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Count how many distinct prime numbers divide the product of all elements in an integer array — equivalent to aggregating the prime factors of each element and returning the number of unique primes. With nums.length up to 10^4 and nums[i] ≤ 1000, efficient per-number factorization (e.g., using trial division or a small sieve) suffices.
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Leetcode 2521. Distinct Prime Factors of Product of Array
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