What is happening with my iphone?

Okay, so I have an iphone 5s. I used it in the morning and it was working perfectly fine. I went to school came back home still it was working perfectly fine. An icon appeard in the settings, it was about updating the new ios 7.0.1. I wanted to install it but I had only 22% of battery and it was said that in order to install it it was needed 50% or to be conected to a charger, so i charged it.

I waited and minutes after I noticed that my iphone has gotten really hot as well as the charger.
At first there was an itunes icon. But I took of the charger cable. Turned off the iphone(completly) then turned it on again. After turning on there was this blue cracked screen and it won't turn on completly.(i don't think its the blue screen of death)

So what should I do now? Are there any chances that it will get back to the begging condition? Or is it broken?

Updating system software is a very heavy task, so its supposed to get hot, you messed it up by unplugging it

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