Hot-keys on this page
r m x p toggle line displays
j k next/prev highlighted chunk
0 (zero) top of page
1 (one) first highlighted chunk
r""" Steiner Quadruple Systems
A Steiner Quadruple System on `n` points is a family `SQS_n \subset \binom {[n]} 4` of `4`-sets, such that any set `S\subset [n]` of size three is a subset of exactly one member of `SQS_n`.
This module implements Haim Hanani's constructive proof that a Steiner Quadruple System exists if and only if `n\equiv 2,4 \pmod 6`. Hanani's proof consists in 6 different constructions that build a large Steiner Quadruple System from a smaller one, and though it does not give a very clear understanding of why it works (to say the least)... it does !
The constructions have been implemented while reading two papers simultaneously, for one of them sometimes provides the informations that the other one does not. The first one is Haim Hanani's original paper [Hanani60]_, and the other one is a paper from Horan and Hurlbert which goes through all constructions [HH12]_.
It can be used through the ``designs`` object::
sage: designs.steiner_quadruple_system(8) Incidence structure with 8 points and 14 blocks
REFERENCES:
.. [Hanani60] Haim Hanani, On quadruple systems, pages 145--157, vol. 12, Canadian Journal of Mathematics, 1960 http://cms.math.ca/cjm/v12/cjm1960v12.0145-0157.pdf
.. [HH12] Victoria Horan and Glenn Hurlbert, *Overlap Cycles for Steiner Quadruple Systems*, 2012, :arxiv:`1204.3215`
AUTHORS:
- Nathann Cohen (May 2013, while listening to "*Le Blues Du Pauvre Delahaye*")
Index -----
This module's main function is the following :
.. csv-table:: :class: contentstable :widths: 15, 20, 65 :delim: |
| :func:`steiner_quadruple_system` | Return a Steiner Quadruple System on `n` points
This function redistributes its work among 6 constructions :
.. csv-table:: :class: contentstable :widths: 15, 20, 65 :delim: |
Construction `1` | :func:`two_n` | Return a Steiner Quadruple System on `2n` points Construction `2` | :func:`three_n_minus_two` | Return a Steiner Quadruple System on `3n-2` points Construction `3` | :func:`three_n_minus_eight` | Return a Steiner Quadruple System on `3n-8` points Construction `4` | :func:`three_n_minus_four` | Return a Steiner Quadruple System on `3n-4` points Construction `5` | :func:`four_n_minus_six` | Return a Steiner Quadruple System on `4n-6` points Construction `6` | :func:`twelve_n_minus_ten` | Return a Steiner Quadruple System on `12n-10` points
It also defines two specific Steiner Quadruple Systems that the constructions require, i.e. `SQS_{14}` and `SQS_{38}` as well as the systems of pairs `P_{\alpha}(m)` and `\overline P_{\alpha}(m)` (see [Hanani60]_).
Functions --------- """ from __future__ import print_function from six.moves import range
from sage.misc.cachefunc import cached_function from sage.combinat.designs.incidence_structures import IncidenceStructure
# Construction 1 def two_n(B): r""" Return a Steiner Quadruple System on `2n` points.
INPUT:
- ``B`` -- A Steiner Quadruple System on `n` points.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import two_n sage: for n in range(4, 30): ....: if (n%6) in [2,4]: ....: sqs = designs.steiner_quadruple_system(n) ....: if not two_n(sqs).is_t_design(3,2*n,4,1): ....: print("Something is wrong !")
"""
# Line 1
# Line 2
# Construction 2 def three_n_minus_two(B): """ Return a Steiner Quadruple System on `3n-2` points.
INPUT:
- ``B`` -- A Steiner Quadruple System on `n` points.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import three_n_minus_two sage: for n in range(4, 30): ....: if (n%6) in [2,4]: ....: sqs = designs.steiner_quadruple_system(n) ....: if not three_n_minus_two(sqs).is_t_design(3,3*n-2,4,1): ....: print("Something is wrong !") """ # relabel function # Line 2.
# Line 3.
else: # Line 1.
# Line 4.
# Line 5.
# Construction 3 def three_n_minus_eight(B): r""" Return a Steiner Quadruple System on `3n-8` points.
INPUT:
- ``B`` -- A Steiner Quadruple System on `n` points.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import three_n_minus_eight sage: for n in range(4, 30): ....: if (n%12) == 2: ....: sqs = designs.steiner_quadruple_system(n) ....: if not three_n_minus_eight(sqs).is_t_design(3,3*n-8,4,1): ....: print("Something is wrong !")
"""
raise ValueError("n must be equal to 2 mod 12")
# Line 1.
# Line 2.
# Line 3.
# Line 4.
# Line 5.
# Construction 4 def three_n_minus_four(B): r""" Return a Steiner Quadruple System on `3n-4` points.
INPUT:
- ``B`` -- A Steiner Quadruple System on `n` points where `n\equiv 10\pmod{12}`.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import three_n_minus_four sage: for n in range(4, 30): ....: if n%12 == 10: ....: sqs = designs.steiner_quadruple_system(n) ....: if not three_n_minus_four(sqs).is_t_design(3,3*n-4,4,1): ....: print("Something is wrong !")
"""
raise ValueError("n must be equal to 10 mod 12")
# Line 1/2.
# Line 3.
# Line 4.
# Line 5.
# Construction 5 def four_n_minus_six(B): """ Return a Steiner Quadruple System on `4n-6` points.
INPUT:
- ``B`` -- A Steiner Quadruple System on `n` points.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import four_n_minus_six sage: for n in range(4, 20): ....: if (n%6) in [2,4]: ....: sqs = designs.steiner_quadruple_system(n) ....: if not four_n_minus_six(sqs).is_t_design(3,4*n-6,4,1): ....: print("Something is wrong !")
"""
# Line 1.
# Line 2/3/4/5
# Line 6/7
# Line 8/9
# Line 10
# Construction 6 def twelve_n_minus_ten(B): """ Return a Steiner Quadruple System on `12n-6` points.
INPUT:
- ``B`` -- A Steiner Quadruple System on `n` points.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import twelve_n_minus_ten sage: for n in range(4, 15): ....: if (n%6) in [2,4]: ....: sqs = designs.steiner_quadruple_system(n) ....: if not twelve_n_minus_ten(sqs).is_t_design(3,12*n-10,4,1): ....: print("Something is wrong !")
"""
# Line 1.
# Line 2
# Line 38.3
# Line 38.4-38.7
# Line 38.8
# Line 38.11 # Line 38.12 # Line 38.13
# Line 38.14
# Line 38.9 # Line 38.10
else: # Line 3
def relabel_system(B): r""" Relabels the set so that `\{n-4, n-3, n-2, n-1\}` is in `B`.
INPUT:
- ``B`` -- a list of 4-uples on `0,...,n-1`.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import relabel_system sage: SQS8 = designs.steiner_quadruple_system(8) sage: relabel_system(SQS8) Incidence structure with 8 points and 14 blocks """
B0[0] : n-4, B0[1] : n-3, B0[2] : n-2, B0[3] : n-1 }
else:
def P(alpha, m): r""" Return the collection of pairs `P_{\alpha}(m)`
For more information on this system, see [Hanani60]_.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import P sage: P(3,4) [(0, 5), (2, 7), (4, 1), (6, 3)] """ raise Exception else: else: else: else: else:
def _missing_pair(n,l): r""" Return the smallest `(x,x+1)` that is not contained in `l`.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import _missing_pair sage: _missing_pair(6, [(0,1), (4,5)]) (2, 3) """
def barP(eps, m): r""" Return the collection of pairs `\overline P_{\alpha}(m)`
For more information on this system, see [Hanani60]_.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import barP sage: barP(3,4) [(0, 4), (3, 5), (1, 2)] """
@cached_function def barP_system(m): r""" Return the 1-factorization of `K_{2m}` `\overline P(m)`
For more information on this system, see [Hanani60]_.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import barP_system sage: barP_system(3) [[(4, 3), (2, 5)], [(0, 5), (4, 1)], [(0, 2), (1, 3)], [(1, 5), (4, 2), (0, 3)], [(0, 4), (3, 5), (1, 2)], [(0, 1), (2, 3), (4, 5)]] """
# The first (shorter) collections of pairs, obtained from P by removing # pairs. Those are added to 'last', a new list of pairs
# Pairs of normal length
# Now the points must be relabeled
else: # The first (shorter) collections of pairs, obtained from P by removing # pairs. Those are added to 'last', a new list of pairs
# Pairs of normal length
# Now the points must be relabeled
# Relabeling the points
# Pairs are sorted first according to their cardinality, then using the # number of the smallest point that they do NOT contain.
@cached_function def steiner_quadruple_system(n, check = False): r""" Return a Steiner Quadruple System on `n` points.
