假设我有一个列表，如下所示：
l = [[1,2,3],[6,5,4,3,7,2],[4,3,2,9],[6,7],[5,1,0],[6,3,2,7]]
我如何编写python代码来检查是否有总是一起出现的元素？例如，在上面的例子中，2,3和6,7总是出现在相同的列表中。 （可能还有其他人，不确定）。
实现这一目标的最简单方法是什么？
我唯一的想法是转换 inner-list1 设置和检查交集 inner-list2 但是当我检查交叉路口时 inner-list3，这些元素可能根本不会发生 inner-list3。
我可以这样做：
for i in range(0,len(lists)):
a=set(lists[i]).intersection(lists[i+1])
if (len(a))==0:
continue
else:
a.intersection(lists[i+1])
这当然不起作用，但我怎么能正式编码这个或者有更好的方法吗？
itertools.combinations：我最初想过用的东西 itertools.combination， 但正如这允许的那样 elements 从一个 list 它们不是彼此相邻的，它不适用于我想到的解决方案。
事实证明，当看非数字输入时 lists， itertools.combinations 是 两种情况都是必要的。我很困惑，因为我认为了 groups 必须是 adjacent。
我认为最适合这种方式的方法是产生可能的方法 elements 那 可以 工作，然后检查每一个 function 反对这 list 的 sub-lists - 而不是做某种组合工作 list 沿着那条路走下去。
所以要检查一下 list 可能的 elements 是'有效'，即如果全部 elements 只发生在一起，我用的很简单 if 用发电机 all() 和 any() 内建的 functions 做这部分工作。
现在这是有效的，需要有一种产生潜力的方法 elements 可能会发生。我刚刚用两个嵌套做了这个 for-loops - 一个 iterating 过了 width 的 window和一个 iterating 在哪里 start 的 window 是。
然后从这里，我们只检查那组 elements 是 valid 并将其添加到另一个 list 如果是！
import itertools
def valid(p):
for s in l:
if any(e in s for e in p) and not all(e in s for e in p):
return False
return True
l = [[1,2,3],[6,5,4,3,7,2],[4,3,2,9],[6,7],[5,1,0],[6,3,2,7]]
els = list(set(b for a in l for b in a))
sol = []
for w in range(2,len(els)+1):
for c in itertools.combinations(els, w):
if valid(c):
sol.append(c)
这使 sol 如：
[(2, 3), (6, 7)]]
这些 2 nested for-loops 实际上可以被扔到一起很好 one-liner （不确定其他人是否认为它是Pythonic）：
sol = [c for w in range(2, len(els)+1) for c in itertools.combinations(els, w) if valid(c)]
它的工作原理相同但只是更短。
由于受欢迎的需求（@Arman），我已经更新了答案，现在它应该适用于其他人 elements 除了 0-9。这是通过引入一个独特的 elements list （els）。
还有一些测试来自 @thanasisp 使用上面相同的代码：
l = [[1, 3, 5, 7],[1, 3, 5, 7]]
给 sol 如：
[(1, 3), (1, 5), (1, 7), (3, 5), (3, 7), (5, 7), (1, 3, 5), (1, 3, 7), (1, 5, 7), (3, 5, 7), (1, 3, 5, 7)]
并再次：
l = [[1, 2, 3, 5, 7], [1, 3, 5, 7]]
得到：
[(1, 3), (1, 5), (1, 7), (3, 5), (3, 7), (5, 7), (1, 3, 5), (1, 3, 7), (1, 5, 7), (3, 5, 7), (1, 3, 5, 7)]
我相信这是正确的 2 不能 像其他所有人一样在任何群体中 elements 是一个不同的 sub-list，所以它永远不能与另一个组成一个团体 element。
另一个具有默认dicts的线性解决方案（元组可用于制作可用密钥）：
from collections import defaultdict
isin,contains = defaultdict(list),defaultdict(list)
for i,s in enumerate(l):
for k in s :
isin[k].append(i)
# isin is {1: [0, 4], 2: [0, 1, 2, 5], 3: [0, 1, 2, 5], 6: [1, 3, 5],
# 5: [1, 4], 4: [1, 2], 7: [1, 3, 5], 9: [2], 0: [4]}
# element 1 is in sets numbered 0 and 4, and so on.
for k,ss in isin.items():
contains[tuple(ss)].append(k)
# contains is {(0, 4): [1], (0, 1, 2, 5): [2, 3], (1, 3, 5): [6, 7],
# (1, 4): [5], (1, 2): [4], (2,): [9], (4,): [0]})
# sets 0 and 4 contains 1, and no other contain 1.
现在，如果您查找按组显示的元素 n （n=2 在这里），键入：
print ([p for p in contains.values() if len(p)==n])
# [[2, 3], [6, 7]]
这是我现在想到的强力选择， dct是每个数字的计数字典，然后我们检查相同的列表 dct 这意味着两个数字出现在相同的列表索引中：
l = [[1,2,3],[6,5,4,3,7,2,1],[4,3,2,9,1],[6,7],[5,1,2,3,0],[6,3,2,7,1]]
dct = defaultdict(list)
for i, v in enumerate(l):
for x in v:
dct[x].append(i)
dct # defaultdict(<class 'list'>, {0: [4], 1: [0, 1, 2, 4, 5], 2: [0, 1, 2, 4, 5], 3: [0, 1, 2, 4, 5], 4: [1, 2], 5: [1, 4], 6: [1, 3, 5], 7: [1, 3, 5], 9: [2]})
new_d = defaultdict(list)
for k, v in dct.items():
for k2, v2 in dct.items():
if(v == v2) and k != k2):
new_d[k].append(k2)
new_d # defaultdict(<class 'list'>, {1: [2, 3], 2: [1, 3], 3: [1, 2], 6: [7], 7: [6]})
它也是一个非常昂贵的操作 O(N*N*M) ： N = list elements 和 M = longest sublist
你可以使用set intersection进行此操作，并且它也适用于每组3个或更多元素：注意我添加了一个 8 到了 6,7 组。
lists = [[1,2,3], [6,5,4,3,7,2,8], [4,3,2,9], [8,6,7], [5,1,0], [6,3,8,2,7]]
首先，我们将每个元素映射到它与之一起出现的所有其他元素的集合：
groups = {}
for lst in lists:
for x in lst:
if x not in groups:
