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Let P(x)P(x)P(x) be a polynomial of degree 99 satisfying P(n)=n⋅99!P(n)=n \cdot 99!P(n)=n⋅99! for n=1,2,3,…,99n= 1,2,3,\ldots,99n=1,2,3,…,99. If P(100)=0P(100)=0P(100)=0, find the value of the coefficient of x98x^{98}x98 in P(x)P(x)P(x).
Notation: !!! denotes the factorial notation. For example, 8!=1×2×3×⋯×88! = 1\times2\times3\times\cdots\times8 8!=1×2×3×⋯×8.
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