_relations()]
    D = DisjointSet(I)
    for a in L:
        for b, c in Subsets(L.upper_covers(a), 2):
            assert a == L.meet(b, c), "The meet of %s and %s is not %s" % (b, c, a)
            d = L.join(b, c)
            D.union((a,b), (c,d))
            D.union((a,c), (b,d))
    return D

def modular_quotient(L):
    L = L.relabel()
    C = L.congruences_lattice()
    c = C.subposet([c for c in C if (L.quotient(c)).is_modular()]).bottom()
    return L.quotient(c)

def statistic(L):
    L_modular = modular_quotient(L)
    return projective_prime_intervals(L_modular).number_of_subsets()

-----------------------------------------------------------------------------
Statistic values:

([],1)                                                                                    => 0
([(0,1)],2)                                                                               => 1
([(0,2),(2,1)],3)                                                                         => 2
([(0,1),(0,2),(1,3),(2,3)],4)                                                             => 2
([(0,3),(2,1),(3,2)],4)                                                                   => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)                                                 => 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)                                                       => 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)                                                       => 3
([(0,4),(2,3),(3,1),(4,2)],5)                                                             => 4
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)                                                       => 3
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)                                     => 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)                                           => 1
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)                                           => 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)                                           => 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)                                                 => 3
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)                                                 => 4
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)                                                 => 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)                                                 => 4
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)                                           => 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)                                                 => 4
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)                                           => 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)                                                 => 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)                                           => 3
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)                                                       => 5
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)                                                 => 3
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)                         => 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)                               => 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)                               => 0
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)                               => 1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)                               => 2
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)                                     => 2
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)                                     => 2
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)                                     => 3
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)                                     => 1
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)                                     => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)                                     => 2
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)                                           => 5
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)                                           => 3
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)                                     => 4
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)                                     => 1
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)                                     => 1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)                                     => 3
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)                               => 0
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)                                     => 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)                                     => 4
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)                               => 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)                                     => 3
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)                               => 2
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)                                     => 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)                               => 2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)                                           => 5
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)                                     => 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)                               => 2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)                                     => 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)                                     => 1
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)                               => 0
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)                                     => 3
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)                                     => 4
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)                                     => 3
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)                                     => 1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)                               => 2
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)                                           => 3
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)                                     => 2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)                                           => 4
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)                                     => 2
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)                               => 2
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)                                     => 3
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)                                           => 2
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)                                           => 5
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)                                     => 1
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)                                           => 4
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)                                           => 2
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)                                           => 4
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)                                     => 3
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)                                                 => 6
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)                                           => 3
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)                                           => 3
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)                                           => 5
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)             => 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8)                   => 1
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8)                   => 0
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8)                   => 0
([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4)],8)                   => 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)                   => 2
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5)],8)                         => 2
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,7)],8)                         => 1
([(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,4),(7,6)],8)                         => 2
([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)                         => 3
([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5)],8)                         => 1
([(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5)],8)                         => 1
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,2),(5,3),(6,7)],8)                         => 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8)                         => 2
([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)                               => 4
([(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(5,3),(5,4),(6,7)],8)                               => 2
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8)                         => 3
([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8)                         => 3
([(0,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7),(7,1)],8)                               => 3
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,4),(7,3)],8)                               => 2
([(0,6),(1,7),(2,7),(3,7),(4,3),(5,2),(6,1),(6,4),(6,5)],8)                               => 2
([(0,5),(1,7),(2,7),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4),(6,7)],8)                         => 1
([(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(6,1),(6,5)],8)                         => 0
([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(5,3),(6,1),(6,5)],8)                         => 1
([(0,5),(1,7),(2,7),(3,7),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3)],8)                         => 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(6,7)],8)                         => 1
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3)],8)                               => 2
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)                               => 5
([(0,3),(0,6),(1,7),(2,7),(3,7),(4,2),(5,1),(6,4),(6,5)],8)                               => 1
([(0,3),(0,5),(1,7),(2,6),(3,7),(4,1),(4,6),(5,2),(5,4),(6,7)],8)                         => 1
([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8)                               => 4
([(0,6),(1,7),(2,7),(3,7),(4,3),(5,1),(5,2),(6,4),(6,5)],8)                               => 2
([(0,5),(1,7),(2,7),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4),(6,7)],8)                         => 3
([(0,5),(1,7),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7)],8)                         => 3
([(0,2),(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,1),(6,5)],8)                         => 1
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2)],8)                         => 0
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3)],8)                         => 1
([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)                         => 3
([(0,2),(0,3),(0,6),(1,7),(2,7),(3,7),(4,5),(5,1),(6,4)],8)                               => 1
([(0,3),(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2)],8)                               => 1
([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)                               => 4
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)                   => 0
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1)],8)                         => 0
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)                         => 0
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)                         => 3
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)                   => 0
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,6),(7,1)],8)                         => 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)                         => 3
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)                   => 1
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)                         => 3
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)                   => 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(7,6)],8)                         => 1
([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)                               => 4
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,6),(6,1),(7,6)],8)                         => 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,1),(5,7),(7,6)],8)                   => 2
([(0,3),(0,4),(0,5),(0,6),(1,7),(3,7),(4,7),(5,7),(6,1),(7,2)],8)                         => 2
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(6,7)],8)                         => 0
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,7),(6,7)],8)                   => 0
([(0,2),(0,3),(0,4),(1,6),(2,7),(3,5),(4,5),(4,7),(5,6),(7,1)],8)                         => 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(5,7),(6,7),(7,1)],8)                         => 3
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(7,5)],8)                               => 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)                         => 1
([(0,2),(0,3),(0,4),(2,7),(3,6),(4,6),(5,1),(6,7),(7,5)],8)                               => 3
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1)],8)                               => 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)                               => 4
([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)                         => 2
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,6),(6,7)],8)                   => 0
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,7),(7,2)],8)                         => 2