groups[x] = set(lst)
else:
groups[x].intersection_update(lst)
# {0: {0, 1, 5}, 1: {1}, 2: {2, 3}, 3: {2, 3}, 4: {2, 3, 4}, 5: {5},
# 6: {8, 6, 7}, 7: {8, 6, 7}, 8: {8, 6, 7}, 9: {9, 2, 3, 4}}
接下来，我们只保留关系是双向的元素：
groups2 = {k: {v for v in groups[k] if k in groups[v]} for k in groups}
# {0: {0}, 1: {1}, 2: {2, 3}, 3: {2, 3}, 4: {4}, 5: {5},
# 6: {8, 6, 7}, 7: {8, 6, 7}, 8: {8, 6, 7}, 9: {9}}
最后，我们获得具有多个元素的唯一组：
groups3 = {frozenset(v) for v in groups2.values() if len(v) > 1}
# {frozenset({8, 6, 7}), frozenset({2, 3})}
以下解决方案有一个 线性 O(n) 复杂性，其中n是所有列表中的数字总数（展平后）。代码是 Python2.x
我正在使用所有可能模式的位图表示（使用python的无限数字）。例如，如果有一个数字 list0 和 list2 但不是 list1，各自的模式将是 ...000101。例如，在给定输入中，值2将具有以下位图模式： 100111 价值3也是如此
l = [[1,2,3],[6,5,4,3,7,2],[4,3,2,9],[6,7],[5,1,0],[6,3,2,7]]
num_to_pattern = {}
for i, sublist in enumerate(l):
for num in sublist:
# turning ON the respective bit for each value
if not num in num_to_pattern:
num_to_pattern[num] = 1 << i
else:
num_to_pattern[num] |= (1 << i)
pattern_to_num_list = {}
# mapping patterns to all their respective numbers
for num, pattern in num_to_pattern.iteritems():
if not pattern in pattern_to_num_list:
pattern_to_num_list[pattern] = [num]
else:
pattern_to_num_list[pattern].append(num)
print pattern_to_num_list
此代码将打印：
{4: [9], 6: [4], 39: [2, 3], 42: [6, 7], 16: [0], 17: [1], 18: [5]}
并且您可以映射和过滤您想要的任何子列表（在您的情况下 - 列表等于或大于2）：
print filter(lambda x: len(x) >= 2, pattern_to_num_list.values())
实现这一目标的最简单方法是什么？
我试图让我的解决方案尽可能短。我也尽可能地优化它。它适用于 任何整数 根据你喜欢的。
这是带有很多注释的代码 说明 它，接着是 更多 基本解释：
注意：在下面的代码中，我使用了 [[1, 2, 3], [2, 1, 4]] 作为原始列表的示例而不是您问题中的列表，使解释更容易。
import itertools
# The original list of lists
org_list = [[1, 2, 3], [2, 1, 4]]
# Sort the lists of org_list to ensure that the resulting tuples of
# itertools.combinations below are sorted also, because later, we
# don't want (1, 2) to be not equal to (2, 1)
org_list = [sorted(l) for l in org_list]
# This list will contain the combinations of the original list
list_of_combinations = []
# --Building list_of_combinations--
# Looping through every list in the original list of lists (org_list)
for i, l in enumerate(org_list):
# Create a new set to hold the combinations for the i-th list of org_list
list_of_combinations.append(set())
# Starting with 2 because we want the combination to contain two
# items at least, and ending at len(org_list[i])+1 because we want
# the maximum length of the combination to be equal to the length
# of its original list
for comb_length in range(2, len(l) + 1):
# Update the set with its combinations of length comb_length
list_of_combinations[i].update(
tuple(itertools.combinations(org_list[i], comb_length))
)
# Now list_of_combinations = [
# {(1, 2), (1, 3), (2, 3), (1, 2, 3)},
# {(1, 2), (1, 2, 4), (2, 4), (1, 4)}
# ]
# This will hold the result. In our case: [2, 3], and [6, 7]
# It is a set because we don't want the result to contain duplicate items
combs = set()
# Looping through the sets in list_of_combinations
for s in list_of_combinations:
# s = {(1, 2), (1, 3), (2, 3), (1, 2, 3)} for example
# Looping through the combinations in the set s
for comb in s:
# comb = (1, 2) for example
# Set a flag (f) initially to 1
f = 1
# Loop through the sets in list_of_combinations
for ind, se in enumerate(list_of_combinations):
# See if comb exists in the set se
if comb not in se:
# If not, see if any number in comb exists in the ind-th list of
# the original list
for n in comb:
if n in org_list[ind]:
# If so, set f to 0
f = 0
break
# if f is still 1, then the current comb satisfy our conditions
# so we add it to the result
if f == 1:
combs.add(comb)
print(combs)
输出：
