A company adopted dollar$-$value LIFO on January $1,2024,$ when the inventory value was $$367,000$ and the cost index was $1\mathrm{.}35.$ On December $31,2024,$ the inventory was valued at year$-$end cost of $$402,000$ and the cost index was $1\mathrm{.}40.$ The company would report a LIFO inventory of:

Note: Round your final answer to the nearest whole dollar amount.

$$387,615.$

$$382,207.$

$$388,407.$

$$418,607.$