Question: The Carrington House is a bungalow located in the hamlet of Cherry Grove in which US state, it is typical of early buildings on Fire Island, the large center island of the outer barrier islands parallel to the south shore of Long Island?

Context articles: Cherry Grove, New York
Outer barrier
Long Beach, New York
Cherry Grove Beach, South Carolina
South Shore Estuary
Invasion of the Pines
Otis Pike Fire Island High Dune Wilderness
Carrington House
Atlantic Beach, New York
Fire Island

Cherry Grove (often referred to locally as The Grove) is a hamlet in the Town of Brookhaven, Suffolk County, New York, United States.
 It is located on Fire Island, a barrier island separated from the southern side of Long Island by the Great South Bay.
 The hamlet has approximately 300 houses on 41 acre , a summer seasonal population of 2,000 and a year-round population of 15.
The outer barrier, also known as the Long Island and New York City barrier islands, refers to the string of barrier islands that divide the lagoons south of Long Island, New York from the Atlantic Ocean.
 These islands include Coney Island, Long Beach Barrier Island, Island Park, Jones Beach Island, Fire Island and Westhampton Island.
 The outer barrier extends 75 mi along the South Shore of Long Island, from Rockaway Beach on the New York City/Nassau County border from Long Beach Barrier Islands' western edge, to Suffolk County's east end of Shinnecock Bay.
Long Beach is a city in Nassau County, New York, United States.
 Just south of Long Island, it is located on Long Beach Barrier Island, which is the westernmost of the outer barrier islands off Long Island's South Shore.
 As of the United States 2010 Census, the city population was 33,275.
 It was incorporated in 1922, and is nicknamed "The City By the Sea" (as seen in Latin on its official seal).
Cherry Grove Beach, sometimes known as Cherry Grove, is a neighborhood of the city of North Myrtle Beach in Horry County, South Carolina, United States.
 It lies along South Carolina Highway 9 and South Carolina Highway 65.
 The Cherry Grove Pier is a popular landmark of Cherry Grove.
 It was built early in the 1950s.
 It has weathered many hurricanes, and was remodeled and lengthened in 1999 after Hurricane Floyd.
 In 1968 Cherry Grove Beach merged with Windy Hill Beach, Ocean Drive Beach, and Crescent Beach to form the city of North Myrtle Beach.
The South Shore Estuary is an estuary located along the south shore of Long Island, between the mainland and the outer barrier islands, in eastern New York state.
 It stretches for over 70 mi from West Bay in Nassau County to the Shinnecock Bay in Suffolk County.
During the summer of 1976, a restaurant in Fire Island Pines, New York, denied entry to a visitor in drag named Terry Warren.
 Fire Island Pines is a beach community on Fire Island east of New York City with a gay majority population that was at the time more affluent and conservative than the population of nearby Cherry Grove.
 When Warren's friends in Cherry Grove heard what had happened, they too dressed up in drag, and, on July 4, 1976, with Cherry Grove's 1976 Homecoming Queen Thom Hansen (aka Panzi) in the lead, sailed to the Pines by water taxi.
 The boatload of drag queens that stormed into the Pines that day—to a surprised but exuberant welcome—was the first "invasion," an event now repeated each year.
The Otis Pike Fire Island High Dune Wilderness, also known as the Otis G. Pike Wilderness Area or the Fire Island Wilderness, is a federally protected wilderness area located on Fire Island, a barrier island off the south shore of Long Island, New York, United States.
 The 1380 acre wilderness is contained within the larger Fire Island National Seashore.
The Carrington House is a bungalow located in the hamlet of Cherry Grove, New York.
 Built around 1912, it was one of the first buildings in the town and constructed for Frederick Marquet.
 It is typical of early buildings on Fire Island.
 It was acquired by theater director Frank Carrington in 1927, who enlarged the house.
 Under his ownership, the house was a popular refuge for LGBT artists like Truman Capote; "Breakfast at Tiffany's" was written there.
Atlantic Beach is an affluent village off the South Shore of Long Island in the Town of Hempstead, Nassau County, New York.
 It is located on Long Beach Barrier Island, one of the outer barrier islands which it shares with Long Beach, East Atlantic Beach, Atlantic Beach Estates, Lido Beach and Point Lookout.
Fire Island is the large center island of the outer barrier islands parallel to the south shore of Long Island, New York.
 In 2012, Hurricane Sandy once again divided Fire Island into two islands.
 Together, these two islands are approximately 31 mi long and vary between 160 and wide.
 Fire Island is part of Suffolk County.
 It lies within the towns of Babylon, Islip, and Brookhaven, containing two villages and a number of hamlets.
 All parts of the island not within village limits are part of the Fire Island census-designated place (CDP), which had a permanent population of 292 at the 2010 census, though that expands to thousands of residents and tourists during the summer months.