The key observation is that once the player activates SP, things can only play
out one way all the way to the beginning of the first phrase that won't be
overlapped. And whatever phrase that is, you will always reach it with 0 seconds
of SP.

Given this insight, it's easy to see that many different paths of play lead to
these identical states, where you are right at the beginning of some phrase,
with 0 SP. This allows for dynamic programming: for each SP phrase in the song,
pretend that the song starts right there and compute the maximum score in that
"sub-song".

Of course, finding the maximum score in a song is the problem itself, so what
we have ended up with now is a divide-and-conquer of sorts. As always, there is
a base case: the sub-song starting with the last phrase. That's only a matter of
finding the highest-scoring single activation (which takes some amount of work
to do, but is a considerably simpler problem). Now, working backwards, we can
find the optimal score from the previous phrase by finding the best singel-
activation-plus-what's-optimal-after-that combination. We already know what's
optimal from whichever phrase an SP activation ends before, so we can just reuse
that result.

And that's how you do it starting from each phrase: just look for the best
single activation ending before each of the subsequent phrases or reaching past
all of them. Just one activation has to be placed in the best way, and a
recursive, memoized, call will take care of the rest.

About optimal activation placement. Given a phrase to start from, just simulate
playing the song. Keep track of the max amount of Star Power at all times. Have
a list of upcoming phrases to reach with emptied SP. At each "step" forward,
check the score one would get if they activated now plus the score from the
phrases never overlapped in earlier steps up to the first phrase beyond a max SP
activation. Then remove all phrases that are less than max SP away from the
list. Keep stepping until the end of the song is reached by max SP. Some more
efficient step than a millisecond at a time or so should be used. You can for
example step to the next note to play, or the next note for SP to end on.

Running time O(np)