Let $a_1, a_2, \cdots, a_n$ be $n > 2$ real numbers. Show that it is possible to select $\epsilon_1, \epsilon_2, \cdots, \epsilon_n \in \{1, -1\}$ such that $$(\sum_{i=1}^na_i)^2 + (\sum_{i=1}^n\epsilon_ia_i)^2 \le (n+1)(\sum_{i=1}^na_i^2)$$