"""Responsible for producing a type DA structure for an arcslide, using

local actions.

"""

def __init__(self, slide):

"""Specifies the arcslide to use. slide should be of type Arcslide.

In addition to recording slide, construct the following:

local_pmc1, mapping1 - restriction of starting pmc to location of slide.

outer_pmc1, outer_mapping1 - complement of slide in starting pmc.

local_pmc2, mapping2, outer_pmc2, outer_mapping2

- same, but for ending pmc.

Moreover, find pattern_fun and translator as appropriate for the case at

hand.

"""

self.slide = slide

self.pmc1, self.pmc2 = slide.start_pmc, slide.end_pmc

n = self.pmc1.n

b1, c1, c2 = slide.b1, slide.c1, slide.c2

b1p, c1p, c2p = [slide.to_r[p] for p in (b1, c1, c2)]

# Note intervals (start, end) with start > end are ignored.

# patterns_base specifies one of the four base patterns of arcslides.

# translator gives the mapping between points in the base pattern and

# points in the pattern at hand.

if b1 == c1 + 1: # downward

if c2 == c1 + 2: # short underslide downward

local_cut1, local_cut2 = ([(c1, c2)], [(c1p, c2p)])

patterns_fun = ArcslideDA._short_underslide_down

if c1 == 0:

translator = ([-1, 0, 1, 2, 3], [-1, 0, 1, 2, 3])

elif c2 == n - 1:

translator = ([0, 1, 2, 3, -1], [0, 1, 2, 3, -1])

else:

translator = None

elif c2 > c1: # general underslide downward

local_cut1, local_cut2 = (

[(c1, b1), (c2, c2)], [(c1p, c1p), (b1p, c2p)])

patterns_fun = ArcslideDA._general_underslide_down

if c1 == 0:

translator = ([-1, 0, 1, 2, 3, 4, 5],

[-1, 0, 1, 2, 3, 4, 5])

elif c2 == n - 1:

translator = ([0, 1, 2, 3, 4, 5, -1],

[0, 1, 2, 3, 4, 5, -1])

else:

translator = None

else: # c2 < c1, general overslide downward

local_cut1, local_cut2 = (

[(c2, c2), (c1, b1)], [(b1p, c2p), (c1p, c1p)])

patterns_fun = ArcslideDA._general_underslide_down

if c2 == 0 and b1 == n - 1:

translator = ([2, 3, 4, -1, -1, 0, 1],

[3, 4, -1, -1, 0, 1, 2])

elif c2 == 0:

translator = ([2, 3, 4, 5, -1, 0, 1],

[3, 4, 5, -1, 0, 1, 2])

elif b1 == n - 1:

translator = ([3, 4, 5, -1, 0, 1, 2],

[4, 5, -1, 0, 1, 2, 3])

else:

translator = ([3, 4, 5, 6, 0, 1, 2], [4, 5, 6, 0, 1, 2, 3])

elif b1 == c1 - 1: # upward

if c2 == c1 - 2: # short underslide upward

local_cut1, local_cut2 = ([(c2, c1)], [(c2p, c1p)])

patterns_fun = ArcslideDA._short_underslide_up

if c2 == 0:

translator = ([-1, 0, 1, 2, 3], [-1, 0, 1, 2, 3])

elif c1 == n - 1:

translator = ([0, 1, 2, 3, -1], [0, 1, 2, 3, -1])

else:

translator = None

elif c2 < c1: # general underslide upward

local_cut1, local_cut2 = (

[(c2, c2), (b1, c1)], [(c2p, b1p), (c1p, c1p)])

patterns_fun = ArcslideDA._general_underslide_up

if c2 == 0:

translator = ([-1, 0, 1, 2, 3, 4, 5],

[-1, 0, 1, 2, 3, 4, 5])

elif c1 == n - 1:

translator = ([0, 1, 2, 3, 4, 5, -1],

[0, 1, 2, 3, 4, 5, -1])

else:

translator = None

else: # c2 > c1, general overslide upward

local_cut1, local_cut2 = (

[(b1, c1), (c2, c2)], [(c1p, c1p), (c2p, b1p)])

patterns_fun = ArcslideDA._general_underslide_up

if b1 == 0 and c2 == n - 1:

translator = ([3, 4, -1, -1, 0, 1, 2],

[2, 3, 4, -1, -1, 0, 1])

elif b1 == 0:

translator = ([3, 4, 5, -1, 0, 1, 2],

[2, 3, 4, 5, -1, 0, 1])

elif c2 == n - 1:

translator = ([4, 5, -1, 0, 1, 2, 3],

[3, 4, 5, -1, 0, 1, 2])

else:

translator = ([4, 5, 6, 0, 1, 2, 3], [3, 4, 5, 6, 0, 1, 2])

else:

# All cases are covered. Should not happen.

raise NotImplementedError(

"This slide pattern is not yet implemented.")

self.patterns_fun = patterns_fun

self.translator = translator

# Necesssary to get local DA structure.

self.splitting1 = PMCSplitting(self.pmc1, local_cut1)

self.splitting2 = PMCSplitting(self.pmc2, local_cut2)

self.local_pmc1 = self.splitting1.local_pmc

self.local_pmc2 = self.splitting2.local_pmc

self.mapping1 = self.splitting1.local_mapping

self.mapping2 = self.splitting2.local_mapping

# Required so the left to right transition on the outside can proceed.

assert self.splitting1.outer_pmc == self.splitting2.outer_pmc

# Initiate the ExtendedDAStructure

ExtendedDAStructure.__init__(

self, self.getLocalDAStructure(), self.splitting1, self.splitting2)

# With generators set, add grading. Any generator can serve as base_gen

for gen in self.generators:

base_gen = gen

break

self.registerHDiagram(getArcslideDiagram(self.slide), base_gen)

def getLocalDAStructure(self, seeds_only = False):

"""Returns the local type DA structure associated to slide. If

seeds_only is set to True, get a local DA structure with incomplete

da_action, that can be completed using the autocompleteda module.

"""

# Compute the set of arrow patterns

patterns_raw = self.patterns_fun(seeds_only = seeds_only)

if self.translator is not None:

patterns_raw = ArcslideDA._restrict_local_arrows(

patterns_raw, self.translator[0], self.translator[1])

arrow_patterns = {}

for pattern in patterns_raw:

coeffs_a = []

for i in range(len(pattern)-1):

coeffs_a.append(self.local_pmc2.sd(pattern[i]))

coeffs_a = tuple(coeffs_a)

if coeffs_a not in arrow_patterns:

arrow_patterns[coeffs_a] = []

arrow_patterns[coeffs_a].append(self.local_pmc1.sd(pattern[-1]))

# Now start construction of the local DA structure.

alg1 = LocalStrandAlgebra(F2, self.local_pmc1)

alg2 = LocalStrandAlgebra(F2, self.local_pmc2)

local_dastr = LocalDAStructure(F2, alg1, alg2)

# Mappings between local starting and ending PMC.

slide = self.slide

local_to_r = dict()

for i in range(slide.start_pmc.n):

if i in self.mapping1:

