Iphone 5s activation failed. Please help

Hello.

I updated my iPhone on 26th and everything was fine, until i put my iPhone to charge that night. I woke up and it only went from below 20% to 77%. So I restarted my phone, typed touch id code and my pin code. After that, my iPhone asked me to activate by putting my apple ID. I did that, and after my iPhone was only searching for my mobile network. No one could call me. So I found some advices on the internet, but nothing worked.

So yesterday I decided to restore. I followed the instructions on the apple support site. Now after it tries to activate, it says that it failed because the server is temporarily unavailable. It also says to activate in iTunes, but iTunes does the same.
Has anyone experienced something like this? I found an discussion where someone said that it's on Apple's side and I should just wait a few days or keep trying. Is that true? Thank you.