My Iphone 5s battery drains fast

Last week the battery of my iPhone 5s ran out. When I got home I connected the charger and I noticed that was really slowly. Anyway I left my phone charging all night as usual.

When I woke up, I left to work and saw that the battery was running out horribly fast. Even with the 3G, wi fi turned off.

I've already restored on iTunes and the problem remains.

Addionalty, I'm from Brazil, and since I bought on USA, they say that the warranty here doesnt work 'cause the model (a1533) its not supported here.

However, I found out that the battery of every iPhone produced in the world is the same! How can I get my Iphone a repair or replacement?

iPhone 5s, iOS 7.0.4