([(0,2),(0,3),(0,5),(1,6),(2,7),(3,7),(4,1),(5,4),(5,7),(7,6)],8)                         => 2
([(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,1),(5,7),(6,2),(7,6)],8)                         => 3
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(6,7)],8)                         => 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)                               => 5
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,7),(5,7),(7,6)],8)                         => 2
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,6),(6,7)],8)                   => 1
([(0,3),(0,5),(1,7),(2,6),(3,6),(4,2),(5,1),(5,4),(6,7)],8)                               => 2
([(0,5),(1,7),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4),(6,7)],8)                               => 3
([(0,6),(1,7),(2,7),(4,2),(5,1),(6,4),(6,5),(7,3)],8)                                     => 4
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,7),(5,1),(5,2),(7,6)],8)                         => 1
([(0,4),(0,6),(1,7),(2,7),(4,7),(5,2),(6,1),(6,5),(7,3)],8)                               => 2
([(0,6),(1,7),(2,7),(3,7),(5,2),(5,3),(6,1),(6,5),(7,4)],8)                               => 3
([(0,4),(0,5),(0,6),(1,7),(2,7),(4,7),(5,7),(6,1),(6,2),(7,3)],8)                         => 1
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(7,6)],8)                         => 1
([(0,3),(0,4),(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(7,5)],8)                               => 3
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,6),(4,1),(5,4),(6,7)],8)                               => 1
([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)                                     => 6
([(0,3),(0,4),(0,5),(2,7),(3,6),(4,6),(5,2),(6,7),(7,1)],8)                               => 2
([(0,3),(0,4),(1,7),(2,6),(3,6),(4,5),(5,1),(5,2),(6,7)],8)                               => 2
([(0,4),(1,7),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3),(6,7)],8)                               => 3
([(0,2),(0,3),(0,5),(1,6),(2,7),(3,7),(4,1),(4,7),(5,4),(7,6)],8)                         => 2
([(0,3),(0,4),(0,6),(1,7),(3,7),(4,7),(5,1),(6,5),(7,2)],8)                               => 2
([(0,4),(0,5),(1,7),(2,7),(4,7),(5,6),(6,1),(6,2),(7,3)],8)                               => 2
([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)                               => 4
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)                         => 0
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,7),(3,5),(4,5),(4,7),(5,6),(7,6)],8)                   => 1
([(0,3),(0,4),(0,5),(2,7),(3,6),(4,6),(5,7),(6,2),(7,1)],8)                               => 2
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)                               => 5
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,6),(5,6),(6,7),(7,1)],8)                         => 1
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(6,1)],8)                         => 1
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,7)],8)                   => 0
([(0,2),(0,3),(0,5),(1,7),(2,7),(3,6),(4,1),(5,4),(5,6),(6,7)],8)                         => 0
([(0,3),(0,4),(1,7),(2,7),(3,6),(4,5),(4,6),(5,1),(5,2),(6,7)],8)                         => 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)                         => 4
([(0,2),(0,3),(0,4),(1,7),(2,5),(3,6),(4,1),(4,5),(5,7),(7,6)],8)                         => 1
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)                               => 5
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,4),(5,7),(7,1)],8)                               => 3
([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)                         => 4
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2)],8)                         => 0
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)                         => 2
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2)],8)                         => 0
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,6),(6,7)],8)                   => 0
([(0,3),(0,5),(1,7),(2,7),(3,6),(4,2),(5,1),(5,4),(5,6),(6,7)],8)                         => 2
([(0,3),(0,4),(1,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(7,6)],8)                         => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6),(5,7),(6,7)],8)                         => 2
([(0,4),(0,5),(1,7),(2,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,3)],8)                         => 3
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,6),(6,3)],8)                         => 2
([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3)],8)                         => 1
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7)],8)                   => 2
([(0,6),(1,7),(2,7),(3,7),(4,5),(5,3),(6,1),(6,2),(6,4)],8)                               => 2
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(6,7)],8)                         => 1
([(0,5),(1,7),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4),(6,7)],8)                               => 2
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,7),(5,1),(5,2),(5,3),(7,6)],8)                         => 2
([(0,6),(1,7),(2,7),(3,7),(5,3),(6,1),(6,2),(6,5),(7,4)],8)                               => 3
([(0,5),(0,6),(1,7),(2,7),(3,7),(5,7),(6,1),(6,2),(6,3),(7,4)],8)                         => 2
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,3),(5,1),(5,2),(5,6),(6,7)],8)                         => 2
([(0,3),(0,6),(1,7),(2,7),(3,7),(4,5),(5,2),(6,1),(6,4)],8)                               => 1
([(0,6),(1,7),(2,7),(3,7),(4,5),(5,2),(5,3),(6,1),(6,4)],8)                               => 2
([(0,6),(1,7),(2,7),(3,4),(4,1),(5,2),(6,3),(6,5)],8)                                     => 3
([(0,5),(1,7),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4),(6,7)],8)                               => 4
([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)                               => 5
([(0,5),(1,7),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4),(6,7)],8)                               => 4
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,6),(5,1),(5,2),(6,7)],8)                         => 0
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,3),(7,2)],8)                               => 2
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,4),(6,7)],8)                               => 2
([(0,6),(2,7),(3,7),(4,3),(5,1),(6,2),(6,4),(7,5)],8)                                     => 5
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(7,6)],8)                         => 1
([(0,4),(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(7,5)],8)                               => 3
([(0,3),(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(5,4),(6,7)],8)                               => 2
([(0,3),(0,4),(1,5),(2,5),(2,6),(3,6),(4,1),(4,2),(5,7),(6,7)],8)                         => 3
([(0,4),(0,5),(2,7),(3,6),(4,6),(5,2),(5,3),(6,7),(7,1)],8)                               => 3
([(0,5),(1,7),(2,6),(3,6),(4,1),(4,3),(5,2),(5,4),(6,7)],8)                               => 3
([(0,3),(0,5),(1,7),(2,6),(3,7),(4,2),(4,7),(5,1),(5,4),(7,6)],8)                         => 2
([(0,5),(0,6),(1,7),(2,7),(3,7),(4,3),(5,1),(6,2),(6,4)],8)                               => 1
([(0,6),(1,7),(2,7),(3,7),(4,3),(5,2),(5,4),(6,1),(6,5)],8)                               => 2
([(0,3),(0,5),(1,7),(2,7),(3,6),(4,2),(4,6),(5,1),(5,4),(6,7)],8)                         => 1
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,3),(5,1),(5,2),(6,7)],8)                               => 2
([(0,6),(1,7),(2,7),(4,5),(5,2),(6,1),(6,4),(7,3)],8)                                     => 4
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(5,3),(6,7)],8)                               => 2
([(0,5),(0,6),(1,7),(2,7),(3,7),(5,3),(6,1),(6,2),(7,4)],8)                               => 2
([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)                                     => 6
([(0,4),(0,5),(2,6),(3,6),(4,7),(5,2),(5,3),(6,7),(7,1)],8)                               => 3
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,2),(4,6),(5,1),(5,6),(6,7)],8)                   => 0
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,2),(4,6),(5,1),(5,6),(6,3)],8)                         => 2
([(0,4),(0,5),(1,7),(2,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)                         => 2
([(0,3),(0,4),(1,6),(2,7),(3,1),(3,5),(4,2),(4,5),(5,7),(7,6)],8)                         => 3
([(0,4),(0,5),(1,7),(2,7),(4,2),(4,6),(5,1),(5,6),(6,7),(7,3)],8)                         => 3
([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2)],8)                         => 0
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,3),(4,6),(5,1),(5,2),(5,6),(6,7)],8)                   => 1
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,2),(4,6),(5,1),(5,3),(6,7)],8)                         => 1
([(0,5),(1,7),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3),(6,7)],8)                               => 4
([(0,4),(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(7,6)],8)                         => 2
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,2),(5,1),(5,6),(6,7)],8)                         => 0
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,1),(5,3),(5,7),(7,2)],8)                               => 3
([(0,4),(0,5),(1,7),(2,6),(3,1),(4,2),(5,3),(5,6),(6,7)],8)                               => 3
([(0,4),(0,5),(1,7),(3,6),(4,3),(5,1),(5,6),(6,7),(7,2)],8)                               => 4
([(0,5),(0,6),(1,7),(2,7),(3,7),(4,3),(5,4),(6,1),(6,2)],8)                               => 1
([(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,2),(6,4)],8)                                     => 3
([(0,4),(1,7),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5)],8)                               => 3
([(0,4),(0,5),(1,7),(2,7),(3,2),(3,6),(4,3),(5,1),(5,6),(6,7)],8)                         => 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,6),(5,1),(6,7)],8)                         => 0
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,6),(5,1),(7,2)],8)                               => 1
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)                               => 4
([(0,3),(0,5),(0,6),(1,7),(2,7),(3,7),(4,1),(5,2),(6,4)],8)                               => 1
([(0,3),(0,5),(1,7),(2,7),(3,7),(4,2),(5,6),(6,1),(6,4)],8)                               => 1
([(0,2),(0,3),(0,5),(1,7),(2,7),(3,6),(4,1),(4,6),(5,4),(6,7)],8)                         => 0
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(4,7),(5,4),(7,1)],8)                               => 3
([(0,4),(0,5),(1,7),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2)],8)                               => 1
([(0,5),(1,7),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(6,4)],8)                               => 3
([(0,3),(0,4),(1,7),(2,7),(3,6),(4,5),(5,1),(5,2),(5,6),(6,7)],8)                         => 2
([(0,2),(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,4)],8)                                     => 2
([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)                                     => 6
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(6,7)],8)                               => 1
([(0,5),(0,6),(2,7),(3,7),(4,1),(5,3),(6,2),(7,4)],8)                                     => 4
([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)                                     => 2
([(0,5),(1,7),(2,7),(3,4),(4,1),(5,6),(6,2),(6,3)],8)                                     => 4
([(0,4),(0,5),(1,7),(2,6),(3,1),(3,6),(4,2),(5,3),(6,7)],8)                               => 3
([(0,2),(0,3),(0,5),(1,6),(2,7),(3,6),(4,1),(5,4),(6,7)],8)                               => 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,5),(5,1),(5,2),(6,7)],8)                               => 2
([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)                                     => 6
([(0,3),(0,6),(2,7),(3,7),(4,2),(5,1),(6,4),(7,5)],8)                                     => 4
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,3),(5,2),(6,1)],8)                               => 1
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,2),(5,1),(5,6),(6,7)],8)                         => 0
([(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,1),(4,5),(4,6),(5,7),(6,7)],8)                   => 1
([(0,2),(0,5),(1,7),(2,6),(3,4),(4,1),(5,3),(5,6),(6,7)],8)                               => 3
([(0,3),(0,5),(2,7),(3,6),(4,2),(5,4),(5,6),(6,7),(7,1)],8)                               => 4
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,6),(5,7),(6,7)],8)                         => 1
([(0,4),(0,5),(1,6),(3,6),(4,7),(5,1),(5,7),(6,2),(7,3)],8)                               => 4
([(0,3),(0,4),(0,5),(1,7),(3,7),(4,6),(5,1),(5,6),(6,7),(7,2)],8)                         => 1
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,7),(7,4)],8)                               => 3
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,7),(4,1),(4,5),(5,7),(7,6)],8)                         => 1
([(0,2),(0,3),(0,4),(1,7),(2,5),(3,5),(3,6),(4,1),(4,6),(5,7),(6,7)],8)                   => 1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)             => 3
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,2),(4,6),(5,1),(5,6),(6,7)],8)                   => 1
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(5,7),(6,7)],8)                         => 2
([(0,4),(0,5),(1,7),(2,6),(3,2),(4,3),(5,1),(5,6),(6,7)],8)                               => 3
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)                               => 5
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,1),(5,2),(5,7),(7,6)],8)                         => 2
([(0,5),(0,6),(1,7),(2,7),(3,4),(4,2),(5,3),(6,1)],8)                                     => 2
([(0,5),(1,7),(2,7),(3,2),(4,1),(5,6),(6,3),(6,4)],8)                                     => 4
([(0,2),(0,5),(1,7),(2,6),(3,1),(4,3),(4,6),(5,4),(6,7)],8)                               => 3
([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8)                               => 4
([(0,5),(1,7),(2,7),(3,6),(4,1),(5,3),(6,2),(6,4)],8)                                     => 5
([(0,2),(0,5),(1,7),(2,6),(3,4),(4,1),(4,6),(5,3),(6,7)],8)                               => 3
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)                                           => 7
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(6,7)],8)                               => 1
([(0,2),(0,3),(0,4),(1,5),(1,6),(2,6),(3,5),(4,1),(5,7),(6,7)],8)                         => 2