{(1, 2)}
正如所料。
对于您问题中的列表，此代码的输出是 {(2, 3), (6, 7)} 这也是预期的。
itertools.combinations？itertools.combinations(iterable, r)：退货 r 来自输入的元素的长度元组 iterable。例如：
list(itertools.combinations([1, 2, 3], 2))
给
[(1, 2), (1, 3), (2, 3)]
在上面的代码中，您可以注意到集合用于保存原始列表中每个列表的组合。这是因为检查集合中的值的成员资格是 非常 快，我们在代码中做了很多这样的检查。
假设我们的原始列表是 [[1, 2, 3], [2, 1, 4]]。
获取原始列表中所需的一组组合：
对于 [1, 2, 3]：组合的集合是 (1, 2), (1, 3), (2, 3), (1, 2, 3)
对于 [2, 1, 4]：组合的集合是 (1, 2), (1, 2, 4), (2, 4), (1, 4)
对于 每 的组合，以及为了在我们的代码的输出（意味着它满足我们的条件），我们要确保为 每 一组组合， 或
让我们来 (1, 3) 来自 第一 一组组合。我们遍历组合集：
为了 第一 设置，我们可以看到 (1, 3) 存在于其中，所以我们向前迈进。
为了 第二 设置，我们可以看到它不存在，所以我们想看看是否存在 任何 其项目存在于相应的清单中（即 第二 原始清单清单： [2, 1, 4]）：
从...开始 1，我们可以看到它存在于相应的列表中 - > (1, 3) 不能在输出中，因为它不满足所需的条件。
首先是数据
data = [[1,2,3],[6,5,4,3,7,2],[4,3,2,9],[6,7],[5,1,0],[6,3,2,7]]
生成组合很昂贵，所以我想尽可能地避免这种情况。
我的“尤里卡！”当我意识到我不需要生成所有对时，我就来了。相反，我可以将每个数字映射到包含它的所有列表。
appears_in = defaultdict(set)
for g in groups:
for number in g:
appears_in[number].add(tuple(g))
结果字典是
{0: {(5, 1, 0)},
1: {(5, 1, 0), (1, 2, 3)},
2: {(4, 3, 2, 9), (6, 3, 2, 7), (6, 5, 4, 3, 7, 2), (1, 2, 3)},
3: {(4, 3, 2, 9), (6, 3, 2, 7), (6, 5, 4, 3, 7, 2), (1, 2, 3)},
4: {(4, 3, 2, 9), (6, 5, 4, 3, 7, 2)},
5: {(5, 1, 0), (6, 5, 4, 3, 7, 2)},
6: {(6, 3, 2, 7), (6, 7), (6, 5, 4, 3, 7, 2)},
7: {(6, 3, 2, 7), (6, 7), (6, 5, 4, 3, 7, 2)},
9: {(4, 3, 2, 9)}}
查看2和3的条目
2: {(4, 3, 2, 9), (6, 3, 2, 7), (6, 5, 4, 3, 7, 2), (1, 2, 3)},
3: {(4, 3, 2, 9), (6, 3, 2, 7), (6, 5, 4, 3, 7, 2), (1, 2, 3)},
包含2的列表集与包含3的列表集相同。因此，我得出结论，2和3总是一起出现。
将其与3和4进行对比
3: {(4, 3, 2, 9), (6, 3, 2, 7), (6, 5, 4, 3, 7, 2), (1, 2, 3)},
4: {(4, 3, 2, 9), (6, 5, 4, 3, 7, 2)},
注意差距在哪里 (6, 3, 2, 7) 和 (1, 2, 3) 应该。我得出结论，3和4并不总是一起出现。
这是完整的代码
from collections import defaultdict
from itertools import combinations
from pprint import pprint
def always_appear_together(groups):
appears_in = defaultdict(set)
for g in groups:
for number in g:
appears_in[number].add(tuple(g))
#pprint(appears_in) # for debugging
return [
(i,j)
for (i,val_i),(j,val_j) in combinations(appears_in.items(),2)
if val_i == val_j
]
运行这个给出
print(always_appear_together(data))
[(2, 3), (6, 7)]
这更像是一个强力解决方案，但是，它将通过生成每个子列表的排列，生成一个大的所有元素列表。 l 并过滤以查找其元素全部出现在子列表中的任何排列 l。如果任何排列通过该条件，则将添加排列 final_pairs：
l = [[1,2,3],[6,5,4,3,7,2],[4,3,2,9],[6,7],[5,1,0],[6,3,2,7]]
import itertools
final_pairs = []
for i in l:
combos = [list(itertools.permutations(i, b)) for b in range(2, len(i))]
for combo in combos:
for b in combo:
if any(all(c in a for c in b) for a in l):
final_pairs.append(combo)
final_data = list(set(itertools.chain.from_iterable(final_pairs)))
输出：
[(2, 5, 6, 7, 3), (7, 3), (2, 6, 3, 7), (5, 3, 2, 6, 7), (5, 6, 4, 7), (7, 2, 5, 4, 6), (6, 7, 3, 4), (5, 2, 3, 7, 6), (7, 4, 3, 2), (6, 4, 7, 2), (4, 7, 6), (7, 3, 4, 6, 2), (5, 3, 7, 2, 6), (5, 7, 6, 4), (7, 4, 6, 2, 5), (7, 5, 4, 6, 3), (4, 2, 7, 3, 5), (4, 7, 3, 2), (2, 5, 4, 7, 3), (6, 5, 7, 2, 4), (4, 6, 7, 2), (2, 7, 5, 6, 3), (2, 6, 7), (5, 4, 2, 3, 7), (2, 3, 4, 6, 5), (5, 7, 2, 3), (3, 2, 4, 7, 6), (2, 6, 3, 5, 7), (3, 6, 5, 4, 7), (6, 5, 7), (2, 4, 6, 7, 5), (4, 3, 5, 2), (2, 3, 5, 7), (4, 5, 7, 3), (4, 6, 7, 2, 5), (3, 4, 5, 7, 2), (2, 4, 5, 6, 3), (3, 5, 2, 7, 6), (6, 3, 5, 7, 2), (5, 2, 7, 3, 6), (6, 3, 5, 4, 2), (2, 7, 4, 5), (2, 5, 3), (3, 2), (3, 2, 6, 7), (5, 3, 7, 6, 4), (4, 5), (2, 7, 3, 6, 4), (6, 4, 2, 5), (7, 5, 4, 2, 6), (2, 4, 3, 7, 6), (3, 2, 6), (4, 5, 3, 6), (7, 4, 3, 6, 5), (7, 3, 4), (5, 3, 4, 6, 7), (6, 5, 3, 2, 4), (6, 4, 2, 3), (5, 2, 7, 6, 3), (5, 4, 6, 3, 7), (3, 2, 6, 5, 7), (6, 5, 4, 3, 7), (3, 5, 2, 6, 4), (7, 3, 6, 2, 5), (2, 3, 7, 6, 4), (3, 4, 5, 2, 7), (7, 3, 5, 2), (2, 4, 5, 7), (2, 3, 6, 4), (7, 5, 6, 4), (7, 