Show that the inequality
\[\sum_{i=1}^{n} \sum_{j=1}^{n} (\sqrt{|x_{i} - x_{j}|}) \leq \sum_{i=1}^{n} \sum_{j=1}^{n} (\sqrt{|x_{i} +x_{j}|})\]
holds for all real numbers $x_1, \ldots, x_n.$
IMO 2021, Problem 2
"Questions we can't answer are far better than answers we can't question"