Auto increment field that is part of unique_together in Django admin

Basketball Game has 4 Quarters. I would like Django to auto increment Quarter.number for each Game in Admin, so I don’t have to always correct them manually. Example

class Game(models.Model):
    name = models.CharField()

class Quarter(models.Model):
    number = models.IntegerField(help_text='quarter number from 1 to 4')
    game = models.ForeignKey(Game)

    class Meta:
        unique_together = ['game', 'number']

So number in Quarter can be 1, 2, 3 or 4 (or more for other sports) and should be set to 1 by default. After saving first quarter for one Game it should suggest number=2 for the next entry of the same Game. The incremented numbers should also get shown correctly in admin.TabularInline if I set Quarter as inline of Game in (in below code Django would by default show 3 entries for a new Game, but all would have default number=1):

class QuarterInline(admin.TabularInline):
    model = Quarter

class Game(admin.ModelAdmin):
    inlines = [QuarterInline]

How can I achieve that number gets incremented by default for each game?

If it’s ok to create the quarters in advance, create them when a new game created (override ), probably easier than other solutions.