# to_r[i] must be in mapping2

local_to_r[self.mapping1[i]] = self.mapping2[slide.to_r[i]]

local_pair_to_r = dict()

for i in range(self.local_pmc1.n):

if i not in self.local_pmc1.endpoints:

local_pair_to_r[self.local_pmc1.pairid[i]] \

= self.local_pmc2.pairid[local_to_r[i]]

b1, c1 = self.slide.b1, self.slide.c1

local_b1, local_c1 = self.mapping1[b1], self.mapping1[c1]

b_pair1 = self.local_pmc1.pairid[local_b1]

c_pair1 = self.local_pmc1.pairid[local_c1]

# Compute the set of local generators. This includes all

# (l_idem, r_idem) where l_idem = r_idem (under the usual identification

# of pairs), or where l_idem has the c_pair and r_idem has the b_pair.

da_idems = []

num_pair = self.local_pmc1.num_pair

for idem in subset(list(range(num_pair))):

da_idems.append((list(idem), [local_pair_to_r[p] for p in idem]))

for idem in subset([p for p in range(num_pair)

if p != b_pair1 and p != c_pair1]):

da_idems.append((list(idem) + [c_pair1],

[local_pair_to_r[p]

for p in (list(idem) + [b_pair1])]))

for i in range(len(da_idems)):

l_idem, r_idem = da_idems[i]

local_dastr.addGenerator(SimpleDAGenerator(

local_dastr, LocalIdempotent(self.local_pmc1, l_idem),

LocalIdempotent(self.local_pmc2, r_idem), "%d" % i))

mod_gens = local_dastr.getGenerators()

# After having added all generators, create u_map:

local_dastr.auto_u_map()

# Add arrows according to arrow_pattern.

for coeffs_a in list(arrow_patterns.keys()):

if len(coeffs_a) == 1 and coeffs_a[0].isIdempotent():

continue

for coeff_d in arrow_patterns[coeffs_a]:

for x, y in itertools.product(mod_gens, mod_gens):

if DAStructure.idemMatchDA(x, y, coeff_d, coeffs_a):

local_dastr.addDelta(x, y, coeff_d, coeffs_a, 1)

return local_dastr

@staticmethod

def _restrict_local_arrows(patterns, point_map_d, point_map_a):

"""Given a list of patterns (in the format of patterns_raw) for more

general local case, restrict to a more special local case using a

mapping from points in the general local PMC to a special local PMC.

point_map_d and point_map_a specifies the point mappings on the D-side

and the A-side.

This function operates entirely by translation using the given point

map, it does not know about formats for local PMCs or local strand

diagrams.

"""

def translate(lst, mapping):

"""lst consists of either integers or pairs of integers. Translate

according to mapping. If any of the translated value is -1, return

None. Otherwise return the translated list.

"""

result = []

for entry in lst:

if isinstance(entry, int):

result.append(mapping[entry])

if result[-1] == -1:

return None

else: # entry must be a pair

result.append((mapping[entry[0]], mapping[entry[1]]))

if result[-1][0] == -1 or result[-1][1] == -1:

return None

return result

new_patterns = []

for pattern in patterns:

new_pattern = [translate(pattern_d, point_map_a)

for pattern_d in pattern[0:-1]]

new_pattern.append(translate(pattern[-1], point_map_d))

if all([entry != None for entry in new_pattern]):

new_patterns.append(new_pattern)

return new_patterns

# The next series of functions specify the local arrows. The format is as

# follows:

# All but the last element of the tuple is a list to be passed to the sd()

# function of the A-side local PMC, specifying the A-side inputs. The last

# element of the tuple is a list to be passed to the sd() function of the

# D-side local PMC, specifying the D-side output.

@staticmethod

def _short_underslide_down(seeds_only = False):

"""Short underslide going down, in the middle of PMC."""

# Local PMC is 0*-1-2-3-4*, with 1 and 3 paired.

patterns_raw = [

#### Initial patterns

([(1, 2)],),

([], []), ([1], [1]), ([2], [2]), ([2], [1]), ([1, 2], [1, 2]),

([(2, 3)], [1]),

([(1, 2)], [(1, 3)]),

([(1, 3)], [(1, 3)]),

([2, (1, 3)], [2, (1, 3)]),

([(1, 2),(2, 3)], [(1, 2),(2, 3)]),

([(2, 3)], [(1, 2)], [(2, 3)]),

([(2, 3)], [(1, 3)], [(2, 3)]),

#### Seeds for top

([(3, 4)], [(3, 4)]),

([2, (3, 4)], [2, (3, 4)]),

#### Seeds for bottom

([(0, 1)], [(0, 1)]),

([2, (0, 1)], [2, (0, 1)]),

]

if seeds_only:

