Unlock Screen Solutions

Consider this problem: Choose a starting point and count the number of unlocking screen solutions. The counting may be assigned with a starting point or include all conditions with any starting point.
The key requirement is that, when the path goes through an unselected point, the point must be included in this path.



Input starting point:(Keep both x and y empty to see the number of all possible solutions)
Input the x chosen from{0,1,2} Input the y chosen from{0,1,2}


Solutions: