In solving the puzzle Phi Proximity Poser, a computer-minded solver might consider trying every possible configuration of formulae, in RPN form, where numbers are pushed onto a stack, and pulled by the dyadic operations, two of them off the stack at a time, replacing them with the result.

But how many formulae can be made so they can be evaluated, assuming one is going to try all possibilities by brute force? The easy part is that there are 9! ways of ordering the digits; the hard part is the placement of the operations.

Determine the overall number of valid formulae for part I of the Proximity puzzle.

Note: It's not expected that you exclude situations where intermediate results of zero are used as divisors.

As a bonus, do this for part II.