return patterns_raw

patterns_raw += [

# From seeds for top

([(2, 3), (3, 4)], [(1, 2)], [(1, 2), (2, 4)]),

([2, (3, 4)], [(2, 3)], [(1, 3)], [1, (2, 4)]),

([(2, 3)], [(1, 4)], [(2, 4)]),

([(2, 4)], [(3, 4)]),

([2, (3, 4)], [(2, 3)], [(1, 2)], [1, (2, 4)]),

([(1, 2), (2, 4)], [(1, 2), (2, 4)]),

([2, (1, 4)], [2, (1, 4)]),

([(1, 4)], [(1, 4)]),

# From seeds for bottom

([(2, 3)], [(0, 2), (3, 4)], [(0, 1), (2, 4)]),

([(0, 2)], [(0, 3)]),

([(0, 1), (1, 4)], [(0, 1), (1, 4)]),

([(0, 1), (2, 4)], [(1, 2)], [1, (0, 4)]),

([2, (0, 1)], [(2, 3), (3, 4)], [(1, 2)], [1, (0, 4)]),

([2, (0, 1)], [(2, 3), (3, 4)], [(1, 2)], [(0, 1), (2, 4)]),

([1, (0, 2), (2, 4)], [1, (0, 2), (2, 4)]),

([2, (0, 1), (3, 4)], [2, (1, 3)], [1, 2, (0, 4)]),

([2, (0, 3), (3, 4)], [2, (0, 1), (1, 4)]),

([(3, 4)], [(0, 2)], [1, (0, 4)]),

([(0, 3)], [(0, 3)]),

([(0, 1), (2, 4)], [(1, 2)], [(0, 1), (2, 4)]),

([(0, 2), (3, 4)], [(0, 1), (1, 4)]),

([(2, 3)], [(0, 3), (3, 4)], [(0, 1), (2, 4)]),

([(2, 3), (3, 4)], [(0, 1), (1, 2)], [(0, 2), (2, 3), (3, 4)]),

([(0, 1), (2, 4)], [(1, 3)], [(0, 1), (2, 4)]),

([(0, 2), (2, 4)], [(0, 2), (2, 4)]),

([(2, 3)], [(0, 1), (1, 2)], [2, (3, 4)], [(0, 1), (2, 4)]),

([(2, 3)], [(0, 1), (1, 2)], [(0, 2), (2, 3)]),

([2, (3, 4)], [2, (0, 3)], [1, 2, (0, 4)]),

([2, (0, 1)], [(2, 3), (3, 4)], [(0, 1), (3, 4)]),

([(2, 4)], [(0, 3)], [(0, 1), (2, 4)]),

([(0, 1), (2, 4)], [(0, 1), (3, 4)]),

([(2, 4)], [(0, 2)], [(0, 1), (2, 4)]),

([(0, 3), (3, 4)], [(0, 1), (1, 4)]),

([(0, 2), (2, 3), (3, 4)], [(0, 2), (2, 3), (3, 4)]),

([(2, 4)], [(0, 2)], [1, (0, 4)]),

([(2, 4)], [(0, 3)], [1, (0, 4)]),

([(0, 1), (3, 4)], [(0, 1), (3, 4)]),

([2, (0, 3)], [2, (0, 3)]),

([2, (0, 1), (1, 4)], [2, (0, 1), (1, 4)]),

([(2, 3)], [(0, 1), (1, 2)], [(2, 3), (3, 4)], [(0, 1), (2, 4)]),

([2, (0, 1)], [1, (0, 2)]),

([(2, 3)], [(0, 1), (1, 4)], [(0, 1), (2, 4)]),

([(3, 4)], [(0, 3)], [1, (0, 4)]),

([(0, 4)], [(0, 4)]),

([(0, 1), (1, 2)], [2, (3, 4)], [(0, 1), (1, 4)]),

([(2, 3), (3, 4)], [(1, 2)], [2, (0, 1)], [1, (0, 2), (2, 4)]),

([2, (0, 3), (3, 4)], [1, (0, 2), (2, 4)]),

([2, (0, 1)], [2, (3, 4)], [(0, 1), (3, 4)]),

([2, (0, 4)], [2, (0, 4)]),

([2, (0, 1)], [(2, 3), (3, 4)], [(1, 3)], [(0, 1), (2, 4)]),

([(0, 1), (1, 2)], [(2, 3), (3, 4)], [(0, 1), (1, 4)]),

([(0, 1), (1, 2), (2, 4)], [(0, 1), (1, 2), (2, 4)]),

([1, (2, 4)], [(0, 1), (1, 2)], [1, (0, 2), (2, 4)]),

([(0, 1), (3, 4)], [(1, 2)], [1, (0, 4)]),

([(0, 1), (3, 4)], [(1, 3)], [1, (0, 4)]),

([(0, 1), (2, 4)], [(1, 3)], [1, (0, 4)]),

([2, (0, 1), (3, 4)], [2, (0, 1), (3, 4)]),

([2, (0, 1)], [(2, 3), (3, 4)], [(1, 3)], [1, (0, 4)]),

([(0, 2), (2, 3)], [(0, 2), (2, 3)]),

]

return patterns_raw

@staticmethod

def _general_underslide_down(seeds_only = False):

"""Underslide of length >= 3 going down, in the middle of PMC."""

# Local PMC at left (D-side) is 0*-1-2-3*, 4*-5-6*, with 1 and 5 paired.

# Local PMC at right (A-side) is 0*-1-2*, 3*-4-5-6*, with 1 and 5

# paired.

patterns_raw = [

#### Initial patterns

([(1, 2)],),

([], []), ([1], [1]), ([4], [2]), ([4], [1]), ([1, 4], [1, 2]),

([(4, 5)], [1]),

#### Seeds for top

([(5, 6)], [(5, 6)]),

([4, (5, 6)], [2, (5, 6)]),

#### Seeds for bottom

([(0, 1)], [(0, 1)]),

([4, (0, 1)], [2, (0, 1)]),

#### Seeds for upper middle

([(3, 4)], [(4, 5)]),

#### Seeds for lower middle

([4, (1, 2)], [1, (2, 3)]),

]

if seeds_only:

