The flag of the United Nations consists of a polar map of the world, with the North Pole as center, extending approximately to $45^{\circ}$ South Latitude. The parallels of latitude are concentric circles with radii proportional to their co-latitudes. Australia is near the periphery of the map and is intersected by the parallel of latitude $30^{\circ} \mathrm{S}$. In the very close vicinity of this parallel, how much are East and West distances exaggerated as compared to North and South distances? The original answer is in the format $m\pi/n\sqrt{j}\sim2.42$, please provide the value of m + n + j.

Let's think step by step and output the final answer within \boxed{}.
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