Given a positive integer $n \geq 2$, non-negative real numbers $a_{i}(1 \leq i \leq n)$ satisfy $\sum_{i=1}^{n} a_{i}=1$, try to find the maximum value of $\sum_{1 \leq i<j \leq n}(j-$ i) $\mathrm{a}_{\mathrm{i}} \mathrm{a}_{\mathrm{j}}$.