$\underline{\text { Folklore }}$

Find any seven consecutive natural numbers, each of which can be changed (increased or decreased) by 1 in such a way that the product of the seven resulting numbers is equal to the product of the seven original numbers.

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For example, the numbers from 3 to 9: we replace 3 with 2, 4 with 5, 5 with 6, and the numbers in each of the pairs $(6,7)$ and $(8,9)$ are swapped with each other. In the end, we get

$3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8 \cdot 9=2 \cdot 5 \cdot 6 \cdot 7 \cdot 6 \cdot 9 \cdot 8$