Iphone 5s contacts with no delete option?

I have some contacts in my iPhone that I can't delete. I press edit then scroll to the bottom but there's nothing there. It's not my Facebook contacts it's usually just some people that I put in my phone then later on decide to delete. However there are other contacts that I can delete and I can't figure out the difference between the two. The way I've kind of dealt with it so far is just delete the number and name but it still shows up in my contact list as a blank or something. It's really frustrating. Can anyone please help me figure out what's wrong and how to fix it?

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