The county has 22 schools; 15 are public schools in 3 school districts, and 7 are private. South Harrison Community Schools is the largest district with 3,141 pupils in 2010. The district covers the southern half of the county and includes Corydon Central High School, Corydon Central Junior High School, South Central Junior & Senior High School, Corydon Intermediate, Corydon Elementary, Heth-Washington Elementary, and New Middletown Elementary. North Harrison Community School Corporation had 2,324 pupils in 2010 enrolled in North Harrison High School, North Harrison Middle School, North Harrison Elementary, and Morgan Elementary. Lanesville Community School Corporation is the smallest district serving only Franklin Township. It consists of Lanesville Junior Senior High School and Lanesville Elementary. In 2010, teachers in the North Harrison district averaged $50,800 in annual salary; South Harrison teachers averaged $48,500; Lanesville teachers averaged $51,500. North Harrison had a 2010 graduation rate of 81.5%; South Harrison 84.6%; Lanesville 91.5%. Lanesville and North Harrison students performed above average on 2010 statewide ISTEP+ tests, while South Harrison students performed below average.
Question: What are the smallest amount of schools in the county, school district or private?
Answer: private