Question: Lincoln County, Kansas has a county seat of a city with a population of what as of 2010?

Context paragraphs:
Lincoln County, Arkansas: Lincoln County is located between the Arkansas Timberlands and Arkansas Delta in the U.S. state of Arkansas.  It is also within the Pine Bluff metro area, and on the outer edge of the Central Arkansas region.  The county is named for Abraham Lincoln, the 16th President of the United States.  Created as Arkansas's 65th county on March 28, 1871, Lincoln County has three incorporated cities, including Star City, the county seat and most populous city.  The county contains 46 unincorporated communities and ghost towns, Cane Creek State Park at the confluence of Cane Creek and Bayou Bartholomew, and nine listings on the National Register of Historic Places to preserve the history and culture of the county.

Kemmerer, Wyoming: Kemmerer is the largest city in and the county seat of Lincoln County, Wyoming, United States.  The population was 2,656 at the 2010 census.  As the county seat of Lincoln County, Kemmerer is the location of the Lincoln County Courthouse.

Hamlin, West Virginia: Hamlin, originally named "Hamline," is a town in Lincoln County, West Virginia, United States, along the Mud River.  The population was recorded as 1,142 at the 2010 census.  It is the county seat of Lincoln County.  Hamlin is a part of the Huntington-Ashland, WV-KY-OH, Metropolitan Statistical Area (MSA).  As of the 2010 census, the MSA had a population of 287,702.  New definitions from February 28, 2013 placed the population at 363,000.

Lincolnton, North Carolina: Lincolnton is a small city in Lincoln County, North Carolina, United States, within the Charlotte metropolitan area.  The population was 10,683 at the 2010 census.  Lincolnton is northwest of Charlotte, on the South Fork of the Catawba River.  The junction of State Highway 27 and U.S. Route 321 is located nearby.  The city is the county seat of Lincoln County, and is the only legally incorporated municipality wholly within the rural county.

Lincoln County, Nebraska: Lincoln County is a county located in the U.S. state of Nebraska.  As of the 2010 census, the population was 36,288.  Its county seat is North Platte.  Despite the county's name, the state capital city of Lincoln is not located in or near Lincoln County.

Merrill, Wisconsin: Merrill is a city in and the county seat of Lincoln County, Wisconsin, United States.  It is located to the south of and adjacent to the Town of Merrill.  The population was 9,661, according to the 2010 census.  Merrill is part of the United States Census Bureau's Merrill MSA, which includes all of Lincoln County.  Together with the Wausau MSA, which includes all of Marathon County, it forms the Wausau-Merrill CSA.

Ivanhoe, Minnesota: Ivanhoe is a city in Lincoln County, Minnesota, United States.  The population was 559 at the 2010 census.  Since 1904 it has been the county seat of Lincoln County and is now the least populous county seat in Minnesota.

Lincoln County, Kansas: Lincoln County (standard abbreviation: LC) is a county located in the U.S. state of Kansas.  As of the 2010 census, the county population was 3,241.  The largest city and county seat is Lincoln Center.

Lincoln Center, Kansas: Lincoln Center, more commonly known as Lincoln, is a city in and the county seat of Lincoln County, Kansas, United States.  As of the 2010 census, the city population was 1,297.

Carrizozo, New Mexico: Carrizozo is a town in Lincoln County, New Mexico and is the county seat with a population of 996 at the 2010 census.  Founded in 1899, the town provided the main railroad access for Lincoln County, and the town experienced significant population growth in the early decades of the 1900s.  However, with declining relevance of the railroad, the population of the town has gradually declined.  The town is located at the intersection of U.S. Route 54 and U.S. Route 380.

Supporting paragraphs: Lincoln County, Kansas Lincoln Center, Kansas
Answer: 1,297