Table schema:
CREATE TABLE table_name_12 (pop_density__per_km2_ INTEGER, district VARCHAR, s_barangay VARCHAR)

Question: What is the lowest population density for the district of Santa Cruz and a Barangay larger than 82?
SQL: SELECT MIN(pop_density__per_km2_) FROM table_name_12 WHERE district = "santa cruz" AND s_barangay > 82