Next Highly Divisible Number

You are given a non-negative integer n. Your task is to find the smallest integer which has strictly more than n divisors.

Recall that the number of divisors of an integer x can be computed by counting all positive integers that evenly divide x. For example, the number 12 has the divisors 1, 2, 3, 4, 6, and 12, making a total of 6 divisors. Formally, if we denote by \(d(x)\) the number of divisors of \(x\), you need to find the minimum integer \(y\) such that \(d(y) > n\).

inputFormat

The input consists of a single line containing one integer n (\(0 \leq n \leq 1000\)).

outputFormat

Output a single integer: the smallest number which has more than n divisors.

5

12