Discrete Centrifugal Jumps
Description
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.
Input
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.
Output
Print single number $k$ — minimal amount of discrete jumps. We can show that an answer always exists.
Samples
5
1 3 1 4 5
3
4
4 2 2 4
1
2
1 1
1
5
100 1 100 1 100
2
Note
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: $1 \rightarrow 3 \rightarrow 5$.