INPUT:
- ``n`` -- an integer such that `n\equiv 2,4\pmod 6`
- ``check`` (boolean) -- whether to check that the system is a Steiner Quadruple System before returning it (`False` by default)
EXAMPLES::
sage: sqs4 = designs.steiner_quadruple_system(4) sage: sqs4 Incidence structure with 4 points and 1 blocks sage: sqs4.is_t_design(3,4,4,1) True
sage: sqs8 = designs.steiner_quadruple_system(8) sage: sqs8 Incidence structure with 8 points and 14 blocks sage: sqs8.is_t_design(3,8,4,1) True
TESTS::
sage: for n in range(4, 100): # long time ....: if (n%6) in [2,4]: # long time ....: sqs = designs.steiner_quadruple_system(n, check=True) # long time """ raise ValueError("n mod 6 must be equal to 2 or 4") sqs = IncidenceStructure(38, _SQS38(), copy = False, check = False) nn = (n+8) // 3 sqs = three_n_minus_eight(steiner_quadruple_system(nn, check = False)) elif n%24 in [2,10]: nn = (n+6) // 4 sqs = four_n_minus_six(steiner_quadruple_system(nn, check = False)) elif n%72 in [14,38]: nn = (n+10) // 12 sqs = twelve_n_minus_ten(steiner_quadruple_system(nn, check = False)) else: raise ValueError("This shouldn't happen !")
raise RuntimeError("Something is very very wrong.")
def _SQS14(): r""" Return a Steiner Quadruple System on 14 points.
Obtained from the La Jolla Covering Repository.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import _SQS14 sage: sqs14 = IncidenceStructure(_SQS14()) sage: sqs14.is_t_design(3,14,4,1) True """ [0, 1, 11, 12], [0, 2, 3, 4], [0, 2, 6, 12], [0, 2, 7, 9], [0, 2, 8, 11], [0, 2, 10, 13], [0, 3, 5, 13], [0, 3, 7, 11], [0, 3, 8, 10], [0, 3, 9, 12], [0, 4, 5, 9], [0, 4, 6, 11], [0, 4, 7, 8], [0, 4, 10, 12], [0, 5, 6, 8], [0, 5, 7, 12], [0, 5, 10, 11], [0, 6, 7, 13], [0, 6, 9, 10], [0, 8, 12, 13], [0, 9, 11, 13], [1, 2, 3, 13], [1, 2, 4, 12], [1, 2, 6, 9], [1, 2, 7, 11], [1, 2, 8, 10], [1, 3, 4, 5], [1, 3, 7, 8], [1, 3, 9, 11], [1, 3, 10, 12], [1, 4, 6, 10], [1, 4, 7, 9], [1, 4, 8, 11], [1, 5, 6, 11], [1, 5, 7, 13], [1, 5, 8, 12], [1, 5, 9, 10], [1, 6, 7, 12], [1, 6, 8, 13], [1, 9, 12, 13], [1, 10, 11, 13], [2, 3, 5, 11], [2, 3, 6, 7], [2, 3, 8, 12], [2, 3, 9, 10], [2, 4, 5, 13], [2, 4, 6, 8], [2, 4, 7, 10], [2, 4, 9, 11], [2, 5, 6, 10], [2, 5, 7, 8], [2, 5, 9, 12], [2, 6, 11, 13], [2, 7, 12, 13], [2, 8, 9, 13], [2, 10, 11, 12], [3, 4, 6, 9], [3, 4, 7, 12], [3, 4, 8, 13], [3, 4, 10, 11], [3, 5, 6, 12], [3, 5, 7, 10], [3, 5, 8, 9], [3, 6, 8, 11], [3, 6, 10, 13], [3, 7, 9, 13], [3, 11, 12, 13], [4, 5, 6, 7], [4, 5, 8, 10], [4, 5, 11, 12], [4, 6, 12, 13], [4, 7, 11, 13], [4, 8, 9, 12], [4, 9, 10, 13], [5, 6, 9, 13], [5, 7, 9, 11], [5, 8, 11, 13], [5, 10, 12, 13], [6, 7, 8, 9], [6, 7, 10, 11], [6, 8, 10, 12], [6, 9, 11, 12], [7, 8, 10, 13], [7, 8, 11, 12], [7, 9, 10, 12], [8, 9, 10, 11]]
def _SQS38(): r""" Return a Steiner Quadruple System on 14 points.
Obtained from the La Jolla Covering Repository.
EXAMPLES::
sage: from sage.combinat.designs.steiner_quadruple_systems import _SQS38 sage: sqs38 = IncidenceStructure(_SQS38()) sage: sqs38.is_t_design(3,38,4,1) True """ # From the La Jolla Covering Repository [0, 1, 7, 12], [0, 1, 8, 36], [0, 1, 9, 10], [0, 1, 11, 18], [0, 1, 13, 37], [0, 1, 15, 35], [0, 1, 16, 22], [0, 1, 19, 33], [0, 1, 20, 25], [0, 1, 21, 23], [0, 1, 24, 32], [0, 1, 26, 28], [0, 1, 29, 30], [0, 2, 3, 10], [0, 2, 4, 9], [0, 2, 5, 28], [0, 2, 6, 15], [0, 2, 7, 36], [0, 2, 8, 23], [0, 2, 11, 22], [0, 2, 12, 13], [0, 2, 16, 25], [0, 2, 17, 18], [0, 2, 19, 30], [0, 2, 20, 35], [0, 2, 21, 29], [0, 2, 24, 34], [0, 2, 26, 31], [0, 2, 27, 32], [0, 2, 33, 37], [0, 3, 4, 18], [0, 3, 5, 23], [0, 3, 6, 32], [0, 3, 7, 19], [0, 3, 8, 20], [0, 3, 9, 17], [0, 3, 11, 25], [0, 3, 12, 24], [0, 3, 13, 27], [0, 3, 14, 31], [0, 3, 15, 22], [0, 3, 16, 28], [0, 3, 21, 33], [0, 3, 26, 36], [0, 3, 29, 35], [0, 3, 30, 37], [0, 4, 5, 7], [0, 4, 6, 28], [0, 4, 8, 25], [0, 4, 10, 30], [0, 4, 11, 20], [0, 4, 12, 32], [0, 4, 13, 36], [0, 4, 14, 29], [0, 4, 15, 27], [0, 4, 16, 35], [0, 4, 17, 22], [0, 4, 19, 23], [0, 4, 21, 34], [0, 4, 24, 33], [0, 4, 26, 37], [0, 5, 6, 24], [0, 5, 8, 26], [0, 5, 9, 29], [0, 5, 10, 20], [0, 5, 11, 13], [0, 5, 12, 14], [0, 5, 15, 33], [0, 5, 16, 37], [0, 5, 17, 35], [0, 5, 18, 19], [0, 5, 21, 25], [0, 5, 22, 30], [0, 5, 31, 32], [0, 5, 34, 36], [0, 6, 7, 30], [0, 6, 8, 33], [0, 6, 9, 12], [0, 6, 10, 18], [0, 6, 11, 37], [0, 6, 13, 31], [0, 6, 14, 35], [0, 6, 16, 29], [0, 6, 19, 25], [0, 6, 20, 27], [0, 6, 21, 36], [0, 6, 22, 23], [0, 6, 26, 34], [0, 7, 8, 11], [0, 7, 9, 33], [0, 7, 10, 21], [0, 7, 13, 20], [0, 7, 14, 22], [0, 7, 15, 31], [0, 7, 16, 34], [0, 7, 17, 29], [0, 7, 18, 24], [0, 7, 23, 26], [0, 7, 25, 32], [0, 7, 27, 28], [0, 7, 35, 37], [0, 8, 9, 37], [0, 8, 10, 27], [0, 8, 12, 18], [0, 8, 13, 30], [0, 8, 14, 15], [0, 8, 16, 21], [0, 8, 17, 19], [0, 8, 22, 35], [0, 8, 24, 31], [0, 8, 28, 34], [0, 8, 29, 32], [0, 9, 11, 30], [0, 9, 13, 23], [0, 9, 14, 18], [0, 9, 15, 25], [0, 9, 16, 26], [0, 9, 19, 28], [0, 9, 20, 36], [0, 9, 21, 35], [0, 9, 22, 24], [0, 9, 27, 31], [0, 9, 32, 34], [0, 10, 11, 36], [0, 10, 12, 15], [0, 10, 13, 26], [0, 10, 14, 16], [0, 10, 17, 37], [0, 10, 19, 29], [0, 10, 22, 31], [0, 10, 23, 32], [0, 10, 24, 35], [0, 10, 25, 34], [0, 10, 28, 33], [0, 11, 12, 16], [0, 11, 14, 24], [0, 11, 15, 26], [0, 11, 17, 31], [0, 11, 19, 21], [0, 11, 23, 34], [0, 11, 27, 29], [0, 11, 28, 35], [0, 11, 32, 33], [0, 12, 17, 20], [0, 12, 19, 35], [0, 12, 21, 28], [0, 12, 22, 25], [0, 12, 23, 27], [0, 12, 26, 29], [0, 12, 30, 33], [0, 12, 31, 34], [0, 12, 36, 37], [0, 13, 14, 33], [0, 13, 15, 