RU-ALLRUSSIAN 1984 Problem 7

$\mathrm{n} > 3$ positive integers are written in a circle. The sum of the two neighbours of each number divided by the number is an integer. Show that the sum of those integers is at least 2n and less than 3n. For example, if the numbers were 3, 7, 11, 15, 4, 1, 2 (with 2 also adjacent to 3), then the sum would be $14 / 7 + 22 / 11 + 15 / 15 + 16 / 4 + 6 / 1 + 4 / 2 + 9 / 3 = 20$ and $14 \leq 20 < 21$ .