Heidi bought a mountain chalet in $2018$ for $$150,000$ and sold it in $2023$ for $$180,000.$ She bought a lakeside cabin in $2019$ for $$100,000$ and sold it in $2023$ for $$130,000.$ She lived full$-$time at the chalet in $2018$ and spent an equal amount of time at the chalet and the cabin during the $5$ years from $2019$ to $2023.$ How should she designate her principal residence exemption for the year $2019$ to minimize her $2023$ taxable capital gains?

$2019$ cannot be designated to either the cabin or the chalet

$2019$ should be split between the cabin and the chalet

$2019$ should be designated to the cabin

$2019$ should be designated to the chalet