Question: What city in Mitchell County, Kansas is both the county seat, and has a Memorial Airport?

Context paragraphs:
Bakersville, North Carolina: Bakersville is a town in Mitchell County, North Carolina, United States.  The population was 464 at the 2010 census.  It is the county seat of Mitchell County.

Moritz Memorial Airport: Moritz Memorial Airport (FAA LID: K61) is a city-owned public-use airport located one mile (2 km) northwest of the central business district of Beloit, a city in Mitchell County, Kansas, United States.

Beloit, Kansas: Beloit is a city and county seat of Mitchell County, Kansas, United States.  As of the 2010 census, the city population was 3,835.

John F. Kennedy Memorial Airport: John F. Kennedy Memorial Airport (IATA: ASX, ICAO: KASX, FAA LID: ASX) is a city and county owned public use airport located two nautical miles (4 km) southwest of the central business district of Ashland, a city in Ashland County, Wisconsin, United States.  It is also known as JFK Memorial Airport.

Mitchell County, Georgia: Mitchell County is a county in the U.S. state of Georgia.  As of the 2010 census, the population was 23,498.  The county seat is Camilla.  Mitchell County was created on December 21, 1857.  It was named for David Brydie Mitchell, 27th Governor of Georgia.

Hailey, Idaho: Hailey is a city in and the county seat of Blaine County, in the Wood River Valley of the central part of the U.S. state of Idaho.  The population was 7,960 at the 2010 census, up from 6,200 in 2000.  Hailey is the site of Friedman Memorial Airport (SUN), the airport for the resort area of Sun Valley/Ketchum, 12 mi north.  The town of Bellevue is a few miles south.  From 1882 to 1895, Hailey was the county seat of now-defunct Alturas County.

Toeterville, Iowa: Toeterville (also Toeter) is an unincorporated community and census-designated place in northwestern Mitchell County, Iowa, United States.  It lies along local roads northwest of the city of Osage, the county seat of Mitchell County.  Its elevation is 1,194 feet (364 m).  Toeterville's post office was established on 1898-02-17 and discontinued on 1985-01-30, when it was attached to the St. Ansgar post office.  Although its post office is gone, Toeterville retains its own ZIP Code, 50481.

Little Cedar, Iowa: Little Cedar is an unincorporated community and census-designated place in central Mitchell County, Iowa, United States.  It lies along local roads northeast of the city of Osage, the county seat of Mitchell County.  Its elevation is 1,194 feet (364 m).  Although Little Cedar is unincorporated, it has a post office, with the ZIP code of 50454.

Friedman Memorial Airport: Friedman Memorial Airport (IATA: SUN, ICAO: KSUN, FAA LID: SUN) is a city-owned public-use airport in the northwest United States, located one nautical mile (2 km) southeast of the central business district of Hailey, the county seat of Blaine County, Idaho.  The airport is operated by the Friedman Memorial Airport Authority under a Joint Powers Agreement between the city of Hailey and Blaine County.  It serves the resort communities of Sun Valley and Ketchum, and the surrounding areas in the Wood River Valley.

Osage, Iowa: Osage is a city in Mitchell County, Iowa, United States.  The population was 3,619 at the 2010 census.  It is the county seat of Mitchell County.

Supporting paragraphs: Moritz Memorial Airport Beloit, Kansas
Answer: Beloit