Barnard Castle has road connections to Bishop Auckland, Spennymoor and central County Durham via the A688 and Darlington, Stockton-on-Tees, and Middlesbrough by the A67. Barnard Castle is also four miles  from the A66, with access to the M6 to the west and the A1 to the east. The B6278 also connects Barnard Castle with Middleton-in-Teesdale. Barnard Castle railway station was closed for passenger trains in 1964. A Bill was approved in 1854 for a line from a junction with the Stockton & Darlington Railway at Darlington to Barnard Castle and opened on 9 July 1856, with intermediate stations at Broomielaw, Winston, Gainford & Piercebridge. The terminus at Darlington only lasted five years.  In 1856 the South Durham & Lancashire Railway proposed a line from Bishop Auckland to Tebay via Barnard Castle and Kirkby Stephen but only the western section was built with the Company receiving its Bill in 1857.  The line opened on 8 August 1861 from a second terminus at Barnard Castle to a junction with the Lancaster & Carlisle Railway at Tebay with intermediate stations at Lartington, Bowes, Barras, Kirkby Stephen, Ravenstondale & Gaisgill. The two stations at Barnard Castle were some distance apart; the earliest station became a through station and closed to passengers on 1 May 1862, but remained in use as a goods depot. The second station was closed for passenger trains under the Beeching cuts in 1964 and completely on 5 April 1965 and the site was eventually built on by Glaxo Smith Kline. Today rail access is via Bishop Auckland, 15 miles  or Darlington, 16 miles .
Question: How many road connections does Barnard Castle have?
Answer: 3