A packaging engineer wants a box count n that can be arranged into exactly k distinct rectangular grid layouts (each divisor pair of n gives one layout), i.e. n must have exactly k positive divisors. Among all such n, she wants the SMALLEST one.
Given k, output the smallest positive integer n such that n has exactly k positive divisors (including 1 and n itself).
Input format
Line 1: a single integer k.
Output format
A single integer: the smallest positive integer with exactly k divisors.
Constraints
- 1 <= k <= 100