Count a factorial

A factorial number \(F\) is any natural number for \(n>0\) such that \(F=n!\). So the first few factorial numbers are \(1, 2, 6, 24, 120, 720 ......\). Implement an algorithm that takes two parameters (low, high) and returns the count of the factorial number in that range. How many factorial numbers are there between \(10^{13}\) and \(10^{1000}\)

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