Michael $($single$)$ purchased his home on July $1,2013.$ He lived in the home as his principal residence until July $1,2021,$ when he moved out of the home, and rented it out until July $1,2022,$ when he moved back into the home. On July $1,2023,$ he sold the home and realized a $$300,000$ gain. What amount of the gain is Michael allowed to exclude from his $2023$ gross income?

$$ $$0$

$$225,000$

$$250,000$

$$300,000$