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python - Find intersection of two nested lists?

I know how to get an intersection of two flat lists:

b1 = [1,2,3,4,5,9,11,15]
b2 = [4,5,6,7,8]
b3 = [val for val in b1 if val in b2]

or

def intersect(a, b):
    return list(set(a) & set(b))
 
print intersect(b1, b2)

But when I have to find intersection for nested lists then my problems starts:

c1 = [1, 6, 7, 10, 13, 28, 32, 41, 58, 63]
c2 = [[13, 17, 18, 21, 32], [7, 11, 13, 14, 28], [1, 5, 6, 8, 15, 16]]

In the end I would like to receive:

c3 = [[13,32],[7,13,28],[1,6]]

Can you guys give me a hand with this?

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You don't need to define intersection. It's already a first-class part of set.

>>> b1 = [1,2,3,4,5,9,11,15]
>>> b2 = [4,5,6,7,8]
>>> set(b1).intersection(b2)
set([4, 5])

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