检查元素是否在所有列表中一起出现？

Question

说我有一个像这样的列表列表:

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为设置和检查交集,inner-list2但当我检查交叉点时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？

Answer 1

使用itertools.combinations:

我最初想过用的东西itertools.combination,但是因为它允许elements来自list不相邻的东西,所以它不适用于我想到的解决方案.

事实证明,在查看非数字输入时lists,在两种情况下itertools.combinations 都是必要的.我很困惑因为我认为groups必须这样做adjacent.

我想会的工作最适合这种情况的方法是将产生的可能elements是可以工作,然后检查了这些每一个function反对list的sub-lists-而不是做的某种组合学工作list,并会沿着这条路走下去.

因此,要检查是否有list可能elements是"有效",即如果所有的elements只发生一起,我用了一个简单的if用一个发电机all()和any()内置functions做这部分工作.

现在这是有效的,需要有一种方法来产生elements可能发生的潜力.我只是用两个嵌套做了这个for-loops- 一个iterating在width它上面window,一个iterating在它的start位置window上.

然后,从这里,我们只检查那组是否elements是valid,如果是的话,将其添加到另一组list!

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)

给出sol如下:

[(2, 3), (6, 7)]]

这些2 nested for-loops实际上可以拼凑成一个很好的one-liner(不确定,如果其他人认为它是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.

由于大众需求(@Arman),我已经更新了答案,以便它现在应该对其他工作elements从分开0-9.这是通过引入unique elements list(els)来完成的.

一些测试@thanasisp来自上面相同的代码:

l = [[1, 3, 5, 7],[1, 3, 5, 7]]

给出sol:

[(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)]

我认为这是正确的,因为2 不应该在任何群体中,因为所有其他群体elements都是不同的sub-list,因此它永远不会与另一群体成为一个群体element.

Answer 2

这更像是一个蛮力解决方案，但是，它会通过生成 中 每个子列表的排列l并过滤以查找其元素全部出现在 的子列表中的任何排列来生成一起出现的所有元素的大列表l。如果任何排列通过该条件，则排列将被添加到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)]