return patterns_raw

patterns_raw += [

# From seeds for top

([(4, 6)], [(5, 6)]),

# From seeds for bottom

([4, (0, 1)], [(4, 5), (5, 6)], [(0, 1), (5, 6)]),

([4, (0, 1), (5, 6)], [2, (0, 1), (5, 6)]),

([4, (0, 1)], [4, (5, 6)], [(0, 1), (5, 6)]),

([(0, 1), (4, 6)], [(0, 1), (5, 6)]),

([4, (0, 1)], [1, (0, 2)]),

([(0, 1), (5, 6)], [(0, 1), (5, 6)]),

# From seed for upper middle

([(3, 4), (4, 6)], [(1, 2), (4, 6)]),

([(0, 1), (3, 4)], [(0, 2), (4, 5)]),

([(3, 5)], [(4, 5)]),

([(3, 4), (4, 6)], [4, (0, 1)], [1, (0, 2), (4, 6)]),

([(3, 4), (4, 5)], [4, (0, 1), (5, 6)], [1, (0, 2), (4, 6)]),

([(0, 1), (3, 4)], [4, (5, 6)], [(0, 1), (4, 6)]),

([1, (3, 4)], [(4, 5), (5, 6)], [1, (4, 6)]),

([4, (0, 1), (3, 6)], [2, (0, 1), (4, 6)]),

([(0, 1), (3, 4)], [(4, 5), (5, 6)], [(0, 1), (4, 6)]),

([(3, 6)], [(4, 6)]),

([4, (3, 6)], [2, (4, 6)]),

([(3, 4), (5, 6)], [(4, 5), (5, 6)]),

([4, (0, 1), (3, 6)], [1, (0, 2), (4, 6)]),

([(4, 5)], [(3, 5), (5, 6)], [1, (4, 6)]),

([(0, 1), (3, 4), (5, 6)], [(0, 2), (4, 5), (5, 6)]),

([4, (3, 5)], [2, (4, 5)]),

([(0, 1), (3, 6)], [(0, 1), (4, 6)]),

([(4, 6)], [(3, 4)], [1, (4, 6)]),

([1, (3, 4)], [(1, 2), (4, 5)]),

([(4, 6)], [(3, 5)], [1, (4, 6)]),

([1, (3, 4)], [4, (5, 6)], [1, (4, 6)]),

([1, (3, 4)], [4, (0, 1), (5, 6)], [1, (0, 2), (4, 6)]),

([1, (3, 6)], [1, (4, 6)]),

([(3, 5), (5, 6)], [(4, 5), (5, 6)]),

([(0, 1), (3, 4), (4, 6)], [(0, 2), (4, 5), (5, 6)]),

([(3, 4), (4, 5)], [(1, 2), (4, 5)]),

([4, (0, 1)], [(3, 4), (4, 5), (5, 6)], [(0, 2), (4, 5), (5, 6)]),

([(4, 5)], [(3, 4), (5, 6)], [1, (4, 6)]),

([4, (3, 5), (5, 6)], [2, (4, 5), (5, 6)]),

([1, 4, (3, 6)], [1, 2, (4, 6)]),

# From seed for lower middle

([(4, 5)], [(0, 2), (3, 4), (5, 6)], [1, (0, 3), (4, 6)]),

([(4, 6)], [(3, 5)], [(1, 2)], [(2, 3), (4, 6)]),

([(1, 2), (3, 6)], [(1, 3), (4, 6)]),

([(0, 2)], [(0, 3)]),

([(4, 5), (5, 6)], [(1, 2)], [(2, 3), (5, 6)]),

([1, 4, (0, 2), (3, 6)], [1, 2, (0, 3), (4, 6)]),

([(3, 4), (4, 5)], [4, (0, 1), (1, 2)], [4, (5, 6)], [(0, 1), (2, 3), (4, 6)]),

([4, (0, 1), (1, 2)], [4, (5, 6)], [(0, 1), (2, 3), (5, 6)]),

([(0, 1), (1, 2), (3, 4)], [4, (5, 6)], [(0, 1), (1, 3), (4, 6)]),

([(0, 1), (1, 2), (4, 6)], [(0, 1), (2, 3), (5, 6)]),

([1, (0, 2)], [1, (0, 3)]),

([(4, 5), (5, 6)], [(1, 2), (3, 5)], [(2, 3), (4, 5), (5, 6)]),

([(1, 2), (4, 6)], [(3, 4)], [1, (2, 3), (4, 6)]),

([(3, 4), (4, 5)], [4, (1, 2)], [(2, 3), (4, 5)]),

([4, (1, 2), (3, 6)], [2, (1, 3), (4, 6)]),

([(1, 2), (3, 5)], [(1, 3), (4, 5)]),

([(1, 2), (3, 4), (4, 6)], [(1, 2), (2, 3), (4, 6)]),

([4, (0, 1), (1, 2)], [(4, 5), (5, 6)], [(0, 1), (2, 3), (5, 6)]),

([4, (1, 2), (3, 5)], [2, (1, 3), (4, 5)]),

([(4, 6)], [(0, 2), (3, 4)], [1, (0, 3), (4, 6)]),

([1, (3, 4)], [(0, 2), (4, 5), (5, 6)], [1, (0, 3), (4, 6)]),

([(4, 5)], [(1, 2), (3, 5)], [(2, 3), (4, 5)]),

([(0, 2), (3, 6)], [(0, 3), (4, 6)]),

([(1, 2), (4, 6)], [(3, 5)], [1, (2, 3), (4, 6)]),

([4, (0, 1), (1, 2)], [(3, 4), (4, 5), (5, 6)], [(0, 2), (2, 3), (4, 5), (5, 6)]),

([(0, 2), (4, 5)], [(3, 5), (5, 6)], [(0, 1), (2, 3), (4, 6)]),

([(1, 2), (3, 4), (4, 5)], [(1, 2), (2, 3), (4, 5)]),

([(1, 2), (4, 5)], [1, (2, 3)]),

([(0, 2), (3, 4), (5, 6)], [(0, 3), (4, 5), (5, 6)]),

([(4, 5)], [(0, 1), (1, 2), (3, 4)], [4, (5, 6)], [(0, 1), (2, 3), (4, 6)]),

([(0, 2), (4, 5)], [(3, 5), (5, 6)], [1, (0, 3), (4, 6)]),

([(3, 4), (4, 5)], [(4, 5), (5, 6)], [(1, 2)], [(2, 3), (4, 6)]),

([(0, 2), (4, 6)], [(0, 3), (5, 6)]),

([1, (3, 4), (4, 6)], [(1, 2), (4, 5)], [1, (2, 3), (4, 6)]),

([(3, 4), (4, 5)], [(1, 2), (4, 6)], [(2, 3), (4, 6)]),

([4, (0, 1)], [(1, 2), (3, 4), (4, 6)], [(0, 1), (2, 3), (4, 6)]),

([4, (0, 1), (1, 2)], [2, (0, 1), (1, 3)]),

([(0, 1), (1, 2), (3, 4), (4, 6)], [(0, 2), (2, 3), (4, 5), (5, 6)]),

([(0, 1), (1, 2)], [(0, 1), (1, 3)]),

([1, (4, 6)], [(1, 2), (3, 5)], [1, (2, 3), (4, 6)]),

([1, (4, 6)], [(1, 2), (3, 4)], [1, (2, 3), (4, 6)]),

([(0, 2), (4, 5)], [(3, 4), (5, 6)], [1, (0, 3), (4, 6)]),

([(4, 5)], [(0, 1), (1, 2), (3, 6)], [(0, 1), (2, 3), (4, 6)]),

([4, (0, 2)], [(0, 1), (2, 3)]),

([(0, 1), (4, 6)], [(1, 2), (3, 5)], [(0, 1), (2, 3), (4, 6)]),

([(0, 2), (3, 5)], [(0, 3), (4, 5)]),

([(0, 1), (3, 4), (4, 6)], [(1, 2), (4, 5)], [(0, 1), (2, 3), (4, 6)]),

([1, (0, 2), (3, 4)], [(4, 5), (5, 6)], [1, (0, 3), (4, 6)]),

([(4, 5)], [(3, 5), (5, 6)], [(0, 1), (1, 2)], [(0, 1), (2, 3), (4, 6)]),

([1, 4, (0, 2)], [1, 2, (0, 3)]),

([(3, 4), (4, 6)], [(4, 5)], [(0, 1), (1, 2)], [(0, 1), (2, 3), (4, 6)]),

([(0, 2), (4, 6)], [(3, 5)], [(0, 1), (2, 3), (4, 6)]),

([4, (0, 2), (5, 6)], [(0, 1), (2, 3), (5, 6)]),

([4, (0, 2)], [1, (0, 3)]),

([(3, 4), (4, 5)], [(0, 2), (4, 5), (5, 6)], [(0, 1), (2, 3), (4, 6)]),

([(0, 2), (3, 4), (4, 6)], [(0, 1), (1, 3), (4, 6)]),

([(0, 2), (3, 4), (4, 5)], [4, (5, 6)], [(0, 1), (2, 3), (4, 6)]),

([(4, 5)], [(0, 1), (1, 2), (3, 4)], [(0, 2), (2, 3), (4, 5)]),

([4, (0, 1), (1, 2)], [1, (0, 2), (2, 3)]),

([(1, 2), (3, 4)], [(1, 3), (4, 5)]),

([4, (0, 2), (3, 5)], [2, (0, 3), (4, 5)]),

([(3, 4), (4, 5)], [(1, 2), (4, 5)], [(2, 3), (4, 5)]),

([(3, 4), (4, 6)], [(4, 5)], [(1, 2)], [(2, 3), (4, 6)]),

([(0, 2), (4, 5)], [1, (0, 3)]),

([(4, 5), (5, 6)], [(1, 2), (3, 4)], [(2, 3), (4, 5), (5, 6)]),

([(0, 2), (4, 5), (5, 6)], [(0, 1), (2, 3), (5, 6)]),

([(4, 5)], [(3, 5), (5, 6)], [(1, 2)], [(2, 3), (4, 6)]),

([(0, 2), (4, 5)], [(0, 1), (2, 3)]),

([(4, 6)], [(0, 2), (3, 5)], [(0, 1), (2, 3), (4, 6)]),

([(3, 4), (4, 6)], [(0, 2), (4, 5)], [(0, 1), (2, 3), (4, 6)]),

([1, (3, 4), (4, 6)], [4, (1, 2)], [1, (2, 3), (4, 6)]),

([(3, 4), (4, 5)], [(4, 5), (5, 6)], [(0, 1), (1, 2)], [(0, 1), (2, 3), (4, 6)]),