6, 2), (3, 9, 4), (4, 6, 5), (6, 4, 5, 3, 2), (6, 7, 3, 2, 5), (3, 5, 7, 6), (2, 5, 3, 4, 6), (5, 3, 6), (2, 3, 4, 6, 7), (6, 5, 2, 3, 7), (6, 3, 5, 2, 4), (5, 4, 2, 3), (5, 7, 6, 3, 2), (4, 6, 5, 2, 7), (7, 5, 2, 3), (4, 5, 2, 6, 3), (5, 7, 6, 3), (2, 7, 3, 4, 6), (2, 3, 6), (7, 4, 3, 5), (4, 3, 5, 6, 7), (7, 3, 6, 5, 2), (6, 2, 5, 3, 7), (5, 6, 4), (5, 2, 7, 6), (4, 6, 2, 3), (4, 3, 2, 6, 7), (3, 2, 7, 5), (6, 7, 2, 4, 5), (4, 3, 6, 2), (4, 3, 6, 7, 2), (6, 7, 4, 3, 2), (5, 1), (5, 7, 4, 3, 2), (6, 3, 7), (6, 7, 3, 4, 2), (7, 6, 3, 5, 2), (4, 9, 3), (4, 7, 5, 2), (5, 4, 2, 7, 6), (5, 3, 7, 2, 4), (3, 2, 5, 4, 7), (4, 2, 5, 7, 6), (3, 7, 6, 4), (7, 3, 2, 6, 4), (7, 2, 5, 3, 6), (2, 3, 5, 6, 4), (4, 5, 2, 3, 6), (5, 6, 7, 4, 3), (4, 2, 6, 5, 7), (6, 2, 3, 7), (7, 4, 5, 3), (5, 3, 4, 2, 7), (5, 7, 3), (5, 7, 3, 2, 6), (3, 5, 2, 7), (2, 7, 6, 5, 4), (4, 6, 5, 7), (3, 4, 7, 6, 5), (6, 2, 3, 5, 7), (6, 5, 3, 4, 2), (5, 4, 7, 2), (5, 7, 4, 6), (7, 6, 2, 5), (3, 4, 9), (6, 4, 5, 7, 2), (4, 7, 5, 3, 2), (3, 5, 6, 2), (4, 7, 2, 6, 3), (5, 4, 7), (5, 3, 7, 6, 2), (2, 4, 3, 5, 7), (1, 0), (3, 2, 6, 7, 5), (2, 3, 4, 7, 6), (6, 5, 2, 7), (7, 5, 2, 4, 3), (5, 3, 6, 2, 4), (2, 7), (2, 3, 6, 5, 7), (5, 3, 2, 6), (2, 6, 3, 4, 5), (6, 3, 7, 4, 5), (5, 6, 4, 2, 3), (2, 6, 5, 3, 4), (3, 4, 2, 7, 5), (5, 7, 3, 6, 4), (6, 3, 4, 5), (7, 4), (6, 7, 5), (7, 4, 6, 2), (6, 4, 3, 2, 7), (3, 5, 6), (3, 5, 6, 4, 2), (7, 2, 4), (2, 3, 6, 4, 5), (4, 2, 3), (2, 5, 3, 4, 7), (5, 2, 3, 6, 7), (4, 7, 6, 2), (3, 4, 6), (4, 3, 7, 6, 5), (7, 2, 4, 6, 5), (5, 3, 6, 7), (4, 6, 2, 5, 7), (6, 4, 3, 7, 2), (7, 4, 5, 2, 6), (3, 6, 7, 4, 5), (3, 6, 2, 5, 7), (3, 6, 2, 5), (5, 3, 4, 2, 6), (6, 5, 4, 3), (7, 4, 2, 3, 5), (2, 4, 5, 6, 7), (3, 7, 4, 5, 2), (2, 4, 7, 5), (5, 7, 3, 4), (7, 5, 4, 6), (4, 7, 6, 5, 3), (4, 3, 2, 6, 5), (7, 6, 2, 4, 5), (6, 3, 4), (3, 4, 6, 2, 5), (2, 5, 4, 6, 3), (2, 6, 3, 7, 5), (6, 7, 2, 5, 4), (6, 5, 7, 3, 2), (4, 7, 3, 2, 6), (2, 6, 7, 4, 5), (2, 3, 5, 6), (3, 2, 5, 4), (5, 7, 6, 4, 2), (2, 4, 5, 7, 3), (7, 5, 4, 2, 3), (7, 6, 3, 5), (6, 5, 4), (3, 6, 5, 7, 4), (2, 7, 3, 6, 5), (4, 5, 2, 7), (7, 3, 5, 6, 4), (5, 7, 4, 2, 6), (7, 4, 3, 5, 6), (3, 4, 6, 2, 7), (2, 5, 4, 7), (2, 7, 6, 3, 4), (5, 7, 3, 2, 4), (2, 6, 7, 3), (3, 4, 2, 5), (3, 7, 2, 4, 6), (7, 6, 4, 2, 3), (3, 2, 7), (7, 6, 5, 2, 3), (7, 6, 4, 3), (5, 6, 3, 2, 4), (6, 5, 3, 4, 7), (9, 2, 4), (6, 7, 3, 5), (2, 3, 4, 7, 5), (7, 6, 4, 5), (6, 2, 5, 4), (5, 6, 7, 2, 4), (4, 6, 5, 7, 3), (4, 2, 3, 5, 6), (4, 5, 7, 3, 2), (4, 2, 6, 7), (6, 3, 4, 5, 7), (4, 7, 6, 2, 5), (7, 6, 3), (2, 6, 7, 3, 4), (6, 7, 3, 4, 5), (4, 6, 7, 5), (7, 5, 3, 4), (5, 6, 7, 3, 2), (5, 2, 6, 7), (3, 4), (7, 5, 3, 4, 6), (5, 7, 3, 6, 2), (7, 3, 6, 2, 4), (4, 7), (4, 5, 7, 6), (5, 6, 4, 2, 7), (3, 6, 7, 4), (5, 6), (7, 2, 5, 6, 4), (4, 5, 6, 7, 3), (2, 4, 3, 6, 5), (2, 3, 7), (7, 6, 3, 2, 4), (6, 4, 3, 5, 7), (6, 2, 7), (6, 3, 2, 7), (3, 5, 4, 6), (7, 6, 5, 4, 2), (6, 4, 7), (3, 7, 4, 2, 6), (3, 4, 2), (6, 2, 7, 5, 4), (2, 6, 5, 7, 3), (6, 2, 4, 5, 3), (4, 5, 3, 7), (4, 2, 6, 7, 3), (2, 4, 3), (4, 7, 3, 6, 5), (2, 4, 6, 3, 5), (6, 5, 7, 4, 3), (3, 7, 4, 6, 5), (7, 2, 4, 3, 6), (6, 7, 3, 2, 4), (6, 2, 7, 5, 3), (3, 4, 7, 2), (7, 4, 5, 6, 3), (2, 6, 5, 4, 7), (3, 6, 4, 7), (5, 7, 2), (2, 4, 5, 6), (2, 7, 4, 3, 6), (4, 5, 6, 2, 7), (5, 2, 3, 6), (4, 9, 2), (5, 4, 6, 7), (7, 3, 4, 6), (3, 2, 5, 7, 6), (7, 5, 4, 6, 2), (3, 7, 2, 5, 6), (3, 6, 5, 2, 4), (6, 4, 2, 3, 5), (6, 3, 2, 4, 7), (5, 4, 3, 7, 2), (5, 4, 3, 7, 6), (5, 7, 2, 4, 3), (3, 7, 2, 4), (4, 3, 2, 6), (4, 2, 6, 3, 5), (7, 4, 2, 6, 3), (4, 3, 6, 7), (2, 7, 5, 4), (5, 2, 4, 3, 7), (7, 3, 