How to make an async game loop in Pygame

game.py

import asyncio

import pygame

class Game:
    def __init__(self):
        pygame.init()
        self.window = pygame.display.set_mode((640, 480))
        self.clock = pygame.time.Clock()
        self.running = True

    def process_input(self):
        for event in pygame.event.get():
            if event.type == pygame.QUIT:
                self.running = False
                break

    def render(self):
        self.window.fill((200, 200, 200))
        pygame.draw.rect(self.window, (0, 0, 255), (120, 120, 400, 240))
        pygame.display.update()

    async def run(self):
        while self.running:
            self.process_input()
            self.render()
            self.clock.tick(60)
            await asyncio.sleep(0)
        pygame.quit()

async def main():
    game = Game()
    await game.run()

if __name__ == "__main__":
    asyncio.run(main())