651. Maximizing Product of Integers

0

Medium

Ram and his friend were playing a game. Ram's friend challenged him to break a given integer n into the sum of k positive integers, where k is greater than or equal to 2, in order to maximize the product of those integers. Your task is to find the maximum product that can be obtained.

Input Format

The first line of input contains a single integer N.

Output Format

Print the maximum product as the output.

Example

Input

10

Output

36

Constraints

2 <= n <= 58

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