29], [0, 13, 16, 24], [0, 13, 17, 21], [0, 13, 18, 34], [0, 13, 19, 32], [0, 13, 22, 28], [0, 13, 25, 35], [0, 14, 17, 26], [0, 14, 19, 20], [0, 14, 21, 32], [0, 14, 23, 36], [0, 14, 25, 28], [0, 14, 27, 30], [0, 14, 34, 37], [0, 15, 16, 36], [0, 15, 17, 23], [0, 15, 18, 20], [0, 15, 19, 34], [0, 15, 21, 37], [0, 15, 24, 28], [0, 15, 30, 32], [0, 16, 17, 32], [0, 16, 18, 27], [0, 16, 19, 31], [0, 16, 20, 33], [0, 16, 23, 30], [0, 17, 24, 27], [0, 17, 25, 33], [0, 17, 28, 36], [0, 17, 30, 34], [0, 18, 21, 26], [0, 18, 22, 29], [0, 18, 23, 28], [0, 18, 25, 31], [0, 18, 30, 35], [0, 18, 32, 37], [0, 18, 33, 36], [0, 19, 22, 26], [0, 19, 24, 37], [0, 19, 27, 36], [0, 20, 21, 31], [0, 20, 22, 37], [0, 20, 23, 24], [0, 20, 26, 30], [0, 20, 28, 32], [0, 20, 29, 34], [0, 21, 22, 27], [0, 21, 24, 30], [0, 22, 32, 36], [0, 22, 33, 34], [0, 23, 25, 29], [0, 23, 31, 37], [0, 23, 33, 35], [0, 24, 25, 26], [0, 24, 29, 36], [0, 25, 27, 37], [0, 25, 30, 36], [0, 26, 27, 33], [0, 26, 32, 35], [0, 27, 34, 35], [0, 28, 29, 37], [0, 28, 30, 31], [0, 29, 31, 33], [0, 31, 35, 36], [1, 2, 3, 15], [1, 2, 4, 35], [1, 2, 5, 32], [1, 2, 6, 28], [1, 2, 7, 18], [1, 2, 8, 13], [1, 2, 9, 37], [1, 2, 10, 11], [1, 2, 12, 19], [1, 2, 16, 36], [1, 2, 17, 23], [1, 2, 20, 34], [1, 2, 21, 26], [1, 2, 22, 24], [1, 2, 25, 33], [1, 2, 27, 29], [1, 2, 30, 31], [1, 3, 4, 11], [1, 3, 5, 10], [1, 3, 6, 29], [1, 3, 7, 16], [1, 3, 8, 37], [1, 3, 9, 24], [1, 3, 12, 23], [1, 3, 13, 14], [1, 3, 17, 26], [1, 3, 18, 19], [1, 3, 20, 31], [1, 3, 21, 36], [1, 3, 22, 30], [1, 3, 25, 35], [1, 3, 27, 32], [1, 3, 28, 33], [1, 4, 5, 19], [1, 4, 6, 24], [1, 4, 7, 33], [1, 4, 8, 20], [1, 4, 9, 21], [1, 4, 10, 18], [1, 4, 12, 26], [1, 4, 13, 25], [1, 4, 14, 28], [1, 4, 15, 32], [1, 4, 16, 23], [1, 4, 17, 29], [1, 4, 22, 34], [1, 4, 27, 37], [1, 4, 30, 36], [1, 5, 6, 8], [1, 5, 7, 29], [1, 5, 9, 26], [1, 5, 11, 31], [1, 5, 12, 21], [1, 5, 13, 33], [1, 5, 14, 37], [1, 5, 15, 30], [1, 5, 16, 28], [1, 5, 17, 36], [1, 5, 18, 23], [1, 5, 20, 24], [1, 5, 22, 35], [1, 5, 25, 34], [1, 6, 7, 25], [1, 6, 9, 27], [1, 6, 10, 30], [1, 6, 11, 21], [1, 6, 12, 14], [1, 6, 13, 15], [1, 6, 16, 34], [1, 6, 18, 36], [1, 6, 19, 20], [1, 6, 22, 26], [1, 6, 23, 31], [1, 6, 32, 33], [1, 6, 35, 37], [1, 7, 8, 31], [1, 7, 9, 34], [1, 7, 10, 13], [1, 7, 11, 19], [1, 7, 14, 32], [1, 7, 15, 36], [1, 7, 17, 30], [1, 7, 20, 26], [1, 7, 21, 28], [1, 7, 22, 37], [1, 7, 23, 24], [1, 7, 27, 35], [1, 8, 9, 12], [1, 8, 10, 34], [1, 8, 11, 22], [1, 8, 14, 21], [1, 8, 15, 23], [1, 8, 16, 32], [1, 8, 17, 35], [1, 8, 18, 30], [1, 8, 19, 25], [1, 8, 24, 27], [1, 8, 26, 33], [1, 8, 28, 29], [1, 9, 11, 28], [1, 9, 13, 19], [1, 9, 14, 31], [1, 9, 15, 16], [1, 9, 17, 22], [1, 9, 18, 20], [1, 9, 23, 36], [1, 9, 25, 32], [1, 9, 29, 35], [1, 9, 30, 33], [1, 10, 12, 31], [1, 10, 14, 24], [1, 10, 15, 19], [1, 10, 16, 26], [1, 10, 17, 27], [1, 10, 20, 29], [1, 10, 21, 37], [1, 10, 22, 36], [1, 10, 23, 25], [1, 10, 28, 32], [1, 10, 33, 35], [1, 11, 12, 37], [1, 11, 13, 16], [1, 11, 14, 27], [1, 11, 15, 17], [1, 11, 20, 30], [1, 11, 23, 32], [1, 11, 24, 33], [1, 11, 25, 36], [1, 11, 26, 35], [1, 11, 29, 34], [1, 12, 13, 17], [1, 12, 15, 25], [1, 12, 16, 27], [1, 12, 18, 32], [1, 12, 20, 22], [1, 12, 24, 35], [1, 12, 28, 30], [1, 12, 29, 36], [1, 12, 33, 34], [1, 13, 18, 21], [1, 13, 20, 36], [1, 13, 22, 29], [1, 13, 23, 26], [1, 13, 24, 28], [1, 13, 27, 30], [1, 13, 31, 34], [1, 13, 32, 35], [1, 14, 15, 34], [1, 14, 16, 30], [1, 14, 17, 25], [1, 14, 18, 22], [1, 14, 19, 35], [1, 14, 20, 33], [1, 14, 23, 29], [1, 14, 26, 36], [1, 15, 18, 27], [1, 15, 20, 21], [1, 15, 22, 33], [1, 15, 24, 37], [1, 15, 26, 29], [1, 15, 28, 31], [1, 16, 17, 37], [1, 16, 18, 24], [1, 16, 19, 21], [1, 16, 20, 35], [1, 16, 25, 29], [1, 16, 31, 33], [1, 17, 18, 33], [1, 17, 19, 28], [1, 17, 20, 32], [1, 17, 21, 34], [1, 17, 24, 31], [1, 18, 25, 28], [1, 18, 26, 34], [1, 18, 29, 37], [1, 18, 31, 35], [1, 19, 22, 27], [1, 19, 23, 30], [1, 19, 24, 29], [1, 19, 26, 32], [1, 19, 31, 36], [1, 19, 34, 37], [1, 20, 23, 27], [1, 20, 28, 37], [1, 21, 22, 32], [1, 21, 24, 25], [1, 21, 27, 31], [1, 21, 29, 33], [1, 21, 30, 35], [1, 22, 23, 28], [1, 22, 25, 31], [1, 23, 33, 37], [1, 23, 34, 35], [1, 24, 26, 30], [1, 24, 34, 36], [1, 25, 26, 27], [1, 25, 30, 37], [1, 26, 31, 37], [1, 27, 28, 34], [1, 27, 33, 36], [1, 28, 35, 36], [1, 29, 31, 32], [1, 30, 32, 34], [1, 32, 36, 37], [2, 3, 4, 16], [2, 3, 5, 36], [2, 3, 6, 33], [2, 3, 7, 29], [2, 3, 8, 19], [2, 3, 9, 14], [2, 3, 11, 12], [2, 3, 13, 20], [2, 3, 17, 37], [2, 3, 18, 24], [2, 3, 21, 35], [2, 3, 22, 27], [2, 3, 23, 25], [2, 3, 26, 34], [2, 3, 28, 30], [2, 3, 31, 32], [2, 4, 5, 12], [2, 4, 6, 11], [2, 4, 7, 30], [2, 4, 8, 17], [2, 4, 10, 25], [2, 4, 13, 24], [2, 4, 14, 15], [2, 4, 18, 27], [2, 4, 19, 20], [2, 4, 21, 32], [2, 4, 22, 37], [2, 4, 23, 31], [2, 4, 26, 36], [2, 4, 28, 33], [2, 4, 29, 34], [2, 5, 6, 20], [2, 5, 7, 25], [2, 5, 8, 34], [2, 5, 9, 21], [2, 5, 10, 22], [2, 5, 11, 19], [2, 5, 13, 27], [2, 5, 14, 26], [2, 5, 15, 29], [2, 5, 16, 33], [2, 5, 17, 24], [2, 5, 18, 30], [2, 5, 23, 35], [2, 5, 31, 37], [2, 6, 7, 9], [2, 6, 8, 30], [2, 6, 10, 27], [2, 6, 12, 32], [2, 6, 13, 22], [2, 6, 14, 34], [2, 6, 16, 31], [2, 6, 17, 29], [2, 6, 18, 37], [2, 6, 19, 24], [2, 6, 21, 25], [2, 6, 23, 36], [2, 6, 26, 35], [2, 7, 8, 26], [2, 7, 10, 28], [2, 7, 11, 31], [2, 7, 12, 22], [2, 7, 13, 15], [2, 7, 14, 16], [2, 7, 17, 35], [2, 7, 19, 37], [2, 7, 20, 21], [2, 7, 23, 27], [2, 7, 24, 32], [2, 7, 33, 34], [2, 8, 9, 32], [2, 8, 10, 