What is what country is ain?

There seems to be a misunderstanding. There isn't a country named "Ain." "Ain" is most commonly a department in the Auvergne-Rhône-Alpes region of France. It's known for its diverse landscapes, ranging from the plains of the Saône valley to the Jura Mountains. It is also recognized for its gastronomy, including Bresse poultry and Comté cheese. The prefecture (capital) of Ain is Bourg-en-Bresse.