([(0,3),(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(7,5)],8)                                     => 5
([(0,3),(0,4),(0,5),(2,6),(3,7),(4,6),(5,2),(6,7),(7,1)],8)                               => 2
([(0,3),(0,6),(1,7),(3,7),(4,5),(5,1),(6,4),(7,2)],8)                                     => 3
([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)                                     => 6
([(0,5),(0,6),(1,7),(2,7),(4,1),(5,2),(6,4),(7,3)],8)                                     => 3
([(0,5),(1,7),(2,7),(4,2),(5,6),(6,1),(6,4),(7,3)],8)                                     => 5
([(0,4),(0,5),(0,6),(1,7),(2,7),(4,7),(5,2),(6,1),(7,3)],8)                               => 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9) => 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1)],9)       => 1
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2)],9)       => 0
([(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3)],9)       => 0
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4)],9)       => 0
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5)],9)       => 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],9)       => 2
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,5),(7,1),(7,2),(7,3),(7,4),(7,6)],9)             => 2
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5),(7,8)],9)             => 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5),(7,8)],9)             => 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5),(8,7)],9)             => 2
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(7,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)             => 3
([(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,4),(7,1),(7,2),(7,3),(7,6)],9)             => 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,4),(6,5),(7,1),(7,2),(7,3),(7,6)],9)             => 1
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,8),(6,1),(6,2),(6,3),(6,4),(7,8)],9)             => 1
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,7),(5,8),(6,1),(6,2),(6,3),(6,4),(7,8)],9)             => 1
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(6,4),(8,7)],9)             => 2
([(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(7,5),(8,6)],9)                   => 4
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5),(8,7)],9)                   => 2
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(6,5),(8,7)],9)             => 3
([(0,6),(1,8),(2,8),(3,8),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5),(8,7)],9)                   => 3
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(8,5)],9)                   => 2
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,3),(6,4),(6,5),(7,8)],9)                   => 1
([(0,5),(1,8),(2,7),(3,6),(4,6),(4,7),(5,1),(5,2),(5,3),(5,4),(6,8),(7,8)],9)             => 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,7),(6,1),(6,3),(6,4),(6,5),(7,8)],9)             => 1
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,8),(7,8)],9)                   => 1
([(0,5),(1,8),(2,8),(3,6),(4,6),(4,8),(5,1),(5,2),(5,3),(5,4),(6,7),(8,7)],9)             => 2
([(0,6),(1,8),(2,8),(4,7),(5,7),(6,1),(6,2),(6,4),(6,5),(7,8),(8,3)],9)                   => 2
([(0,5),(1,6),(2,6),(3,7),(4,8),(5,1),(5,2),(5,3),(5,4),(6,8),(8,7)],9)                   => 2
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,8),(6,1),(6,2),(6,3),(6,4),(7,5)],9)                   => 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,3),(7,1),(7,2),(7,5),(7,6)],9)                   => 2
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(6,4),(6,5),(7,8)],9)             => 1
([(0,4),(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,3),(7,1),(7,2),(7,6)],9)             => 0
([(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,3),(6,4),(7,1),(7,2),(7,6)],9)             => 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,3),(6,4),(6,5),(7,1),(7,2),(7,6)],9)             => 1
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,8),(6,1),(6,2),(6,3),(7,8)],9)             => 0
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,8),(5,8),(6,1),(6,2),(6,3),(7,8)],9)             => 1
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4)],9)                   => 2
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(8,4),(8,5)],9)                   => 4
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(6,2),(6,3),(6,5),(7,8)],9)                   => 1
([(0,4),(0,5),(1,7),(2,6),(3,6),(3,7),(4,8),(5,1),(5,2),(5,3),(6,8),(7,8)],9)             => 1
([(0,5),(1,7),(2,8),(3,6),(4,6),(4,8),(5,2),(5,3),(5,4),(6,7),(8,1)],9)                   => 3
([(0,5),(2,7),(3,6),(4,6),(4,7),(5,2),(5,3),(5,4),(6,8),(7,8),(8,1)],9)                   => 4
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(5,7),(6,2),(6,3),(6,5),(7,8)],9)             => 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,8),(6,1),(6,2),(6,5),(8,4)],9)                   => 3
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(6,3),(6,4),(6,5),(7,8)],9)                   => 2
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,4),(6,5),(7,8)],9)             => 2
([(0,5),(1,6),(2,6),(3,7),(4,3),(4,8),(5,1),(5,2),(5,4),(6,8),(8,7)],9)                   => 3
([(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7)],9)                   => 2
([(0,6),(1,8),(3,7),(4,7),(5,2),(6,1),(6,3),(6,4),(7,8),(8,5)],9)                         => 4
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(6,5),(8,3)],9)                         => 2
([(0,5),(1,7),(2,8),(3,8),(4,6),(5,2),(5,3),(5,4),(6,7),(8,1),(8,6)],9)                   => 3
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,8),(6,1),(6,2),(6,3),(7,4)],9)                   => 1
([(0,6),(1,8),(2,7),(3,7),(4,8),(5,8),(6,1),(6,2),(6,3),(7,4),(7,5)],9)                   => 1
([(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(6,2),(7,1),(7,5),(7,6)],9)                   => 1
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(5,7),(6,1),(6,3),(6,5),(7,8)],9)             => 1
([(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(5,7),(6,1),(6,3),(6,5),(7,4)],9)                   => 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,2),(6,3),(7,1),(7,5),(7,6)],9)                   => 1
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,3),(5,7),(6,1),(6,4),(6,5),(7,8)],9)             => 1
([(0,6),(1,8),(2,8),(3,8),(4,3),(4,7),(5,2),(5,7),(6,1),(6,4),(6,5),(7,8)],9)             => 1
([(0,7),(1,8),(2,8),(3,8),(4,3),(5,2),(6,1),(7,4),(7,5),(7,6)],9)                         => 2
([(0,6),(1,8),(2,8),(3,7),(4,2),(5,1),(5,7),(6,3),(6,4),(6,5),(7,8)],9)                   => 1
([(0,5),(1,8),(2,7),(3,6),(4,1),(4,6),(4,7),(5,2),(5,3),(5,4),(6,8),(7,8)],9)             => 2
([(0,5),(1,8),(2,6),(3,6),(3,7),(4,1),(4,7),(5,2),(5,3),(5,4),(6,8),(7,8)],9)             => 2
([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)       => 4
([(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,1),(5,7),(6,3),(6,4),(6,5),(7,8)],9)             => 2
([(0,5),(1,6),(2,8),(3,7),(4,3),(4,6),(5,1),(5,2),(5,4),(6,8),(8,7)],9)                   => 2
([(0,3),(0,4),(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,2),(7,1),(7,6)],9)             => 0
([(0,4),(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,2),(6,3),(7,1),(7,6)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,4),(6,7),(7,1),(7,2),(7,3)],9)             => 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,5),(6,7),(7,1),(7,2),(7,3),(7,4)],9)             => 2
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,8)],9)             => 1
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3)],9)                   => 1
([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4)],9)                   => 1
([(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4),(7,5)],9)                   => 4
([(0,3),(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,2),(6,1),(7,5),(7,6)],9)                   => 0
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,8),(5,1),(5,7),(6,2),(6,5),(7,8)],9)             => 0
([(0,4),(0,6),(1,8),(2,7),(3,8),(4,8),(5,1),(5,7),(6,2),(6,5),(7,3)],9)                   => 1
([(0,6),(1,8),(2,7),(3,8),(4,8),(5,1),(5,7),(6,2),(6,5),(7,3),(7,4)],9)                   => 3
([(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(6,1),(6,2),(7,5),(7,6)],9)                   => 1
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,1),(5,2),(5,7),(6,3),(6,5),(7,8)],9)             => 1
([(0,6),(1,8),(2,8),(3,7),(4,8),(5,1),(5,2),(5,7),(6,3),(6,5),(7,4)],9)                   => 3
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,4),(6,5),(6,7),(7,1),(7,2),(7,3)],9)                   => 2
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)             => 3
([(0,3),(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8)],9)             => 1
([(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,3)],9)                   => 3
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(5,4),(6,1),(6,2),(7,5),(7,6)],9)                   => 1
([(0,6),(1,8),(2,8),(3,8),(4,3),(4,7),(5,1),(5,2),(5,7),(6,4),(6,5),(7,8)],9)             => 2
([(0,3),(0,4),(0,6),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(6,5),(7,8)],9)                   => 1
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3)],9)                         => 2
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)                         => 5
([(0,2),(0,3),(0,4),(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,1),(7,6)],9)             => 1
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2)],9)             => 0
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4)],9)             => 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],9)             => 3
([(0,2),(0,3),(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,1),(7,5)],9)                   => 1
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2)],9)                   => 0
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3)],9)                   => 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],9)                   => 4
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)       => 0
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,1)],9)             => 0
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,1),(7,2)],9)             => 0
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,1),(7,2),(7,3)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,1),(7,2),(7,3),(7,4)],9)             => 3
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)       => 0
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,7),(8,1)],9)             => 0
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,7),(8,1),(8,2)],9)             => 0
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,8),(5,8),(6,8),(8,1),(8,2),(8,3)],9)             => 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(8,7)],9)       => 0
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,8),(6,7),(8,1)],9)             => 1
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,8),(8,1),(8,2)],9)             => 3
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)       => 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(8,7)],9)             => 3
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8),(8,1)],9)       => 2
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,8),(6,1),(8,7)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(2,8),(3,8),(4,8),(5,8),(6,1),(7,6),(8,7)],9)                   => 4
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,8),(3,8),(4,8),(5,8),(6,7),(7,1),(8,7)],9)             => 2
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,8),(6,1),(6,8),(8,7)],9)       => 2
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(3,8),(4,8),(5,8),(6,8),(7,1),(8,2)],9)             => 2
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,7),(6,1),(7,8)],9)             => 0
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(8,6)],9)                   => 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,8),(5,6),(6,7),(8,6)],9)             => 1
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(8,2)],9)                   => 1
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(8,2),(8,6)],9)                   => 3
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,8),(5,6),(6,7),(8,1),(8,6)],9)             => 2
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(6,8),(8,7)],9)       => 0
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,8),(8,2)],9)             => 2
([(0,2),(0,3),(0,4),(0,6),(1,7),(2,8),(3,8),(4,8),(5,1),(6,5),(6,8),(8,7)],9)             => 2
([(0,3),(0,4),(0,5),(0,6),(1,7),(3,8),(4,8),(5,8),(6,1),(6,8),(7,2),(8,7)],9)             => 3
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,7),(6,1),(6,2),(7,8)],9)             => 1
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(8,6)],9)                   => 4
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,8),(5,1),(5,6),(6,7),(8,6)],9)             => 2
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(6,8),(8,7)],9)       => 1
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(8,7)],9)             => 1
([(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(4,8),(5,8),(6,8),(7,1),(7,2),(8,3)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(8,7)],9)             => 1
([(0,3),(0,4),(0,5),(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(8,6)],9)                   => 3
([(0,2),(0,3),(0,4),(0,6),(1,7),(2,8),(3,8),(4,8),(5,1),(6,5),(8,7)],9)                   => 1
([(0,2),(0,3),(0,4),(2,8),(3,8),(4,8),(5,6),(6,1),(7,5),(8,7)],9)                         => 5
([(0,2),(0,3),(0,4),(0,5),(2,8),(3,8),(4,8),(5,7),(6,1),(7,6),(8,7)],9)                   => 3
([(0,3),(0,4),(0,5),(0,6),(1,7),(3,8),(4,8),(5,8),(6,1),(7,2),(8,7)],9)                   => 2
([(0,2),(0,3),(0,4),(0,6),(1,7),(2,8),(3,8),(4,8),(5,1),(5,8),(6,5),(8,7)],9)             => 2
([(0,3),(0,4),(0,7),(1,8),(3,8),(4,8),(5,6),(6,1),(7,5),(8,2)],9)                         => 2
([(0,4),(0,6),(1,8),(2,8),(4,8),(5,7),(6,5),(7,1),(7,2),(8,3)],9)                         => 2
([(0,6),(1,8),(2,8),(3,8),(5,7),(6,5),(7,1),(7,2),(7,3),(8,4)],9)                         => 5
([(0,3),(0,4),(0,5),(0,7),(1,8),(3,8),(4,8),(5,8),(6,1),(7,6),(8,2)],9)                   => 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,6),(6,7),(8,7)],9)             => 0
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,7),(5,8),(7,6),(8,6)],9)       => 0
([(0,3),(0,4),(0,5),(0,6),(1,7),(3,8),(4,8),(5,8),(6,7),(7,2),(8,1)],9)                   => 2
