Harry potter/hunger games crossover

Panem used to have its own wizarding school, but it was fully controlled by the capitol and it was very strict.
Panem saw the witches and wizards as freaks, that's why they organized 'the hunger games' in the first place.
From the outside it might seem like they picked random children between 12 and 18, but they secretly only picked witches and wizards.
Fortunately, the brave witch Katniss Everdeen undermined the Capitol and thanks to her, the Capitol has fallen.

The wizards and witches who are still young enough to go to school, will be randomly sorted into Dumstrang, hogwarts or ......

(I know that the hunger games is in the future and harry potter is in the past, but I changed it so it would fit in the plot. The revolution in the Capitol was before the Hogwarts war, and Peeta, katniss, Gale and finnick are 16 when the story starts, although Gale and finnick are originally older)