Description

A sequence of numbers represents the ground profile’s elevation changes. The height values are integers, and adjacent heights are connected by straight line segments. Find and count how many low-lying depressions could hold water.

As shown: the elevation changes are $[0,1,0,2,1,2,0,0,2,0]$.

Input Format

Two lines.

• Line 1: $n$, the number of heights.
• Line 2: $n$ integers giving the ground profile heights, with the first and last equal to $0$. $(3 \le n \le 10000, 0 \le$ height $\le 1000)$.

Output Format

A single integer: the number of depressions that can potentially hold water.

10
0 1 0 2 1 2 0 0 2 0

3

Hint

Translated by ChatGPT 5