Given a number N, let P be the set of all the prime divisors of N. Now, let S be another set of all the divisors of N (including 1 and N). Let's define the term Prime Score of a prime divisor x as the number of elements in S which have x as a prime divisor. Output the product of prime scores of all the elements in P modulo 1000003.
For example, let N be 12. Set P will be {2, 3} and set S will be {1, 2, 3, 4, 6, 12}. Now, 2 is a prime divisor of 4 elements in S (2, 4, 6, 12) and 3 is a prime divisor of 3 elements in S (3, 6, 12). So, the prime scores of 2 and 3 would be 4 and 3. respectively. So. the output will be 4*3 mod 1000003 = 12 .
What I have tried:
can anyone give me a solution?
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