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“גוט שבת, גוט שבת”

My father, passing someone on the street on שבת, says "גוט שבת, גוט שבת" (Yiddish, "good sabbath, good sabbath"). I thought it might be his own idio-custom — until I came across someone else who does the same. Neither could really explain to me why he does it, though the one not my father told me "that's the minhag [=custom]!". Does anyone know where this comes from or why people do it?