([(0,4),(0,5),(0,6),(1,7),(2,7),(4,8),(5,8),(6,8),(7,3),(8,1),(8,2)],9)                   => 4
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8),(8,1)],9)             => 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,6),(5,8),(6,7),(8,7)],9)       => 1
([(0,3),(0,4),(0,5),(0,6),(2,8),(3,8),(4,8),(5,7),(6,7),(7,2),(8,1)],9)                   => 1
([(0,4),(0,5),(0,6),(2,8),(3,8),(4,8),(5,7),(6,7),(7,2),(7,3),(8,1)],9)                   => 1
([(0,5),(0,6),(2,8),(3,8),(4,8),(5,7),(6,7),(7,2),(7,3),(7,4),(8,1)],9)                   => 4
([(0,2),(0,3),(0,4),(0,5),(0,6),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8),(8,1)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,8)],9)             => 0
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)       => 0
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,8),(4,6),(5,6),(5,7),(6,8),(7,1)],9)             => 0
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,6),(5,7),(6,8),(7,1),(7,2)],9)             => 1
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)             => 1
([(0,2),(0,3),(0,4),(2,7),(3,6),(4,6),(4,7),(5,1),(6,8),(7,8),(8,5)],9)                   => 4
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,8),(5,7),(5,8),(7,2),(8,1)],9)                   => 2
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,8),(4,5),(4,8),(5,7),(7,6),(8,1),(8,7)],9)             => 3
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(4,7),(5,1),(6,8),(7,8)],9)             => 0
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(4,7),(5,8),(6,8),(7,8)],9)       => 1
([(0,2),(0,3),(0,4),(1,8),(2,6),(3,7),(4,6),(4,7),(5,1),(6,8),(7,5)],9)                   => 2
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,5),(3,6),(4,5),(4,6),(5,8),(6,7),(7,8)],9)             => 1
([(0,3),(0,4),(0,5),(2,8),(3,6),(4,7),(5,6),(5,7),(6,8),(7,2),(8,1)],9)                   => 3
([(0,2),(0,3),(0,4),(0,5),(2,8),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8),(8,1)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(4,7),(5,1),(5,7),(6,8),(7,8)],9)       => 0
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9) => 1
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(4,8),(5,1),(6,7),(8,7)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,6)],9)                   => 0
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,6),(6,7),(7,8)],9)             => 0
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,8),(3,6),(4,7),(5,7),(7,8),(8,1)],9)                   => 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,7),(7,8),(8,1),(8,2)],9)                   => 3
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,2)],9)                   => 0
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,2),(7,6)],9)                   => 0
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,8),(5,6),(6,8),(7,1),(7,6)],9)             => 0
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,7),(7,1),(7,8),(8,2)],9)                   => 2
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,2),(7,3)],9)                   => 0
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,2),(7,3),(7,6)],9)                   => 3
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,1),(7,2),(7,6)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,7),(7,8)],9)       => 0
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,7),(6,2),(6,8),(8,1)],9)             => 0
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,8),(5,8),(6,3),(6,8),(8,1),(8,2)],9)             => 1
([(0,2),(0,3),(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(6,5),(6,7),(7,8)],9)             => 0
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,8),(4,8),(5,1),(5,8),(6,7),(8,6)],9)             => 1
([(0,3),(0,4),(0,6),(1,7),(2,7),(3,8),(4,8),(5,1),(6,5),(6,8),(8,2)],9)                   => 2
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,8),(5,2),(5,8),(6,7),(8,1),(8,6)],9)             => 3
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(5,7),(6,1),(6,2),(7,8)],9)             => 1
([(0,2),(0,3),(0,5),(1,7),(2,8),(3,8),(4,1),(4,6),(5,4),(5,8),(6,7),(8,6)],9)             => 3
([(0,2),(0,3),(0,6),(1,7),(2,8),(3,8),(4,5),(5,1),(6,4),(6,8),(8,7)],9)                   => 2
([(0,3),(0,4),(0,6),(2,7),(3,8),(4,8),(5,1),(6,2),(6,8),(7,5),(8,7)],9)                   => 4
([(0,3),(0,4),(0,6),(1,7),(3,8),(4,8),(5,1),(6,5),(6,8),(7,2),(8,7)],9)                   => 3
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(7,6)],9)                   => 0
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(5,1),(5,7),(6,7),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,2),(5,8),(7,8),(8,1)],9)                   => 2
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(7,3)],9)                   => 1
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(7,3),(7,6)],9)                   => 3
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,2),(5,6),(6,8),(7,1),(7,6)],9)             => 1
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,7),(7,8)],9)       => 0
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,8),(5,8),(6,2),(6,3),(6,8),(8,1)],9)             => 1
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(6,7),(7,8)],9)             => 1
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,8),(5,1),(5,2),(5,8),(6,7),(8,6)],9)             => 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,8),(5,1),(5,2),(5,8),(6,7),(8,7)],9)             => 1
([(0,4),(0,5),(0,6),(2,8),(3,8),(4,7),(5,7),(6,2),(6,3),(6,7),(7,8),(8,1)],9)             => 2
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(7,8)],9)             => 1
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(7,6)],9)                   => 4
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(5,1),(5,2),(5,7),(6,7),(7,8)],9)             => 1
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(6,7),(7,8)],9)       => 1
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5),(7,8)],9)                   => 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5),(7,8)],9)                   => 2
([(0,6),(1,8),(2,7),(3,7),(4,3),(5,2),(6,1),(6,4),(6,5),(7,8)],9)                         => 2
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(7,8)],9)             => 0
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(6,1),(6,3),(6,5),(8,7)],9)                   => 2
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,3),(6,1),(6,4),(6,5),(8,7)],9)                   => 2
([(0,7),(1,8),(2,8),(3,8),(5,3),(6,2),(7,1),(7,5),(7,6),(8,4)],9)                         => 3
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,8),(6,1),(6,2),(6,3),(8,7)],9)             => 1
([(0,5),(0,7),(1,8),(2,8),(3,8),(5,8),(6,3),(7,1),(7,2),(7,6),(8,4)],9)                   => 2
([(0,7),(1,8),(2,8),(3,8),(4,8),(6,3),(6,4),(7,1),(7,2),(7,6),(8,5)],9)                   => 2
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(5,8),(6,8),(7,1),(7,2),(7,3),(8,4)],9)             => 1
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,7),(5,7),(6,1),(6,2),(7,8)],9)             => 0
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,8),(6,1),(6,2),(8,3)],9)                   => 1
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(8,7)],9)             => 1
([(0,4),(0,5),(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(8,6)],9)                   => 2
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(7,8)],9)                   => 1
([(0,3),(0,4),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(6,5),(8,6)],9)                         => 5
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,6),(4,1),(5,4),(5,8),(6,8),(8,7)],9)                   => 2
([(0,3),(0,4),(0,5),(2,8),(3,6),(4,6),(5,2),(5,7),(6,7),(7,8),(8,1)],9)                   => 3
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,6),(4,6),(5,1),(5,2),(6,8),(8,7)],9)                   => 2
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,3),(6,1),(6,5),(7,8)],9)                   => 1
([(0,5),(1,8),(2,8),(3,7),(4,7),(5,2),(5,6),(6,1),(6,3),(6,4),(7,8)],9)                   => 2
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,7),(6,1),(6,5),(7,8)],9)             => 0
([(0,3),(0,6),(1,8),(2,7),(3,7),(4,1),(5,2),(6,4),(6,5),(7,8)],9)                         => 2
([(0,4),(0,6),(2,8),(3,7),(4,7),(5,3),(6,2),(6,5),(7,8),(8,1)],9)                         => 3
([(0,3),(0,6),(1,8),(2,7),(3,8),(4,1),(5,2),(5,8),(6,4),(6,5),(8,7)],9)                   => 2
([(0,6),(1,8),(2,8),(3,7),(4,3),(4,8),(5,1),(5,2),(6,4),(6,5),(8,7)],9)                   => 3
([(0,6),(1,8),(2,7),(3,7),(4,3),(5,1),(5,2),(6,4),(6,5),(7,8)],9)                         => 3
([(0,6),(1,8),(2,8),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8),(8,3)],9)                   => 4
([(0,6),(1,8),(2,7),(3,7),(4,1),(5,2),(5,3),(6,4),(6,5),(7,8)],9)                         => 3
([(0,6),(1,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,5),(7,8),(8,2)],9)                         => 4
([(0,5),(1,7),(2,6),(3,6),(4,2),(4,3),(4,7),(5,1),(5,4),(6,8),(7,8)],9)                   => 3
([(0,6),(1,8),(2,8),(4,7),(5,1),(5,2),(5,7),(6,4),(6,5),(7,8),(8,3)],9)                   => 4
([(0,3),(0,5),(1,7),(2,6),(3,6),(4,2),(4,7),(5,1),(5,4),(6,8),(7,8)],9)                   => 2
([(0,4),(0,6),(1,8),(3,7),(4,8),(5,1),(5,7),(6,3),(6,5),(7,8),(8,2)],9)                   => 2
([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9)                         => 5
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,8),(5,2),(6,1),(6,5),(8,7)],9)                   => 1
([(0,4),(0,5),(0,6),(1,8),(2,7),(4,8),(5,8),(6,1),(6,2),(7,3),(8,7)],9)                   => 2
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(5,3),(6,1),(6,5),(8,7)],9)                   => 2
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,3),(5,6),(6,1),(6,2),(6,4),(8,7)],9)                   => 3
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,8),(5,2),(5,8),(6,1),(6,5),(8,7)],9)             => 1
([(0,4),(0,5),(0,7),(1,8),(2,8),(4,8),(5,8),(6,2),(7,1),(7,6),(8,3)],9)                   => 1
([(0,5),(0,7),(1,8),(2,8),(3,8),(5,8),(6,2),(6,3),(7,1),(7,6),(8,4)],9)                   => 2
([(0,6),(1,8),(2,8),(3,8),(4,8),(6,4),(6,7),(7,1),(7,2),(7,3),(8,5)],9)                   => 3
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(6,8),(7,8)],9)                   => 1
([(0,4),(0,5),(2,8),(3,8),(4,7),(5,7),(6,2),(6,3),(7,6),(8,1)],9)                         => 6
([(0,4),(0,5),(0,6),(1,8),(2,8),(4,7),(5,7),(6,1),(6,2),(7,8),(8,3)],9)                   => 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(2,8),(3,8),(4,8),(5,1),(5,2),(6,7),(8,7)],9)             => 2
([(0,5),(0,6),(1,7),(2,7),(4,8),(5,8),(6,1),(6,2),(7,4),(8,3)],9)                         => 3
([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)                         => 6
([(0,4),(0,5),(0,6),(2,7),(3,7),(4,8),(5,8),(6,2),(6,3),(7,8),(8,1)],9)                   => 2
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,8),(5,1),(6,2),(6,5),(8,7)],9)                   => 1
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,1),(5,2),(6,3),(6,5),(8,7)],9)                   => 2
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(8,7)],9)                   => 3
([(0,4),(0,7),(1,8),(2,8),(4,8),(5,2),(6,1),(7,5),(7,6),(8,3)],9)                         => 2
([(0,7),(1,8),(2,8),(3,8),(5,3),(6,1),(6,2),(7,5),(7,6),(8,4)],9)                         => 3
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,7),(5,7),(6,1),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,7),(6,1),(8,2)],9)                   => 1
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,8),(6,1),(8,2),(8,3)],9)                   => 3
([(0,2),(0,3),(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(6,5),(7,8)],9)                   => 0
([(0,2),(0,3),(0,4),(1,8),(2,7),(3,7),(4,8),(5,1),(6,5),(7,6)],9)                         => 1
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(6,8),(8,7)],9)                   => 1
([(0,3),(0,4),(0,6),(1,8),(3,7),(4,7),(5,2),(6,1),(7,8),(8,5)],9)                         => 3
([(0,3),(0,4),(0,6),(1,7),(2,7),(3,8),(4,8),(5,2),(6,5),(8,1)],9)                         => 1
([(0,3),(0,4),(1,7),(2,7),(3,8),(4,8),(5,6),(6,2),(8,1),(8,5)],9)                         => 4
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,8),(5,2),(6,7),(8,1),(8,6)],9)                   => 2
([(0,2),(0,3),(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,7),(6,5),(7,8)],9)             => 0
([(0,3),(0,4),(0,6),(1,7),(2,7),(3,8),(4,8),(5,1),(5,8),(6,5),(8,2)],9)                   => 2
([(0,2),(0,3),(0,6),(1,7),(2,8),(3,8),(4,1),(5,4),(5,8),(6,5),(8,7)],9)                   => 2
([(0,3),(0,4),(0,6),(1,7),(3,8),(4,8),(5,1),(5,8),(6,5),(7,2),(8,7)],9)                   => 3
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(7,8)],9)                   => 1
([(0,3),(0,4),(1,7),(2,7),(3,8),(4,8),(5,6),(6,1),(6,2),(8,5)],9)                         => 6
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,6),(4,1),(4,8),(5,4),(6,8),(8,7)],9)                   => 2
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(7,8)],9)                   => 1
([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4),(7,8)],9)                   => 2
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(6,7),(7,8)],9)             => 1
([(0,3),(0,4),(0,5),(1,8),(2,7),(3,8),(4,8),(5,6),(6,1),(6,2),(8,7)],9)                   => 1
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,8),(5,6),(6,1),(6,2),(6,3),(8,7)],9)                   => 2
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4),(8,7)],9)                   => 3
([(0,4),(0,5),(0,6),(1,8),(2,8),(4,8),(5,8),(6,7),(7,1),(7,2),(8,3)],9)                   => 1
([(0,5),(0,6),(1,8),(2,8),(3,8),(5,8),(6,7),(7,1),(7,2),(7,3),(8,4)],9)                   => 2
([(0,6),(1,8),(2,8),(3,8),(4,8),(6,7),(7,1),(7,2),(7,3),(7,4),(8,5)],9)                   => 4
([(0,2),(0,3),(0,6),(1,7),(2,8),(3,7),(4,5),(5,1),(6,4),(7,8)],9)                         => 1
([(0,3),(0,7),(2,8),(3,8),(4,2),(5,4),(6,1),(7,5),(8,6)],9)                               => 4
([(0,3),(0,5),(1,7),(2,7),(3,8),(4,6),(5,4),(6,1),(6,2),(7,8)],9)                         => 2
([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)                               => 7
([(0,2),(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(6,5),(8,7)],9)                   => 1
([(0,3),(0,4),(0,7),(2,8),(3,8),(4,8),(5,2),(6,1),(7,5),(8,6)],9)                         => 3
([(0,2),(0,3),(0,6),(1,8),(2,7),(3,7),(4,5),(5,1),(6,4),(7,8)],9)                         => 1
([(0,2),(0,3),(2,8),(3,8),(4,6),(5,4),(6,1),(7,5),(8,7)],9)                               => 7