5, 4, 2), (3, 5, 2, 4, 6), (3, 2, 7, 6), (5, 7, 4, 6, 3), (9, 2, 3), (3, 2, 4, 5, 6), (2, 7, 5, 6, 4), (5, 3, 7, 6), (4, 7, 5, 3), (7, 3, 5, 2, 6), (6, 2, 7, 3), (7, 3, 4, 2, 5), (3, 7, 6, 5), (7, 2, 5), (5, 6, 2, 4), (7, 4, 5, 6), (2, 7, 6, 4, 3), (6, 2, 7, 5), (3, 6, 4, 7, 2), (2, 4, 3, 7, 5), (2, 6, 5, 7), (2, 5, 3, 6, 7), (3, 5, 2, 4), (1, 3), (4, 7, 3, 5, 6), (4, 5, 7, 3, 6), (2, 5), (2, 4, 7, 3, 5), (5, 4, 7, 3), (6, 5, 4, 2, 7), (5, 3, 2, 4, 7), (7, 3, 2, 6, 5), (7, 6, 2, 4), (5, 2, 3), (6, 7), (3, 6, 5, 7), (7, 6), (2, 7, 6, 3), (7, 5, 6, 2, 4), (4, 6, 2, 5, 3), (2, 6, 5), (6, 7, 5, 2), (3, 7, 5, 6), (6, 5, 2, 4, 7), (5, 4, 7, 2, 3), (5, 4, 3, 6), (4, 6, 2, 7, 5), (4, 2, 6, 7, 5), (5, 3, 2, 7), (5, 2, 4, 3), (7, 4, 6, 3, 2), (6, 4, 3, 2, 5), (3, 7, 4, 5, 6), (3, 7, 2), (7, 6, 3, 4, 2), (6, 2, 5, 7, 4), (2, 5, 4, 6, 7), (6, 3, 4, 2, 7), (7, 5, 2, 3, 6), (7, 6, 4, 5, 3), (5, 3, 6, 4, 7), (5, 3, 6, 2), (4, 7, 2, 5, 3), (4, 7, 6, 5), (4, 2, 7, 6), (7, 5, 6), (2, 6, 4, 5), (2, 4, 7, 6, 3), (3, 2, 4), (5, 3, 6, 4), (3, 7, 2, 5, 4), (7, 3, 6), (5, 3, 2, 7, 6), (2, 3, 7, 4, 5), (6, 3, 2, 5, 4), (2, 6, 4, 3), (3, 7, 6, 5, 2), (9, 4, 3), (6, 7, 2, 3, 5), (7, 4, 5, 3, 6), (3, 1), (2, 4, 5, 3, 6), (3, 6, 2, 4), (2, 5, 3, 4), (5, 2, 7, 3, 4), (4, 3, 6), (3, 2, 4, 6, 7), (3, 4, 5, 6), (5, 7, 3, 4, 6), (3, 6, 4, 5), (3, 4, 7, 5), (2, 4, 3, 5), (4, 6, 7), (5, 4, 3, 6, 2), (7, 3, 6, 4), (3, 2, 4, 6, 5), (4, 5, 6, 3), (4, 6, 7, 5, 2), (6, 7, 5, 2, 4), (6, 4, 7, 5, 3), (6, 5, 4, 2, 3), (4, 2, 3, 5, 7), (5, 6, 2, 7, 4), (4, 5, 2, 6), (6, 3, 5, 4), (7, 2, 5, 4, 3), (3, 6, 4, 2), (9, 4), (6, 2, 3, 5, 4), (4, 6, 5, 3, 2), (6, 3, 5, 2), (2, 5, 4, 6), (7, 6, 4, 3, 2), (7, 5, 3, 4, 2), (7, 4, 2, 5, 3), (2, 7, 3, 4), (5, 6, 2, 3, 7), (7, 2, 5, 6), (4, 3, 2, 7, 6), (5, 6, 4, 3), (4, 7, 6, 3, 5), (3, 4, 2, 7, 6), (2, 6, 7, 4), (2, 5, 7, 6, 4), (4, 3, 6, 5, 2), (2, 6, 3, 5), (7, 6, 4, 2), (4, 6, 7, 3, 2), (3, 6), (6, 7, 3, 2), (7, 2, 4, 6, 3), (6, 2, 5, 7), (3, 2, 5, 6, 7), (5, 7, 6, 2), (5, 6, 4, 3, 7), (6, 4, 3, 7, 5), (5, 4), (6, 5, 4, 3, 2), (7, 5, 6, 2, 3), (6, 2, 4, 5, 7), (7, 3, 5, 4, 6), (2, 6, 4, 3, 5), (3, 5, 2, 7, 4), (5, 3, 4, 7, 6), (2, 3, 4, 6), (4, 2, 5), (4, 6, 3, 5), (5, 3, 7, 4, 6), (6, 7, 5, 4, 3), (6, 4, 7, 3, 2), (4, 2, 5, 3, 6), (4, 5, 6), (5, 2, 6, 4, 7), (3, 6, 7, 5), (6, 3, 4, 2, 5), (6, 5, 7, 3, 4), (5, 6, 3, 4, 2), (3, 2, 6, 5, 4), (2, 5, 7, 4, 6), (2, 3, 4, 5, 7), (3, 5, 4, 7), (4, 2, 7, 3, 6), (5, 2, 4), (4, 5, 3, 2), (2, 7, 5, 3, 6), (4, 2, 5, 3), (6, 4, 2, 7), (2, 5, 4, 3, 7), (2, 5, 7, 6, 3), (3, 5, 4), (3, 2, 5, 7, 4), (7, 2, 6, 4, 5), (4, 3, 5, 7, 6), (3, 2, 6, 4, 5), (7, 6, 5, 4), (6, 2, 4, 5), (2, 4, 5, 3), (2, 7, 3), (2, 5, 6, 3, 7), (3, 7, 5), (6, 2), (6, 2, 4, 3), (5, 3, 4, 6), (7, 5, 6, 2), (3, 6, 2, 4, 7), (5, 2, 3, 7), (5, 4, 2, 6, 7), (5, 6, 2, 3, 4), (4, 3, 2, 7), (3, 5, 7, 4), (5, 4, 2, 7), (4, 6, 5, 2, 3), (4, 7, 5), (5, 4, 3, 2, 7), (2, 5, 6, 4, 3), (4, 6, 3, 7, 5), (6, 2, 4, 3, 7), (5, 2, 3, 4, 6), (7, 5, 3, 6, 2), (3, 7, 2, 5), (2, 3, 4, 5, 6), (5, 4, 2, 7, 3), (3, 2, 7, 6, 5), (2, 6, 4), (7, 4, 2), (7, 5, 3, 2, 4), (6, 2, 7, 3, 5), (5, 2, 7, 4), (4, 6, 2, 5), (7, 4, 3, 2, 6), (2, 4, 6, 5, 3), (4, 7, 5, 6), (2, 7, 5, 3), (7, 3, 6, 4, 5), (6, 5, 2), (2, 5, 7, 3, 6), (5, 3, 2, 6, 4), (3, 6, 7, 2, 4), (6, 4, 5, 3), (6, 2, 7, 4, 5), (6, 4, 5, 3, 7), (2, 3), (3, 6, 5, 4, 2), (2, 5, 6), (5, 6, 2, 3), (2, 3, 7, 6, 5), (6, 3, 2, 7, 4), (6, 5, 2, 4, 3), (6, 2, 7, 4), (6, 4, 2, 5, 7), (6, 5), (5, 6, 4, 3, 2), (6, 2, 3, 5), (4, 6, 5, 3), (4, 3, 5, 6, 2), (5, 4, 7, 6, 2), (5, 4, 7, 6), (7, 3, 2, 4, 5), (6, 5, 4, 7, 3), (4, 2, 3, 6, 7), (2, 