Let the maximum value of $\sin x \cos x$ for $x \in \mathbb{R}$ be $M$. If the value of $x$ for which $\sin x \cos x$ is maximum, where $0< x < \pi$, can be expressed as $\dfrac{A\pi}{B}$ for positive coprime integers $A$ and $B$, compute $M+A+B$.

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