Peak Order Flow Rate Detection

During continuous trading sessions, automated monitoring engines at Citadel and Optiver track instantaneous market message rates. An array of integers rates of length $N$ records message arrival counts per millisecond across an auction period.

A peak rate occurs at index $i$ if rates[i] is strictly greater than its immediate neighbors: $rates[i] > rates[i-1] \quad \text{and} \quad rates[i] > rates[i+1]$ For the boundary elements, assume virtual neighbors $rates[-1] = rates[N] = -\infty$. You are guaranteed that no two adjacent elements are equal (rates[i] != rates[i+1] for all $0 \le i < N - 1$).

Your Task

Implement the function find_peak_flow_rate_index(rates: list[int]) -> int that finds the index of any peak rate in $\mathcal{O}(\log N)$ time.

Constraints

• $1 \le \text{len}(rates) \le 10^5$
• $-2^{31} \le rates[i] \le 2^{31} - 1$
• rates[i] != rates[i+1] for all valid $i$.

Examples

rates = [1, 2, 3, 1]
# Index 2 (value 3) is greater than 2 and 1.
# Output: 2

rates = [1, 2, 1, 3, 5, 6, 4]
# Valid peak indices: 1 or 5.
# Output: 1 or 5