Napkin math

The Napkin blocks the door of the design review: no system gets built until someone says how much load it takes. Its first question is about a chat app.

Write peak_qps(daily_users: int, requests_per_user: int, peak_factor: int) -> int:

• Every user sends requests_per_user requests a day, and a day has 86,400 seconds.
• The average load is daily_users * requests_per_user / 86,400 requests per second.
• The busiest second of the day carries peak_factor times the average.
• Return that peak, rounded up to a whole number. Round once, at the very end: never round the average first.

peak_qps(10_000_000, 20, 3)   # 6945: 200M requests / 86,400 s ≈ 2,314.8 per second, x3 ≈ 6,944.4, up to 6,945
peak_qps(100_000, 1, 2)       # 3:    ≈ 1.157 per second, x2 ≈ 2.31, up to 3 (rounding the average to 2 first gives 4)
peak_qps(86_400, 5, 1)        # 5:    exactly 5 per second, nothing to round
peak_qps(1_000, 1, 2)         # 1:    a tiny app still needs room for 1 request per second

1 <= daily_users <= 10^9, 1 <= requests_per_user <= 10^4, 1 <= peak_factor <= 100.