Smallest Integer with a Given Number of Divisors

Given a positive integer n, determine the smallest positive integer x such that the number of positive divisors of x is exactly n.

Recall that the number of divisors of a number \(x\), denoted as \(d(x)\), is defined as the number of positive integers that divide \(x\) evenly, i.e., all \(d\) such that \(x \mod d = 0\). For example, when \(n = 3\), the answer is \(4\) because the divisors of \(4\) are \(\{1, 2, 4\}\), and thus \(d(4) = 3\).

Your task is to implement a function (or program) which reads \(n\) as input and outputs the smallest \(x\) that satisfies \(d(x) = n\).

inputFormat

The input consists of a single positive integer n provided via standard input.

outputFormat

Output the smallest positive integer \(x\) such that the number of its divisors equals n by writing the result to standard output.

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