The partition function \(P(n) \) counts the number of distinct ways we can represent \(n\) as the sum of positive integers. Currently, there is no known closed form for \(P(n)\), so computing it for large arguments is done recursively using computers. However, it is computationally intensive and can cause your program to crash if implemented naively.

Implement a program to compute \(P(n)\) exactly and enter the value of \( P(8000) \pmod {10^{10}} \).

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