At December $31,$ Moore Company's inventory records indicated a balance of $$420,000.$ Upon further investigation it was determined that this amount included the following:

$(1)$ $$54,000$ in inventory purchases made by Moore shipped from the seller December $29$ terms FOB destination, but not due to be received until January $2.$

$(2)$ $$25,000$ in inventory purchases made by Moore shipped from the seller December $29$ terms FOB shipping point, but not due to be received until January $2.$

$(3)$ $$6,000$ in goods sold by Moore with terms FOB shipping point on December $29.$ The goods are not expected to reach their destination until January $4.$

$(4)$ $$7,000$ in goods sold by Moore with terms FOB destination on December

$29.$ The goods are not expected to reach their destination until January $5.$

$(5)$ $$15,000$ of goods owned by Moore Company held on consignment by Dollywood Company.

What is Moore's correct ending inventory balance at December $31?$

$$345,000$

$$392,000$

$$373,000$

$$351,000$

$$360,000$