1. $n$ is a positive integer greater than 1, and the product of the following expression is a perfect square. The minimum value of $n$ is $\qquad$.
$$
\sqrt{1+\frac{1}{2}} \times \sqrt{1+\frac{1}{3}} \times \sqrt{1+\frac{1}{4}} \times \cdots \times \sqrt{1+\frac{1}{n+1}}
$$
$30$