Mountain Sequence Checker

You are given several sequences of integers. Your task is to determine whether each sequence forms a mountain sequence.

A sequence is considered a mountain sequence if and only if it satisfies the following conditions:

• The sequence contains at least 3 elements.
• There exists an index \( i \) (with \(1 \leq i \leq n-2\)) such that the subsequence \(a_0, a_1, \dots, a_i\) is strictly increasing and the subsequence \(a_i, a_{i+1}, \dots, a_{n-1}\) is strictly decreasing.
• The peak element \(a_i\) is greater than both of its immediate neighbors (i.e. \(a_{i-1} a_{i+1}\)).

Input/Output Method: Read input from standard input (stdin) and write the result to standard output (stdout).

inputFormat

The first line of input contains an integer \(T\), representing the number of sequences.

For each sequence, the first number is an integer \(n\) representing the number of elements in the sequence, followed by \(n\) integers.

Example:

3
7
1 2 3 4 3 2 1
5
1 2 3 2 1
5
1 2 3 4 5

outputFormat

For each sequence, output a single line containing either YES if the sequence is a mountain sequence, or NO otherwise.

Example output:

YES
YES
NO

## sample

3
7
1 2 3 4 3 2 1
5
1 2 3 2 1
5
1 2 3 4 5

YES
YES
NO

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