Spouses, Chip and Carrie Carson, purchased a principal residence in Richmond for $375,000$ on September $1,20$x$5.$ Carrie obtained a job in Boston, and on December $1,206,$ they sold their home in Richmond for $$650,000$ and moved to Boston. How much gain, if any must Chip and Carrie recognize on their $206$ joint federal income tax return?

$\backslash$table$[[$A$,$$$500,000$