计算
$$
D=\left|\begin{array}{cccccc}
4 & 3 & 3 & \cdots & 3 & 3 \\
3 & 5 & 3 & \cdots & 3 & 3 \\
3 & 3 & 6 & \cdots & 3 & 3 \\
\vdots & \vdots & \vdots & & \vdots & \vdots \\
3 & 3 & 3 & \cdots & n+2 & 3 \\
3 & 3 & 3 & \cdots & 3 & n+3
\end{array}\right|
$$