35], [2, 8, 11, 14], [2, 8, 12, 20], [2, 8, 15, 33], [2, 8, 16, 37], [2, 8, 18, 31], [2, 8, 21, 27], [2, 8, 22, 29], [2, 8, 24, 25], [2, 8, 28, 36], [2, 9, 10, 13], [2, 9, 11, 35], [2, 9, 12, 23], [2, 9, 15, 22], [2, 9, 16, 24], [2, 9, 17, 33], [2, 9, 18, 36], [2, 9, 19, 31], [2, 9, 20, 26], [2, 9, 25, 28], [2, 9, 27, 34], [2, 9, 29, 30], [2, 10, 12, 29], [2, 10, 14, 20], [2, 10, 15, 32], [2, 10, 16, 17], [2, 10, 18, 23], [2, 10, 19, 21], [2, 10, 24, 37], [2, 10, 26, 33], [2, 10, 30, 36], [2, 10, 31, 34], [2, 11, 13, 32], [2, 11, 15, 25], [2, 11, 16, 20], [2, 11, 17, 27], [2, 11, 18, 28], [2, 11, 21, 30], [2, 11, 23, 37], [2, 11, 24, 26], [2, 11, 29, 33], [2, 11, 34, 36], [2, 12, 14, 17], [2, 12, 15, 28], [2, 12, 16, 18], [2, 12, 21, 31], [2, 12, 24, 33], [2, 12, 25, 34], [2, 12, 26, 37], [2, 12, 27, 36], [2, 12, 30, 35], [2, 13, 14, 18], [2, 13, 16, 26], [2, 13, 17, 28], [2, 13, 19, 33], [2, 13, 21, 23], [2, 13, 25, 36], [2, 13, 29, 31], [2, 13, 30, 37], [2, 13, 34, 35], [2, 14, 19, 22], [2, 14, 21, 37], [2, 14, 23, 30], [2, 14, 24, 27], [2, 14, 25, 29], [2, 14, 28, 31], [2, 14, 32, 35], [2, 14, 33, 36], [2, 15, 16, 35], [2, 15, 17, 31], [2, 15, 18, 26], [2, 15, 19, 23], [2, 15, 20, 36], [2, 15, 21, 34], [2, 15, 24, 30], [2, 15, 27, 37], [2, 16, 19, 28], [2, 16, 21, 22], [2, 16, 23, 34], [2, 16, 27, 30], [2, 16, 29, 32], [2, 17, 19, 25], [2, 17, 20, 22], [2, 17, 21, 36], [2, 17, 26, 30], [2, 17, 32, 34], [2, 18, 19, 34], [2, 18, 20, 29], [2, 18, 21, 33], [2, 18, 22, 35], [2, 18, 25, 32], [2, 19, 26, 29], [2, 19, 27, 35], [2, 19, 32, 36], [2, 20, 23, 28], [2, 20, 24, 31], [2, 20, 25, 30], [2, 20, 27, 33], [2, 20, 32, 37], [2, 21, 24, 28], [2, 22, 23, 33], [2, 22, 25, 26], [2, 22, 28, 32], [2, 22, 30, 34], [2, 22, 31, 36], [2, 23, 24, 29], [2, 23, 26, 32], [2, 24, 35, 36], [2, 25, 27, 31], [2, 25, 35, 37], [2, 26, 27, 28], [2, 28, 29, 35], [2, 28, 34, 37], [2, 29, 36, 37], [2, 30, 32, 33], [2, 31, 33, 35], [3, 4, 5, 17], [3, 4, 6, 37], [3, 4, 7, 34], [3, 4, 8, 30], [3, 4, 9, 20], [3, 4, 10, 15], [3, 4, 12, 13], [3, 4, 14, 21], [3, 4, 19, 25], [3, 4, 22, 36], [3, 4, 23, 28], [3, 4, 24, 26], [3, 4, 27, 35], [3, 4, 29, 31], [3, 4, 32, 33], [3, 5, 6, 13], [3, 5, 7, 12], [3, 5, 8, 31], [3, 5, 9, 18], [3, 5, 11, 26], [3, 5, 14, 25], [3, 5, 15, 16], [3, 5, 19, 28], [3, 5, 20, 21], [3, 5, 22, 33], [3, 5, 24, 32], [3, 5, 27, 37], [3, 5, 29, 34], [3, 5, 30, 35], [3, 6, 7, 21], [3, 6, 8, 26], [3, 6, 9, 35], [3, 6, 10, 22], [3, 6, 11, 23], [3, 6, 12, 20], [3, 6, 14, 28], [3, 6, 15, 27], [3, 6, 16, 30], [3, 6, 17, 34], [3, 6, 18, 25], [3, 6, 19, 31], [3, 6, 24, 36], [3, 7, 8, 10], [3, 7, 9, 31], [3, 7, 11, 28], [3, 7, 13, 33], [3, 7, 14, 23], [3, 7, 15, 35], [3, 7, 17, 32], [3, 7, 18, 30], [3, 7, 20, 25], [3, 7, 22, 26], [3, 7, 24, 37], [3, 7, 27, 36], [3, 8, 9, 27], [3, 8, 11, 29], [3, 8, 12, 32], [3, 8, 13, 23], [3, 8, 14, 16], [3, 8, 15, 17], [3, 8, 18, 36], [3, 8, 21, 22], [3, 8, 24, 28], [3, 8, 25, 33], [3, 8, 34, 35], [3, 9, 10, 33], [3, 9, 11, 36], [3, 9, 12, 15], [3, 9, 13, 21], [3, 9, 16, 34], [3, 9, 19, 32], [3, 9, 22, 28], [3, 9, 23, 30], [3, 9, 25, 26], [3, 9, 29, 37], [3, 10, 11, 14], [3, 10, 12, 36], [3, 10, 13, 24], [3, 10, 16, 23], [3, 10, 17, 25], [3, 10, 18, 34], [3, 10, 19, 37], [3, 10, 20, 32], [3, 10, 21, 27], [3, 10, 26, 29], [3, 10, 28, 35], [3, 10, 30, 31], [3, 11, 13, 30], [3, 11, 15, 21], [3, 11, 16, 33], [3, 11, 17, 18], [3, 11, 19, 24], [3, 11, 20, 22], [3, 11, 27, 34], [3, 11, 31, 37], [3, 11, 32, 35], [3, 12, 14, 33], [3, 12, 16, 26], [3, 12, 17, 21], [3, 12, 18, 28], [3, 12, 19, 29], [3, 12, 22, 31], [3, 12, 25, 27], [3, 12, 30, 34], [3, 12, 35, 37], [3, 13, 15, 18], [3, 13, 16, 29], [3, 13, 17, 19], [3, 13, 22, 32], [3, 13, 25, 34], [3, 13, 26, 35], [3, 13, 28, 37], [3, 13, 31, 36], [3, 14, 15, 19], [3, 14, 17, 27], [3, 14, 18, 29], [3, 14, 20, 34], [3, 14, 22, 24], [3, 14, 26, 37], [3, 14, 30, 32], [3, 14, 35, 36], [3, 15, 20, 23], [3, 15, 24, 31], [3, 15, 25, 28], [3, 15, 26, 30], [3, 15, 29, 32], [3, 15, 33, 36], [3, 15, 34, 37], [3, 16, 17, 36], [3, 16, 18, 32], [3, 16, 19, 27], [3, 16, 20, 24], [3, 16, 21, 37], [3, 16, 22, 35], [3, 16, 25, 31], [3, 17, 20, 29], [3, 17, 22, 23], [3, 17, 24, 35], [3, 17, 28, 31], [3, 17, 30, 33], [3, 18, 20, 26], [3, 18, 21, 23], [3, 18, 22, 37], [3, 18, 27, 31], [3, 18, 33, 35], [3, 19, 20, 35], [3, 19, 21, 30], [3, 19, 22, 34], [3, 19, 23, 36], [3, 19, 26, 33], [3, 20, 27, 30], [3, 20, 28, 36], [3, 20, 33, 37], [3, 21, 24, 29], [3, 21, 25, 32], [3, 21, 26, 31], [3, 21, 28, 34], [3, 22, 25, 29], [3, 23, 24, 34], [3, 23, 26, 27], [3, 23, 29, 33], [3, 23, 31, 35], [3, 23, 32, 37], [3, 24, 25, 30], [3, 24, 27, 33], [3, 25, 36, 37], [3, 26, 28, 32], [3, 27, 28, 29], [3, 29, 30, 36], [3, 31, 33, 34], [3, 32, 34, 36], [4, 5, 6, 18], [4, 5, 8, 35], [4, 5, 9, 31], [4, 5, 10, 21], [4, 5, 11, 16], [4, 5, 13, 14], [4, 5, 15, 22], [4, 5, 20, 26], [4, 5, 23, 37], [4, 5, 24, 29], [4, 5, 25, 27], [4, 5, 28, 36], [4, 5, 30, 32], [4, 5, 33, 34], [4, 6, 7, 14], [4, 6, 8, 13], [4, 6, 9, 32], [4, 6, 10, 19], [4, 6, 12, 27], [4, 6, 15, 26], [4, 6, 16, 17], [4, 6, 20, 29], [4, 6, 21, 22], [4, 6, 23, 34], [4, 6, 25, 33], [4, 6, 30, 35], [4, 6, 31, 36], [4, 7, 8, 22], [4, 7, 9, 27], [4, 7, 10, 36], [4, 7, 11, 23], [4, 7, 12, 24], [4, 7, 13, 21], [4, 7, 15, 29], [4, 7, 16, 28], [4, 7, 17, 31], [4, 7, 18, 35], [4, 7, 19, 26], [4, 7, 20, 32], [4, 7, 25, 37], [4, 8, 9, 11], [4, 8, 10, 32], [4, 8, 12, 29], [4, 8, 14, 34], [4, 8, 15, 24], [4, 8, 16, 36], [4, 8, 18, 33], [4, 8, 19, 31], [4, 8, 21, 26], [4, 