Đếm cực tiểu cục bộ (Count Local Minima)

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given an integer sequence $a_1,a_2,\ldots,a_n$.

An element $a_i$ is a strict local minimum when $2\le i\le n-1$ and

The endpoints $a_1$ and $a_n$ are never considered local minima. If $n<3$, the answer is $0$.

Count the strict local minima.

Input

The first line contains integer $n$. The second line contains $n$ space-separated integers $a_1,a_2,\ldots,a_n$.

Output

Print one integer: the number of strict local minima.

Subtasks

Subtask 1 (100 points): $1\le n\le 2\cdot 10^5$; $|a_i|\le 10^9$.

Example

Input

7
5 1 4 2 6 0 3

Output

3

Explanation

Positions $i=2,4,6$ contain $1,2,0$ respectively, each strictly smaller than both neighbors.