Long Contest and Cook Off Overlaps

Each month, a CodeChef Long Contest starts at 3 PM IST (UTC+5:30) on the first Friday and it lasts for exactly $10$ days (i.e. $240$ hours). Also, a Cook-Off starts at 9:30 PM IST on the second-to-last (i.e. penultimate) Sunday and it lasts for $2.5$ hours. Let's denote a month by a pair $(m, y)$, where $m$ is one of the twelve months (numbered $1$ through $12$) and $y$ is a year. You are given