Question: Which  castle in the border region of Scotland did Hermitage Water passes through 

full_context: Document 1: Craigmillar Castle: Craigmillar Castle is a ruined medieval castle in Edinburgh, Scotland. It is 3 mi south-east of the city centre, on a low hill to the south of the modern suburb of Craigmillar. The Preston family of Craigmillar, the local feudal barons, began building the castle in the late 14th century and building works continued through the 15th and 16th centuries. In 1660 the castle was sold to Sir John Gilmour, Lord President of the Court of Session, who made further alterations. The Gilmours left Craigmillar in the 18th century, and the castle fell into ruin. It is now in the care of Historic Environment Scotland.
Document 2: Hermitage Water: The Hermitage Water is a river in Liddesdale, in the Scottish Borders area of Scotland. Among its many feeder burns are Braidley Burn, Dinley Burn, Gorrenberry Burn and Twislehope Burn. The Water flows through the hamlets of Dinley and Gorrenberry, and through the village of Hermitage, and past Hermitage Castle. It continues past Toftholm where it meets the B6399, and passes Newlands, Longhaugh, Leahaugh and Redheugh. At Sandholm it joins the Liddel Water and the dismantled railway.
Document 3: Lane, West Yorkshire: Lane Village is a small hamlet 3 miles southwest of Holmfirth and approximately half a mile southwest of Holme Village on the A6024 Woodhead Road. It lies on the edge of Holme Moss just inside the Peak District National Park boundary. The rainwater springs seeping from Holme Moss and Kaye Edge provide the source of the River Holme.
Document 4: 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 5: 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 6: Hermitage Castle: Hermitage Castle is a semi-ruined castle in the border region of Scotland. It is under the care of Historic Scotland. The castle has a reputation, both from its history and its appearance, as one of the most sinister and atmospheric in Scotland.
Document 7: Cowie Water: The Cowie Water (Scottish Gaelic: "Uisge Chollaidh" ) is a river rising in the Grampian Mountains in Aberdeenshire, Scotland that discharges to the North Sea in the northern part of Stonehaven. south of the ruined Cowie Castle. Tributaries of the Cowie Water include the Burn of Monboys, which drains the area to the north, in which the archaeological site Raedykes Roman Camp is situated; and Cowton Burn.
Document 8: Luther Water: Luther Water is a generally southerly flowing river in Aberdeenshire, Scotland that discharges to the River North Esk; this watercourse rises in the Howe of the Mearns somewhat south of Drumelzie Forest. Draining chiefly agricultural lands, this stream has a notable lack of turbidity and a pH level of approximately 8.26 measured near the Mains of Luther. Turbidity has been measured at 70 centimetres by the Secchi disc protocol. summer temperatures are approximately 16 degrees Celsius and electrical conductivity is 21 micro-siemens per centimetre. Armouring of the stream bottom consists of small rounded stones varying typically from about one centimeter to four centimeters in diameter, some of which are quartzite in composition, leading to a golden-green effect in some locations. Other nearby watercourses discharging to the North Sea include Cowie Water to the north.
Document 9: River Calder, Lancashire: The River Calder is a major tributary of the River Ribble, starting in Cliviger close to Burnley in Lancashire, England and is around 15 mi in length. Its source is very close to that of the West Yorkshire river with the same name, and that of the River Irwell. It flows through Towneley Park passing Unity College and Fulledge Recreation Ground. It passes through a culvert in the Burnley Embankment on the Leeds and Liverpool Canal and on through Burnley town centre where it is joined by the River Brun at Active Way. It then flows north through the site of Burnley College and out of the town, where it is joined by Pendle Water before turning west past Ightenhill and Gawthorpe Hall and through the town of Padiham. It flows through Altham and Whalley, passing the ruins of Whalley Abbey, then being crossed by the red brick Whalley Viaduct. It meets the Ribble near Great Mitton.
Document 10: Stirling Castle: Stirling Castle, located in Stirling, is one of the largest and most important castles in Scotland, both historically and architecturally. The castle sits atop Castle Hill, an intrusive crag, which forms part of the Stirling Sill geological formation. It is surrounded on three sides by steep cliffs, giving it a strong defensive position. Its strategic location, guarding what was, until the 1890s, the farthest downstream crossing of the River Forth, has made it an important fortification from the earliest times.
Document 11: River Irvine: The River Irvine (Scottish Gaelic: "Irbhinn" ) is a river that flows through southwest Scotland. Its watershed is on the Lanarkshire border of Ayrshire at an altitude of 810 ft above sea-level, near Loudoun Hill, Drumclog, and 7 mi SW by W of Strathaven. It flows 29½ miles westward, dividing the old district of Cunninghame from that of Kyle, until it reaches the sea via Irvine Harbour in the form of the Firth of Clyde, and flows into Irvine Bay by the town of Irvine. It has many tributaries, some of which form parish, district and other boundaries.
Document 12: Kildrummy Castle: Kildrummy Castle is a ruined castle near Kildrummy, in Aberdeenshire, Scotland. Though ruined, it is one of the most extensive castles dating from the 13th century to survive in eastern Scotland, and was the seat of the Earls of Mar. It is owned today by Historic Scotland and is open to the public as a scheduled ancient monument.
Document 13: Fetteresso Castle: Fetteresso Castle is a 14th-century towerhouse, rebuilt in 1761 as a Scottish gothic style Palladian manor, with clear evidence of prehistoric use of the site. It is situated immediately west of the town of Stonehaven in Kincardineshire slightly to the west of the A90 dual carriageway. Other notable historic fortified houses or castles in this region are Dunnottar Castle, Muchalls Castle, Fiddes Castle, Cowie Castle and Monboddo House.
Document 14: Water of Aven: The Water of Aven (or A'an) (Scottish Gaelic: "an t-Uisge Bàn" ) is a tributary of the Water of Feugh, itself the largest tributary of the River Dee, Aberdeenshire, Scotland. The Water of Aven rises at Loch Tennet, where the historic counties of Aberdeenshire, Angus and Kincardineshire meet and flows for approximately 15 km to its confluence with the Feugh near Whitestone. The Water of Aven forms the historic boundary between Aberdeenshire and Kincardineshire for its entire length and the lower 4.5 km are designated as part of the River Dee Special Area of Conservation, due to its importance for Atlantic salmon and Eurasian otter.
Document 15: Carlisle Castle: Carlisle Castle is situated in Carlisle, in the English county of Cumbria, near the ruins of Hadrian's Wall. The castle is over 900 years old and has been the scene of many historical episodes in British history. Given the proximity of Carlisle to the border between England and Scotland, it has been the centre of many wars and invasions. Today the castle is managed by English Heritage and is open to the public. The castle until recently was the administrative headquarters of the former King's Own Royal Border Regiment now county headquarters to the Duke of Lancaster's Regiment and a museum to the regiment is within the castle walls.
ground_truth: Hermitage Castle