Show

The chief director of the show wants the participants to be able to line up in exactly $n$ different ways, with each lineup having the same number of people in each column.

Your task is to determine the minimum number of people, $m$, required to achieve this. For example, if n = 3, you would need m = 4 people, as they can be arranged in $1$, $2$, and $4$ columns. If for a given $n$, the number of people needed exceeds 10^9, you should inform the director that it is impossible to gather the required number of people.