([(0,3),(0,4),(0,6),(2,8),(3,7),(4,7),(5,2),(6,5),(7,8),(8,1)],9)                         => 2
([(0,3),(0,5),(1,8),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(7,8)],9)                         => 2
([(0,5),(1,8),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3),(7,8)],9)                         => 4
([(0,2),(0,3),(0,6),(1,7),(2,8),(3,8),(4,5),(5,1),(5,8),(6,4),(8,7)],9)                   => 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)             => 0
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)       => 0
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,8),(4,8),(5,7),(5,8),(7,1),(8,6)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(2,8),(3,8),(4,6),(5,6),(5,8),(6,7),(7,1),(8,7)],9)             => 2
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,6),(5,8),(6,7),(8,1)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,8),(4,8),(5,6),(6,7),(8,1)],9)                   => 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,8),(5,8),(6,7),(8,1),(8,2)],9)                   => 1
([(0,3),(0,4),(0,5),(2,7),(3,8),(4,8),(5,7),(6,1),(7,6),(8,2)],9)                         => 3
([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)                         => 6
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(5,7),(6,8),(8,7)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(2,8),(3,8),(4,7),(5,7),(6,1),(7,8),(8,6)],9)                   => 2
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,6),(6,7),(8,1)],9)                   => 0
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,8),(5,6),(6,7),(8,1),(8,2)],9)                   => 1
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,8),(6,7),(8,1),(8,2),(8,3)],9)                   => 3
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,8),(5,8),(7,1),(7,8),(8,6)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8),(8,1)],9)                   => 1
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(7,8)],9)                   => 0
([(0,3),(0,4),(0,6),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(8,5)],9)                         => 1
([(0,3),(0,4),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(8,5),(8,6)],9)                         => 4
([(0,2),(0,3),(0,4),(1,7),(2,6),(3,6),(4,8),(5,1),(6,5),(6,8),(8,7)],9)                   => 2
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,1),(6,8),(8,7)],9)                   => 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)             => 2
([(0,2),(0,3),(0,4),(2,8),(3,7),(4,7),(5,1),(6,5),(7,8),(8,6)],9)                         => 4
([(0,2),(0,3),(0,4),(0,5),(2,7),(3,8),(4,6),(5,6),(6,7),(7,8),(8,1)],9)                   => 2
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,7),(7,8)],9)             => 0
([(0,3),(0,4),(0,6),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(6,8),(8,5)],9)                   => 2
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,1),(5,8),(6,7),(8,6)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,8),(3,8),(4,6),(5,1),(5,8),(6,7),(8,7)],9)             => 0
([(0,4),(0,5),(0,6),(1,7),(2,7),(4,8),(5,8),(6,1),(6,8),(7,3),(8,2)],9)                   => 3
([(0,3),(0,4),(0,5),(0,6),(2,8),(3,8),(4,7),(5,7),(6,2),(6,7),(7,8),(8,1)],9)             => 1
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,2),(5,8),(6,1),(6,8),(8,7)],9)       => 1
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(4,7),(5,1),(5,6),(6,8),(7,8)],9)       => 1
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,1),(6,2),(6,8),(8,7)],9)             => 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,8),(3,8),(4,6),(4,8),(5,1),(6,7),(8,7)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(6,8),(7,8)],9)             => 0
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,7),(4,6),(4,7),(5,8),(6,8),(7,8)],9)       => 0
([(0,2),(0,3),(0,4),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(6,5),(7,8)],9)                   => 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)             => 1
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2)],9)                   => 2
([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)                   => 5
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,6),(4,6),(5,1),(5,8),(6,8),(8,7)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,1),(5,6),(5,7),(6,8),(7,8)],9)       => 0
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,1),(5,6),(6,7),(8,7)],9)             => 1
([(0,4),(0,5),(0,6),(1,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,3),(8,2)],9)                   => 1
([(0,5),(0,6),(1,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,3),(7,4),(8,2)],9)                   => 3
([(0,3),(0,4),(0,5),(0,6),(1,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,8),(8,2)],9)             => 1
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,6),(5,1),(5,8),(6,7),(8,2)],9)                   => 1
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,1),(5,8),(6,7),(8,2),(8,3)],9)                   => 3
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,1),(5,6),(6,8),(8,7)],9)             => 1
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,1),(6,2),(8,7)],9)                   => 1
([(0,3),(0,4),(0,7),(2,8),(3,8),(4,8),(5,1),(6,5),(7,2),(8,6)],9)                         => 4
([(0,3),(0,4),(0,5),(0,6),(1,8),(3,8),(4,8),(5,7),(6,1),(7,2),(8,7)],9)                   => 2
([(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(4,8),(5,8),(6,2),(7,1),(8,3)],9)                   => 2
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(6,8),(7,8)],9)                   => 0
([(0,3),(0,4),(0,5),(2,8),(3,8),(4,7),(5,7),(6,2),(7,6),(8,1)],9)                         => 2
([(0,4),(0,5),(0,6),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3)],9)                         => 2
([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)                         => 5
([(0,3),(0,4),(0,5),(2,8),(3,6),(4,7),(5,7),(6,8),(7,2),(7,6),(8,1)],9)                   => 3
([(0,3),(0,4),(0,5),(0,6),(1,8),(3,8),(4,7),(5,7),(6,1),(7,8),(8,2)],9)                   => 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(1,8),(2,8),(3,8),(4,6),(5,1),(6,7),(8,7)],9)             => 1
([(0,4),(0,5),(0,6),(1,8),(3,7),(4,7),(5,8),(6,1),(7,2),(8,3)],9)                         => 2
([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)                         => 5
([(0,3),(0,4),(0,5),(0,6),(2,7),(3,8),(4,8),(5,7),(6,2),(7,8),(8,1)],9)                   => 1
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,2),(7,1)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,8)],9)       => 0
([(0,2),(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(6,5),(6,7),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(5,7),(6,1),(6,2),(7,8)],9)             => 0
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(5,7),(6,1),(6,2),(6,3),(7,8)],9)             => 2
([(0,3),(0,4),(1,8),(2,8),(3,6),(4,5),(4,6),(5,1),(5,2),(5,7),(6,7),(7,8)],9)             => 3
([(0,2),(0,3),(0,5),(1,8),(2,8),(3,6),(4,1),(4,7),(5,4),(5,6),(6,7),(7,8)],9)             => 0
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(4,8),(5,4),(5,7),(7,8),(8,1)],9)                   => 4
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(5,7),(6,1),(6,2),(7,3)],9)                   => 2
([(0,3),(0,5),(1,8),(2,8),(3,7),(4,2),(4,6),(5,4),(5,7),(6,8),(7,1),(7,6)],9)             => 3
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,1),(5,6),(6,7),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2)],9)                   => 1
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)                   => 5
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(6,5),(6,7),(7,2)],9)                   => 0
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,8),(5,2),(5,7),(6,8),(7,1),(7,6)],9)             => 0
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(6,5),(6,7),(7,2),(7,3)],9)                   => 2
([(0,4),(0,5),(1,8),(2,8),(3,6),(4,7),(5,3),(5,7),(6,8),(7,1),(7,2),(7,6)],9)             => 3
([(0,2),(0,3),(0,6),(1,8),(2,8),(3,7),(4,5),(5,1),(6,4),(6,7),(7,8)],9)                   => 0
([(0,2),(0,3),(0,5),(1,8),(2,6),(3,7),(4,1),(5,4),(5,6),(6,8),(8,7)],9)                   => 1
([(0,3),(0,6),(2,8),(3,7),(4,2),(5,1),(6,4),(6,7),(7,8),(8,5)],9)                         => 5
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,5),(5,2),(6,4),(6,8),(8,1)],9)                         => 3
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,2),(7,8),(8,3)],9)                   => 4
([(0,3),(0,5),(1,7),(2,6),(3,8),(4,2),(5,4),(5,8),(6,7),(8,1),(8,6)],9)                   => 4
([(0,3),(0,5),(1,8),(2,8),(3,7),(4,6),(5,4),(5,7),(6,1),(6,2),(7,8)],9)                   => 2
([(0,2),(0,5),(1,7),(2,6),(3,4),(4,1),(4,8),(5,3),(5,6),(6,8),(8,7)],9)                   => 4
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,2)],9)             => 0
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,2),(7,3)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,7),(7,2),(7,3),(7,4)],9)             => 2
([(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,3),(7,1),(7,2)],9)             => 0
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,7),(7,8)],9)       => 0
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,5),(6,7),(7,8)],9)             => 0
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,3),(6,1),(6,5),(6,7),(7,8)],9)             => 1
([(0,3),(0,5),(1,8),(2,8),(3,6),(4,2),(4,7),(5,1),(5,4),(5,6),(6,7),(7,8)],9)             => 1
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,1),(5,2),(5,6),(6,7),(7,8)],9)             => 0
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,3),(5,7),(7,8),(8,2)],9)                   => 2
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,5),(6,7),(7,3)],9)                   => 2
([(0,4),(0,5),(1,8),(2,8),(3,6),(4,7),(5,2),(5,3),(5,7),(6,8),(7,1),(7,6)],9)             => 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,1),(5,2),(5,7),(6,8),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,7),(5,1),(5,2),(5,6),(6,8),(8,7)],9)             => 1
([(0,4),(0,6),(2,8),(3,8),(4,7),(5,1),(6,2),(6,3),(6,7),(7,8),(8,5)],9)                   => 4
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,2),(5,3),(5,8),(6,7),(8,1)],9)                   => 2
([(0,4),(0,5),(1,8),(2,8),(3,6),(4,7),(5,1),(5,2),(5,7),(7,3),(7,8),(8,6)],9)             => 3
([(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,2),(5,3),(5,6),(6,7),(8,1)],9)                   => 2
([(0,4),(0,5),(2,6),(3,6),(4,7),(5,2),(5,3),(5,7),(6,8),(7,8),(8,1)],9)                   => 3
([(0,3),(0,6),(1,8),(2,8),(3,7),(4,2),(5,1),(6,4),(6,5),(6,7),(7,8)],9)                   => 2
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,4),(5,6),(6,8),(7,8)],9)             => 1
([(0,3),(0,4),(1,5),(2,5),(2,7),(3,6),(4,1),(4,2),(4,6),(5,8),(6,7),(7,8)],9)             => 3
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,8),(5,1),(5,4),(5,6),(6,8),(8,7)],9)             => 3
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(5,1),(5,4),(5,6),(6,8),(8,7)],9)                   => 2
([(0,3),(0,4),(1,7),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6),(5,7),(6,8),(7,8)],9)             => 3
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,7),(7,3)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,7),(7,3),(7,4)],9)             => 1
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,4),(7,1),(7,2),(7,3)],9)             => 0
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(6,7),(7,8)],9)       => 0
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,5),(6,7),(7,8)],9)             => 2
([(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7),(7,8)],9)             => 1
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,2),(5,3),(5,7),(6,8),(7,8)],9)             => 1
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,1),(5,2),(5,3),(5,6),(6,8),(8,7)],9)             => 2
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,1),(5,2),(5,3),(5,6),(6,7),(8,7)],9)             => 2
([(0,5),(0,6),(1,8),(2,8),(3,8),(5,7),(6,1),(6,2),(6,3),(6,7),(7,8),(8,4)],9)             => 3
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(6,7),(7,4)],9)             => 2
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,5),(7,1),(7,2),(7,3),(7,4)],9)             => 1
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(6,4),(6,7),(7,8)],9)       => 2
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,4),(7,1),(7,2),(7,3),(7,5)],9)                   => 2
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(7,8)],9)             => 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5),(7,8)],9)                   => 1
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(7,8)],9)             => 1
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,4),(6,5),(8,7)],9)                   => 2
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,8),(6,1),(6,2),(6,3),(6,4),(8,7)],9)             => 2
([(0,7),(1,8),(2,8),(3,8),(4,8),(6,4),(7,1),(7,2),(7,3),(7,6),(8,5)],9)                   => 3
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(6,8),(7,1),(7,2),(7,3),(7,4),(8,5)],9)             => 2
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(6,1),(6,2),(6,3),(6,7),(7,8)],9)             => 2
([(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,3),(7,1),(7,2),(7,5)],9)                   => 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,3),(6,4),(7,1),(7,2),(7,5)],9)                   => 1
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,7),(6,1),(6,2),(6,3),(7,8)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,7),(6,1),(6,2),(6,3),(7,4)],9)                   => 1
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,3),(6,1),(6,2),(6,5),(7,8)],9)                   => 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,4),(6,5),(8,3)],9)                         => 2
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,7),(6,1),(6,2),(6,3),(7,8)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,8),(6,1),(6,2),(6,3),(8,4)],9)                   => 2
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,5),(8,7)],9)                   => 2
([(0,7),(2,8),(3,8),(4,8),(5,4),(6,1),(7,2),(7,3),(7,5),(8,6)],9)                         => 4
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,1),(6,2),(6,3),(8,7)],9)             => 1
([(0,5),(0,7),(2,8),(3,8),(4,8),(5,8),(6,1),(7,2),(7,3),(7,4),(8,6)],9)                   => 3
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,3),(6,1),(6,2),(6,5),(8,7)],9)                   => 2
([(0,5),(0,6),(1,8),(2,8),(3,7),(5,8),(6,1),(6,2),(6,3),(7,4),(8,7)],9)                   => 3
