Discrete Centrifugal Jumps

有 $n$ 个高楼排成一行，每个楼有一个高度 $h_i$。称可以从楼 $i$ 跳到 楼 $j$，当 $i$, $j$ ( $i < j$ )满足以下三个条件之一： * $i+1=j$ * $\max(h_{i+1},h_{i+2},\cdots,h_{j-1})<\min(h_i,h_j)$ * $\min(h_{i+1},h_{i+2},\cdots,h_{j-1})>\max(h_i,h_j)$ 现在你在楼 $1$，请求出跳到楼 $n$ 最少要跳几次。 $2 \leq n \leq 3\cdot 10^5$, $1\leq h_i \leq 10^9$。

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.

5
1 3 1 4 5

3

4
4 2 2 4

1

2
1 1

1

5
100 1 100 1 100

2

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 $ .