Question: North Berwick was set off from Berwick in 1831 after the other half of the town did so in 1814, which is home to what day school?

Context paragraphs:
North Berwick: North Berwick ( ; Scottish Gaelic: "Bearaig a Tuath" ) is a seaside town and former royal burgh in East Lothian, Scotland.  It is situated on the south shore of the Firth of Forth, approximately 25 mi north-east of Edinburgh.  North Berwick became a fashionable holiday resort in the nineteenth century because of its two sandy bays, the East (or Milsey) Bay and the West Bay, and continues to attract holidaymakers.  Golf courses at the ends of each bay are open to visitors.

Noble High School (Maine): Noble High School is a public high school in North Berwick, Maine serving students in grades 8-12 from the towns of Berwick, North Berwick, and Lebanon.  NOBLE is an acronym for the three towns that NHS serves (NOrth Berwick, Berwick, and LEbanon).  Noble High School is a member of the Coalition of Essential Schools.

South Berwick, Maine: South Berwick is a town in York County, Maine, United States.  The population was 7,220 at the 2010 census.  South Berwick is home to Berwick Academy, a private, co-educational university-preparatory day school founded in 1791.

North Berwick railway station: North Berwick railway station is a railway station serving the seaside town of North Berwick in East Lothian, Scotland.  It is the terminus of the Edinburgh to North Berwick Line, 22+1/4 mi east of Edinburgh Waverley .

North Berwick (CDP), Maine: North Berwick is a census-designated place (CDP) consisting of the primary settlement in the town of North Berwick in York County, Maine, United States.  The population was 1,615 at the 2010 census, out of a total town population of 4,576.  It is part of the Portland–South Portland–Biddeford, Maine Metropolitan Statistical Area.

North Berwick, Maine: North Berwick is a town in York County, Maine, United States.  The town was set off from Berwick in 1831, following South Berwick in 1814.

North Berwick Law: North Berwick Law is a conical hill which rises conspicuously from the surrounding landscape (this is the definition of the Lowland Scots word "law").  It overlooks the East Lothian town of North Berwick and stands at 613 ft (187 m) above sea level.

Drem railway station: Drem railway station serves the village of Drem in East Lothian, 5 mi from the seaside town of North Berwick in Scotland.  It is located on the East Coast Main Line (ECML) 18 mi east of Edinburgh Waverley.  Passenger services are provided on the Abellio ScotRail North Berwick Line, and the junction where the North Berwick branch diverges from the ECML is a short distance to the east of the station.

North Berwick High School: North Berwick High School is a non-denominational state secondary school located in North Berwick, East Lothian, Scotland.

Mary R. Hurd House: The Mary R. Hurd House is a historic house at 2 Elm Street in North Berwick, Maine.  Built in 1894, the house is architecturally one of the finest Queen Anne/Eastlake houses in southern Maine.  It was built by Mary Hurd, who was the proprietor of the North Berwick Woolen Mill for nearly 60 years, and a major benefactor to the town.  Now a bed and breakfast inn, the house was listed on the National Register of Historic Places on September 11, 1979.

Supporting paragraphs: North Berwick, Maine South Berwick, Maine
Answer: Berwick Academy