8, 23, 27], [4, 8, 28, 37], [4, 9, 10, 28], [4, 9, 12, 30], [4, 9, 13, 33], [4, 9, 14, 24], [4, 9, 15, 17], [4, 9, 16, 18], [4, 9, 19, 37], [4, 9, 22, 23], [4, 9, 25, 29], [4, 9, 26, 34], [4, 9, 35, 36], [4, 10, 11, 34], [4, 10, 12, 37], [4, 10, 13, 16], [4, 10, 14, 22], [4, 10, 17, 35], [4, 10, 20, 33], [4, 10, 23, 29], [4, 10, 24, 31], [4, 10, 26, 27], [4, 11, 12, 15], [4, 11, 13, 37], [4, 11, 14, 25], [4, 11, 17, 24], [4, 11, 18, 26], [4, 11, 19, 35], [4, 11, 21, 33], [4, 11, 22, 28], [4, 11, 27, 30], [4, 11, 29, 36], [4, 11, 31, 32], [4, 12, 14, 31], [4, 12, 16, 22], [4, 12, 17, 34], [4, 12, 18, 19], [4, 12, 20, 25], [4, 12, 21, 23], [4, 12, 28, 35], [4, 12, 33, 36], [4, 13, 15, 34], [4, 13, 17, 27], [4, 13, 18, 22], [4, 13, 19, 29], [4, 13, 20, 30], [4, 13, 23, 32], [4, 13, 26, 28], [4, 13, 31, 35], [4, 14, 16, 19], [4, 14, 17, 30], [4, 14, 18, 20], [4, 14, 23, 33], [4, 14, 26, 35], [4, 14, 27, 36], [4, 14, 32, 37], [4, 15, 16, 20], [4, 15, 18, 28], [4, 15, 19, 30], [4, 15, 21, 35], [4, 15, 23, 25], [4, 15, 31, 33], [4, 15, 36, 37], [4, 16, 21, 24], [4, 16, 25, 32], [4, 16, 26, 29], [4, 16, 27, 31], [4, 16, 30, 33], [4, 16, 34, 37], [4, 17, 18, 37], [4, 17, 19, 33], [4, 17, 20, 28], [4, 17, 21, 25], [4, 17, 23, 36], [4, 17, 26, 32], [4, 18, 21, 30], [4, 18, 23, 24], [4, 18, 25, 36], [4, 18, 29, 32], [4, 18, 31, 34], [4, 19, 21, 27], [4, 19, 22, 24], [4, 19, 28, 32], [4, 19, 34, 36], [4, 20, 21, 36], [4, 20, 22, 31], [4, 20, 23, 35], [4, 20, 24, 37], [4, 20, 27, 34], [4, 21, 28, 31], [4, 21, 29, 37], [4, 22, 25, 30], [4, 22, 26, 33], [4, 22, 27, 32], [4, 22, 29, 35], [4, 23, 26, 30], [4, 24, 25, 35], [4, 24, 27, 28], [4, 24, 30, 34], [4, 24, 32, 36], [4, 25, 26, 31], [4, 25, 28, 34], [4, 27, 29, 33], [4, 28, 29, 30], [4, 30, 31, 37], [4, 32, 34, 35], [4, 33, 35, 37], [5, 6, 7, 19], [5, 6, 9, 36], [5, 6, 10, 32], [5, 6, 11, 22], [5, 6, 12, 17], [5, 6, 14, 15], [5, 6, 16, 23], [5, 6, 21, 27], [5, 6, 25, 30], [5, 6, 26, 28], [5, 6, 29, 37], [5, 6, 31, 33], [5, 6, 34, 35], [5, 7, 8, 15], [5, 7, 9, 14], [5, 7, 10, 33], [5, 7, 11, 20], [5, 7, 13, 28], [5, 7, 16, 27], [5, 7, 17, 18], [5, 7, 21, 30], [5, 7, 22, 23], [5, 7, 24, 35], [5, 7, 26, 34], [5, 7, 31, 36], [5, 7, 32, 37], [5, 8, 9, 23], [5, 8, 10, 28], [5, 8, 11, 37], [5, 8, 12, 24], [5, 8, 13, 25], [5, 8, 14, 22], [5, 8, 16, 30], [5, 8, 17, 29], [5, 8, 18, 32], [5, 8, 19, 36], [5, 8, 20, 27], [5, 8, 21, 33], [5, 9, 10, 12], [5, 9, 11, 33], [5, 9, 13, 30], [5, 9, 15, 35], [5, 9, 16, 25], [5, 9, 17, 37], [5, 9, 19, 34], [5, 9, 20, 32], [5, 9, 22, 27], [5, 9, 24, 28], [5, 10, 11, 29], [5, 10, 13, 31], [5, 10, 14, 34], [5, 10, 15, 25], [5, 10, 16, 18], [5, 10, 17, 19], [5, 10, 23, 24], [5, 10, 26, 30], [5, 10, 27, 35], [5, 10, 36, 37], [5, 11, 12, 35], [5, 11, 14, 17], [5, 11, 15, 23], [5, 11, 18, 36], [5, 11, 21, 34], [5, 11, 24, 30], [5, 11, 25, 32], [5, 11, 27, 28], [5, 12, 13, 16], [5, 12, 15, 26], [5, 12, 18, 25], [5, 12, 19, 27], [5, 12, 20, 36], [5, 12, 22, 34], [5, 12, 23, 29], [5, 12, 28, 31], [5, 12, 30, 37], [5, 12, 32, 33], [5, 13, 15, 32], [5, 13, 17, 23], [5, 13, 18, 35], [5, 13, 19, 20], [5, 13, 21, 26], [5, 13, 22, 24], [5, 13, 29, 36], [5, 13, 34, 37], [5, 14, 16, 35], [5, 14, 18, 28], [5, 14, 19, 23], [5, 14, 20, 30], [5, 14, 21, 31], [5, 14, 24, 33], [5, 14, 27, 29], [5, 14, 32, 36], [5, 15, 17, 20], [5, 15, 18, 31], [5, 15, 19, 21], [5, 15, 24, 34], [5, 15, 27, 36], [5, 15, 28, 37], [5, 16, 17, 21], [5, 16, 19, 29], [5, 16, 20, 31], [5, 16, 22, 36], [5, 16, 24, 26], [5, 16, 32, 34], [5, 17, 22, 25], [5, 17, 26, 33], [5, 17, 27, 30], [5, 17, 28, 32], [5, 17, 31, 34], [5, 18, 20, 34], [5, 18, 21, 29], [5, 18, 22, 26], [5, 18, 24, 37], [5, 18, 27, 33], [5, 19, 22, 31], [5, 19, 24, 25], [5, 19, 26, 37], [5, 19, 30, 33], [5, 19, 32, 35], [5, 20, 22, 28], [5, 20, 23, 25], [5, 20, 29, 33], [5, 20, 35, 37], [5, 21, 22, 37], [5, 21, 23, 32], [5, 21, 24, 36], [5, 21, 28, 35], [5, 22, 29, 32], [5, 23, 26, 31], [5, 23, 27, 34], [5, 23, 28, 33], [5, 23, 30, 36], [5, 24, 27, 31], [5, 25, 26, 36], [5, 25, 28, 29], [5, 25, 31, 35], [5, 25, 33, 37], [5, 26, 27, 32], [5, 26, 29, 35], [5, 28, 30, 34], [5, 29, 30, 31], [5, 33, 35, 36], [6, 7, 8, 20], [6, 7, 10, 37], [6, 7, 11, 33], [6, 7, 12, 23], [6, 7, 13, 18], [6, 7, 15, 16], [6, 7, 17, 24], [6, 7, 22, 28], [6, 7, 26, 31], [6, 7, 27, 29], [6, 7, 32, 34], [6, 7, 35, 36], [6, 8, 9, 16], [6, 8, 10, 15], [6, 8, 11, 34], [6, 8, 12, 21], [6, 8, 14, 29], [6, 8, 17, 28], [6, 8, 18, 19], [6, 8, 22, 31], [6, 8, 23, 24], [6, 8, 25, 36], [6, 8, 27, 35], [6, 8, 32, 37], [6, 9, 10, 24], [6, 9, 11, 29], [6, 9, 13, 25], [6, 9, 14, 26], [6, 9, 15, 23], [6, 9, 17, 31], [6, 9, 18, 30], [6, 9, 19, 33], [6, 9, 20, 37], [6, 9, 21, 28], [6, 9, 22, 34], [6, 10, 11, 13], [6, 10, 12, 34], [6, 10, 14, 31], [6, 10, 16, 36], [6, 10, 17, 26], [6, 10, 20, 35], [6, 10, 21, 33], [6, 10, 23, 28], [6, 10, 25, 29], [6, 11, 12, 30], [6, 11, 14, 32], [6, 11, 15, 35], [6, 11, 16, 26], [6, 11, 17, 19], [6, 11, 18, 20], [6, 11, 24, 25], [6, 11, 27, 31], [6, 11, 28, 36], [6, 12, 13, 36], [6, 12, 15, 18], [6, 12, 16, 24], [6, 12, 19, 37], [6, 12, 22, 35], [6, 12, 25, 31], [6, 12, 26, 33], [6, 12, 28, 29], [6, 13, 14, 17], [6, 13, 16, 27], [6, 13, 19, 26], [6, 13, 20, 28], [6, 13, 21, 37], [6, 13, 23, 35], [6, 13, 24, 30], [6, 13, 29, 32], [6, 13, 33, 34], [6, 14, 16, 33], [6, 14, 18, 24], [6, 14, 19, 36], [6, 14, 20, 21], [6, 14, 22, 27], [6, 14, 23, 25], [6, 14, 30, 37], [6, 15, 17, 36], [6, 15, 19, 29], [6, 15, 20, 24], [6, 15, 21, 31], [6, 15, 22, 32], [6, 15, 25, 