If we know that $\dot{q} = \frac{\partial H}{\partial p}$ and $\dot{p} = -\frac{\partial H}{\partial q}$

And $Q$ and $P$ are $q$ and $p$ at a later time step. How could we prove that:

$Q = q + {\Delta}t\frac{\partial H}{\partial p}(q,p) $, $P = p - {\Delta}t\frac{\partial H}{\partial q}(q,p) $

Is not symplectic,

While:

$Q = q - {\Delta}t\frac{\partial H}{\partial p}(q,p) $, $P = p + {\Delta}t\frac{\partial H}{\partial q}(q,p) $

is symplectic