The roads of boston city form a 1x26 grid with the meeting point of roads forming nodes. A route from node A to B is a path that does not traverse the same road twice. The length of the route is the number of roads in the path. There are different routes joining the upper left and lower right nodes with some having the same length. Which of the numbers below is the length of fewest routes?

As an illustration, a 1x4 grid is shown with 2 possible routes of length 7 from node A to B.