([(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5),(8,7)],9)                   => 2
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,8),(5,3),(5,8),(6,1),(6,2),(6,5),(8,7)],9)             => 2
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,3),(6,5),(7,8)],9)                   => 1
([(0,4),(0,5),(1,6),(2,7),(3,8),(4,6),(5,1),(5,2),(5,3),(6,8),(8,7)],9)                   => 2
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,4),(6,1),(6,3),(6,5),(7,8)],9)                   => 1
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,7),(6,1),(6,3),(6,5),(7,8)],9)             => 1
([(0,6),(1,8),(2,7),(3,7),(4,3),(5,1),(6,2),(6,4),(6,5),(7,8)],9)                         => 2
([(0,6),(2,8),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5),(7,8),(8,1)],9)                         => 3
([(0,6),(1,8),(2,8),(3,7),(4,2),(5,3),(5,8),(6,1),(6,4),(6,5),(8,7)],9)                   => 3
([(0,5),(1,6),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(6,8),(7,8)],9)                   => 2
([(0,6),(1,8),(2,8),(4,7),(5,2),(5,7),(6,1),(6,4),(6,5),(7,8),(8,3)],9)                   => 2
([(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(5,3),(6,8),(7,8)],9)                   => 1
([(0,4),(0,5),(1,8),(2,8),(3,6),(3,8),(4,6),(5,1),(5,2),(5,3),(6,7),(8,7)],9)             => 2
([(0,5),(0,6),(1,8),(2,8),(4,7),(5,7),(6,1),(6,2),(6,4),(7,8),(8,3)],9)                   => 2
([(0,4),(0,5),(1,8),(2,6),(3,6),(3,8),(4,8),(5,1),(5,2),(5,3),(6,7),(8,7)],9)             => 2
([(0,6),(1,7),(2,7),(3,8),(5,8),(6,1),(6,2),(6,3),(7,5),(8,4)],9)                         => 3
([(0,5),(0,6),(1,8),(3,7),(4,7),(5,8),(6,1),(6,3),(6,4),(7,8),(8,2)],9)                   => 2
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,1),(7,2),(7,3),(7,5)],9)                   => 1
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,3),(6,5),(7,1),(7,2),(7,6)],9)                   => 1
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(6,5),(7,8)],9)             => 1
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(7,8)],9)                   => 1
([(0,6),(1,8),(2,7),(3,7),(4,5),(5,3),(6,1),(6,2),(6,4),(7,8)],9)                         => 2
([(0,7),(1,8),(2,8),(3,8),(4,2),(5,6),(6,3),(7,1),(7,4),(7,5)],9)                         => 2
([(0,6),(1,8),(2,8),(3,7),(4,3),(5,1),(5,7),(6,2),(6,4),(6,5),(7,8)],9)                   => 1
([(0,6),(1,8),(2,8),(3,7),(4,2),(5,4),(5,7),(6,1),(6,3),(6,5),(7,8)],9)                   => 1
([(0,5),(1,6),(2,7),(3,8),(4,3),(4,6),(5,1),(5,2),(5,4),(6,8),(8,7)],9)                   => 2
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,3),(6,4),(7,8)],9)                   => 1
([(0,4),(0,5),(1,8),(2,6),(3,6),(3,7),(4,7),(5,1),(5,2),(5,3),(6,8),(7,8)],9)             => 1
([(0,5),(1,6),(2,7),(3,6),(3,7),(4,2),(5,1),(5,3),(5,4),(6,8),(7,8)],9)                   => 3
([(0,4),(0,5),(1,6),(2,6),(3,7),(4,3),(5,1),(5,2),(5,7),(6,8),(7,8)],9)                   => 2
([(0,5),(0,6),(1,8),(2,8),(4,7),(5,4),(6,1),(6,2),(6,7),(7,8),(8,3)],9)                   => 3
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,4),(8,7)],9)                   => 2
([(0,7),(1,8),(2,8),(3,8),(5,6),(6,3),(7,1),(7,2),(7,5),(8,4)],9)                         => 3
([(0,6),(1,8),(2,7),(3,7),(4,5),(5,1),(6,2),(6,3),(6,4),(7,8)],9)                         => 2
([(0,6),(1,8),(2,8),(3,7),(4,3),(5,4),(5,8),(6,1),(6,2),(6,5),(8,7)],9)                   => 3
([(0,6),(1,8),(2,8),(3,7),(5,3),(5,8),(6,1),(6,2),(6,5),(7,4),(8,7)],9)                   => 4
([(0,6),(2,8),(3,7),(4,7),(5,2),(6,3),(6,4),(6,5),(7,8),(8,1)],9)                         => 3
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(6,1),(6,2),(6,3),(8,7)],9)                   => 2
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(6,4),(7,1),(7,2),(7,3),(8,5)],9)                   => 2
([(0,7),(2,8),(3,8),(4,8),(5,1),(6,5),(7,2),(7,3),(7,4),(8,6)],9)                         => 5
([(0,5),(0,6),(1,8),(2,8),(3,8),(5,7),(6,1),(6,2),(6,3),(7,4),(8,7)],9)                   => 3
([(0,6),(1,7),(2,8),(3,8),(4,7),(5,4),(6,1),(6,2),(6,3),(8,5)],9)                         => 2
([(0,4),(0,5),(1,6),(2,6),(3,7),(4,8),(5,1),(5,2),(5,3),(6,8),(8,7)],9)                   => 2
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,3),(6,1),(6,2),(6,7),(7,8)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,3),(6,1),(6,2),(6,7),(7,4)],9)                   => 2
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(5,3),(6,1),(6,4),(6,7),(7,8)],9)                   => 2
([(0,4),(0,5),(1,6),(2,7),(3,8),(4,1),(5,2),(5,3),(5,6),(6,8),(8,7)],9)                   => 2
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,5),(7,1),(7,2),(7,3)],9)                   => 1
([(0,7),(1,8),(2,8),(3,8),(4,6),(5,3),(6,5),(7,1),(7,2),(7,4)],9)                         => 2
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,3),(4,7),(5,4),(6,1),(6,2),(6,7),(7,8)],9)             => 1
([(0,3),(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,2),(7,1),(7,5)],9)                   => 0
([(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,2),(6,3),(7,1),(7,5)],9)                   => 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,4),(6,5),(7,1),(7,2),(7,3)],9)                   => 2
([(0,3),(0,7),(1,8),(2,8),(3,8),(4,1),(5,6),(6,2),(7,4),(7,5)],9)                         => 1
([(0,3),(0,6),(1,8),(2,7),(3,8),(4,1),(5,4),(5,7),(6,2),(6,5),(7,8)],9)                   => 1
([(0,6),(1,8),(2,8),(3,7),(4,5),(4,7),(5,1),(5,2),(6,3),(6,4),(7,8)],9)                   => 3
([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)                   => 5
([(0,3),(0,5),(1,6),(2,8),(3,7),(4,2),(4,6),(5,1),(5,4),(6,8),(8,7)],9)                   => 2
([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)                         => 6
([(0,6),(1,8),(2,7),(3,7),(4,5),(4,8),(5,3),(6,1),(6,4),(8,2)],9)                         => 4
([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)                   => 5
([(0,3),(0,6),(1,8),(2,7),(3,8),(4,5),(5,1),(5,7),(6,2),(6,4),(7,8)],9)                   => 1
([(0,6),(1,8),(2,7),(3,7),(4,5),(5,3),(5,8),(6,1),(6,4),(8,2)],9)                         => 4
([(0,7),(1,8),(2,8),(3,8),(4,3),(5,6),(6,1),(6,2),(7,4),(7,5)],9)                         => 2
([(0,6),(1,8),(2,8),(3,7),(4,5),(5,1),(5,2),(5,7),(6,3),(6,4),(7,8)],9)                   => 3
([(0,6),(1,8),(2,8),(3,4),(4,1),(4,7),(5,2),(5,7),(6,3),(6,5),(7,8)],9)                   => 3
([(0,3),(0,6),(1,8),(2,7),(3,8),(4,2),(5,1),(5,7),(6,4),(6,5),(7,8)],9)                   => 1
([(0,6),(1,8),(2,7),(3,7),(4,1),(5,3),(5,8),(6,4),(6,5),(8,2)],9)                         => 4
([(0,7),(1,8),(2,8),(3,8),(4,5),(5,3),(6,1),(6,2),(7,4),(7,6)],9)                         => 2
([(0,6),(1,8),(2,8),(3,7),(4,3),(5,1),(5,2),(5,7),(6,4),(6,5),(7,8)],9)                   => 3
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,7),(6,1),(6,2),(7,8)],9)             => 0
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,7),(6,1),(6,2),(7,3)],9)                   => 0
([(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,7),(6,1),(6,2),(7,3),(7,4)],9)                   => 1
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,7),(6,1),(6,2),(7,8)],9)             => 0
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,7),(6,1),(6,2),(8,3)],9)                   => 1
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,8),(6,1),(6,2),(8,3),(8,4)],9)                   => 3
([(0,4),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(6,1),(7,2),(7,5)],9)                   => 0
([(0,4),(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(6,2),(6,5),(7,1),(7,6)],9)                   => 1
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,7),(6,1),(6,5),(7,8)],9)             => 0
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,7),(6,1),(6,5),(7,3)],9)                   => 1
([(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,2),(6,3),(7,1),(7,6)],9)                   => 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,4),(6,3),(6,7),(7,1),(7,2),(7,5)],9)                   => 2
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,3),(5,7),(6,1),(6,5),(7,8)],9)             => 1
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,8),(4,1),(5,2),(6,4),(6,7),(7,8)],9)                   => 0
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,3),(5,6),(5,7),(6,1),(6,2),(7,8)],9)                   => 2
([(0,4),(0,5),(1,6),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(6,8),(8,7)],9)                   => 4
([(0,3),(0,4),(0,5),(1,6),(2,8),(3,7),(4,1),(5,2),(5,6),(6,8),(8,7)],9)                   => 1
([(0,5),(0,6),(1,8),(3,7),(4,2),(5,3),(6,1),(6,7),(7,8),(8,4)],9)                         => 5
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,2),(5,1),(6,4),(6,8),(8,3)],9)                         => 3
([(0,4),(0,5),(1,7),(2,8),(3,6),(4,2),(5,3),(5,8),(6,7),(8,1),(8,6)],9)                   => 4
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,3),(6,1),(6,2),(7,8)],9)                   => 0
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,5),(5,2),(6,1),(6,4),(7,8)],9)                         => 2
([(0,7),(2,8),(3,8),(4,5),(5,3),(6,1),(7,2),(7,4),(8,6)],9)                               => 5
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,1),(5,2),(6,3),(6,4),(7,8)],9)                         => 2
([(0,6),(1,8),(2,7),(3,7),(4,3),(5,1),(5,4),(6,2),(6,5),(7,8)],9)                         => 3
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,3),(4,8),(5,1),(6,2),(6,4),(8,7)],9)                   => 2
([(0,5),(0,6),(2,8),(3,7),(4,7),(5,4),(6,2),(6,3),(7,8),(8,1)],9)                         => 3
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,4),(8,3)],9)                         => 2
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,2),(5,3),(6,4),(7,1),(7,5)],9)                         => 1
([(0,7),(1,8),(2,8),(3,8),(4,5),(5,3),(6,2),(6,4),(7,1),(7,6)],9)                         => 2
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,3),(6,1),(6,4),(7,8)],9)                   => 1
([(0,5),(1,8),(2,8),(3,8),(4,3),(5,6),(6,2),(6,7),(7,1),(7,4)],9)                         => 3
([(0,5),(0,6),(1,8),(2,8),(3,1),(4,2),(4,7),(5,4),(6,3),(6,7),(7,8)],9)                   => 2
([(0,4),(0,5),(1,8),(2,7),(3,2),(3,6),(4,3),(5,1),(5,6),(6,8),(8,7)],9)                   => 3
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,4),(6,1),(6,3),(7,8)],9)                   => 1
([(0,6),(1,8),(2,7),(3,5),(4,3),(5,1),(5,7),(6,2),(6,4),(7,8)],9)                         => 4
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,7),(5,1),(6,2),(6,5),(7,8)],9)                   => 0
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(5,3),(6,2),(6,5),(7,8)],9)                   => 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,4),(6,1),(6,5),(8,3)],9)                         => 3
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,7),(5,1),(5,7),(6,2),(6,5),(7,8)],9)             => 0
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,2),(5,8),(6,1),(6,5),(8,3)],9)                   => 2
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(6,3),(6,5),(7,8)],9)                   => 2
([(0,5),(1,8),(2,8),(3,7),(4,7),(5,4),(5,6),(6,1),(6,2),(6,3),(7,8)],9)                   => 2
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(5,7),(6,3),(6,5),(7,8)],9)             => 1
([(0,3),(0,5),(1,6),(2,7),(3,6),(4,2),(4,8),(5,1),(5,4),(6,8),(8,7)],9)                   => 3
([(0,3),(0,4),(0,5),(1,6),(2,8),(3,6),(4,7),(5,1),(5,2),(6,8),(8,7)],9)                   => 1
([(0,4),(0,6),(1,8),(3,7),(4,7),(5,2),(6,1),(6,3),(7,8),(8,5)],9)                         => 4
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,3),(6,1),(6,5),(8,2)],9)                         => 2
([(0,4),(0,5),(1,7),(2,8),(3,6),(4,8),(5,2),(5,3),(6,7),(8,1),(8,6)],9)                   => 3
([(0,3),(0,4),(0,5),(1,6),(2,6),(2,7),(3,8),(4,7),(5,1),(5,2),(6,8),(7,8)],9)             => 0
([(0,4),(0,5),(1,7),(2,6),(3,6),(3,8),(4,8),(5,2),(5,3),(6,7),(8,1)],9)                   => 3
([(0,4),(0,5),(2,6),(3,6),(3,7),(4,7),(5,2),(5,3),(6,8),(7,8),(8,1)],9)                   => 4
([(0,4),(0,5),(1,7),(2,8),(3,6),(3,8),(4,6),(5,2),(5,3),(6,7),(8,1)],9)                   => 3
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,5),(8,7)],9)                   => 1
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,3),(6,1),(6,5),(8,7)],9)                   => 2
([(0,7),(2,8),(3,8),(4,8),(5,1),(6,3),(6,4),(7,2),(7,6),(8,5)],9)                         => 4
([(0,4),(0,7),(2,8),(3,8),(4,8),(5,3),(6,1),(7,2),(7,5),(8,6)],9)                         => 3
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(6,2),(6,3),(7,8)],9)                   => 1
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(8,7)],9)                   => 1
([(0,6),(0,7),(2,8),(3,8),(4,8),(5,1),(6,2),(7,3),(7,4),(8,5)],9)                         => 3
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,8)],9)                         => 2
([(0,4),(1,8),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5),(7,8)],9)                         => 4
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,3),(4,8),(5,4),(6,1),(6,2),(8,7)],9)                   => 2
([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)                               => 7
([(0,5),(0,6),(2,8),(3,7),(4,7),(5,2),(6,3),(6,4),(7,8),(8,1)],9)                         => 3
([(0,4),(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(6,1),(6,2),(8,5)],9)                         => 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,8),(5,1),(5,2),(6,8),(8,7)],9)                   => 1
([(0,4),(0,6),(2,7),(3,7),(4,8),(5,1),(6,2),(6,3),(7,8),(8,5)],9)                         => 4
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3)],9)                         => 2
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)                         => 5
([(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,2),(5,3),(6,7),(8,1),(8,6)],9)                   => 3
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,3),(5,2),(6,1),(7,4),(7,5)],9)                         => 1
([(0,7),(1,8),(2,8),(3,8),(4,2),(5,3),(6,1),(6,5),(7,4),(7,6)],9)                         => 2
([(0,6),(1,8),(2,8),(3,7),(4,2),(5,1),(5,4),(5,7),(6,3),(6,5),(7,8)],9)                   => 3
([(0,5),(1,6),(2,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(8,7)],9)                   => 3
([(0,6),(1,8),(2,8),(3,2),(4,3),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8)],9)                   => 3
([(0,5),(1,7),(2,8),(3,1),(3,6),(4,2),(4,6),(5,3),(5,4),(6,8),(8,7)],9)                   => 4
