In the context of model-assisted survey sampling, a calibration estimator $\hat{Y}_{cal} = \sum_{i \in s} w_i y_i$ is constructed by minimizing a distance function $D(w_i, d_i)$ (where $d_i = 1/\pi_i$) subject to the calibration constraint $\sum_{i \in s} w_i x_i = X$. If the distance function is the Chi-square distance $D = \sum_{i \in s} \frac{(w_i - d_i)^2}{d_i q_i}$, what is the resulting form of the calibrated weight $w_i$?