JMO 2025 Problem 1

Let $n$ be an integer greater than or equal to $2$ . Consider real numbers $a_1, a_2, \dots, a_{2n}$ satisfying the condition $$|a_k - a_{n+k}| \geqslant 1 \text{for all } 1 \leqslant k \leqslant n.$$ Determine the minimum possible value of $$(a_1 - a_2)^2 + (a_2 - a_3)^2 + \dots + (a_{2n-1} - a_{2n})^2 + (a_{2n} - a_1)^2.$$