Counting depth or the deepest level a nested list goes to

A have a real problem (and a headache) with an assignment...

I'm in an introductory programming class, and I have to write a function that, given a list, will return the "maximum" depth it goes to... For example: [1,2,3] will return 1, [1,[2,3]] will return 2...

I've written this piece of code (it's the best I could get T_T)

def flat(l):
    count=0
    for item in l:
        if isinstance(item,list):
            count+= flat(item)
    return count+1

However, It obviously doens't work like it should, because if there are lists that do not count for the maximum deepness, it still raises the counter...

For example: when I use the function with [1,2,[3,4],5,[6],7] it should return 2, but it returns 3...

Any ideas or help would be greatly appreciated ^^ thanks a lot!! I've been strugling with this for weeks now...

Breadth-first, without recursion, and it also works with other sequence types:

from collections import Sequence
from itertools import chain, count

def depth(seq):
    for level in count():
        if not seq:
            return level
        seq = list(chain.from_iterable(s for s in seq if isinstance(s, Sequence)))

The same idea, but with much less memory consumption:

from collections import Sequence
from itertools import chain, count

def depth(seq):
    seq = iter(seq)
    try:
        for level in count():
            seq = chain([next(seq)], seq)
            seq = chain.from_iterable(s for s in seq if isinstance(s, Sequence))
    except StopIteration:
        return level