A certain factory produces Xn specialized parts on day n, where Xn are independent and identically distributed random variables with mean 6 and variance 9. Let S be the total number of specialized parts produced from day 1 to day n. Using central limit theorem, determine the total number of parts, a, the said factory can guarantee to produce by day 50 with at least 99.9% certainty, i.e. determine the maximum value of a so that P(S50 ≥ a) ≥ 0.999. Note: This maximum value must be a whole number.

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