I wonder if a 30-min nap improves the situation. But I need to tell the brain to hold the flushing until the nap.
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I pop up 5 minutes later and feel completely refreshed.
My experience after sleeplessness nights is that even few seconds help significantly, especially when you're almost unable to function anymore.
If the nap lasts longer than 30 minutes, though, you have a good chance of feeling groggy afterwards.