A14089 | Let's Go Hiking

On a weekend, Qingshan suggests that she and her friend Daniel go hiking. Unfortunately, they are busy high school students, so they can only go hiking on scratch paper.

A permutation $p$ is written from left to right on the paper. First Qingshan chooses an integer index $x$ ( $1\le x\le n$ ) and tells it to Daniel. After that, Daniel chooses another integer index $y$ ( $1\le y\le n$ , $y \ne x$ ).

The game progresses turn by turn and as usual, Qingshan moves first. The rules follow:

- If it is Qingshan's turn, Qingshan must change $x$ to such an index $x'$ that $1\le x'\le n$ , $|x'-x|=1$ , $x'\ne y$ , and $p_{x'}<p_x$ at the same time.
- If it is Daniel's turn, Daniel must change $y$ to such an index $y'$ that $1\le y'\le n$ , $|y'-y|=1$ , $y'\ne x$ , and $p_{y'}>p_y$ at the same time.

The person who can't make her or his move loses, and the other wins. You, as Qingshan's fan, are asked to calculate the number of possible $x$ to make Qingshan win in the case both players play optimally.

The first line contains a single integer $n$ ( $2\le n\le 10^5$ ) — the length of the permutation.

The second line contains $n$ distinct integers $p_1,p_2,\dots,p_n$ ( $1\le p_i\le n$ ) — the permutation.

Print the number of possible values of $x$ that Qingshan can choose to make her win.