# What now? Minimum? Complicating...

Level pending

Consider all sequences of positive real numbers $$x_i$$, $$i = 1,2, \ldots, 333$$ that satisfy $$\sum_{i=1}^{333} x_i = 1$$. The minimum value of

$$\sum_{i=1}^{333} \frac{x_i}{1+\sum_{i \neq j, j=1}^{333} x_j}$$

is $$M$$. Let $$M = \frac{a}{b}$$. Find the value of $$a+b$$.

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