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?

full_context: Document 1: Babylon, New York: Babylon is one of ten towns in Suffolk County, New York, United States. Located on Long Island, the town population was 214,191 as of the 2014 census. Parts of Jones Beach Island, Captree Island and Fire Island are in the southernmost part of the town. It borders Nassau County to the West, and the Atlantic Ocean to the South. At its westernmost point, its location is approximately 20 mi from New York City at the Queens border, and approximately 30 mi from Manhattan. There is also a village of Babylon located within the town.
Document 2: Long Island: The Long Island is a large, densely-populated island off the East Coast of the United States, beginning at New York Harbor just 0.35 miles (0.56 km) from Manhattan Island and extending eastward into the Atlantic Ocean. The island comprises four counties in the U.S. state of New York: Kings and Queens (which comprise the New York City boroughs of Brooklyn and Queens, respectively) to the west; and Nassau and Suffolk to the east. However, many people in the New York metropolitan area (even those living in Brooklyn and Queens) colloquially use the term "Long Island" (or "The Island") exclusively to refer to the Nassau–Suffolk county area collectively, which is mainly suburban in character. The majority of New York City residents now live on Long Island.
Document 3: Fire Island: 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.
Document 4: Long Island Central Pine Barrens: The Long Island Central Pine Barrens (also known as the Long Island Pine Barrens) is a large area of publicly protected pine barrens in Suffolk County, New York, on Long Island, covering more than 100000 acre .
Document 5: Bay Shore, New York: Bay Shore is a hamlet and census-designated place (CDP) in the Town of Islip, Suffolk County, New York, United States. It is situated on the South Shore of Long Island, adjoining the Great South Bay. In 2008, Bay Shore celebrated the 300th anniversary of the purchase of the land from the Secatogue Native Americans. The population of the CDP was 26,337 at the time of the 2010 census.
Document 6: Von Sternberg House: The Von Sternberg House was mini-mansion designed by the architect Richard Neutra. With only one bedroom, plus bedrooms for servants, it was built in 1935 at 10000 Tampa Avenue, Northridge, Chatsworth, on a plot of 13 acres (5 hectares) in California's then-rural San Fernando Valley for the movie director Josef von Sternberg. The house was demolished in 1972 to make way for a housing development.
Document 7: Outer barrier: 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.
Document 8: Invasion of the Pines: 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.
Document 9: Fire Island Lighthouse: The Fire Island Lighthouse is a visible landmark on the Great South Bay, in southern Suffolk County, New York on the western end of Fire Island, a barrier island off the southern coast of Long Island. The lighthouse is located within Fire Island National Seashore and just to the east of Robert Moses State Park. It is part of the Fire Island Light Station which contains the light, keepers quarters, the lens building containing the original first-order Fresnel lens, and a boat house.
Document 10: Cherry Grove, New York: 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.
Document 11: Carrington House: 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.
Document 12: Rachel Carson House (Colesville, Maryland): The Rachel Carson House is a historic house at 11701 Berwick Road in Colesville, Maryland, an unincorporated area near Silver Spring, Maryland. Built in 1956, this typical suburban ranch-style house was where writer Rachel Carson wrote her classic work "Silent Spring" in 1962. The house was designated a National Historic Landmark in 1991 for its association with Carson.
Document 13: Cupsogue Beach County Park: Cupsogue Beach County Park is a 296 acre park at the east end of Fire Island and the west end of Westhampton Island, known locally as Dune Road, one of Long Island's easternmost barrier islands. The park is surrounded by the Atlantic Ocean, Moriches Inlet and Moriches Bay.
Document 14: Hawaiian Cottage: The Hawaiian Cottage (or simply "The Cottage") was a Polynesian style restaurant in Cherry Hill, New Jersey, United States. It opened in 1938, on Cherry Hill's western side, on Route 38, nearby the Cherry Hill Mall (which later opened in 1961). The Cottage was established by Michael Egidi and Mary Egidi-Pietrafesa. Started as a roadhouse, the restaurant soon emerged into what was considered a South Jersey landmark. The restaurant's exterior was known for its vivid yellow, pineapple-shaped dome, burning Polynesian torches at the entrance, and a Hawaiian atmosphere that included a luau show. After Mr. Egidi's death in a car accident in the early 1940s, Mrs. Egidi continued to operate the business. Her second husband, John Muresan, helped with the restaurant's growth. On July 1, 1978, the restaurant was destroyed by a fire. The site is now occupied by an Olive Garden Restaurant.
Document 15: Monte Cristo Cottage: Monte Cristo Cottage, also known as Eugene O'Neill Summer House, was the summer home of acclaimed Irish-American actor James O'Neill, and of his family, notably his son (with his wife Ella O'Neill), the acclaimed Nobel prize-winning American playwright, Eugene O'Neill. A National Historic Landmark, it is located at 325 Pequot Avenue in New London, Connecticut.
ground_truth: New York