The Hamiltonian for a one-dimensional system with mass \( m \), position \( q \), and momentum \( p \) is:
\[
H(p, q) = \frac{p^2}{2m} + q^2 A(q)
\]
where \( A(q) \) is a real function of \( q \). If
\[
m \frac{d^2 q}{dt^2} = -5q A(q),
\]
then
\[
\frac{d A(q)}{d q} = n \frac{A(q)}{q}.
\]
The value of \( n \) (in integer) is: