Metro Manila Detour

Metro Manila currently has five circumferential roads arranged in concentric semicircles, with a sixth to be constructed linking the north and the south. From the center (Manila), there are ten radial roads that connect the inner and outer areas of Metro Manila.

Figure 1 Ideal road network of Metro Manila

In this problem, you are to find the shortest distance from point A to point B. Each point is determined by the intersection of a circumferential and a radial road, denoted as (\textbf{C\#}, \textbf{R\#}), and the center is represented as (\textbf{C0}, \textbf{R0}).

For calculation purposes, the distance for each segment along a radial road is equal to $1$ unit, while each arc along a circumferential road has length equal to the circumferential road's number. For example, the distance from (\textbf{C1}, \textbf{R3}) to (\textbf{C2}, \textbf{R3}) is $1$ unit, and the distance from (\textbf{C3}, \textbf{R1}) to (\textbf{C3}, \textbf{R2}) is $3$ units. The shortest distance from (\textbf{C1}, \textbf{R2}) to (\textbf{C5}, \textbf{R1}) is $5$ units (see the darkened path). It is assumed that $\text{C6}$ is passable for this problem.

However, with the new number coding scheme, vehicles are not allowed to use a radial road if its number matches the last digit of the vehicle's plate number. For instance, a vehicle with the plate number ABC-123 cannot use $\text{R3}$. Furthermore, circumferential roads (except for $\text{C6}$) also have restrictions: plate numbers ending in $1$ and $2$ are not allowed on $\text{C1}$, $3$ and $4$ are not allowed on $\text{C2}$, $5$ and $6$ on $\text{C3}$, $7$ and $8$ on $\text{C4}$, and $9$ and $0$ on $\text{C5}$. Thus, the shortest path from (\textbf{C1}, \textbf{R2}) to (\textbf{C5}, \textbf{R1}) is $5$ units for a vehicle with plate number ABC-123, but $9$ units for a vehicle with plate number CBA-321. Note that there may be instances in which a vehicle cannot reach the destination at all.