Count Months Whose First Day Is Sunday

## Problem Given inclusive start and end years, count how many months in that range begin on a Sunday. Use the proleptic Gregorian calendar and do not use a built-in date or calendar library. You may use the anchor that January 1, 2000 was a Saturday. ### Function Contract Implement `count_sunday_month_starts(start_year, end_year) -> int`. ### Constraints - `1900 <= start_year <= end_year <= 9999`. - A leap year is divisible by 400, or divisible by 4 but not by 100. - Count January through December in both boundary years. - Weekday arithmetic must work for ranges before as well as after 2000. ### Examples - `start_year = 2000`, `end_year = 2024` returns `43`. - The year 2000 is a leap year; 1900 is not. ```hint Track the first weekday Once the weekday of a month's first day is known, add that month's length modulo seven to reach the next month. ``` ```hint Reach the starting year from the anchor Move year by year forward or backward from 2000 using 365 or 366 days modulo seven. ``` ### Edge Cases - Century leap-year rules affect 1900, 2000, and 2100 differently. - A one-year range still includes all twelve months. - Do not assume the start year is at or after 2000.