([(0,3),(0,6),(1,8),(2,8),(3,7),(4,2),(5,1),(5,7),(6,4),(6,5),(7,8)],9)                   => 1
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,6),(5,1),(5,4),(6,8),(8,7)],9)                   => 2
([(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,1),(5,3),(6,4),(6,5),(7,8)],9)                   => 2
([(0,3),(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8)],9)             => 1
([(0,3),(0,5),(1,8),(2,6),(2,7),(3,6),(4,1),(4,7),(5,2),(5,4),(6,8),(7,8)],9)             => 2
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8)],9)                   => 1
([(0,3),(0,5),(1,8),(2,6),(3,7),(4,1),(4,6),(4,7),(5,2),(5,4),(6,8),(7,8)],9)             => 2
([(0,4),(0,5),(1,6),(2,7),(3,6),(3,7),(4,2),(5,1),(5,3),(6,8),(7,8)],9)                   => 3
([(0,6),(1,7),(2,8),(3,7),(4,3),(4,8),(5,1),(6,2),(6,4),(8,5)],9)                         => 4
([(0,3),(0,5),(1,6),(2,7),(3,8),(4,2),(4,6),(5,1),(5,4),(6,8),(8,7)],9)                   => 2
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,7),(5,2),(6,1),(6,5),(7,8)],9)                   => 0
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,2),(5,3),(6,1),(6,5),(7,8)],9)                   => 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(6,3),(6,5),(8,4)],9)                         => 3
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(6,3),(6,5),(8,2)],9)                         => 2
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,2),(5,1),(6,4),(6,5),(7,8)],9)                         => 2
([(0,7),(2,8),(3,8),(4,3),(5,2),(6,1),(7,4),(7,5),(8,6)],9)                               => 5
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,8)],9)       => 0
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,3)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,3),(7,4)],9)             => 2
([(0,3),(0,5),(0,6),(1,8),(2,8),(3,8),(4,1),(5,2),(5,7),(6,4),(6,7),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,1),(4,6),(5,2),(5,6),(6,7),(7,8)],9)             => 0
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,3),(4,7),(5,1),(5,7),(7,8),(8,2)],9)                   => 3
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,1),(5,2),(5,7),(6,4),(6,7),(7,3)],9)                   => 2
([(0,4),(0,5),(1,8),(2,8),(3,6),(4,2),(4,7),(5,3),(5,7),(6,8),(7,1),(7,6)],9)             => 2
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,3),(4,7),(5,6),(5,7),(6,1),(6,2),(7,8)],9)             => 1
([(0,4),(0,5),(1,8),(2,8),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7),(7,8)],9)             => 2
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,2),(4,6),(5,1),(5,6),(6,8),(8,7)],9)             => 1
([(0,5),(0,6),(2,8),(3,8),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8),(8,4)],9)                   => 4
([(0,4),(0,5),(1,8),(2,8),(3,6),(4,2),(4,7),(5,1),(5,7),(7,3),(7,8),(8,6)],9)             => 3
([(0,5),(0,6),(1,8),(2,8),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7),(7,8)],9)                   => 2
([(0,4),(0,5),(1,8),(2,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)                   => 3
([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)             => 4
([(0,4),(0,5),(1,8),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)             => 3
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,3),(6,4),(7,1),(7,2)],9)             => 0
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,3),(5,7),(6,1),(6,2),(6,7),(7,8)],9)       => 0
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,3),(5,1),(5,7),(6,2),(6,4),(6,7),(7,8)],9)             => 1
([(0,4),(0,5),(1,7),(2,8),(3,8),(4,3),(4,6),(5,1),(5,2),(5,6),(6,7),(7,8)],9)             => 1
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,1),(4,7),(5,2),(5,3),(5,7),(6,8),(7,8)],9)             => 2
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,3),(4,6),(5,1),(5,2),(5,6),(6,8),(8,7)],9)             => 2
([(0,5),(0,6),(1,8),(2,8),(3,8),(5,3),(5,7),(6,1),(6,2),(6,7),(7,8),(8,4)],9)             => 2
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,2),(4,6),(5,1),(5,3),(5,6),(6,8),(8,7)],9)             => 2
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,3),(5,7),(6,1),(6,2),(6,7),(7,4)],9)             => 1
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,3),(5,4),(5,7),(6,1),(6,2),(6,7),(7,8)],9)             => 1
([(0,4),(0,5),(1,7),(2,8),(3,8),(4,1),(4,6),(5,2),(5,3),(5,6),(6,7),(7,8)],9)             => 2
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,4),(6,5),(7,1),(7,2),(7,3)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,4),(5,7),(6,1),(6,2),(6,3),(6,7),(7,8)],9)       => 1
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(6,4),(7,8)],9)             => 1
([(0,6),(1,8),(2,8),(3,7),(4,5),(5,1),(5,7),(6,2),(6,3),(6,4),(7,8)],9)                   => 1
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,7),(6,1),(6,3),(6,4),(7,8)],9)             => 1
([(0,6),(1,8),(2,8),(3,7),(4,5),(5,3),(5,8),(6,1),(6,2),(6,4),(8,7)],9)                   => 3
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,4),(5,8),(6,1),(6,2),(6,3),(8,7)],9)             => 2
([(0,5),(1,7),(2,6),(3,6),(3,7),(4,3),(5,1),(5,2),(5,4),(6,8),(7,8)],9)                   => 3
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,3),(5,4),(5,7),(6,1),(6,2),(6,7),(7,8)],9)       => 0
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,4),(6,1),(6,2),(6,7),(7,8)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,7),(7,8)],9)             => 1
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(5,7),(6,1),(6,3),(7,8)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,2),(5,7),(6,1),(6,3),(7,4)],9)                   => 1
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(5,7),(6,2),(6,3),(7,8)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,8),(6,1),(6,2),(8,4)],9)                   => 2
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,3),(5,4),(5,8),(6,1),(6,2),(8,7)],9)                   => 2
([(0,5),(0,6),(1,8),(2,8),(3,7),(5,3),(5,8),(6,1),(6,2),(7,4),(8,7)],9)                   => 3
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(5,1),(5,7),(6,3),(6,4),(7,8)],9)                   => 1
([(0,4),(0,5),(1,6),(2,8),(3,7),(4,3),(4,6),(5,1),(5,2),(6,8),(8,7)],9)                   => 2
([(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,1),(5,4),(6,3),(6,5),(7,8)],9)                   => 2
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,1),(5,7),(6,3),(6,4),(7,8)],9)             => 1
([(0,5),(0,6),(1,8),(2,8),(4,7),(5,2),(5,7),(6,1),(6,4),(7,8),(8,3)],9)                   => 2
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(5,4),(5,7),(6,1),(6,3),(7,8)],9)                   => 1
([(0,4),(0,5),(1,6),(2,7),(3,8),(4,3),(4,6),(5,1),(5,2),(6,8),(8,7)],9)                   => 2
([(0,6),(1,8),(2,7),(3,5),(4,1),(5,4),(5,7),(6,2),(6,3),(7,8)],9)                         => 4
([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9)                         => 5
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,2),(6,3),(7,1),(7,5)],9)                   => 0
([(0,7),(1,8),(2,8),(3,8),(4,8),(5,2),(5,6),(6,3),(6,4),(7,1),(7,5)],9)                   => 2
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,3),(4,7),(5,1),(5,7),(6,2),(6,4),(7,8)],9)             => 1
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,3),(6,1),(6,4),(7,8)],9)                   => 0
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,1),(5,2),(6,3),(6,4),(7,8)],9)                   => 1
([(0,4),(0,5),(1,8),(2,6),(3,6),(3,7),(4,1),(4,7),(5,2),(5,3),(6,8),(7,8)],9)             => 2
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(5,2),(6,3),(6,4),(8,7)],9)                   => 1
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(6,3),(6,4),(7,1),(7,2),(8,5)],9)                   => 1
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(8,5)],9)                         => 6
([(0,4),(0,5),(1,6),(2,6),(3,7),(4,3),(4,8),(5,1),(5,2),(6,8),(8,7)],9)                   => 3
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,2),(6,1),(6,7),(7,8)],9)             => 0
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,2),(6,1),(6,7),(7,3)],9)                   => 0
([(0,5),(0,6),(1,8),(2,7),(3,8),(4,8),(5,2),(6,1),(6,7),(7,3),(7,4)],9)                   => 2
([(0,4),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(6,5),(7,1),(7,2)],9)                   => 0
([(0,3),(0,7),(1,8),(2,8),(3,8),(4,6),(5,2),(6,5),(7,1),(7,4)],9)                         => 1
([(0,7),(1,8),(2,8),(3,8),(4,5),(5,6),(6,2),(6,3),(7,1),(7,4)],9)                         => 2
([(0,7),(1,8),(2,8),(3,5),(4,3),(5,2),(6,1),(7,4),(7,6)],9)                               => 3
([(0,6),(1,8),(2,7),(3,4),(4,1),(5,3),(5,7),(6,2),(6,5),(7,8)],9)                         => 4
([(0,6),(2,8),(3,7),(4,2),(5,4),(5,7),(6,3),(6,5),(7,8),(8,1)],9)                         => 5
([(0,6),(1,8),(2,7),(3,2),(4,3),(5,1),(5,7),(6,4),(6,5),(7,8)],9)                         => 4
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,8),(5,7),(6,2),(6,3),(7,1),(7,6)],9)                   => 1
([(0,5),(1,8),(2,8),(3,8),(4,8),(5,6),(6,4),(6,7),(7,1),(7,2),(7,3)],9)                   => 3
([(0,3),(0,5),(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,4),(6,1),(6,7),(7,8)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,4),(6,1),(6,7),(7,3)],9)                   => 2
([(0,5),(0,7),(1,8),(2,8),(3,8),(4,8),(5,6),(6,3),(6,4),(7,1),(7,2)],9)                   => 0
([(0,5),(1,8),(2,8),(3,8),(4,8),(5,7),(6,3),(6,4),(7,1),(7,2),(7,6)],9)                   => 2
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,1),(5,7),(6,2),(6,3),(6,7),(7,8)],9)             => 1
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,8),(4,2),(5,4),(6,1),(6,7),(7,8)],9)                   => 0
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,1),(5,4),(6,3),(6,8),(8,2)],9)                         => 3
([(0,3),(0,5),(1,8),(2,7),(3,8),(4,1),(4,7),(5,6),(6,2),(6,4),(7,8)],9)                   => 1
([(0,5),(1,8),(2,7),(3,7),(4,3),(4,8),(5,6),(6,1),(6,4),(8,2)],9)                         => 5
([(0,5),(0,6),(1,8),(2,7),(3,2),(4,1),(5,3),(6,4),(6,7),(7,8)],9)                         => 3
([(0,5),(0,6),(1,8),(3,7),(4,3),(5,4),(6,1),(6,7),(7,8),(8,2)],9)                         => 4
([(0,5),(1,8),(2,7),(3,1),(4,3),(4,7),(5,6),(6,2),(6,4),(7,8)],9)                         => 5
([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)                         => 6
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(7,2)],9)                   => 0
([(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(7,2),(7,3)],9)                   => 0
([(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(7,2),(7,3),(7,4)],9)                   => 3
([(0,3),(0,4),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,1),(6,2),(7,5)],9)                   => 1
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(6,7),(7,1),(7,5)],9)                   => 0
([(0,3),(0,4),(0,5),(1,7),(2,7),(3,8),(4,8),(5,6),(6,1),(6,2),(7,8)],9)                   => 1
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3)],9)                         => 2
([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)                         => 6
([(0,2),(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(5,7),(6,5),(7,8)],9)             => 0
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(5,7),(6,5),(7,2)],9)                   => 0
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(5,7),(6,5),(7,2),(7,3)],9)                   => 2
([(0,2),(0,3),(0,6),(1,8),(2,8),(3,7),(4,1),(5,4),(5,7),(6,5),(7,8)],9)                   => 0
([(0,2),(0,3),(0,5),(1,8),(2,6),(3,7),(4,1),(4,6),(5,4),(6,8),(8,7)],9)                   => 1
([(0,3),(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,4),(7,8),(8,5)],9)                         => 5
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,5),(4,8),(5,2),(6,4),(8,1)],9)                         => 3
([(0,3),(0,5),(1,7),(2,6),(3,8),(4,2),(4,8),(5,4),(6,7),(8,1),(8,6)],9)                   => 4
([(0,3),(0,5),(1,8),(2,8),(3,7),(4,6),(4,7),(5,4),(6,1),(6,2),(7,8)],9)                   => 2
([(0,2),(0,5),(1,7),(2,6),(3,4),(3,6),(4,1),(4,8),(5,3),(6,8),(8,7)],9)                   => 4
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,3),(6,7),(7,1),(7,2)],9)                   => 0
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,8),(5,3),(6,7),(7,1),(7,2),(7,5)],9)                   => 1
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,1),(6,2),(6,7),(7,8)],9)             => 0
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,1),(6,2),(6,7),(7,3)],9)                   => 2
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(7,3)],9)                   => 1
([(0,6),(1,8),(2,8),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(7,3),(7,5)],9)                   => 3
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,1),(6,2),(6,3),(6,7),(7,8)],9)             => 2
([(0,3),(0,4),(0,5),(1,8),(2,7),(3,8),(4,7),(5,6),(6,1),(6,2),(7,8)],9)                   => 0
([(0,4),(0,5),(1,8),(2,7),(3,7),(4,8),(5,6),(6,1),(6,2),(6,3),(7,8)],9)                   => 1
([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(6,4),(8,3)],9)                         => 3
([(0,4),(0,5),(1,8),(2,7),(3,7),(4,8),(5,6),(6,1),(6,3),(8,2)],9)                         => 2
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,1),(6,2),(8,7)],9)                   => 1
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,1),(6,2),(6,3),(8,7)],9)                   => 2
([(0,6),(2,8),(3,8),(4,8),(5,1),(6,7),(7,2),(7,3),(7,4),(8,5)],9)                         => 5
([(0,4),(0,6),(2,8),(3,8),(4,8),(5,1),(6,7),(7,2),(7,3),(8,5)],9)                         => 3
([(0,2),(0,3),(0,7),(1,8),(2,8),(3,8),(4,6),(5,4),(6,1),(7,5)],9)                         => 1
([(0,3),(0,6),(1,8),(2,8),(3,8),(4,5),(5,7),(6,4),(7,1),(7,2)],9)                         => 1
([(0,6),(1,8),(2,8),(3,8),(4,5),(5,7),(6,4),(7,1),(7,2),(7,3)],9)                         => 5
([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(7,8)],9)                   => 0
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(8,3)],9)                         => 1
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(8,3),(8,4)],9)                         => 4
([(0,3),(0,6),(0,7),(1,8),(2,8),(3,8),(4,2),(5,1),(6,4),(7,5)],9)                         => 1
([(0,3),(0,6),(1,8),(2,8),(3,8),(4,5),(5,2),(6,7),(7,1),(7,4)],9)                         => 1
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,8),(4,1),(4,7),(5,2),(6,4),(7,8)],9)                   => 0
([(0,5),(0,6),(1,8),(2,7),(3,7),(4,2),(4,8),(5,1),(6,4),(8,3)],9)                         => 3
