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In-hand object reorientation has been a challenging problem in robotics due to high dimensional actuation space and the frequent change in contact state between the fingers and the objects. We present a simple model-free framework that can learn to reorient objects with both the hand facing upwards and downwards. We demonstrate the capability of reorienting over $2000$ geometrically different objects in both cases. The learned policies show strong zero-shot transfer performance on new objects. We provide evidence that these policies are amenable to real-world operation by distilling them to use observations easily available in the real world. The videos of the learned policies are available at: https://taochenshh.github.io/projects/in-hand-reorientation.