def prime_factorize_factorial(self, n):
    res = dict()
    for i in range(2, (n + 1)):
        for (p, c) in self.prime_factorize(i).items():
            res[p] = (res.get(p, 0) + c)
    return res
def prime_factorize_factorial(self, n):
    res = dict()
    for i in range(2, (n + 1)):
        for (p, c) in self.prime_factorize(i).items():
            res[p] = (res.get(p, 0) + c)
    return res