Find the minimum value of the expression

Over all sets of positive reals $\{ x_i \}$ with $n$ elements that sum to $\frac16,$ what is the minimum possible value of $\frac{ 1 - x_1 } { 1 + x_1 } \times \frac{ 1 - x_2 } { 1 + x_2 } \times \cdots \times \frac{ 1 - x_n } { 1 + x_n } ?$ Give your answer to 3 decimal places.

$$
Clarification: $n$ can be any positive integer.