([(3, 4), (4, 5)], [(0, 1), (1, 2), (4, 6)], [(0, 1), (2, 3), (4, 6)]),

([(3, 4), (4, 5)], [4, (0, 1), (1, 2)], [(0, 2), (2, 3), (4, 5)]),

([(0, 1), (3, 4), (4, 6)], [4, (1, 2)], [1, (0, 3), (4, 6)]),

([(1, 2), (3, 4), (4, 6)], [4, (0, 1)], [1, (0, 2), (2, 3), (4, 6)]),

([(4, 5)], [(1, 2)], [(2, 3)]),

([1, (0, 2), (3, 6)], [1, (0, 3), (4, 6)]),

([4, (1, 2)], [2, (1, 3)]),

([(3, 4), (4, 5)], [4, (0, 1), (1, 2)], [(4, 5), (5, 6)], [(0, 1), (2, 3), (4, 6)]),

([(0, 2), (3, 4), (4, 5)], [(0, 2), (2, 3), (4, 5)]),

([(4, 5)], [(0, 1), (1, 2), (3, 4)], [(4, 5), (5, 6)], [(0, 1), (2, 3), (4, 6)]),

([4, (0, 1), (1, 2), (3, 6)], [2, (0, 1), (1, 3), (4, 6)]),

([(3, 4), (4, 5), (5, 6)], [4, (1, 2)], [(2, 3), (4, 5), (5, 6)]),

([(4, 6)], [(0, 2), (3, 5)], [1, (0, 3), (4, 6)]),

([4, (0, 1), (1, 2), (3, 6)], [1, (0, 2), (2, 3), (4, 6)]),

([(1, 2), (4, 5)], [(3, 4), (5, 6)], [1, (2, 3), (4, 6)]),

([(4, 5)], [(1, 2), (3, 6)], [(2, 3), (4, 6)]),

([4, (0, 2), (5, 6)], [2, (0, 3), (5, 6)]),

([4, (0, 2)], [2, (0, 3)]),

([(0, 2), (5, 6)], [(0, 3), (5, 6)]),

([(1, 2), (4, 5)], [(3, 5), (5, 6)], [1, (2, 3), (4, 6)]),

([(0, 1), (4, 6)], [(1, 2), (3, 4)], [1, (0, 3), (4, 6)]),

([4, (0, 2), (3, 5), (5, 6)], [2, (0, 3), (4, 5), (5, 6)]),

([(0, 1), (4, 6)], [(1, 2), (3, 5)], [1, (0, 3), (4, 6)]),

([4, (0, 2), (3, 6)], [2, (0, 3), (4, 6)]),

([1, (0, 2), (3, 4)], [4, (5, 6)], [1, (0, 3), (4, 6)]),

([(0, 1), (3, 4), (4, 6)], [(1, 2), (4, 5)], [1, (0, 3), (4, 6)]),

([(0, 2), (3, 4)], [(0, 3), (4, 5)]),

([(0, 1), (1, 2), (3, 6)], [(0, 1), (1, 3), (4, 6)]),

([(0, 2), (3, 4), (4, 5), (5, 6)], [(0, 2), (2, 3), (4, 5), (5, 6)]),

([(4, 5)], [(1, 2), (3, 4)], [(2, 3), (4, 5)]),

([(1, 2)], [(1, 3)]),

([(0, 2), (3, 5), (5, 6)], [(0, 3), (4, 5), (5, 6)]),

([(1, 2), (3, 4), (4, 5)], [4, (0, 1), (5, 6)], [1, (0, 2), (2, 3), (4, 6)]),

([(3, 4), (4, 5), (5, 6)], [4, (0, 1), (1, 2)], [(0, 2), (2, 3), (4, 5), (5, 6)]),

([1, (3, 4)], [4, (0, 2), (5, 6)], [1, (0, 3), (4, 6)]),

([(0, 2), (3, 4), (4, 6)], [(4, 5)], [(0, 1), (2, 3), (4, 6)]),

([(4, 5)], [(0, 1), (1, 2)], [(0, 1), (2, 3)]),

([(4, 5)], [(0, 2), (3, 5), (5, 6)], [1, (0, 3), (4, 6)]),

([4, (0, 2)], [(3, 4), (4, 6)], [(0, 1), (2, 3), (4, 6)]),

([(4, 5), (5, 6)], [(0, 1), (1, 2)], [(0, 1), (2, 3), (5, 6)]),

([(4, 5)], [(0, 2), (3, 5), (5, 6)], [(0, 1), (2, 3), (4, 6)]),

([(0, 2), (4, 6)], [(3, 5)], [1, (0, 3), (4, 6)]),

([(1, 2), (4, 6)], [(2, 3), (5, 6)]),

([(0, 1), (1, 2), (3, 4)], [(4, 5), (5, 6)], [(0, 1), (1, 3), (4, 6)]),

([(0, 2), (4, 6)], [(3, 4)], [1, (0, 3), (4, 6)]),

([(4, 6)], [(3, 5)], [(0, 1), (1, 2)], [(0, 1), (2, 3), (4, 6)]),

([(3, 4), (4, 5), (5, 6)], [(1, 2), (4, 5)], [(2, 3), (4, 5), (5, 6)]),

([4, (0, 2), (3, 6)], [(0, 1), (2, 3), (4, 6)]),

([(4, 5), (5, 6)], [(0, 1), (1, 2), (3, 4)], [(0, 2), (2, 3), (4, 5), (5, 6)]),

]

return patterns_raw

@staticmethod

def _short_underslide_up(seeds_only = False):

"""Short underslide going up, in the middle of PMC."""

# Local PMC is 0*-1-2-3-4*, with 1 and 3 paired.

patterns_raw = [

#### Initial patterns

([(2, 3)],),

([], []), ([1], [1]), ([2], [2]), ([2], [1]), ([1, 2], [1, 2]),

([(1, 2)], [1]),

([(2, 3)], [(1, 3)]),

([(1, 3)], [(1, 3)]),

([2, (1, 3)], [2, (1, 3)]),

([(1, 2),(2, 3)], [(1, 2),(2, 3)]),

([(2, 3)], [(1, 2)], [(1, 2)]),

([(1, 3)], [(1, 2)], [(1, 2)]),

#### Seeds for top

([(3, 4)], [(3, 4)]),

([2, (3, 4)], [2, (3, 4)]),

#### Seeds for bottom

([(0, 1)], [(0, 1)]),

([2, (0, 1)], [2, (0, 1)]),

]

if seeds_only:

