Matrices And Determinants

Let \(a, b\) and \(c\) be such that \(b+c \neq 0\) and
$$\begin{aligned} & \left|\begin{array}{ccc} a & a+1 & a-1 \\ -b & b+1 & b-1 \\ c & c-1 & c+1 \end{array}\right| \\ & +\left|\begin{array}{ccc} a+1 & b+1 & c-1 \\ a-1 & b-1 & c+1 \\ (-1)^{n+2} a & (-1)^{n-1} b & (-1)^n c \end{array}\right|=0 \text {, } \\ & \end{aligned}$$

then the value of \(n\) is