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G = \sum_{p=1}^{N^{\uparrow}_P}} G^{\uparrow}_{ut,p} \cdot q^{\uparrow}_{t, p} - \sum_{i=1}^{N^{\downarrow}_W} G^{\downarrow}_w \cdot q^{\downarrow}_{w, i} - \sum_{j=1}^{N^{\downarrow}_G} G^{\downarrow}_g \cdot q^{\downarrow}_{g, i} \rightarrow \rm max |
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