War in Middle Earth

Crossover also with Lord of the Rings. Katniss somehow was magically taken to Middle Earth in search for who brought her there, Frodo. Harry is in search for why he and his whole school was also taken to Middle Earth. How does this all end up with a war? Harry Potter & Hogwarts vs Katniss & Middle Earth. Who'll win? During Mockingjay book. During Deathly Hallows. After LOTR.