34], [6, 15, 28, 30], [6, 15, 33, 37], [6, 16, 18, 21], [6, 16, 19, 32], [6, 16, 20, 22], [6, 16, 25, 35], [6, 16, 28, 37], [6, 17, 18, 22], [6, 17, 20, 30], [6, 17, 21, 32], [6, 17, 23, 37], [6, 17, 25, 27], [6, 17, 33, 35], [6, 18, 23, 26], [6, 18, 27, 34], [6, 18, 28, 31], [6, 18, 29, 33], [6, 18, 32, 35], [6, 19, 21, 35], [6, 19, 22, 30], [6, 19, 23, 27], [6, 19, 28, 34], [6, 20, 23, 32], [6, 20, 25, 26], [6, 20, 31, 34], [6, 20, 33, 36], [6, 21, 23, 29], [6, 21, 24, 26], [6, 21, 30, 34], [6, 22, 24, 33], [6, 22, 25, 37], [6, 22, 29, 36], [6, 23, 30, 33], [6, 24, 27, 32], [6, 24, 28, 35], [6, 24, 29, 34], [6, 24, 31, 37], [6, 25, 28, 32], [6, 26, 27, 37], [6, 26, 29, 30], [6, 26, 32, 36], [6, 27, 28, 33], [6, 27, 30, 36], [6, 29, 31, 35], [6, 30, 31, 32], [6, 34, 36, 37], [7, 8, 9, 21], [7, 8, 12, 34], [7, 8, 13, 24], [7, 8, 14, 19], [7, 8, 16, 17], [7, 8, 18, 25], [7, 8, 23, 29], [7, 8, 27, 32], [7, 8, 28, 30], [7, 8, 33, 35], [7, 8, 36, 37], [7, 9, 10, 17], [7, 9, 11, 16], [7, 9, 12, 35], [7, 9, 13, 22], [7, 9, 15, 30], [7, 9, 18, 29], [7, 9, 19, 20], [7, 9, 23, 32], [7, 9, 24, 25], [7, 9, 26, 37], [7, 9, 28, 36], [7, 10, 11, 25], [7, 10, 12, 30], [7, 10, 14, 26], [7, 10, 15, 27], [7, 10, 16, 24], [7, 10, 18, 32], [7, 10, 19, 31], [7, 10, 20, 34], [7, 10, 22, 29], [7, 10, 23, 35], [7, 11, 12, 14], [7, 11, 13, 35], [7, 11, 15, 32], [7, 11, 17, 37], [7, 11, 18, 27], [7, 11, 21, 36], [7, 11, 22, 34], [7, 11, 24, 29], [7, 11, 26, 30], [7, 12, 13, 31], [7, 12, 15, 33], [7, 12, 16, 36], [7, 12, 17, 27], [7, 12, 18, 20], [7, 12, 19, 21], [7, 12, 25, 26], [7, 12, 28, 32], [7, 12, 29, 37], [7, 13, 14, 37], [7, 13, 16, 19], [7, 13, 17, 25], [7, 13, 23, 36], [7, 13, 26, 32], [7, 13, 27, 34], [7, 13, 29, 30], [7, 14, 15, 18], [7, 14, 17, 28], [7, 14, 20, 27], [7, 14, 21, 29], [7, 14, 24, 36], [7, 14, 25, 31], [7, 14, 30, 33], [7, 14, 34, 35], [7, 15, 17, 34], [7, 15, 19, 25], [7, 15, 20, 37], [7, 15, 21, 22], [7, 15, 23, 28], [7, 15, 24, 26], [7, 16, 18, 37], [7, 16, 20, 30], [7, 16, 21, 25], [7, 16, 22, 32], [7, 16, 23, 33], [7, 16, 26, 35], [7, 16, 29, 31], [7, 17, 19, 22], [7, 17, 20, 33], [7, 17, 21, 23], [7, 17, 26, 36], [7, 18, 19, 23], [7, 18, 21, 31], [7, 18, 22, 33], [7, 18, 26, 28], [7, 18, 34, 36], [7, 19, 24, 27], [7, 19, 28, 35], [7, 19, 29, 32], [7, 19, 30, 34], [7, 19, 33, 36], [7, 20, 22, 36], [7, 20, 23, 31], [7, 20, 24, 28], [7, 20, 29, 35], [7, 21, 24, 33], [7, 21, 26, 27], [7, 21, 32, 35], [7, 21, 34, 37], [7, 22, 24, 30], [7, 22, 25, 27], [7, 22, 31, 35], [7, 23, 25, 34], [7, 23, 30, 37], [7, 24, 31, 34], [7, 25, 28, 33], [7, 25, 29, 36], [7, 25, 30, 35], [7, 26, 29, 33], [7, 27, 30, 31], [7, 27, 33, 37], [7, 28, 29, 34], [7, 28, 31, 37], [7, 30, 32, 36], [7, 31, 32, 33], [8, 9, 10, 22], [8, 9, 13, 35], [8, 9, 14, 25], [8, 9, 15, 20], [8, 9, 17, 18], [8, 9, 19, 26], [8, 9, 24, 30], [8, 9, 28, 33], [8, 9, 29, 31], [8, 9, 34, 36], [8, 10, 11, 18], [8, 10, 12, 17], [8, 10, 13, 36], [8, 10, 14, 23], [8, 10, 16, 31], [8, 10, 19, 30], [8, 10, 20, 21], [8, 10, 24, 33], [8, 10, 25, 26], [8, 10, 29, 37], [8, 11, 12, 26], [8, 11, 13, 31], [8, 11, 15, 27], [8, 11, 16, 28], [8, 11, 17, 25], [8, 11, 19, 33], [8, 11, 20, 32], [8, 11, 21, 35], [8, 11, 23, 30], [8, 11, 24, 36], [8, 12, 13, 15], [8, 12, 14, 36], [8, 12, 16, 33], [8, 12, 19, 28], [8, 12, 22, 37], [8, 12, 23, 35], [8, 12, 25, 30], [8, 12, 27, 31], [8, 13, 14, 32], [8, 13, 16, 34], [8, 13, 17, 37], [8, 13, 18, 28], [8, 13, 19, 21], [8, 13, 20, 22], [8, 13, 26, 27], [8, 13, 29, 33], [8, 14, 17, 20], [8, 14, 18, 26], [8, 14, 24, 37], [8, 14, 27, 33], [8, 14, 28, 35], [8, 14, 30, 31], [8, 15, 16, 19], [8, 15, 18, 29], [8, 15, 21, 28], [8, 15, 22, 30], [8, 15, 25, 37], [8, 15, 26, 32], [8, 15, 31, 34], [8, 15, 35, 36], [8, 16, 18, 35], [8, 16, 20, 26], [8, 16, 22, 23], [8, 16, 24, 29], [8, 16, 25, 27], [8, 17, 21, 31], [8, 17, 22, 26], [8, 17, 23, 33], [8, 17, 24, 34], [8, 17, 27, 36], [8, 17, 30, 32], [8, 18, 20, 23], [8, 18, 21, 34], [8, 18, 22, 24], [8, 18, 27, 37], [8, 19, 20, 24], [8, 19, 22, 32], [8, 19, 23, 34], [8, 19, 27, 29], [8, 19, 35, 37], [8, 20, 25, 28], [8, 20, 29, 36], [8, 20, 30, 33], [8, 20, 31, 35], [8, 20, 34, 37], [8, 21, 23, 37], [8, 21, 24, 32], [8, 21, 25, 29], [8, 21, 30, 36], [8, 22, 25, 34], [8, 22, 27, 28], [8, 22, 33, 36], [8, 23, 25, 31], [8, 23, 26, 28], [8, 23, 32, 36], [8, 24, 26, 35], [8, 25, 32, 35], [8, 26, 29, 34], [8, 26, 30, 37], [8, 26, 31, 36], [8, 27, 30, 34], [8, 28, 31, 32], [8, 29, 30, 35], [8, 31, 33, 37], [8, 32, 33, 34], [9, 10, 11, 23], [9, 10, 14, 36], [9, 10, 15, 26], [9, 10, 16, 21], [9, 10, 18, 19], [9, 10, 20, 27], [9, 10, 25, 31], [9, 10, 29, 34], [9, 10, 30, 32], [9, 10, 35, 37], [9, 11, 12, 19], [9, 11, 13, 18], [9, 11, 14, 37], [9, 11, 15, 24], [9, 11, 17, 32], [9, 11, 20, 31], [9, 11, 21, 22], [9, 11, 25, 34], [9, 11, 26, 27], [9, 12, 13, 27], [9, 12, 14, 32], [9, 12, 16, 28], [9, 12, 17, 29], [9, 12, 18, 26], [9, 12, 20, 34], [9, 12, 21, 33], [9, 12, 22, 36], [9, 12, 24, 31], [9, 12, 25, 37], [9, 13, 14, 16], [9, 13, 15, 37], [9, 13, 17, 34], [9, 13, 20, 29], [9, 13, 24, 36], [9, 13, 26, 31], [9, 13, 28, 32], [9, 14, 15, 33], [9, 14, 17, 35], [9, 14, 19, 29], [9, 14, 20, 22], [9, 14, 21, 23], [9, 14, 27, 28], [9, 14, 30, 34], [9, 15, 18, 21], [9, 15, 19, 27], [9, 15, 28, 34], [9, 15, 29, 36], [9, 15, 31, 32], [9, 16, 17, 20], [9, 16, 19, 30], [9, 16, 22, 29], [9, 16, 23, 31], [9, 16, 27, 33], [9, 16, 32, 35], [9, 16, 36, 37], [9, 17, 19, 36], [9, 17, 21, 27], [9, 17, 23, 24], [9, 17, 25, 30], [9, 17, 26, 28], [9, 