Build the Longest Spike Sequence

Question

We use the word spike for a run of numbers that keeps climbing (each value bigger than the one before) and afterwards keeps dropping (each value smaller than the one before). The peak, the largest value, is shared by the rising part and the falling part. So [3, 8, 9, 4, 1] is a spike, while [2, 4, 4, 9, 1] is not, since its rising part repeats the value 4 and therefore does not go strictly up. ...