Maximum Four-Person Families in a Cinema

### Problem The cinema has n rows and 10 numbered seats per row. A four-person family may occupy exactly one of these blocks within a row: seats 2..5,4..7,or 6..9. Reserved seats cannot be used, and families cannot share seats. Return the maximum number of families that can be seated. ```cpp class Solution { public: int maxNumberOfFamilies(int n, vector<vector<int>>& reservedSeats); }; ``` ### Examples **Example 1:** ```text Input: n = 2, reservedSeats = [[1,4],[2,7]] Output: 2 Explanation: Use seats6..9 in row1 and seats2..5 in row2; neither row permits two families. ``` **Example 2:** ```text Input: n = 3, reservedSeats = [[2,1],[2,10]] Output: 6 Explanation: Seats1 and10 belong to none of the allowed blocks, so every row still fits two families. ``` ### Constraints - `1 <= n <= 1000000000`. - There are 1 to min(10*n,10000) distinct reserved seat pairs. - Each pair has row in `[1,n]` and seat in `[1,10]`. ### Contract considerations The three stated blocks encode the aisle rule, including the permitted split across the aisle. ```hint Read the boundary condition Check overlapping family placements and reservations at the outside seats. Count families across all rows, including rows without reservations. ``` ### Boundary reminders The three stated blocks encode the aisle rule, including the permitted split across the aisle.