Equilibrium constants are given for the following two equilibria:
\[
(i)\; A_2(g) + B_2(g) \rightleftharpoons 2AB(g); \quad K_1 = 2 \times 10^{-4}
\]
\[
(ii)\; 2AB(g) + C_2(g) \rightleftharpoons 2ABC(g); \quad K_2 = 2 \times 10^{-2}\, L\, mol^{-1}
\]
Calculate the equilibrium constant for:
\[
ABC(g) \rightleftharpoons \frac{1}{2}A_2(g) + \frac{1}{2}B_2(g) + \frac{1}{2}C_2(g)
\]