\( x_1, x_2, \ldots, x_n \) are positive numbers that sum to \( \frac{1}{2} \). The minimum value of

\[ \prod_{i=1}^n \frac{ 1 - x_i } { 1 + x_i } \]

can be expressed as \( \frac{a}{b} \) for positive coprime integers \(a\) and \(b\). What is the value of \( a+b \)?

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