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itertools.groupby

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I have a file such as:

$ cat my_data
Starting a new group
a
b
c
Starting a new group
1
2
3
4
Starting a new group
X
Y
Z
Starting a new group

I am wanting a list of lists:
['a', 'b', 'c']
['1', '2', '3', '4']
['X', 'Y', 'Z']
[]

I wrote this:
------------------------------------
#!/usr/bin/python3
from itertools import groupby

def get_lines_from_file(file_name):
    with open(file_name) as reader:
        for line in reader.readlines():
            yield(line.strip())

counter = 0
def key_func(x):
    if x.startswith("Starting a new group"):
        global counter
        counter += 1
    return counter

for key, group in groupby(get_lines_from_file("my_data"), key_func):
    print(list(group)[1:])
------------------------------------

I get the output I desire, but I'm wondering if there is a solution without
the global counter.

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itertools.groupby Jason Friedman <jsf80238@gmail.com> - 2013-04-20 11:09 -0600
  Re: itertools.groupby Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-04-21 00:13 +0000
    Re: itertools.groupby Joshua Landau <joshua.landau.ws@gmail.com> - 2013-04-22 04:09 +0100
  Re: itertools.groupby Neil Cerutti <neilc@norwich.edu> - 2013-04-22 14:24 +0000
    Re: itertools.groupby Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2013-04-22 15:49 +0100
      Re: itertools.groupby Neil Cerutti <neilc@norwich.edu> - 2013-04-22 15:04 +0000
    Re: itertools.groupby Chris Angelico <rosuav@gmail.com> - 2013-04-23 01:14 +1000

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