return patterns_raw

patterns_raw += [

# From seeds for top

([(2, 3), (3, 4)], [(1, 2)], [(1, 2), (2, 4)]),

([(2, 4)], [(1, 4)]),

([(1, 4)], [(1, 4)]),

([2, (1, 4)], [2, (1, 4)]),

([2, (3, 4)], [1, (2, 4)]),

([(1, 2), (2, 4)], [(1, 2), (2, 4)]),

# From seeds for bottom

([(1, 3)], [1, (0, 2)], [1, (0, 2)]),

([(1, 3)], [(0, 2), (3, 4)], [1, (0, 4)]),

([(2, 3)], [(0, 2), (3, 4)], [(0, 2), (3, 4)]),

([(0, 2), (3, 4)], [(0, 1), (3, 4)]),

([(1, 4)], [(0, 1)], [1, (0, 4)]),

([(0, 1), (1, 2), (2, 4)], [(0, 1), (1, 2), (2, 4)]),

([(0, 1), (1, 2)], [(2, 3), (3, 4)], [(1, 2)], [(0, 2), (3, 4)]),

([(1, 3)], [(0, 2), (3, 4)], [(0, 2), (3, 4)]),

([(0, 2)], [(0, 1)]),

([1, (0, 2), (2, 4)], [1, (0, 2), (2, 4)]),

([(0, 1), (1, 4)], [(1, 2)], [(0, 2), (3, 4)]),

([(0, 3)], [(0, 3)]),

([2, (0, 1), (1, 4)], [1, (0, 2), (2, 4)]),

([2, (0, 1), (1, 4)], [2, (0, 3), (3, 4)]),

([(0, 2), (2, 3), (3, 4)], [(0, 2), (2, 3), (3, 4)]),

([(0, 1), (2, 4)], [(1, 2)], [(0, 2), (3, 4)]),

([(2, 3), (3, 4)], [1, (0, 2)], [1, (0, 2), (2, 4)]),

([(0, 1), (2, 4)], [(0, 3), (3, 4)]),

([2, (1, 3)], [2, (0, 1), (3, 4)], [1, 2, (0, 4)]),

([(2, 3)], [(0, 1), (1, 2)], [(0, 1), (1, 2)]),

([(0, 2), (2, 4)], [(0, 2), (2, 4)]),

([(2, 4)], [(0, 1)], [1, (0, 4)]),

([(0, 1), (1, 4)], [(0, 3), (3, 4)]),

([(2, 4)], [(0, 2)], [1, (0, 4)]),

([2, (0, 1)], [(2, 3), (3, 4)], [(1, 2)], [(0, 2), (3, 4)]),

([(1, 3)], [(0, 1), (3, 4)], [1, (0, 4)]),

([(2, 3)], [(0, 1), (3, 4)], [1, (0, 4)]),

([(0, 1), (1, 2)], [(2, 3), (3, 4)], [(0, 3), (3, 4)]),

([2, (0, 3), (3, 4)], [2, (0, 3), (3, 4)]),

([(1, 4)], [(0, 2)], [(0, 2), (3, 4)]),

([(0, 1), (1, 2)], [2, (3, 4)], [(0, 1), (3, 4)]),

([(2, 3), (3, 4)], [(0, 1), (1, 2)], [(0, 1), (1, 2), (2, 4)]),

([(0, 1), (3, 4)], [(0, 1), (3, 4)]),

([2, (0, 3)], [2, (0, 3)]),

([(0, 3), (3, 4)], [(1, 2)], [(0, 2), (3, 4)]),

([(1, 4)], [(0, 2)], [1, (0, 4)]),

([(0, 4)], [(0, 4)]),

([2, (1, 4)], [2, (0, 1)], [1, 2, (0, 4)]),

([(2, 3)], [1, (0, 2)], [1, (0, 2)]),

([2, (0, 4)], [2, (0, 4)]),

([2, (0, 1)], [2, (3, 4)], [(0, 1), (3, 4)]),

([(2, 3)], [(0, 2), (3, 4)], [1, (0, 4)]),

([(0, 3)], [(1, 2)], [(0, 2)]),

([2, (0, 1)], [(2, 3), (3, 4)], [(0, 3), (3, 4)]),

([(1, 3)], [(0, 1), (1, 2)], [(0, 1), (1, 2)]),

([(2, 4)], [(0, 2)], [(0, 2), (3, 4)]),

([(0, 3), (3, 4)], [(0, 3), (3, 4)]),

([2, (0, 1), (3, 4)], [2, (0, 1), (3, 4)]),

([(0, 2), (2, 3)], [(0, 2), (2, 3)]),

]

return patterns_raw

@staticmethod

def _general_underslide_up(seeds_only = False):

"""Underslide of length >= 3 going up, in the middle of PMC."""

# Local PMC at left (D-side) is 0*-1-2*, 3*-4-5-6*, with 1 and 5 paired.

# Local PMC at right (A-side) is 0*-1-2-3*, 4*-5-6*, with 1 and 5

# paired.

patterns_raw = [

#### Initial patterns

([(4, 5)],),

([], []), ([1], [1]), ([2], [4]), ([2], [1]), ([1, 2], [1, 4]),

([(1, 2)], [1]),

#### Seeds for top

([(5, 6)], [(5, 6)]),

([2, (5, 6)], [4, (5, 6)]),

#### Seeds for bottom

([(0, 1)], [(0, 1)]),

([2, (0, 1)], [4, (0, 1)]),

#### Seed for upper middle

([2, (4, 5)], [1, (3, 4)]),

#### Seed for lower middle

([(2, 3)], [(1, 2)]),

]

if seeds_only:

