If $\begin{vmatrix}x^n&x^{n+2}&x^{n+3}\\y^n&y^{n+2}&y^{n+3}\\z^n&z^{n+2}&z^{n+3}\end{vmatrix}$ = $(y-z)(z-x)(x-y)(\large\frac{1}{x}+\frac{1}{y}+\frac{1}{z})$ then $n$ is equal to

Question

$(a)\;2\qquad(b)\;-2\qquad(c)\;-1\qquad(d)\;1$