A Smith number is a composite number such that the sum of its digits is equal to the sum of the digits of its prime factors. For example, the prime factorization of 852 is 2 2 3 1 71 1, and so the sum of the digits of its prime factors is 2 + 2 + 3 + 7 + 1 = 15 which is equal to the sum of its digits, 8 + 5 + 2 = 15. Write a program to find all Smith numbers less than 10 000.

Develop auxiliary functions for one-, two-, and three-dimensional offlattice random walks. Then create a function offLatticeWalk[steps, dim] that uses these auxiliary functions to return an off-lattice walk of length steps, in dimension dim. Finally, modify RandomWalk to include an option LatticeWalk, that, when set to True, calls the latticeWalk auxiliary function and when set to False, calls this new offLatticeWalk auxiliary function.