Please answer the following question: Given the following context: Buckton was a small highland enclosure castle with a 2.8-metre-thick (9 ft) sandstone curtain wall; nothing survives above ground. It is roughly oval and measures 35.6 by 26.2 metres (117 by 86 ft), covering an area of 730 square metres (0.18 acres). The castle is surrounded by a 10-metre-wide (33 ft) ditch apart from the south-west part where the steep slope of the hill makes the ditch unnecessary. When the ditch was dug some of the material was used to raise the interior of the castle by 1.5 metres (4 ft 11 in).Buckton is similar in size to Clitheroe Castle's inner enclosure, which is also oval (31.8 by 26 metres (104 by 85 ft)) and has a 2.6-metre-thick (9 ft) curtain wall. Clitheroe was also built on a rocky peak and the small size of its great tower may be due to its naturally defensible position and location in an economically deprived area.Buckton Castle was entered through a gatehouse in the north-west measuring 9.3 by 7.5 metres (31 by 25 ft). The east side was occupied by the gate passage and the west by a chamber. Though the structure no longer survives above ground, it was probably at least two storeys tall. Constructed in the 12th century, Buckton's gatehouse was the earliest in North West England, and was one of six stone gatehouses in the region that were built in the 12th or 13th centuries: Buckton, Egremont, Brough, Clitheroe, Carlisle's inner gatehouse, and the Agricola Tower at Chester. They are broadly similar in size, and take the form of a gate passage piercing a single tower with rooms in the floors above. Buckton's gatehouse differs slightly in having the passage offset to one side.In the 1770s, the antiquarian Thomas Percival recorded a well within the castle, close to the south curtain, and walls of buildings inside the castle still standing to a height of 2 metres (7 ft). A plan created by the Saddleworth Geological Society in 1842 recorded a ruined structure within the castle's south-east area in addition to the well Percival noted. Trenches in the castle's interior did not reveal... answer the following question: What are the exact names of the six stone gatehouses built in North West England in the 12th or 13th centuries?
A:
Carlisle's inner gatehouse