3. Given an integer $n \geqslant 2$. Let $a_{1}, a_{2}, \cdots, a_{n}, b_{1}, b_{2}, \cdots, b_{n}>0$, satisfying
$$
a_{1}+a_{2}+\cdots+a_{n}=b_{1}+b_{2}+\cdots+b_{n} \text {, }
$$

and for any $i, j(1 \leqslant i<j \leqslant n)$, we have $a_{i} a_{j} \geqslant b_{i}+b_{j}$. Find the minimum value of $a_{1}+a_{2}+\cdots+a_{n}$.