5, 6, 4, 7), (3, 6, 5, 2), (6, 7, 4, 3, 5), (2, 3, 7, 6), (6, 3, 2), (4, 3, 7), (2, 5, 4, 7, 6), (3, 6, 5, 4), (3, 7, 2, 6), (2, 6, 5, 4, 3), (4, 2, 7, 5, 3), (6, 5, 2, 3), (6, 2, 3, 7, 4), (3, 5, 2, 6, 7), (5, 6, 2, 4, 7), (2, 7, 5, 3, 4), (6, 7, 5, 3), (2, 7, 3, 4, 5), (5, 4, 3, 7), (7, 4, 6, 5, 2), (2, 5, 7, 3, 4), (3, 5, 7, 2, 6), (5, 3, 2, 4), (7, 5, 4, 3, 2), (6, 7, 5, 3, 2), (4, 3, 7, 6, 2), (2, 4, 6, 5, 7), (4, 3, 7, 2), (5, 7, 3, 4, 2), (6, 3, 4, 7), (5, 6, 7, 2), (6, 2, 5), (2, 6, 7, 5, 3), (5, 6, 7), (7, 4, 5, 2, 3), (5, 3, 6, 7, 4), (3, 6, 2, 7, 5), (2, 3, 6, 5, 4), (6, 4, 7, 2, 3), (6, 3, 5, 7, 4), (7, 2, 6, 5, 3), (7, 4, 2, 3), (3, 2, 4, 7), (5, 4, 2), (4, 7, 2, 5), (2, 4, 5), (2, 5, 6, 7, 4), (5, 7, 2, 3, 6), (3, 6, 7), (4, 3, 5, 2, 6), (5, 7, 6, 2, 3), (4, 7, 2, 3), (6, 2, 4, 7, 3), (3, 4, 6, 5, 2), (5, 6, 3, 7, 4), (3, 6, 2, 7), (3, 5, 7, 6, 4), (2, 3, 6, 7, 4), (3, 2, 7, 5, 6), (3, 4, 5, 7), (7, 3, 4, 2, 6), (5, 7, 3, 2), (2, 3, 5, 6, 7), (4, 2, 7, 5, 6), (3, 5, 4, 6, 7), (7, 3, 6, 5), (3, 6, 2, 7, 4), (6, 5, 3, 7), (3, 6, 2, 4, 5), (4, 5, 6, 2), (4, 5, 3, 7, 2), (4, 5, 7), (7, 3, 4, 5, 2), (3, 5, 4, 2, 6), (5, 7, 6, 4, 3), (2, 5, 4, 3), (3, 7, 5, 6, 2), (7, 5, 2, 3, 4), (6, 5, 7, 2), (4, 7, 2), (3, 9), (3, 7, 4, 5), (6, 2, 4, 3, 5), (4, 3), (7, 4, 2, 5), (6, 4, 3, 2), (5, 6, 4, 7, 2), (5, 2), (4, 3, 9), (5, 6, 4, 2), (5, 2, 6, 4, 3), (5, 3, 6, 2, 7), (2, 5, 6, 4), (4, 7, 6, 2, 3), (2, 6, 3, 4), (7, 3, 5, 6), (7, 2, 3), (4, 7, 5, 2, 3), (3, 4, 5, 2, 6), (4, 2, 6, 3), (3, 5, 6, 7, 2), (4, 5, 6, 7, 2), (7, 4, 2, 6, 5), (2, 7, 4), (4, 2, 3, 7, 5), (3, 7, 4), (2, 4, 6, 5), (7, 4, 3, 2, 5), (4, 7, 3, 5), (6, 7, 4, 5, 2), (4, 3, 7, 2, 6), (3, 6, 5, 7, 2), (3, 5, 7, 2, 4), (2, 4, 6, 3), (7, 5, 3, 2), (4, 6, 3, 5, 7), (2, 3, 5, 4), (4, 3, 5, 7, 2), (3, 2, 7, 4, 5), (5, 7, 2, 6), (4, 2, 5, 7, 3), (4, 6, 3, 2), (2, 6, 5, 7, 4), (1, 5), (3, 5, 4, 2), (5, 2, 7, 6, 4), (4, 7, 3, 6, 2), (2, 6, 3), (7, 4, 3), (6, 3, 2, 5), (4, 2, 3, 6, 5), (2, 6), (2, 7, 4, 6), (2, 6, 5, 4), (5, 2, 7, 4, 6), (2, 7, 3, 5, 6), (4, 6, 3, 2, 7), (5, 7, 2, 3, 4), (7, 2, 6, 5), (2, 3, 7, 5, 6), (6, 5, 3), (6, 2, 4, 7, 5), (7, 5), (7, 2, 6, 3), (4, 3, 5, 2, 7), (2, 6, 4, 5, 7), (3, 5, 7, 6, 2), (5, 3, 2), (5, 6, 7, 4, 2), (2, 5, 7), (3, 5, 6, 2, 4), (3, 2, 7, 4, 6), (2, 3, 5, 4, 7), (2, 3, 6, 7), (7, 6, 5, 3, 4), (7, 6, 3, 2, 5), (4, 5, 2, 3, 7), (7, 5, 4), (6, 5, 7, 2, 3), (5, 4, 6, 3), (7, 3, 4, 2), (5, 3, 4, 7), (5, 4, 2, 3, 6), (7, 5, 6, 3), (5, 2, 3, 4), (2, 3, 9), (5, 4, 2, 6), (3, 4, 5), (4, 7, 2, 5, 6), (3, 6, 4, 5, 2), (3, 2, 6, 7, 4), (6, 4, 2, 5, 3), (2, 7, 4, 5, 3), (4, 5, 6, 2, 3), (4, 6, 5, 7, 2), (7, 5, 2, 6), (6, 4, 5, 7, 3), (6, 3, 7, 4), (5, 2, 7, 3), (2, 5, 3, 7, 6), (2, 1), (5, 2, 6, 3, 7), (2, 7, 5, 6), (7, 2, 3, 4), (2, 6, 4, 7, 5), (2, 3, 7, 4, 6), (3, 4, 5, 6, 7), (4, 6, 3, 5, 2), (4, 5, 6, 3, 7), (3, 6, 7, 4, 2), (7, 2), (5, 3, 7, 4), (2, 4, 7, 5, 6), (6, 4, 5, 2), (6, 2, 4), (4, 3, 6, 2, 7), (5, 6, 2, 4, 3), (4, 2, 5, 3, 7), (2, 4, 7, 3, 6), (2, 5, 6, 7), (7, 2, 5, 6, 3), (2, 6, 7, 4, 3), (2, 6, 5, 3), (2, 6, 5, 3, 7), (2, 5, 4, 3, 6), (4, 6, 7, 3, 5), (5, 2, 3, 6, 4), (5, 6, 7, 2, 3), (6, 5, 7, 4, 2), (6, 2, 3, 4), (5, 4, 3), (4, 6, 5, 2), (7, 2, 6, 4, 3), (6, 4, 3, 5, 2), (2, 7, 4, 6, 3), (3, 6, 4), (6, 3, 4, 7, 2), (7, 5, 2, 6, 4), (4, 5, 2, 7, 3), (3, 4, 2, 6, 5), (3, 4, 7, 2, 6), (4, 2, 5, 6, 7), (5, 3, 4, 6, 2), (3, 7, 5, 2, 6), (4, 7, 5, 6, 3), (4, 3, 7, 2, 5), (3, 6, 2, 5, 4), (6, 5, 3, 2, 7), (3, 4, 2, 6, 7), (3, 4, 6, 7, 2), (3, 7, 6, 2, 5), (3, 5, 2), (6, 3, 2, 4, 5), (6, 7, 4, 2, 3), (2, 3, 7, 5, 4), (3, 5), (4, 2, 7), (5, 2, 4, 7), (4, 