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I'm just going to walk through all of it. If something is too pedantic, skip it. Module[{f,g}... creates a scoping construct so the definitions of f and g are local to this code. Tally[a] produces a list of all the elements in a and a count for each element. For instance, Tally[{a,a,b,c,a,d,d}] would give {{a,3},{b,1},{c,1},{d,2}}. The strange ...

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