Question: The Chiefs of Clan Mackay was once seated at the castle near what village?

Context paragraphs:
Chiefs of Clan Mackay: The Clan Mackay is a highland Scottish clan.  The clan chief of Clan Mackay has from early times been designated "of Strathnaver".  The chief was also from early times seated at Castle Varrich but later moved to Tongue House in Tongue, Highland.  In the 17th century the chief of Clan Mackay was made Lord Reay.  The following is a list of the chiefs of Clan Mackay.

Iye Mackay, 4th of Strathnaver: Iye Mackay, 4th of Strathnaver (died 1370) was the chief of the ancient Clan Mackay, a Scottish clan of the Scottish Highlands.  He was murdered along with his eldest son Donald at Dingwall Castle during a feud with the Earl of Sutherland, chief of the Clan Sutherland.

Castle Varrich: Castle Varrich (Scottish Gaelic: "Caisteal Bharraich" ) is in the far north of the Scottish Highlands, near the village of Tongue.  The castle is on a local high point of rock, overlooking both the Kyle of Tongue and the village of Tongue.  The castle's precise origins and age are unknown.

Huistean Du Mackay, 13th of Strathnaver: Huistean Du Mackay (Hugh Mackay) (d. 1614) of Strathnaver was the thirteenth chief of the Clan Mackay, a Highland Scottish clan.

Battle of Alltan-Beath: The Battle of Alltan-Beath also known as the Battle of Ailtan-Beath was a Scottish clan battle said to have taken place in the year 1542 in the village of Knockarthur (or Knockartel), in Sutherland, in the Scottish Highlands.  It was fought between men of the Clan Mackay and men of the Clan Sutherland whose chiefs were the Gordon, Earls of Sutherland.

Clan Mackay: Clan Mackay (Scottish Gaelic: "Clann Mhic Aoidh" ] ) is an ancient and once-powerful Scottish clan from the far North of the Scottish Highlands, but with roots in the old kingdom of Moray.  They supported Robert the Bruce during the Wars of Scottish Independence in the 14th century.  In the centuries that followed they were anti-Jacobite.  The territory of the Clan Mackay consisted of the parishes of Farr, Tongue, Durness and Eddrachillis, and was known as Strathnaver, in the north-west of the county of Sutherland.  However, it was not until 1829 that Strathnaver was considered part of Sutherland when the chief sold his lands to the Earls of Sutherland and the Highland Clearances then had dire consequences for the clan.  In the 17th century the Mackay chief's territory had extended to the east to include the parish of Reay in the west of the neighbouring county of Caithness.  The chief of the clan is Lord Reay and the lands of Strathnaver later became known as the Reay Country.

Battle of Drumnacoub: The Battle of Drumnacoub (Battle of Druim na coub, Drum-ne-coub) was a Scottish clan battle involving factions of the Clan Mackay fought in the far northwest of Scotland, some time between 1427 and 1433.  It took place on a hill called Carn Fada at the southern end of the Kyle of Tongue, between Ben Loyal and the village of Tongue.  It was fought between members of the Clan Mackay and men of the Clan Sutherland.

Mackay of Aberach: The Mackays of Aberach also known as the Clan Aberach are a Scottish family and a branch of the ancient Clan Mackay of the Scottish Highlands.  They were the senior cadet branch of the Clan Mackay and were seated at Achness, in Strathnaver, which is in modern-day Sutherland.  In Scottish Gaelic they are known as the Sleaght-ean Aberigh (descendants of John Aberach).

Neil Mackay, 8th of Strathnaver: Neil Mackay, 8th of Strathnaver was a chief of the ancient Clan Mackay, a Scottish clan of the Scottish Highlands.  He is sometimes also recorded as Neil "Bass" Mackay or Neil "Wasse" Mackay which was a nickname taken from the fact that for a time he was a prisoner on the Bass Rock.

Mackay of Scoury: The Mackays of Scoury were a minor noble Scottish family and a branch of the ancient Clan Mackay, a Highland Scottish clan.  They were seated at Scourie Castle, in Scourie (modern spelling), in the parish of Eddrachillis, county of Sutherland.  However, Scourie was part of the Mackay chief’s province of “Strathnaver” until it was sold to the Earl of Sutherland in 1829.

Supporting paragraphs: Chiefs of Clan Mackay Castle Varrich
Answer: Tongue