18, 22, 32], [9, 18, 23, 27], [9, 18, 24, 34], [9, 18, 25, 35], [9, 18, 28, 37], [9, 18, 31, 33], [9, 19, 21, 24], [9, 19, 22, 35], [9, 19, 23, 25], [9, 20, 21, 25], [9, 20, 23, 33], [9, 20, 24, 35], [9, 20, 28, 30], [9, 21, 26, 29], [9, 21, 30, 37], [9, 21, 31, 34], [9, 21, 32, 36], [9, 22, 25, 33], [9, 22, 26, 30], [9, 22, 31, 37], [9, 23, 26, 35], [9, 23, 28, 29], [9, 23, 34, 37], [9, 24, 26, 32], [9, 24, 27, 29], [9, 24, 33, 37], [9, 25, 27, 36], [9, 26, 33, 36], [9, 27, 30, 35], [9, 27, 32, 37], [9, 28, 31, 35], [9, 29, 32, 33], [9, 30, 31, 36], [9, 33, 34, 35], [10, 11, 12, 24], [10, 11, 15, 37], [10, 11, 16, 27], [10, 11, 17, 22], [10, 11, 19, 20], [10, 11, 21, 28], [10, 11, 26, 32], [10, 11, 30, 35], [10, 11, 31, 33], [10, 12, 13, 20], [10, 12, 14, 19], [10, 12, 16, 25], [10, 12, 18, 33], [10, 12, 21, 32], [10, 12, 22, 23], [10, 12, 26, 35], [10, 12, 27, 28], [10, 13, 14, 28], [10, 13, 15, 33], [10, 13, 17, 29], [10, 13, 18, 30], [10, 13, 19, 27], [10, 13, 21, 35], [10, 13, 22, 34], [10, 13, 23, 37], [10, 13, 25, 32], [10, 14, 15, 17], [10, 14, 18, 35], [10, 14, 21, 30], [10, 14, 25, 37], [10, 14, 27, 32], [10, 14, 29, 33], [10, 15, 16, 34], [10, 15, 18, 36], [10, 15, 20, 30], [10, 15, 21, 23], [10, 15, 22, 24], [10, 15, 28, 29], [10, 15, 31, 35], [10, 16, 19, 22], [10, 16, 20, 28], [10, 16, 29, 35], [10, 16, 30, 37], [10, 16, 32, 33], [10, 17, 18, 21], [10, 17, 20, 31], [10, 17, 23, 30], [10, 17, 24, 32], [10, 17, 28, 34], [10, 17, 33, 36], [10, 18, 20, 37], [10, 18, 22, 28], [10, 18, 24, 25], [10, 18, 26, 31], [10, 18, 27, 29], [10, 19, 23, 33], [10, 19, 24, 28], [10, 19, 25, 35], [10, 19, 26, 36], [10, 19, 32, 34], [10, 20, 22, 25], [10, 20, 23, 36], [10, 20, 24, 26], [10, 21, 22, 26], [10, 21, 24, 34], [10, 21, 25, 36], [10, 21, 29, 31], [10, 22, 27, 30], [10, 22, 32, 35], [10, 22, 33, 37], [10, 23, 26, 34], [10, 23, 27, 31], [10, 24, 27, 36], [10, 24, 29, 30], [10, 25, 27, 33], [10, 25, 28, 30], [10, 26, 28, 37], [10, 27, 34, 37], [10, 28, 31, 36], [10, 29, 32, 36], [10, 30, 33, 34], [10, 31, 32, 37], [10, 34, 35, 36], [11, 12, 13, 25], [11, 12, 17, 28], [11, 12, 18, 23], [11, 12, 20, 21], [11, 12, 22, 29], [11, 12, 27, 33], [11, 12, 31, 36], [11, 12, 32, 34], [11, 13, 14, 21], [11, 13, 15, 20], [11, 13, 17, 26], [11, 13, 19, 34], [11, 13, 22, 33], [11, 13, 23, 24], [11, 13, 27, 36], [11, 13, 28, 29], [11, 14, 15, 29], [11, 14, 16, 34], [11, 14, 18, 30], [11, 14, 19, 31], [11, 14, 20, 28], [11, 14, 22, 36], [11, 14, 23, 35], [11, 14, 26, 33], [11, 15, 16, 18], [11, 15, 19, 36], [11, 15, 22, 31], [11, 15, 28, 33], [11, 15, 30, 34], [11, 16, 17, 35], [11, 16, 19, 37], [11, 16, 21, 31], [11, 16, 22, 24], [11, 16, 23, 25], [11, 16, 29, 30], [11, 16, 32, 36], [11, 17, 20, 23], [11, 17, 21, 29], [11, 17, 30, 36], [11, 17, 33, 34], [11, 18, 19, 22], [11, 18, 21, 32], [11, 18, 24, 31], [11, 18, 25, 33], [11, 18, 29, 35], [11, 18, 34, 37], [11, 19, 23, 29], [11, 19, 25, 26], [11, 19, 27, 32], [11, 19, 28, 30], [11, 20, 24, 34], [11, 20, 25, 29], [11, 20, 26, 36], [11, 20, 27, 37], [11, 20, 33, 35], [11, 21, 23, 26], [11, 21, 24, 37], [11, 21, 25, 27], [11, 22, 23, 27], [11, 22, 25, 35], [11, 22, 26, 37], [11, 22, 30, 32], [11, 23, 28, 31], [11, 23, 33, 36], [11, 24, 27, 35], [11, 24, 28, 32], [11, 25, 28, 37], [11, 25, 30, 31], [11, 26, 28, 34], [11, 26, 29, 31], [11, 29, 32, 37], [11, 30, 33, 37], [11, 31, 34, 35], [11, 35, 36, 37], [12, 13, 14, 26], [12, 13, 18, 29], [12, 13, 19, 24], [12, 13, 21, 22], [12, 13, 23, 30], [12, 13, 28, 34], [12, 13, 32, 37], [12, 13, 33, 35], [12, 14, 15, 22], [12, 14, 16, 21], [12, 14, 18, 27], [12, 14, 20, 35], [12, 14, 23, 34], [12, 14, 24, 25], [12, 14, 28, 37], [12, 14, 29, 30], [12, 15, 16, 30], [12, 15, 17, 35], [12, 15, 19, 31], [12, 15, 20, 32], [12, 15, 21, 29], [12, 15, 23, 37], [12, 15, 24, 36], [12, 15, 27, 34], [12, 16, 17, 19], [12, 16, 20, 37], [12, 16, 23, 32], [12, 16, 29, 34], [12, 16, 31, 35], [12, 17, 18, 36], [12, 17, 22, 32], [12, 17, 23, 25], [12, 17, 24, 26], [12, 17, 30, 31], [12, 17, 33, 37], [12, 18, 21, 24], [12, 18, 22, 30], [12, 18, 31, 37], [12, 18, 34, 35], [12, 19, 20, 23], [12, 19, 22, 33], [12, 19, 25, 32], [12, 19, 26, 34], [12, 19, 30, 36], [12, 20, 24, 30], [12, 20, 26, 27], [12, 20, 28, 33], [12, 20, 29, 31], [12, 21, 25, 35], [12, 21, 26, 30], [12, 21, 27, 37], [12, 21, 34, 36], [12, 22, 24, 27], [12, 22, 26, 28], [12, 23, 24, 28], [12, 23, 26, 36], [12, 23, 31, 33], [12, 24, 29, 32], [12, 24, 34, 37], [12, 25, 28, 36], [12, 25, 29, 33], [12, 26, 31, 32], [12, 27, 29, 35], [12, 27, 30, 32], [12, 32, 35, 36], [13, 14, 15, 27], [13, 14, 19, 30], [13, 14, 20, 25], [13, 14, 22, 23], [13, 14, 24, 31], [13, 14, 29, 35], [13, 14, 34, 36], [13, 15, 16, 23], [13, 15, 17, 22], [13, 15, 19, 28], [13, 15, 21, 36], [13, 15, 24, 35], [13, 15, 25, 26], [13, 15, 30, 31], [13, 16, 17, 31], [13, 16, 18, 36], [13, 16, 20, 32], [13, 16, 21, 33], [13, 16, 22, 30], [13, 16, 25, 37], [13, 16, 28, 35], [13, 17, 18, 20], [13, 17, 24, 33], [13, 17, 30, 35], [13, 17, 32, 36], [13, 18, 19, 37], [13, 18, 23, 33], [13, 18, 24, 26], [13, 18, 25, 27], [13, 18, 31, 32], [13, 19, 22, 25], [13, 19, 23, 31], [13, 19, 35, 36], [13, 20, 21, 24], [13, 20, 23, 34], [13, 20, 26, 33], [13, 20, 27, 35], [13, 20, 31, 37], [13, 21, 25, 31], [13, 21, 27, 28], [13, 21, 29, 34], [13, 21, 30, 32], [13, 22, 26, 36], [13, 22, 27, 31], [13, 22, 35, 37], [13, 23, 25, 28], [13, 23, 27, 29], [13, 24, 25, 29], [13, 24, 27, 37], [13, 24, 32, 34], [13, 25, 30, 33], [13, 26, 29, 37], [13, 26, 30, 34], [13, 27, 