Total inductance (multiloop circuit)

1. The problem statement, all variables and given/known data
Essentially I have a circuit that looks like this:

Code:
         A
-------|--------
|      |        |
L1     |        L3
|      |        |
----------L4-----
|      |        |
L2     |        L5
|      |        |
-------|---------
B
L1 = 2
L2 = 10
L3 = 4
L4 = 6
L5 = 8

How can one find the total inductance between A and B?

3. The attempt at a solution

I know inductance rules are the same as resistance rules--but if this is so, the total inductance would be zero because there is a direct path from A to B. But something tells me this isn't right.

Any help would be appreciated!

Much obliged,

- Steve.
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