Paxton is a mechanical engineer, and while unemployed invents a switching device for computer networks. Paxton patents the device but does not reduce it to practice. Paxton has a zero tax basis for the patent. In consideration of $$300,000$ plus a $$1$ royalty per device sold, Paxton assigns the patent to a computer manufacturing company. Paxton assigned all substantial rights in the patent. Which of the following statements is true?

a$.$ Paxton automatically has long$-$term capital gain from the lump$-$sum payment but not from the royalty payments.

b$.$ Paxton automatically has long$-$term capital gain from the royalty payments but not from the lump$-$sum payment.

c$.$ Paxton automatically has long$-$term capital gain from both the lump$-$sum payment and the royalty payments.

d$.$ Paxton has long$-$term capital gain from the lump$-$sum payment and a short$-$term capital gain from the royalty payments.

e$.$ Paxton does not have automatic long$-$term capital gain from either the lump$-$sum payment or the royalty payments.