5, 2, 7, 6), (4, 6), (2, 3, 7, 5), (7, 2, 4, 6), (5, 7), (3, 2, 5, 4, 6), (5, 4, 6, 3, 2), (4, 5, 7, 6, 2), (5, 2, 4, 7, 3), (5, 6, 7, 3), (4, 2, 3, 5), (7, 2, 4, 3), (4, 7, 3), (4, 7, 5, 2, 6), (7, 6, 2, 3), (5, 2, 6), (7, 2, 4, 5, 6), (2, 6, 3, 4, 7), (2, 5, 7, 3), (4, 3, 7, 5, 6), (6, 4, 5, 2, 3), (2, 6, 4, 7), (7, 4, 3, 5, 2), (7, 3, 2, 5), (5, 2, 7, 4, 3), (5, 2, 6, 7, 3), (4, 7, 2, 3, 6), (3, 7, 2, 6, 5), (3, 2, 6, 4, 7), (3, 4, 7, 5, 6), (5, 4, 3, 2), (2, 3, 6, 7, 5), (3, 4, 5, 2), (2, 5, 7, 4, 3), (2, 3, 4, 5), (2, 7, 5), (5, 4, 6, 2, 3), (3, 7, 2, 6, 4), (4, 3, 6, 2, 5), (2, 4, 7, 6), (3, 5, 6, 7), (2, 4, 3, 7), (2, 6, 7, 3, 5), (6, 2, 3, 4, 7), (6, 5, 3, 7, 2), (3, 5, 7, 4, 2), (3, 5, 6, 4), (3, 6, 4, 5, 7), (7, 6, 3, 2), (5, 7, 4, 6, 2), (7, 3, 4, 6, 5), (2, 7, 6, 5, 3), (2, 7, 6, 4, 5), (6, 7, 5, 4), (4, 3, 6, 5, 7), (2, 7, 6, 5), (3, 7, 5, 4), (2, 6, 3, 5, 4), (6, 5, 7, 3), (2, 7, 6, 4), (6, 7, 5, 3, 4), (4, 3, 2, 7, 5), (2, 9, 4), (3, 5, 7, 4, 6), (6, 4, 3, 5), (7, 6, 5, 4, 3), (3, 4, 7, 5, 2), (6, 5, 2, 3, 4), (7, 3, 2, 5, 6), (7, 2, 5, 4), (2, 4, 6, 7, 3), (3, 7, 5, 2, 4), (6, 4, 2, 7, 5), (6, 2, 5, 3), (3, 2, 7, 5, 4), (7, 6, 2, 4, 3), (2, 5, 4), (7, 3, 5, 2, 4), (2, 4, 6, 3, 7), (7, 4, 3, 6), (6, 5, 2, 7, 3), (4, 6, 7, 5, 3), (4, 7, 6, 5, 2), (0, 5), (7, 5, 3), (4, 7, 2, 6, 5), (7, 4, 2, 5, 6), (4, 7, 3, 6), (4, 7, 3, 2, 5), (5, 3, 6, 4, 2), (5, 3, 7, 4, 2), (5, 6, 3, 7, 2), (2, 4), (7, 5, 6, 4, 2), (2, 6, 4, 5, 3), (5, 2, 6, 4), (4, 6, 3, 7), (7, 3, 6, 4, 2), (6, 5, 4, 2), (4, 3, 5), (6, 3, 2, 5, 7), (3, 2, 5), (7, 3, 6, 5, 4), (4, 3, 5, 6), (2, 7, 4, 3), (2, 4, 3, 6, 7), (6, 7, 3, 5, 2), (2, 3, 6, 4, 7), (4, 5, 7, 6, 3), (3, 2, 6, 5), (6, 3, 2, 4), (4, 2, 5, 7), (4, 5, 3, 6, 7), (3, 5, 2, 4, 7), (5, 7, 6), (7, 2, 6, 4), (7, 4, 6, 3), (3, 2, 4, 5, 7), (2, 9, 3), (5, 6, 3, 2, 7), (5, 6, 7, 4), (7, 2, 6, 3, 4), (7, 6, 4, 2, 5), (6, 2, 3), (2, 6, 4, 7, 3), (6, 5, 2, 7, 4), (4, 2, 3, 7, 6), (6, 4, 3), (5, 2, 6, 3, 4), (5, 6, 2, 7, 3), (7, 6, 5, 2), (6, 2, 4, 7), (5, 3, 4, 2), (3, 7, 5, 6, 4), (5, 7, 2, 6, 4), (4, 3, 7, 6), (5, 4, 6, 2), (6, 3, 7, 4, 2), (9, 3), (2, 4, 7), (3, 5, 4, 2, 7), (3, 6, 5), (4, 2, 6, 5, 3), (7, 3, 4, 5, 6), (6, 7, 4, 5), (7, 3, 4, 5), (5, 3, 2, 7, 4), (3, 5, 7, 2), (9, 3, 4), (6, 7, 2, 5, 3), (3, 5, 6, 4, 7), (2, 5, 7, 4), (5, 4, 7, 3, 6), (6, 7, 4, 3), (4, 3, 2, 5), (3, 6, 4, 2, 5), (7, 4, 6, 5), (6, 3, 7, 5), (3, 7, 4, 2, 5), (6, 4, 7, 2, 5), (7, 3, 2, 5, 4), (4, 2, 6), (4, 2, 3, 6), (7, 2, 3, 5), (2, 7, 4, 5, 6), (4, 6, 2, 7), (2, 7, 6, 3, 5), (7, 4, 5, 3, 2), (2, 6, 3, 7, 4), (6, 4, 5, 7), (5, 3, 6, 7, 2), (7, 6, 2, 3, 4), (7, 4, 2, 3, 6), (3, 7, 6, 2), (5, 6, 2, 7), (5, 7, 6, 2, 4), (5, 2, 4, 6, 3), (4, 3, 6, 7, 5), (5, 4, 2, 6, 3), (5, 2, 7), (9, 4, 2), (2, 7, 4, 3, 5), (7, 2, 4, 3, 5), (4, 6, 3, 2, 5), (6, 3, 7, 2, 5), (6, 7, 2), (3, 7, 6, 4, 5), (4, 5, 3, 7, 6), (6, 3, 7, 2, 4), (7, 2, 3, 5, 4), (3, 7), (7, 6, 5, 3, 2), (4, 5, 3, 2, 6), (3, 7, 5, 4, 2), (5, 6, 4, 7, 3), (4, 5, 2, 6, 7), (2, 5, 3, 7, 4), (2, 7, 6), (5, 7, 4, 2), (7, 6, 3, 4), (3, 7, 6), (4, 3, 7, 5, 2), (5, 4, 7, 6, 3), (5, 2, 4, 3, 6), (6, 4, 2, 3, 7), (6, 4, 5, 2, 7), (7, 6, 5, 2, 4), (7, 3, 2, 4), (3, 6, 7, 5, 4), (2, 6, 7, 5, 4), (3, 2, 4, 6), (5, 2, 4, 6), (7, 5, 6, 4, 3), (7, 2, 3, 6, 4), (6, 3, 7, 5, 2), (6, 2, 7, 4, 3), (7, 2, 4, 5), (3, 6, 4, 2, 7), (5, 2, 4, 7, 6), (2, 7, 5, 4, 6), (7, 5, 2, 4, 6), (2, 3, 5, 7, 6), (7, 4, 5), (3, 5, 4, 7, 6), (2, 5, 7, 6), (3, 4, 6, 5, 7), (4, 2, 7, 5), (7, 6, 3, 5, 4), (6, 7, 2, 3), (4, 2, 7, 3), (7, 4, 6, 2, 3), (4, 6, 3), (7, 3, 2, 6), (2, 4, 5, 3, 7), (6, 7, 2, 5), (5, 6, 3, 7), (5, 3, 2, 