([(0,5),(0,6),(1,8),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3)],9)                         => 1
([(0,6),(1,8),(2,8),(3,8),(4,5),(5,3),(6,7),(7,1),(7,2),(7,4)],9)                         => 3
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,3),(5,6),(6,1),(6,2),(6,7),(7,8)],9)                   => 2
([(0,5),(1,8),(2,8),(3,8),(4,7),(5,6),(6,3),(6,4),(7,1),(7,2)],9)                         => 3
([(0,5),(0,6),(1,8),(2,8),(3,2),(3,7),(4,1),(4,7),(5,3),(6,4),(7,8)],9)                   => 2
([(0,3),(0,5),(0,6),(1,7),(2,7),(3,8),(4,1),(5,2),(6,4),(7,8)],9)                         => 1
([(0,3),(0,5),(1,7),(2,7),(3,8),(4,2),(5,6),(6,1),(6,4),(7,8)],9)                         => 2
([(0,6),(2,8),(3,8),(4,3),(5,1),(6,7),(7,2),(7,4),(8,5)],9)                               => 6
([(0,6),(0,7),(2,8),(3,8),(4,2),(5,1),(6,4),(7,3),(8,5)],9)                               => 4
([(0,2),(0,3),(0,4),(0,6),(1,7),(2,8),(3,8),(4,7),(5,1),(6,5),(7,8)],9)                   => 0
([(0,3),(0,4),(0,6),(1,8),(2,7),(3,8),(4,7),(5,1),(6,5),(8,2)],9)                         => 1
([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(6,5),(8,2),(8,3)],9)                         => 4
([(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,3),(6,2),(7,1)],9)                   => 1
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,7),(7,8)],9)             => 0
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,1),(5,6),(5,7),(6,8),(7,8)],9)       => 0
([(0,2),(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(5,4),(5,6),(5,7),(6,8),(7,8)],9)             => 1
([(0,2),(0,3),(0,4),(1,7),(2,5),(3,6),(4,1),(4,5),(4,6),(5,8),(6,7),(7,8)],9)             => 1
([(0,3),(0,4),(0,5),(1,8),(3,7),(4,6),(5,1),(5,6),(5,7),(6,8),(7,8),(8,2)],9)             => 2
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,2),(5,6),(5,7),(6,8),(7,1)],9)             => 1
([(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,1),(4,5),(4,6),(5,8),(6,8),(8,7)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,8),(3,6),(4,7),(5,1),(5,7),(6,8),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,8),(5,2),(5,8),(6,7),(8,1)],9)                   => 1
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,7),(5,1),(5,6),(6,8),(8,7)],9)             => 1
([(0,3),(0,4),(0,6),(2,8),(3,8),(4,7),(5,1),(6,2),(6,7),(7,8),(8,5)],9)                   => 2
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,6),(5,2),(5,8),(6,7),(8,1)],9)                   => 1
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,3),(5,8),(6,7),(8,1),(8,2)],9)                   => 3
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,8),(5,1),(5,7),(7,2),(7,8),(8,6)],9)             => 1
([(0,3),(0,4),(0,5),(2,6),(3,6),(4,7),(5,2),(5,7),(6,8),(7,8),(8,1)],9)                   => 2
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,2),(5,6),(6,7),(8,1)],9)                   => 1
([(0,4),(0,6),(2,7),(3,7),(4,8),(5,1),(6,2),(6,8),(7,5),(8,3)],9)                         => 5
([(0,3),(0,5),(0,6),(1,8),(2,8),(3,7),(4,1),(5,2),(6,4),(6,7),(7,8)],9)                   => 0
([(0,3),(0,5),(1,8),(2,8),(3,7),(4,2),(5,6),(5,7),(6,1),(6,4),(7,8)],9)                   => 2
([(0,3),(0,4),(1,7),(2,8),(3,6),(4,5),(4,6),(5,1),(5,2),(6,8),(8,7)],9)                   => 3
([(0,2),(0,5),(1,7),(2,6),(3,1),(4,3),(4,8),(5,4),(5,6),(6,8),(8,7)],9)                   => 4
([(0,2),(0,3),(0,5),(1,8),(2,6),(3,7),(4,1),(4,7),(5,4),(5,6),(6,8),(7,8)],9)             => 0
([(0,3),(0,5),(1,7),(2,6),(3,8),(4,1),(4,6),(5,4),(5,8),(6,7),(8,2)],9)                   => 4
([(0,2),(0,3),(0,5),(1,7),(2,8),(3,6),(4,1),(4,8),(5,4),(5,6),(6,8),(8,7)],9)             => 1
([(0,2),(0,3),(0,4),(1,5),(1,7),(2,5),(3,6),(4,1),(4,6),(5,8),(6,7),(7,8)],9)             => 2
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,2),(5,1),(6,4),(6,8),(8,5)],9)                         => 3
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(5,1),(5,6),(6,4),(6,8),(8,7)],9)                   => 4
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,8),(4,1),(5,4),(5,6),(6,8),(8,7)],9)                   => 1
([(0,2),(0,3),(0,4),(1,7),(2,5),(3,6),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)             => 2
([(0,3),(0,4),(0,5),(2,8),(3,7),(4,6),(5,2),(5,6),(6,7),(7,8),(8,1)],9)                   => 2
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,6),(4,1),(5,2),(5,6),(6,8),(8,7)],9)                   => 1
([(0,3),(0,4),(0,5),(2,7),(3,8),(4,6),(5,2),(5,6),(6,7),(7,8),(8,1)],9)                   => 2
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,8),(4,2),(5,1),(6,4),(6,8),(8,7)],9)                   => 2
([(0,4),(0,5),(0,6),(1,8),(2,7),(4,8),(5,1),(6,2),(6,8),(7,3),(8,7)],9)                   => 3
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,7),(4,1),(5,4),(5,6),(6,8),(7,8)],9)                   => 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,5),(4,7),(5,1),(5,2),(6,8),(7,8)],9)                   => 3
([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)                   => 5
([(0,4),(0,5),(1,8),(2,8),(4,7),(5,6),(5,7),(6,1),(6,2),(7,8),(8,3)],9)                   => 3
([(0,4),(0,6),(1,7),(3,7),(4,8),(5,1),(6,5),(6,8),(7,2),(8,3)],9)                         => 4
([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)                   => 5
([(0,3),(0,4),(0,6),(1,8),(3,8),(4,7),(5,1),(6,5),(6,7),(7,8),(8,2)],9)                   => 1
([(0,3),(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,7),(7,5)],9)                   => 0
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,8),(4,6),(5,1),(5,6),(6,7),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,2),(5,7),(7,8),(8,1)],9)                   => 1
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,7),(7,3)],9)                   => 0
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,7),(7,3),(7,5)],9)                   => 2
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,2),(5,7),(6,8),(7,1),(7,6)],9)             => 0
([(0,2),(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(4,7),(5,1),(5,7),(6,8),(7,8)],9)       => 0
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(4,7),(5,2),(5,7),(6,8),(7,1)],9)             => 1
([(0,1),(0,2),(0,3),(0,4),(1,8),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9) => 0
([(0,2),(0,3),(0,4),(1,8),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,1)],9)       => 3
([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)       => 4
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(4,7),(5,2),(5,6),(6,8),(7,1)],9)             => 1
([(0,2),(0,3),(0,4),(1,7),(2,5),(3,5),(3,6),(4,1),(4,6),(5,8),(6,8),(8,7)],9)             => 2
([(0,2),(0,3),(0,5),(1,8),(2,6),(3,6),(3,7),(4,1),(5,4),(5,7),(6,8),(7,8)],9)             => 1
([(0,2),(0,3),(0,4),(1,7),(2,5),(3,5),(3,6),(4,1),(4,6),(5,8),(6,7),(7,8)],9)             => 2
([(0,3),(0,4),(0,5),(1,8),(3,6),(4,6),(4,7),(5,1),(5,7),(6,8),(7,8),(8,2)],9)             => 2
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(5,7),(6,1),(6,7),(7,8)],9)       => 0
([(0,3),(0,5),(0,6),(1,8),(2,8),(3,7),(4,1),(5,2),(5,7),(6,4),(6,7),(7,8)],9)             => 1
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,1),(4,8),(5,2),(5,8),(6,7),(8,6)],9)             => 2
([(0,4),(0,5),(0,6),(2,8),(3,8),(4,7),(5,3),(5,7),(6,2),(6,7),(7,8),(8,1)],9)             => 2
([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,8),(5,3),(5,8),(6,2),(6,8),(8,1)],9)             => 1
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,1),(4,6),(5,2),(5,7),(6,8),(7,8)],9)             => 0
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9)                   => 4
([(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,2),(4,8),(5,1),(5,6),(6,8),(8,7)],9)             => 1
([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(7,6)],9)                   => 2
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,2),(4,7),(5,1),(5,6),(6,7),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(4,7),(5,1),(5,2),(5,7),(6,8),(7,8)],9)       => 1
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(6,7),(7,8)],9)       => 0
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,6),(4,7),(5,1),(5,2),(6,8),(7,8)],9)             => 1
([(0,3),(0,5),(1,6),(2,6),(2,7),(3,7),(4,2),(5,1),(5,4),(6,8),(7,8)],9)                   => 3
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,6),(4,6),(4,8),(5,1),(5,2),(6,7),(8,7)],9)             => 2
([(0,5),(1,6),(2,7),(3,6),(3,7),(4,2),(4,3),(5,1),(5,4),(6,8),(7,8)],9)                   => 4
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,3),(5,1),(5,7),(6,2),(6,4),(7,8)],9)                   => 1
([(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,3),(5,4),(6,1),(6,5),(7,8)],9)                   => 2
([(0,6),(1,8),(2,7),(3,5),(4,2),(5,1),(5,7),(6,3),(6,4),(7,8)],9)                         => 4
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(5,7),(6,1),(6,3),(7,8)],9)             => 0
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(5,3),(5,8),(6,1),(6,4),(8,7)],9)                   => 2
([(0,6),(1,8),(2,8),(3,7),(4,3),(4,8),(5,2),(5,4),(6,1),(6,5),(8,7)],9)                   => 3
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,8),(5,3),(5,8),(6,1),(6,2),(8,7)],9)             => 1
([(0,2),(0,3),(0,4),(0,5),(1,7),(2,8),(3,6),(4,6),(4,7),(5,1),(6,8),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,6),(4,6),(4,8),(5,2),(6,7),(8,1)],9)                   => 2
([(0,3),(0,4),(0,5),(1,7),(2,6),(3,8),(4,6),(4,8),(5,2),(6,7),(8,1)],9)                   => 2
([(0,3),(0,4),(0,5),(2,6),(3,7),(4,6),(4,7),(5,2),(6,8),(7,8),(8,1)],9)                   => 3
([(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,8),(4,7),(5,2),(6,1),(6,7),(7,8)],9)             => 0
([(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(4,8),(5,1),(6,2),(6,8),(8,3)],9)                   => 2
([(0,3),(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8)],9)                   => 0
([(0,2),(0,6),(1,8),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7),(7,8)],9)                         => 3
([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)                         => 6
([(0,3),(0,6),(2,8),(3,7),(4,5),(5,2),(6,4),(6,7),(7,8),(8,1)],9)                         => 4
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,7),(6,8),(7,8)],9)                   => 1
([(0,4),(0,6),(1,8),(3,8),(4,7),(5,3),(6,1),(6,7),(7,5),(8,2)],9)                         => 4
([(0,4),(0,5),(0,6),(1,8),(2,8),(4,7),(5,2),(6,1),(6,7),(7,8),(8,3)],9)                   => 1
([(0,3),(0,6),(1,7),(2,7),(3,8),(4,2),(5,4),(6,1),(6,8),(8,5)],9)                         => 3
([(0,3),(0,4),(0,5),(1,7),(2,8),(3,6),(4,2),(5,1),(5,6),(6,8),(8,7)],9)                   => 1
([(0,3),(0,5),(1,8),(2,8),(3,7),(4,2),(4,7),(5,6),(6,1),(6,4),(7,8)],9)                   => 1
([(0,2),(0,3),(0,5),(1,8),(2,6),(3,6),(3,7),(4,1),(4,7),(5,4),(6,8),(7,8)],9)             => 1
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,1),(5,7),(6,2),(6,3),(7,8)],9)                   => 1
([(0,5),(1,8),(2,8),(3,7),(4,2),(4,7),(5,6),(6,1),(6,3),(6,4),(7,8)],9)                   => 2
([(0,3),(0,5),(0,6),(1,8),(2,8),(3,7),(4,2),(4,7),(5,4),(6,1),(6,7),(7,8)],9)             => 1
([(0,2),(0,3),(0,5),(1,7),(2,6),(3,6),(3,7),(4,1),(5,4),(6,8),(7,8)],9)                   => 2
([(0,3),(0,4),(1,6),(2,6),(2,7),(3,7),(4,5),(5,1),(5,2),(6,8),(7,8)],9)                   => 3
([(0,4),(1,7),(2,6),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,8),(7,8)],9)                   => 4
([(0,3),(0,5),(0,6),(1,8),(2,7),(3,8),(4,1),(5,4),(6,2),(6,8),(8,7)],9)                   => 2
([(0,3),(0,5),(1,8),(2,7),(3,8),(4,2),(4,8),(5,6),(6,1),(6,4),(8,7)],9)                   => 2
([(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,3),(5,8),(6,1),(6,2),(8,7)],9)                   => 2
([(0,5),(1,8),(2,8),(3,7),(4,3),(4,8),(5,6),(6,1),(6,2),(6,4),(8,7)],9)                   => 4
([(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,4),(6,3),(7,1),(7,2)],9)                   => 0
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,7),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,1),(5,2),(5,6),(5,7),(6,8),(7,8)],9)       => 1
([(0,3),(0,6),(1,8),(2,8),(3,7),(4,5),(5,2),(6,1),(6,4),(6,7),(7,8)],9)                   => 2
([(0,3),(0,5),(1,7),(2,8),(3,6),(4,2),(5,1),(5,4),(5,6),(6,8),(8,7)],9)                   => 2
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,2),(5,7),(6,8),(7,8)],9)             => 0
([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,1),(5,3),(5,8),(6,7),(8,2)],9)                   => 2
([(0,3),(0,4),(0,5),(1,8),(2,7),(3,8),(4,6),(5,1),(5,2),(5,6),(6,8),(8,7)],9)             => 1
([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,4),(5,7),(6,8),(7,8)],9)                   => 2
([(0,4),(0,5),(2,7),(3,8),(4,6),(5,2),(5,3),(5,6),(6,7),(7,8),(8,1)],9)                   => 3
([(0,4),(0,6),(1,8),(2,8),(4,7),(5,2),(6,1),(6,5),(6,7),(7,8),(8,3)],9)                   => 3
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,8),(4,6),(5,1),(5,2),(5,6),(6,7),(8,7)],9)             => 1
([(0,5),(0,6),(1,8),(2,8),(4,8),(5,7),(6,1),(6,2),(6,7),(7,4),(8,3)],9)                   => 3
([(0,4),(0,5),(0,6),(1,8),(2,8),(4,8),(5,7),(6,1),(6,2),(6,7),(7,8),(8,3)],9)             => 1
([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,3),(6,1),(6,2),(6,7),(7,5)],9)                   => 2
([(0,3),(0,4),(0,5),(1,8),(2,8),(3,7),(4,6),(5,1),(5,2),(5,6),(6,7),(7,8)],9)             => 0
([(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,2),(5,1),(5,6),(5,7),(6,8),(7,8)],9)             => 1
([(0,5),(0,6),(1,8),(2,8),(3,7),(4,3),(5,4),(6,1),(6,2),(6,7),(7,8)],9)                   => 2
([(0,4),(1,8),(2,8),(3,7),(4,5),(5,3),(5,6),(6,1),(6,2),(6,7),(7,8)],9)                   => 4
([(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(6,1),(6,2),(6,7),(7,8)],9)             => 1
([(0,6),(0,7),(1,8),(2,8),(3,8),(4,5),(5,3),(6,1),(7,2),(7,4)],9)                         => 1
([(0,7),(1,8),(2,8),(3,8),(4,3),(5,2),(6,4),(6,5),(7,1),(7,6)],9)                         => 2
([(0,3),(0,6),(1,8),(2,8),(3,7),(4,2),(5,4),(5,7),(6,1),(6,5),(7,8)],9)                   => 1
([(0,3),(0,5),(1,7),(2,8),(3,6),(4,2),(4,6),(5,1),(5,4),(6,8),(8,7)],9)                   => 2
([(0,7),(1,8),(2,8),(3,8),(4,6),(5,3),(6,2),(6,5),(7,1),(7,4)],9)                         => 2
([(0,3),(0,6),(1,8),(2,8),(3,7),(4,5),(5,1),(5,7),(6,2),(6,4),(7,8)],9)                   => 1

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Created: Sep 29, 2020 at 17:15 by Martin Rubey

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Last Updated: Feb 08, 2021 at 23:11 by Martin Rubey