Covariance of absolute value of variables

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I have some relatively complicated variables I am working with.

I need to find the covariance: $\text{cov}(\left|x\right|,\left|y\right|)$, is there a simplification of $\text{cov}(\left|x\right|,\left|y\right|)$ in terms of $\text{cov}(x,y)$?