Construct a list containing the prime factors and their multiplicity. Alternately, use a map for the result.

### Example

(deftest p36-prime-factors-multiplicity (is (= {3 2, 5 1, 7 1} (prime-factors-multiplicity 315) )))

### Solution

If you have been following this series this problem might sound familiar. In fact it is just a slight variation on the combination of Problem 35 (prime factors) and Problem 10 (run-length encoding). I followed Phil Gold in using a map as the output format to make the problem a bit more interesting.

While you could reimplement the solution from scratch, I think it is good practice to reuse existing code. In this case all we have to do is call prime-factors on the input, run-length encode, reverse the individual pairs of primes and their multiplicity as required by the problem description. Turning it into a map is then just a matter of flattening the result and applying the assoc function to an empty map and our intermediate result. Try it yourself before you look at the code.

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