Multi-Window Throttling Gateway

An electronic market-making gateway at Citadel processes an incoming stream of client order requests. To safeguard low-latency order matching engines and prevent cascading exchange connectivity failures, the gateway enforces three simultaneous sliding-window throttling rules:

1. 1-Second Rule: No more than $3$ requests are permitted within any $1$-second rolling window $[t, t]$.
2. 10-Second Rule: No more than $20$ requests are permitted within any $10$-second rolling window $[t-9, t]$.
3. 60-Second Rule: No more than $60$ requests are permitted within any $60$-second rolling window $[t-59, t]$.

You are given an array of integers request_times sorted in non-decreasing order, where each element represents the arrival timestamp (in seconds) of a client request. A request arriving at time $t$ is dropped if processing it would cause the number of recorded requests in any of the three windows ending at $t$ to exceed the respective limit.

Crucial Protocol Specification: All requests (both successfully delivered and dropped) remain logged in the gateway's sequence and are counted in the evaluation of all subsequent throttling windows.

Your Task

Implement the function count_dropped_requests(request_times: list[int]) -> int that calculates the total number of dropped order requests.

Constraints

• $1 \le \text{len}(request\_times) \le 10^5$
• $1 \le request\_times[i] \le 10^6$
• request_times is sorted in non-decreasing order ($request\_times[i] \le request\_times[i+1]$).

Examples

# Example 1
request_times = [1, 1, 1, 1, 2]
# Output: 1 (at index 3, 4th request at t=1 exceeds 3 requests per 1 sec)

# Example 2
request_times = [1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7]
# Output: 2