in fact one way you could Mathematica think of it as just the thing of it is whatever make XT and XT plus on one variable as if it's one variable we ignore that it's really two variables then exactly the same calculation can be done and then when you unpack this one variable you'll see that you'll have to introduce an XT plus 1 given XT into it because you're unpacking the details otherwise it's just the same thing to compute these forward and backward messages and then when you are hitting the middle point you essentially just