Question: In what country is the are two Baronies separated by the Lugton Water or the Bungle Burn running through Burnhouse?

Context paragraphs:
Auchentiber: The hamlet of Auchentiber (Scottish Gaelic, "Achadh an Tiobair") is in North Ayrshire, Parish of Kilwinning, Scotland.  Auchentiber is 4 mi NE of Kilwinning on the Lochlibo Road, 2.2 mi from the hamlet of Burnhouse and 2.6 mi from the village of Barrmill.  Grid Ref.  NS3647.  Some new housing has been built, but the settlement is still very much a hamlet.  The settlement is on the Lugton Water, which runs into the River Garnock after running through Montgreenan and Eglinton Country Park in Irvine.

North West Liberties of Londonderry: The North West Liberties of Londonderry is a barony in County Londonderry, Northern Ireland.  It is bordered by two other baronies in Northern Ireland; Tirkeeran to the east, across Lough Foyle; and Strabane Lower to the south.  It also borders two baronies in the Republic of Ireland: Raphoe North, to the south-west; and Inishowen West to the north.

Baron Marmion: There have been four different baronies held by the Marmion family, two feudal baronies and two baronies by writ.

Lugton Water: The Lugton Water, the largest tributary of the River Garnock, runs 14 mi from Loch Libo (395 feet above sea-level) in Uplawmoor, through Lugton and the parishes of Neilston, Beith, Dunlop, Stewarton and Kilwinning.  The Lugton joins the Garnock below the tidal limit, shortly after passing through Eglinton Country Park, developed around the ancient estate of the Earl of Eglinton.

Baron Conyers: Baron Conyers is a title in the Peerage of England.  It was created on 17 October 1509 for William Conyers, the son-in-law of William Neville, 1st Earl of Kent.  The abeyance after the death of the 3rd baron was terminated for the 7th Baron Darcy de Knayth, these baronies were held together until the abeyance of 1888, after which the abeyance of these two baronies were separately terminated.  Since 1509, the Barons Conyers had held a part of the "right" to the barony Fauconberg, i.e. the part for which the abeyance was terminated in 1903; and since the termination of the abeyance of the barony Fauconberg, the two baronies, Conyers and Fauconberg, had been held together; from 1948 they were abeyant between the two daughters of the 5th Earl of Yarborough.  On the death of the younger daughter in 2012 the abeyance terminated automatically in favour of her elder sister, the 15th holder of the title.  Since the death of the latter in 2013, the title is in abeyance once more.

Orior Upper: Orior Upper (from Irish: "Airthir" , the name of an ancient Gaelic territory) is a barony in County Armagh, Northern Ireland.  It lies in the south-east of the county and borders the Republic of Ireland with its southern boundary.  It is bordered by five other baronies in Northern Ireland: Fews Upper and an enclave of Fews Lower to the west; Orior Lower to the north; Iveagh Upper, Upper Half to its west, which is divided in two by the Lordship of Newry.  It also borders two baronies in the Republic of Ireland: Dundalk Lower and Dundalk Upper to the south.

Strabane Lower: Strabane Lower (named after Strabane) is a barony in County Tyrone, Northern Ireland.  It is bordered by five other baronies in Northern Ireland: North West Liberties of Londonderry to the north; Tirkeeran to the north-east; Strabane Upper to the east; Omagh East to the south; and Omagh West to the south-west.  It also borders two baronies in the Republic of Ireland: Raphoe North and Raphoe South to the west.

Barony and Castle of Giffen: The Barony of Giffen and its associated 15th-century castle were in the parish of Beith in the former District of Cunninghame, now North Ayrshire.  The site may be spelled Giffen or Giffin and lay within the Lordship of Giffin, which included the Baronies of Giffen, Trearne, Hessilhead, Broadstone, Roughwood and Ramshead; valued at £3788 9s 10d.  The Barony of Giffen comprised a number of properties, including Greenhills, Thirdpart, Drumbuie, Nettlehirst and Balgray, covering about half of the parish of Beith.  Giffen was a hundred merk land, separated from the Barony of Beith, a forty-pound land, by the Powgree Burn which rises on Cuff hill.  The Lugton Water or the Bungle Burn running through Burnhouse may have been the Giffen barony boundary with that of the adjacent barony and lands of Aiket castle.

Lugton: Lugton is a small village or hamlet in East Ayrshire, Scotland with a population of 80 people.  The A736 road runs through on its way from Glasgow, 15 mi to the north, to Irvine in North Ayrshire.  Uplawmoor is the first settlement on this 'Lochlibo Road' to the north and Burnhouse is to the south.  The settlement lies on the Lugton Water which forms the boundary between East Ayrshire and East Renfrewshire as well as that of the parishes of Dunlop and Beith.

Greenhills, North Ayrshire: Greenhills is a small village or hamlet in North Ayrshire, Parish of Beith, Scotland.  It lies between the settlements of Barrmill and Burnhouse on a crossroads of the B706 and the lanes to Nettlehirst and Tandlehill via Thirdpart.  It is named after the 'Green Hill' an artificial mound, a Moot, Law or Justice hill that once stood here.  The settlement lay within the old Barony of Giffen; the castle no longer exists.  The village lies within Barrmill and District Community Association's area and is also covered by Beith Community Council.

Supporting paragraphs: Greenhills, North Ayrshire Barony and Castle of Giffen
Answer: Scotland