Schedule a one-day conference with these constraints: TALKS: A (90min), B (60min), C (45min), D (30min), E (30min), F (45min) ROOMS: Main Hall (capacity 500), Room 2 (capacity 100), Room 3 (capacity 50) TIME: 9:00 AM - 5:00 PM, with mandatory lunch break 12:00-1:00 PM CONSTRAINTS: 1. Talk A must be in Main Hall (expected attendance: 400) 2. Talk B and C cannot overlap (same speaker) 3. Talk D must be before Talk E (E builds on D's content) 4. Talk F requires Room 2's AV equipment 5. No room can have more than 3 talks total 6. At least one talk must be running at all times (except lunch) 7. Talk A cannot start before 10:00 AM (speaker arriving late) 8. Talk E must end by 3:00 PM (speaker leaving early) Find a valid schedule or prove none exists.