Slept through interview. Am I screwed?

I've had a really bad sleep schedule lately and haven't been able to get to sleep until like 4 am every day. Therefore, since I had an interview at noon today, I decided the best plan would be for me to just stay up, go to the interview, and sleep after it. This was a mistake. I passed out at 9:30 am and woke up at 2 pm in a panic.

I immediately sent an email apologizing and explaining the situation, but I didn't have a specific email for a person so I had to send it to a generic jobs@companyname.com type email. I also didn't have a phone number to call so I couldn't do that.

Am I screwed? Or is there some way to fix this?

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