Question: Design a fast algorithm to compute (n) ! for large values of (n), using Java's BigInteger class. Use your program to compute the longest run

Design a fast algorithm to compute $n$ ! for large values of $n$, using Java's BigInteger class. Use your program to compute the longest run of consecutive $9 \mathrm{~s}$ in 1000000 !. Develop and validate a hypothesis for the order of growth of the running time of your algorithm.

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