For reaction : $\mathrm{SO}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_3(\mathrm{~g}), \mathrm{K}_{\mathrm{P}}=2 \times 10^{12}$ at $27^{\circ} \mathrm{C}$ and 1 atm pressure. The $\mathrm{K}_{\mathrm{c}}$ for the same reaction is $\_\_\_\_$ $\times 10^{13}$. (Nearest integer) $\left(\right.$ Given $\left.\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$