return patterns_raw

patterns_raw += [

# From seeds for top

([2, (5, 6)], [1, (4, 6)]),

# From seeds for bottom

([2, (0, 1)], [2, (5, 6)], [(0, 1), (5, 6)]),

([(0, 2), (5, 6)], [(0, 1), (5, 6)]),

([2, (0, 1), (5, 6)], [4, (0, 1), (5, 6)]),

([(0, 2)], [(0, 1)]),

([(0, 1), (1, 2)], [2, (5, 6)], [(0, 1), (5, 6)]),

([(0, 1), (5, 6)], [(0, 1), (5, 6)]),

# From seed for upper middle

([2, (4, 5)], [4, (3, 5)]),

([1, (4, 6)], [1, (3, 6)]),

([(0, 2), (4, 5), (5, 6)], [(0, 1), (3, 4), (5, 6)]),

([(4, 5)], [(3, 5)]),

([(0, 1), (1, 2), (4, 6)], [(0, 1), (3, 4), (5, 6)]),

([2, (4, 6)], [4, (3, 6)]),

([2, (0, 1)], [2, (4, 5), (5, 6)], [(0, 1), (3, 4), (5, 6)]),

([(4, 5), (5, 6)], [(1, 2)], [(3, 4), (5, 6)]),

([(1, 2), (4, 6)], [(3, 4), (5, 6)]),

([(0, 1), (4, 6)], [(0, 1), (3, 6)]),

([1, 2, (4, 6)], [1, 4, (3, 6)]),

([(4, 5)], [(1, 2)], [(3, 4)]),

([(1, 2), (4, 5)], [1, (3, 4)]),

([2, (0, 1), (4, 6)], [4, (0, 1), (3, 6)]),

([2, (4, 6)], [1, (3, 6)]),

([(0, 1), (1, 2)], [2, (4, 5), (5, 6)], [(0, 1), (3, 4), (5, 6)]),

([(0, 2), (4, 5)], [(0, 1), (3, 4)]),

([2, (4, 6)], [(3, 4), (5, 6)]),

([(4, 5), (5, 6)], [(3, 5), (5, 6)]),

([(4, 6)], [(3, 6)]),

([2, (4, 5), (5, 6)], [1, (3, 4), (4, 6)]),

([(1, 2), (4, 6)], [1, (3, 6)]),

([2, (0, 1), (4, 6)], [(0, 1), (3, 4), (5, 6)]),

([2, (4, 5), (5, 6)], [4, (3, 5), (5, 6)]),

([(0, 2), (4, 6)], [(0, 1), (3, 6)]),

([(4, 5)], [(0, 1), (1, 2)], [(0, 1), (3, 4)]),

([(4, 5), (5, 6)], [(0, 1), (1, 2)], [(0, 1), (3, 4), (5, 6)]),

# From seed for lower middle

([2, (0, 3), (4, 5), (5, 6)], [4, (0, 2), (3, 5), (5, 6)]),

([2, (0, 3), (5, 6)], [4, (0, 2), (5, 6)]),

([(2, 3), (5, 6)], [(0, 1)], [1, (0, 2), (4, 6)]),

([(1, 3), (4, 5)], [(1, 2)], [(1, 2), (3, 4)]),

([(0, 2), (4, 5), (5, 6)], [(1, 2), (2, 3)], [(0, 2), (3, 4), (5, 6)]),

([(1, 3)], [(0, 2), (4, 5)], [1, (0, 2), (3, 4)]),

([2, (4, 5)], [(0, 1), (1, 2), (2, 3)], [(0, 1), (1, 2), (3, 4)]),

([2, (1, 3)], [2, (0, 1), (4, 6)], [1, 4, (0, 2), (3, 6)]),

([(0, 3), (4, 5)], [(0, 2), (3, 5)]),

([(0, 2), (2, 3)], [2, (4, 6)], [(0, 2), (3, 4), (5, 6)]),

([(1, 3), (4, 5)], [(0, 2), (5, 6)], [(0, 2), (3, 4), (5, 6)]),

([(2, 3), (4, 5)], [(0, 1), (1, 2)], [(0, 1), (1, 2), (3, 4)]),

([(0, 1), (1, 2), (2, 3)], [2, (5, 6)], [(0, 1), (1, 2), (4, 6)]),

([(2, 3), (4, 5)], [(0, 2), (5, 6)], [1, (0, 2), (3, 6)]),

([2, (1, 3), (4, 6)], [2, (0, 1)], [1, 4, (0, 2), (3, 6)]),

([(0, 1), (1, 2), (4, 6)], [(1, 2), (2, 3)], [(0, 2), (3, 4), (5, 6)]),

([1, 2, (0, 3)], [1, 4, (0, 2)]),

([(0, 1), (1, 3), (4, 6)], [(1, 2)], [(0, 2), (3, 4), (5, 6)]),

([2, (0, 3), (4, 6)], [4, (0, 2), (3, 6)]),

([(4, 5)], [(1, 3)], [(0, 2)], [(0, 2), (3, 4)]),

([(2, 3)], [(0, 2), (4, 6)], [1, (0, 2), (3, 6)]),

([(0, 1), (2, 3)], [(5, 6)], [(0, 2), (5, 6)]),

([(0, 1), (1, 2)], [2, (4, 5), (5, 6)], [(1, 2), (2, 3)], [(0, 2), (3, 4), (5, 6)]),

([(0, 1), (1, 3)], [(1, 2), (4, 6)], [(0, 2), (3, 4), (5, 6)]),

([(2, 3)], [(0, 1)], [1, (0, 2)]),

([2, (0, 1), (1, 3), (4, 6)], [1, (0, 2), (3, 4), (4, 6)]),

([(1, 3), (4, 6)], [(1, 2), (3, 6)]),

([(1, 2), (4, 6)], [(0, 2), (2, 3)], [(0, 2), (3, 4), (5, 6)]),

([(1, 3), (4, 5)], [(0, 1), (1, 2)], [(0, 1), (1, 2), (3, 4)]),

([1, (4, 6)], [(0, 1), (1, 3)], [1, (0, 2), (3, 6)]),

([(1, 2), (2, 3), (4, 6)], [(1, 2), (3, 4), (4, 6)]),

([2, (0, 1)], [(2, 3), (4, 5), (5, 6)], [(1, 2)], [(0, 2), (3, 4), (5, 6)]),

([2, (0, 3), (4, 5)], [4, (0, 2), (3, 5)]),

([2, (0, 1), (1, 3)], [1, 2, (4, 6)], [1, 4, (0, 2), (3, 6)]),

([(1, 2)], [(0, 2), (2, 3), (4, 6)], [(0, 2), (3, 4), (5, 6)]),

([(4, 5)], [(0, 1), (1, 2)], [(1, 2), (2, 3)], [(0, 2), (3, 4)]),

([2, (1, 3), (4, 5)], [2, (0, 1), (5, 6)], [1, 4, (0, 2), (3, 6)]),

([(4, 5), (5, 6)], [(0, 1), (1, 3)], [(1, 2)], [(0, 2), (3, 4), (5, 6)]),

([2, (1, 3)], [4, (1, 2)]),

([1, (2, 3)], [(1, 2), (4, 5)]),

([2, (4, 5)], [(1, 2), (2, 3)], [(1, 2), (3, 4)]),

([(0, 2), (2, 3), (4, 5), (5, 6)], [(0, 1), (1, 2), (3, 4), (4, 6)]),

([(2, 3)], [(0, 2)], [1, (0, 2)]),

([(0, 2), (4, 5)], [(1, 2), (2, 3)], [(0, 2), (3, 4)]),

([(2, 3)], [(0, 1), (4, 6)], [1, (0, 2), (3, 6)]),

([1, (0, 2), (2, 3)], [2, (5, 6)], [1, (0, 2), (4, 6)]),

([(4, 5), (5, 6)], [(1, 2)], [(0, 2), (2, 3)], [(0, 2), (3, 4), (5, 6)]),

([2, (4, 5), (5, 6)], [(1, 2), (2, 3)], [(1, 2), (3, 4), (4, 6)]),

([(1, 2), (4, 5)], [1, (0, 2), (2, 3)], [1, (0, 2), (3, 4)]),

([(0, 1), (1, 3)], [(1, 2), (4, 6)], [1, (0, 2), (3, 6)]),

([(0, 1), (1, 3)], [(1, 2), (4, 5)], [1, (0, 2), (3, 4)]),

([(0, 1), (2, 3)], [(4, 5), (5, 6)], [(1, 2)], [(0, 2), (3, 4), (5, 6)]),

([(1, 3), (4, 5)], [(0, 1), (5, 6)], [1, (0, 2), (3, 6)]),

([(2, 3), (4, 5), (5, 6)], [(0, 1), (1, 2)], [(0, 1), (1, 2), (3, 4), (4, 6)]),

([(4, 5)], [(1, 2)], [(0, 2), (2, 3)], [(0, 2), (3, 4)]),

([(1, 3), (4, 6)], [(0, 2)], [(0, 2), (3, 4), (5, 6)]),

([(0, 2), (2, 3)], [(0, 2), (4, 5)]),

([1, (0, 3)], [1, (0, 2)]),

([(4, 5), (5, 6)], [(1, 3)], [(0, 2)], [(0, 2), (3, 4), (5, 6)]),

([(1, 3), (4, 5)], [(1, 2), (3, 5)]),

([(2, 3), (5, 6)], [(1, 2), (4, 6)]),

([2, (1, 3), (4, 5)], [4, (1, 2), (3, 5)]),

([2, (0, 1)], [2, (4, 5), (5, 6)], [(1, 2), (2, 3)], [(0, 2), (3, 4), (5, 6)]),

([(2, 3), (4, 5)], [(0, 1), (5, 6)], [1, (0, 2), (3, 6)]),

([(0, 1), (2, 3)], [(1, 2), (4, 6)], [(0, 2), (3, 4), (5, 6)]),

([(2, 3), (4, 6)], [(0, 1)], [1, (0, 2), (3, 6)]),

([(0, 3), (4, 5), (5, 6)], [(1, 2)], [(0, 2), (3, 4), (5, 6)]),

([2, (0, 3), (4, 6)], [(0, 2), (3, 4), (5, 6)]),

([(1, 2), (4, 5)], [(0, 2), (2, 3), (5, 6)], [(0, 2), (3, 4), (5, 6)]),

([2, (4, 5), (5, 6)], [(0, 1), (1, 2), (2, 3)], [(0, 1), (1, 2), (3, 4), (4, 6)]),