4, 6), (5, 7, 2, 6, 3), (4, 7, 5, 6, 2), (3, 4, 5, 6, 2), (2, 4, 7, 3), (5, 7, 3, 6), (2, 5, 3, 7), (7, 5, 2), (4, 5, 7, 2, 3), (4, 6, 2, 7, 3), (6, 2, 5, 3, 4), (2, 3, 4), (7, 3, 2), (7, 5, 4, 2), (7, 5, 4, 3, 6), (5, 6, 2), (7, 5, 3, 2, 6), (3, 2, 5, 6), (3, 4, 7), (6, 3, 5, 2, 7), (3, 7, 4, 6, 2), (7, 4, 5, 6, 2), (7, 2, 3, 6, 5), (6, 3, 5), (4, 3, 2), (3, 4, 6, 7, 5), (6, 7, 4, 2, 5), (7, 6, 4), (4, 5, 2, 3), (6, 3, 5, 7), (7, 6, 4, 5, 2), (6, 4, 2, 7, 3), (6, 5, 7, 4), (2, 4, 5, 7, 6), (7, 2, 5, 3), (6, 2, 5, 4, 3), (4, 2, 7, 6, 3), (7, 2, 3, 5, 6), (6, 4, 7, 5), (4, 6, 2, 3, 5), (3, 4, 6, 2), (2, 5, 3, 6), (6, 7, 2, 3, 4), (4, 6, 3, 7, 2), (6, 4, 7, 3), (6, 2, 5, 4, 7), (7, 3, 5, 4), (3, 7, 6, 5, 4), (6, 4, 2), (4, 2, 6, 5), (4, 5, 3, 6, 2), (4, 5, 2), (6, 4), (7, 5, 2, 6, 3), (4, 7, 2, 3, 5), (3, 5, 6, 7, 4), (3, 7, 6, 2, 4), (2, 4, 6, 7), (4, 6, 7, 3), (7, 5, 3, 6), (2, 4, 6), (3, 6, 2), (6, 7, 5, 2, 3), (6, 4, 7, 5, 2), (4, 7, 3, 5, 2), (6, 5, 4, 7), (7, 2, 6, 5, 4), (5, 2, 6, 3), (3, 6, 7, 2), (6, 3, 4, 5, 2), (5, 7, 2, 4), (2, 3, 5, 7, 4), (4, 5, 7, 2), (6, 5, 3, 7, 4), (5, 2, 3, 4, 7), (4, 3, 5, 7), (3, 2, 4, 7, 5), (7, 6, 4, 3, 5), (3, 4, 2, 5, 6), (7, 2, 6), (2, 5, 3, 6, 4), (9, 2), (3, 2, 6, 4), (3, 2, 5, 6, 4), (4, 2, 5, 6), (6, 2, 3, 4, 5), (7, 5, 6, 3, 4), (3, 5, 4, 6, 2), (5, 4, 7, 3, 2), (3, 6, 5, 2, 7), (7, 6, 2, 5, 3), (2, 4, 3, 6), (2, 7, 3, 5, 4), (2, 7, 4, 6, 5), (5, 7, 4, 2, 3), (5, 4, 6, 7, 2), (4, 6, 5, 3, 7), (7, 2, 3, 4, 5), (7, 6, 5, 3), (3, 4, 7, 6), (6, 3, 2, 7, 5), (2, 3, 6, 5), (5, 3, 4), (3, 4, 5, 7, 6), (7, 2, 6, 3, 5), (6, 7, 3), (5, 4, 6, 2, 7), (6, 7, 5, 4, 2), (6, 4, 7, 3, 5), (7, 3, 2, 4, 6), (5, 2, 6, 7, 4), (4, 2, 9), (7, 6, 2, 5, 4), (2, 6, 4, 3, 7), (6, 7, 4, 2), (9, 3, 2), (4, 3, 6, 5), (2, 4, 7, 5, 3), (7, 5, 2, 4), (6, 3, 7, 2), (4, 2, 7, 6, 5), (6, 2, 3, 7, 5), (3, 2, 7, 4), (3, 7, 6, 4, 2), (4, 6, 2, 3, 7), (7, 2, 3, 6), (3, 7, 5, 4, 6), (5, 7, 2, 4, 6), (4, 3, 2, 5, 6), (5, 0), (7, 3, 5), (3, 6, 4, 7, 5), (2, 3, 7, 4), (5, 3, 7, 2), (4, 2, 5, 6, 3), (2, 5, 6, 3), (5, 2, 4, 6, 7), (4, 5, 7, 2, 6), (7, 4, 6), (3, 6, 7, 2, 5), (4, 3, 2, 5, 7), (5, 4, 3, 6, 7), (4, 2), (2, 4, 7, 6, 5), (7, 4, 5, 2), (5, 3), (4, 2, 6, 3, 7), (2, 4, 9), (3, 5, 2, 6), (3, 4, 2, 5, 7), (6, 3, 5, 4, 7), (4, 5, 3, 2, 7), (4, 6, 2), (0, 1), (7, 2, 3, 4, 6), (2, 3, 5, 4, 6), (5, 4, 3, 2, 6), (5, 3, 7), (4, 7, 6, 3, 2), (3, 5, 4, 7, 2), (3, 7, 4, 2), (3, 9, 2), (5, 7, 4, 3, 6), (4, 6, 7, 2, 3), (5, 2, 3, 7, 4), (7, 4, 6, 5, 3), (5, 7, 4, 3), (3, 6, 7, 5, 2), (3, 2, 7, 6, 4), (2, 3, 5), (2, 7, 5, 4, 3), (6, 2, 7, 3, 4), (3, 5, 6, 2, 7), (6, 5, 2, 4), (5, 6, 3), (7, 5, 6, 3, 2), (6, 4, 5), (7, 3, 5, 6, 2), (3, 2, 4, 5), (3, 7, 5, 2), (7, 2, 4, 5, 3), (5, 7, 6, 3, 4), (6, 3, 4, 2), (7, 6, 5), (4, 3, 7, 5), (1, 2), (5, 4, 7, 2, 6), (6, 7, 2, 4, 3), (2, 4, 3, 5, 6), (4, 9), (4, 2, 3, 7), (2, 9), (7, 2, 5, 3, 4), (4, 7, 6, 3), (7, 4, 2, 6), (5, 3, 4, 7, 2), (4, 7, 5, 3, 6), (5, 7, 4), (6, 3), (5, 4, 6, 7, 3), (6, 2, 5, 7, 3), (5, 6, 3, 2), (6, 5, 4, 7, 2), (4, 7, 2, 6), (3, 4, 2, 7), (6, 7, 2, 4), (5, 6, 3, 4), (7, 6, 2, 3, 5), (4, 5, 6, 3, 2), (5, 6, 3, 4, 7), (3, 2, 9), (5, 6, 7, 3, 4), (7, 5, 3, 6, 4), (4, 5, 3), (2, 3, 4, 7), (2, 7, 3, 6), (5, 4, 6), (7, 4, 3, 6, 2), (7, 3, 6, 2), (6, 5, 3, 4), (7, 5, 4, 3), (6, 7, 4, 5, 3), (3, 4, 7, 6, 2), (3, 2, 5, 7), (6, 5, 3, 2), (4, 5, 6, 7), (7, 4, 6, 3, 5), (3, 7, 2, 4, 5), (6, 7, 3, 5, 4), (6, 3, 4, 7, 5), (7, 6, 3, 4, 5), (2, 7, 3, 5), (6, 7, 4), (2, 5, 6, 3, 4), (3, 4, 7, 2, 5), (3, 5, 7), (3, 7, 4, 6), (6, 3, 7, 5, 4), (3, 4, 2, 6), (3, 4, 6, 5), (3, 4, 6, 7), (6, 4, 3, 7), (2, 6, 7, 5)]