Iphone 5s alarm not working?

I set up the alarm (on my new iPhone 5s) and then hit save. It just displays 'NO alarms'
What am I doing wrong? Am I missing something? I just want to set an alarm ;'0

Try to restart your phone by holding the lock and home button at the same time until the Apple logo appears and try the alarm again. If that doesn't work then make an appointment at the Genius Bar.

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