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-0.592(alpha_{[x],mathrm{max}} alpha_{[y],mathrm{max}}+alpha_{[y],mathrm{max}}alpha_{[z],mathrm{max}}+alpha_{[z],mathrm{max}}alpha_{[x],mathrm{max}})
pi_{[a]}=frac{0.246+frac{0.05}{3}-0.246(pi_{[y]}+pi_{[z]})}{alpha_{[a],mathrm{max}}-0.592}
alpha_{[x],mathrm{max}}=0.838-0.246timesfrac{pi_{[x]}+pi_{[y]}+pi_{[z]}}{pi_{[x]}}+frac{0.246+frac{0.05}{3}}{pi_{[x]}}
alpha_{[a-c-*]}=0.838-0.246timesfrac{pi_{[a-b-*]}+pi_{[b-c-*]}+pi_{[a-c-*]}}{pi_{[a-c-*]}}+frac{0.246}{pi_{[a-c-*]}}
alpha_{[b]}=0.838-0.246timesfrac{pi_{[a]}+pi_{[b]}+pi_{[c]}}{pi_{[b]}}+frac{0.246+frac{0.05}{3}}{pi_{[b]}}