Customizing a Picker That Contains a List

I'm still new Xamarin and I'm having some trouble in my code.
I have a picker that contains a list of areas. There are over 3000 items. It will be very hard and not user friendly to scroll down all of them.
So I want to add at the top of it a text entry so that the user can enter the first letters and the list is automatically filtered. Then he chooses the preferred area.
I'm only trying this in Android so far. A snapshot is attached to give an idea about my work.
Any help is much appreciated.