A13704. Discrete Centrifugal Jumps

There are $n$ beautiful skyscrapers in New York, the height of the $i$ -th one is $h_i$ . Today some villains have set on fire first $n - 1$ of them, and now the only safety building is $n$ -th skyscraper.

Let's call a jump from $i$ -th skyscraper to $j$ -th ( $i < j$ ) discrete, if all skyscrapers between are strictly lower or higher than both of them. Formally, jump is discrete, if $i < j$ and one of the following conditions satisfied:

- $i + 1 = j$
- $\max(h_{i + 1}, \ldots, h_{j - 1}) < \min(h_i, h_j)$
- $\max(h_i, h_j) < \min(h_{i + 1}, \ldots, h_{j - 1})$ .

At the moment, Vasya is staying on the first skyscraper and wants to live a little longer, so his goal is to reach $n$ -th skyscraper with minimal count of discrete jumps. Help him with calcualting this number.

The first line contains a single integer $n$ ( $2 \le n \le 3 \cdot 10^5$ ) — total amount of skyscrapers.

The second line contains $n$ integers $h_1, h_2, \ldots, h_n$ ( $1 \le h_i \le 10^9$ ) — heights of skyscrapers.

Print single number $k$ — minimal amount of discrete jumps. We can show that an answer always exists.

In the first testcase, Vasya can jump in the following way: $1 \rightarrow 2 \rightarrow 4 \rightarrow 5$ .

In the second and third testcases, we can reach last skyscraper in one jump.

Sequence of jumps in the fourth testcase: $1 \rightarrow 3 \rightarrow 5$ .