Pyramidal Sequence Checker

A sequence of non-negative integers is defined as pyramidal if and only if there exists an index \(k\) (with \(2 \le k \le n-1\)) such that the following conditions hold:

• \(a_1 < a_2 < \cdots < a_k\) (strictly increasing), and
• \(a_k > a_{k+1} > \cdots > a_n\) (strictly decreasing).

Your task is to determine whether a given sequence is pyramidal. Note that the sequence must have at least 3 elements to form a valid pyramid.

inputFormat

The input is given via stdin and consists of two lines:

1. The first line contains a single integer \(n\) (the length of the sequence).
2. The second line contains \(n\) space-separated non-negative integers.

outputFormat

Output a single line to stdout with the word "YES" if the sequence forms a pyramidal sequence according to the definition, otherwise output "NO".

7
1 2 3 4 3 2 1

YES