<image>On Misha's new phone, a passlock consists of six circles arranged in a $2\times 3$ rectangle. The lock is opened by a continuous path connecting the six circles; the path cannot pass through a circle  on the way between two others (e.g. the top left and right circles cannot be adjacent).  For example, the left path shown below is allowed but the right path is not.  (Paths are considered to be oriented, so that a path starting at $A$ and ending at $B$ is different from a path starting at $B$ and ending at $A$.  However, in the diagrams below, the paths are valid/invalid regardless of orientation.)  How many passlocks are there consisting of all six circles?\n