Đếm cực đại cục bộ (Count Local Maxima)

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 maximum when $2\le i\le n-1$ and

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

Count the strict local maxima.

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 maxima.

Subtasks

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

Example

Input

7
1 5 2 4 4 6 1

Output

2

Explanation

The strict local maxima are $a_2=5$ and $a_6=6$. The adjacent equal values $4,4$ do not form a strict maximum.