A standart way of solution  has appeared too slow(TLE14)!
Standard way is to make Hermit form above __int64
of the matrix
A=
[p q -p -q]
[q p q   p]
or form
[0 0 * *]
[0 0 0 *]
by Gauss operations on columns in int ring.
For initial A and Hermit form answer is equel.
I were very suprized what for so small matrix we have big Time. This is due to many operations need to make zeros.