Question: Where does the ruined castle lies which is near by the Montgreenan?

full_context: Document 1: Eglinton Tournament Bridge: The Eglinton Tournament Bridge is a bridge located within Eglinton Country Park near Kilwinning, North Ayrshire, Scotland. The bridge crosses the Lugton Water a short distance northwest of Eglinton Castle (grid reference [ NS 3206 4224] ) and was named after the Eglinton Tournament of 1839. The castle and surrounding grounds were once home to the Montgomerie family, Earls of Eglinton and chiefs of the Clan Montgomery.
Document 2: Ardrossan Castle: Ardrossan Castle is situated on the west coast of Scotland in the town of Ardrossan, Ayrshire. The castle, defended by a moat, stands on a ridge above the town. There is a keep dating from the fifteenth century, and a vaulted range containing a kitchen and cellars. In a deep passageway there is a well. Part of the keep remains up to the corbels of the parapet, but it is in ruins. The original castle, owned by Clan Barclay, was partly destroyed during the Wars of Scottish Independence. This event, in which the English garrison were slaughtered, became known as "Wallace's Larder," a name which is still applied to the remaining vaults. Rebuilt by Clan Montgomery in the 15th century, Ardrossan later fell into disuse and was partially demolished by the soldiers of Oliver Cromwell in the 17th century who used the stones to help construct the Ayr Citadel.
Document 3: Eglinton Country Park: Eglinton Country Park is located in the grounds of the old Eglinton Castle estate, Kilwinning, North Ayrshire, Scotland (map reference NS 3227 4220). Eglinton Park is situated in the parish of Kilwinning, part of the former district of Cunninghame, and covers an area of 400 hectares (98 acre of which are woodland). The central iconic feature of the country park is the ruined Eglinton Castle, once home to the Eglinton family and later the Montgomeries, Earls of Eglinton and chiefs of the Clan Montgomery. Eglinton Country Park is managed and maintained by North Ayrshire Council and its Ranger Service.
Document 4: 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.
Document 5: Dundarg Castle: Dundarg Castle is a ruined castle about 2 km north-northeast of New Aberdour, Aberdeenshire, Scotland, built within the ramparts of an earlier iron age promontory fort. It was described by W. Douglas Simpson as one of the nine castles of the Knuckle, referring to the rocky headland of north-east Aberdeenshire.
Document 6: Dunderave Castle: Dunderave Castle is an L-plan castle built in the 16th century as the Scottish seat of the MacNaughton clan. The castle lies on a small promontory on the northern shores of Loch Fyne, around 5 km north-east of Inveraray, Argyll. The castle is in use as a residence. The present castle was built after their previous castle was destroyed following a Plague infection. The old castle, and remnants of McNaughton crannógs, can still be seen on the lochan known as the Dubh Loch at the head of Glen Shira.
Document 7: Auchenharvie Castle: Auchenharvie Castle is a ruined castle near Torranyard on the A 736 Glasgow to Irvine road. Burnhouse lies to the north and Irvine to the south. It lies in North Ayrshire, Scotland.
Document 8: Seagate Castle: Seagate Castle is a castle in North Ayrshire, in the town of Irvine, close to the River Irvine, Scotland. The castle was formerly a stronghold, a town house, and later a dower house of the Montgomery Clan. The castle overlooks the oldest street in Irvine, which was once the main route between the town and the old harbour at Seagatefoot, which by 1606, was useless and abandoned due to silting. The remains of the castle are protected as a scheduled ancient monument.
Document 9: 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.
Document 10: Auchinhove: Auchinhove, located to the east of Keith in Moray, Scotland, is the site of a Roman marching camp, first discovered by aerial photography in 1949.
Document 11: Montgreenan: Montgreenan is an estate in North Ayrshire, Parish of Kilwinning, Scotland. The Lugton Water runs through the policies and farmland of Montgreenan. Nearby are the hamlets of Torranyard and Auchentiber.
Document 12: Inverugie Castle: Inverugie Castle or Cheyne's Tower is the ruins of a motte-and-bailey castle in Aberdeenshire, Scotland.
Document 13: Industry and the Eglinton Castle estate: The Eglinton Castle estate was situated at Irvine, on the outskirts of Kilwinning, North Ayrshire, Scotland (map reference NS 3227 42200) in the former district of Cunninghame. Eglinton Castle, was once home to the Montgomeries, Earls of Eglinton and chiefs of the Clan Montgomery. Eglinton Country Park now occupies part of the site.
Document 14: Castle and Barony of Robertland: The Castle and Barony of Robertland (NS 4428 4693) is located near Stewarton, off the B769 road, in the old district of Cunninghame, Parish of Stewarton, and now part of East Ayrshire, Scotland.
Document 15: Gree Goods station: Gree Goods station or Gree Depot as it was listed in the Caledonian Railway Working Timetable was a relatively short lived railway freight facility located approximately one miles south of Lugton on the A736 Lochlibo Road, North Ayrshire, Scotland. Gree Goods served the industrial and agricultural requirements for transportation in the vicinity, with the village of Burnhouse not far away, sitting on the crossroads to Barrmill, Dunlop and Irvine. Over Gree, High Gree, Nether Gree, Gree and Brownhills Farms were located nearby. Gree Goods was close to the Lugton East Junction, just south of the 11 arch Gree Viaduct. The nearest passenger station on the line north was Lugton High and to the south was Giffen.
ground_truth: North Ayrshire, Scotland