A contour integral is defined as \[ I_n = \oint_C \frac{dz}{(z - n)^2 + \pi^2} \] where \( n \) is a positive integer and \( C \) is the closed contour, as shown in the figure, consisting of the line from \( -100 \) to \( 100 \) and the semicircle traversed in the counter-clockwise sense. The value of \( \sum_{n=1}^5 I_n \) (in integer) is \(\underline{\hspace{2cm}}\).
