Give an example of a sequence $ (A_n) $ of the connected subset of $ mathbb {R} ^ 2 $ such that $ A_ {n + 1} subset A_n $ for $ n in mathbb {N} $ but $ bigcap limits_n A_n $ it is not connected

My attempt: I take $ A_n = (- frac {1} {n} -1, frac {1} {n} +1) $ but $ bigcap limits_ {n = 1} ^ { infty} (- frac {1} {n} -1, frac {1} {n} +1) = (-1,1). $ what is connected

I can't really find the example that $ bigcap limits _n A_n $ it is not connected?