Longest Platonic Range

You are given an integer n and a list of integers representing the heights of hills. Your task is to find the length of the longest platonic range in the list.

A platonic range is defined as a contiguous subarray that consists of a strictly increasing sequence followed by a strictly decreasing sequence. Formally, a subarray from index l to r (with l < r) is a platonic range if there exists an index i (with l < i < r) such that:

$a_l < a_{l+1} < \cdots < a_i$ and $a_i > a_{i+1} > \cdots > a_r$,

with the requirement that both the increasing and decreasing parts contain at least one element. If no such range exists, output 0.

inputFormat

The input is read from standard input (stdin) and consists of:

• An integer n representing the number of hills.
• A line containing n space-separated integers representing the heights of the hills.

For example: 10\n2 1 4 7 3 2 5 6 8 4

outputFormat

Output a single integer to standard output (stdout): the length of the longest platonic range. If none exists, output 0.

10
2 1 4 7 3 2 5 6 8 4

5