grammar - I think that she thinks that I think she is dumb

Just trying have some fun with Japanese grammar, but the sentence in the title has me stumped. I just don't understand Japanese particles enough to even know where to begin. Here is my best attempt at something resembling this sentence, but its gotta be wrong, so please help understand how to construct this sentence in the best way.

I think that she thinks that I think she is dumb
私は彼女が私は彼女がバカとおもうとおもっているとおもう。(LOL, there is just no way...)

Answer

How about...

I think she is dumb.
彼女のことをバカだと僕は思っている。
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She thinks that I think she is dumb.
彼女のことをバカだと僕が思っていると彼女は思っている。
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I think that she thinks that I think she is dumb.
彼女のことをバカだと僕が思っていると彼女が思っていると僕は思っている。
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X thinks that I think that she thinks that I think she is dumb.
彼女のことをバカだと僕が思っていると彼女が思っていると僕が思っているとXさんは思っている。
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Y thinks that X thinks that I think that she thinks that I think she is dumb.
彼女のことをバカだと僕が思っていると彼女が思っていると僕が思っているとXさんが思っているとYさんは思っている。
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... and it can go on and on...