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A casual LTI system has zero initial conditions and impulse response $h(t)$. Its input $x(t)$ and output $y(t)$ are related through the linear constant-coefficient differential equation $$\frac{d^2y(t)}{dt^2} + a \frac{dy(t)}{dt}+a^2y(t)=x(t).$$ Let another signal $g(t)$ be defined as $$g(t)=a^2 \int_0^t h(\tau) d \tau +\frac{dh(t)}{dt}+ah(t).$$ If $G(s)$ is the Laplace transform of $g(t)$, then the number of poles of $G(s)$ is _________.
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