Circuit Breaker

When a downstream dependency starts failing, hammering it with retries makes things worse — you pile load onto a service that is already struggling and you make your own callers wait on calls that are doomed to fail. The circuit breaker pattern fixes this by failing fast: after enough failures it stops calling the dependency entirely for a cooldown period, then cautiously tests whether it has recovered.

A breaker has three states:

• CLOSED — normal operation; requests pass through. Consecutive failures are counted, and hitting the failure threshold trips the breaker to OPEN.
• OPEN — the dependency is presumed down; every request fails immediately without being attempted. After a cooldown period elapses, the breaker moves to HALF_OPEN.
• HALF_OPEN — a limited trial: the next request(s) are allowed through to probe recovery. A success closes the breaker again; a failure reopens it immediately and restarts the cooldown.

Implement CircuitBreaker:

• __init__(self, failure_threshold: int, cooldown_ms: int, success_threshold: int = 1)
• call(self, timestamp_ms: int, succeeds: bool) -> bool — process one request arriving at timestamp_ms. succeeds is what the underlying dependency would return if called. Return True if the request was allowed through and succeeded; return False if it was rejected (OPEN) or if it was allowed through but failed.

Behavior:

• CLOSED + failure → increment failure count; at failure_threshold consecutive failures, trip to OPEN (record the time).
• CLOSED + success → reset the failure count to 0.
• OPEN + request within cooldown → reject (return False), do not call the dependency.
• OPEN + request at/after cooldown_ms since opening → move to HALF_OPEN and treat this request as a trial.
• HALF_OPEN + success → count it; at success_threshold successes, close the breaker. Return True.
• HALF_OPEN + failure → reopen immediately, record the new open time, return False.

Constraints:

• timestamp_ms is non-decreasing across calls
• failure_threshold >= 1, cooldown_ms >= 0, success_threshold >= 1