Benny and Alice Jackson bought their principal residence located in New York City in $2017.$ In $2023$ they decided to move to New Jersey and sold their house at a gain of $$550,000.$ They paid $$895,000$ for their new house. If they file a joint return in $2023,$ how much of the $$550,000$ gain must they report in $2023?$

$$0$

$$550,000$

$$50,000$

$$500,000$