You are buying a set of fireworks for the New Year's firework show you are hosting on January 1, 2025!

The show will consist of 100,000 fireworks launched one at a time. The firework store measures each firework's power in “booms”. To create a beautiful show, the first firework must have a power of 4 booms, and the 100,000th firework must have a power of 12,848 booms.

Moreover, you want each firework's power to differ by exactly 2 booms from the previous firework's power. For example, since the first firework has a power of 4 booms, the second firework must have a power of 2 or 6 booms. It is possible for fireworks to have 0 or negative booms.

How many possible firework shows can you display to satisfy these requirements?

Hint: You don't need a calculator to solve this problem. The number of possible shows is very small.