32, 33], [13, 28, 30, 36], [13, 28, 31, 33], [13, 33, 36, 37], [14, 15, 16, 28], [14, 15, 20, 31], [14, 15, 21, 26], [14, 15, 23, 24], [14, 15, 25, 32], [14, 15, 30, 36], [14, 15, 35, 37], [14, 16, 17, 24], [14, 16, 18, 23], [14, 16, 20, 29], [14, 16, 22, 37], [14, 16, 25, 36], [14, 16, 26, 27], [14, 16, 31, 32], [14, 17, 18, 32], [14, 17, 19, 37], [14, 17, 21, 33], [14, 17, 22, 34], [14, 17, 23, 31], [14, 17, 29, 36], [14, 18, 19, 21], [14, 18, 25, 34], [14, 18, 31, 36], [14, 18, 33, 37], [14, 19, 24, 34], [14, 19, 25, 27], [14, 19, 26, 28], [14, 19, 32, 33], [14, 20, 23, 26], [14, 20, 24, 32], [14, 20, 36, 37], [14, 21, 22, 25], [14, 21, 24, 35], [14, 21, 27, 34], [14, 21, 28, 36], [14, 22, 26, 32], [14, 22, 28, 29], [14, 22, 30, 35], [14, 22, 31, 33], [14, 23, 27, 37], [14, 23, 28, 32], [14, 24, 26, 29], [14, 24, 28, 30], [14, 25, 26, 30], [14, 25, 33, 35], [14, 26, 31, 34], [14, 27, 31, 35], [14, 28, 33, 34], [14, 29, 31, 37], [14, 29, 32, 34], [15, 16, 17, 29], [15, 16, 21, 32], [15, 16, 22, 27], [15, 16, 24, 25], [15, 16, 26, 33], [15, 16, 31, 37], [15, 17, 18, 25], [15, 17, 19, 24], [15, 17, 21, 30], [15, 17, 26, 37], [15, 17, 27, 28], [15, 17, 32, 33], [15, 18, 19, 33], [15, 18, 22, 34], [15, 18, 23, 35], [15, 18, 24, 32], [15, 18, 30, 37], [15, 19, 20, 22], [15, 19, 26, 35], [15, 19, 32, 37], [15, 20, 25, 35], [15, 20, 26, 28], [15, 20, 27, 29], [15, 20, 33, 34], [15, 21, 24, 27], [15, 21, 25, 33], [15, 22, 23, 26], [15, 22, 25, 36], [15, 22, 28, 35], [15, 22, 29, 37], [15, 23, 27, 33], [15, 23, 29, 30], [15, 23, 31, 36], [15, 23, 32, 34], [15, 24, 29, 33], [15, 25, 27, 30], [15, 25, 29, 31], [15, 26, 27, 31], [15, 26, 34, 36], [15, 27, 32, 35], [15, 28, 32, 36], [15, 29, 34, 35], [15, 30, 33, 35], [16, 17, 18, 30], [16, 17, 22, 33], [16, 17, 23, 28], [16, 17, 25, 26], [16, 17, 27, 34], [16, 18, 19, 26], [16, 18, 20, 25], [16, 18, 22, 31], [16, 18, 28, 29], [16, 18, 33, 34], [16, 19, 20, 34], [16, 19, 23, 35], [16, 19, 24, 36], [16, 19, 25, 33], [16, 20, 21, 23], [16, 20, 27, 36], [16, 21, 26, 36], [16, 21, 27, 29], [16, 21, 28, 30], [16, 21, 34, 35], [16, 22, 25, 28], [16, 22, 26, 34], [16, 23, 24, 27], [16, 23, 26, 37], [16, 23, 29, 36], [16, 24, 28, 34], [16, 24, 30, 31], [16, 24, 32, 37], [16, 24, 33, 35], [16, 25, 30, 34], [16, 26, 28, 31], [16, 26, 30, 32], [16, 27, 28, 32], [16, 27, 35, 37], [16, 28, 33, 36], [16, 29, 33, 37], [16, 30, 35, 36], [16, 31, 34, 36], [17, 18, 19, 31], [17, 18, 23, 34], [17, 18, 24, 29], [17, 18, 26, 27], [17, 18, 28, 35], [17, 19, 20, 27], [17, 19, 21, 26], [17, 19, 23, 32], [17, 19, 29, 30], [17, 19, 34, 35], [17, 20, 21, 35], [17, 20, 24, 36], [17, 20, 25, 37], [17, 20, 26, 34], [17, 21, 22, 24], [17, 21, 28, 37], [17, 22, 27, 37], [17, 22, 28, 30], [17, 22, 29, 31], [17, 22, 35, 36], [17, 23, 26, 29], [17, 23, 27, 35], [17, 24, 25, 28], [17, 24, 30, 37], [17, 25, 29, 35], [17, 25, 31, 32], [17, 25, 34, 36], [17, 26, 31, 35], [17, 27, 29, 32], [17, 27, 31, 33], [17, 28, 29, 33], [17, 29, 34, 37], [17, 31, 36, 37], [17, 32, 35, 37], [18, 19, 20, 32], [18, 19, 24, 35], [18, 19, 25, 30], [18, 19, 27, 28], [18, 19, 29, 36], [18, 20, 21, 28], [18, 20, 22, 27], [18, 20, 24, 33], [18, 20, 30, 31], [18, 20, 35, 36], [18, 21, 22, 36], [18, 21, 25, 37], [18, 21, 27, 35], [18, 22, 23, 25], [18, 23, 29, 31], [18, 23, 30, 32], [18, 23, 36, 37], [18, 24, 27, 30], [18, 24, 28, 36], [18, 25, 26, 29], [18, 26, 30, 36], [18, 26, 32, 33], [18, 26, 35, 37], [18, 27, 32, 36], [18, 28, 30, 33], [18, 28, 32, 34], [18, 29, 30, 34], [19, 20, 21, 33], [19, 20, 25, 36], [19, 20, 26, 31], [19, 20, 28, 29], [19, 20, 30, 37], [19, 21, 22, 29], [19, 21, 23, 28], [19, 21, 25, 34], [19, 21, 31, 32], [19, 21, 36, 37], [19, 22, 23, 37], [19, 22, 28, 36], [19, 23, 24, 26], [19, 24, 30, 32], [19, 24, 31, 33], [19, 25, 28, 31], [19, 25, 29, 37], [19, 26, 27, 30], [19, 27, 31, 37], [19, 27, 33, 34], [19, 28, 33, 37], [19, 29, 31, 34], [19, 29, 33, 35], [19, 30, 31, 35], [20, 21, 22, 34], [20, 21, 26, 37], [20, 21, 27, 32], [20, 21, 29, 30], [20, 22, 23, 30], [20, 22, 24, 29], [20, 22, 26, 35], [20, 22, 32, 33], [20, 23, 29, 37], [20, 24, 25, 27], [20, 25, 31, 33], [20, 25, 32, 34], [20, 26, 29, 32], [20, 27, 28, 31], [20, 28, 34, 35], [20, 30, 32, 35], [20, 30, 34, 36], [20, 31, 32, 36], [21, 22, 23, 35], [21, 22, 28, 33], [21, 22, 30, 31], [21, 23, 24, 31], [21, 23, 25, 30], [21, 23, 27, 36], [21, 23, 33, 34], [21, 25, 26, 28], [21, 26, 32, 34], [21, 26, 33, 35], [21, 27, 30, 33], [21, 28, 29, 32], [21, 29, 35, 36], [21, 31, 33, 36], [21, 31, 35, 37], [21, 32, 33, 37], [22, 23, 24, 36], [22, 23, 29, 34], [22, 23, 31, 32], [22, 24, 25, 32], [22, 24, 26, 31], [22, 24, 28, 37], [22, 24, 34, 35], [22, 26, 27, 29], [22, 27, 33, 35], [22, 27, 34, 36], [22, 28, 31, 34], [22, 29, 30, 33], [22, 30, 36, 37], [22, 32, 34, 37], [23, 24, 25, 37], [23, 24, 30, 35], [23, 24, 32, 33], [23, 25, 26, 33], [23, 25, 27, 32], [23, 25, 35, 36], [23, 27, 28, 30], [23, 28, 34, 36], [23, 28, 35, 37], [23, 29, 32, 35], [23, 30, 31, 34], [24, 25, 31, 36], [24, 25, 33, 34], [24, 26, 27, 34], [24, 26, 28, 33], [24, 26, 36, 37], [24, 28, 29, 31], [24, 29, 35, 37], [24, 30, 33, 36], [24, 31, 32, 35], [25, 26, 32, 37], [25, 26, 34, 35], [25, 27, 28, 35], [25, 27, 29, 34], [25, 29, 30, 32], [25, 31, 34, 37], [25, 32, 33, 36], [26, 27, 35, 36], [26, 28, 29, 36], [26, 28, 30, 35], [26, 30, 31, 33], [26, 33, 34, 37], [27, 28, 36, 37], [27, 29, 30, 37], [27, 29, 31, 36], [27, 31, 32, 34], [28, 30, 32, 37], [28, 32, 33, 35], [29, 33, 34, 36], [30, 34, 35, 37]] |