([(0, 1), (2, 3)], [(0, 2), (4, 5)]),

([(2, 3), (4, 6)], [(0, 2)], [1, (0, 2), (3, 6)]),

([(2, 3), (4, 5)], [(1, 2)], [(1, 2), (3, 4)]),

([(0, 1), (1, 2)], [(2, 3), (4, 5), (5, 6)], [(0, 2), (3, 5), (5, 6)]),

([(0, 1), (1, 3)], [1, (4, 6)], [1, (0, 2), (3, 6)]),

([(0, 1), (2, 3), (4, 6)], [(0, 2), (3, 5), (5, 6)]),

([2, (1, 3), (4, 6)], [4, (1, 2), (3, 6)]),

([(1, 3)], [(1, 2)]),

([2, (0, 3)], [4, (0, 2)]),

([1, (2, 3)], [(0, 1), (5, 6)], [1, (0, 2), (4, 6)]),

([2, (0, 1)], [(1, 2), (2, 3), (4, 6)], [(0, 2), (3, 4), (5, 6)]),

([(0, 2), (2, 3), (5, 6)], [2, (4, 5)], [1, (0, 2), (3, 4), (4, 6)]),

([(0, 1), (1, 2), (2, 3)], [2, (4, 5), (5, 6)], [(0, 1), (1, 2), (3, 4), (4, 6)]),

([(0, 1), (1, 2)], [(2, 3), (5, 6)], [(0, 2), (5, 6)]),

([(2, 3), (5, 6)], [(0, 2)], [1, (0, 2), (4, 6)]),

([(4, 5)], [(0, 1), (1, 3)], [(1, 2)], [(0, 2), (3, 4)]),

([(0, 3), (4, 5), (5, 6)], [(0, 2), (3, 5), (5, 6)]),

([2, (0, 1), (5, 6)], [(1, 2), (2, 3), (4, 5)], [1, (0, 2), (3, 4), (4, 6)]),

([(0, 3), (5, 6)], [(0, 2), (5, 6)]),

([(0, 1), (2, 3), (5, 6)], [(0, 2), (4, 5), (5, 6)]),

([1, 2, (4, 6)], [2, (0, 1), (1, 3)], [1, 4, (0, 2), (3, 6)]),

([(0, 2), (2, 3), (4, 6)], [(0, 2), (3, 5), (5, 6)]),

([(1, 3), (4, 6)], [(0, 2)], [1, (0, 2), (3, 6)]),

([(1, 3), (4, 5)], [(0, 2), (5, 6)], [1, (0, 2), (3, 6)]),

([(0, 2), (2, 3), (5, 6)], [(0, 2), (4, 5), (5, 6)]),

([(1, 2), (4, 5)], [(0, 1), (1, 2), (2, 3)], [(0, 1), (1, 2), (3, 4)]),

([2, (4, 5)], [1, (0, 2), (2, 3)], [1, (0, 2), (3, 4)]),

([(1, 3)], [(0, 2), (4, 6)], [(0, 2), (3, 4), (5, 6)]),

([(1, 3)], [(0, 2)], [1, (0, 2)]),

([(2, 3), (4, 5), (5, 6)], [(1, 2)], [(1, 2), (3, 4), (4, 6)]),

([(0, 1), (2, 3), (5, 6)], [(1, 2), (4, 5)], [1, (0, 2), (3, 4), (4, 6)]),

([(0, 1), (1, 3)], [(0, 1), (1, 2)]),

([2, (0, 1), (1, 3), (4, 6)], [4, (0, 2), (3, 5), (5, 6)]),

([(0, 2), (2, 3), (4, 5)], [2, (5, 6)], [(0, 2), (3, 4), (5, 6)]),

([2, (0, 3), (4, 5), (5, 6)], [1, (0, 2), (3, 4), (4, 6)]),

([2, (0, 1)], [(2, 3), (5, 6)], [(0, 2), (5, 6)]),

([(0, 1), (2, 3)], [(4, 5), (5, 6)], [(0, 2), (3, 5), (5, 6)]),

([(0, 2), (2, 3), (4, 5)], [(0, 2), (3, 4), (4, 5)]),

([(1, 3)], [(0, 2), (4, 6)], [1, (0, 2), (3, 6)]),

([(1, 3), (4, 6)], [(0, 1)], [1, (0, 2), (3, 6)]),

([(0, 3), (4, 5)], [(1, 2)], [(0, 2), (3, 4)]),

([(2, 3)], [(0, 2), (4, 5)], [1, (0, 2), (3, 4)]),

([(0, 3)], [(0, 2)]),

([(0, 3), (4, 6)], [(0, 2), (3, 6)]),

([(0, 1), (1, 2), (2, 3), (4, 6)], [(0, 1), (1, 2), (3, 4), (4, 6)]),

([(2, 3), (4, 5)], [(1, 2), (3, 5)]),

([(1, 2), (2, 3), (4, 5)], [(1, 2), (3, 4), (4, 5)]),

([(0, 1), (1, 3)], [(1, 2)], [1, (0, 2)]),

([(0, 1), (1, 2)], [(2, 3), (4, 5), (5, 6)], [(1, 2)], [(0, 2), (3, 4), (5, 6)]),

([(0, 1), (1, 3), (4, 6)], [(0, 2), (3, 5), (5, 6)]),

([(1, 2)], [(0, 1), (2, 3)], [1, (0, 2)]),

([(1, 3)], [(0, 1), (4, 6)], [1, (0, 2), (3, 6)]),

([(2, 3), (4, 5)], [1, (0, 2)], [1, (0, 2), (3, 4)]),

([(2, 3), (4, 6)], [(1, 2), (3, 6)]),

([2, (0, 1), (1, 3)], [4, (0, 1), (1, 2)]),

([(4, 5), (5, 6)], [(0, 1), (1, 2)], [(1, 2), (2, 3)], [(0, 2), (3, 4), (5, 6)]),

([2, (0, 1)], [(2, 3), (4, 5), (5, 6)], [(0, 2), (3, 5), (5, 6)]),

([2, (5, 6)], [(0, 2), (2, 3), (4, 5)], [1, (0, 2), (3, 4), (4, 6)]),

([(1, 2), (4, 5)], [(1, 2), (2, 3)], [(1, 2), (3, 4)]),

([(0, 1), (1, 2)], [1, (2, 3)], [1, (0, 2)]),

([(1, 3), (4, 5)], [1, (0, 2)], [1, (0, 2), (3, 4)]),

([1, (2, 3)], [(0, 2), (5, 6)], [1, (0, 2), (4, 6)]),

([(1, 2), (2, 3)], [(1, 2), (4, 5)]),

]