Pyramid Blocks

Given an array of integers representing the heights of blocks, determine whether these blocks can form a pyramid-like structure. A pyramid-like structure is defined as a sequence that strictly increases to a single peak and then strictly decreases. In other words, there must exist an index (i) (with (1 < i < n)) such that (a_1 < a_2 < \cdots < a_i) and (a_i > a_{i+1} > \cdots > a_n). The sequence must contain at least three elements since the pyramid requires both an increasing and a decreasing part.

For example:

• [1, 2, 3, 4, 3, 2, 1] forms a pyramid and should output True.
• [1, 3, 2] forms a pyramid and should output True.
• [1, 2, 3] does not form a pyramid and should output False.

Your task is to read the input from standard input (stdin) and print the result to standard output (stdout).

inputFormat

The first line contains an integer (n) (the number of blocks). The second line contains (n) space-separated integers (a_1, a_2, \ldots, a_n) representing the heights of the blocks.

outputFormat

Output a single line containing either True if the blocks can form a pyramid-like structure, or False otherwise.## sample

7
1 2 3 4 3 2 1

True