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class Solution:
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    def numPrimeArrangements(self, n: int) -> int:
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        primes = set()
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        for i in range(2, n + 1):
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            if all(i % p != 0 for p in primes):
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                primes.add(i)
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        M = 10**9 + 7
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        def fact(k):
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            res = 1
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            for i in range(2, k + 1):
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                res = (res * i) % M
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            return res
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        return fact(len(primes)) * fact(n - len(primes)) % M