D. Discrete Centrifugal Jumpstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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.InputThe 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.OutputPrint single number k — minimal amount of discrete jumps. We can show that an answer always exists.ExamplesInput
5
1 3 1 4 5
Output
3Input
4
4 2 2 4
Output
1Input
2
1 1
Output
1Input
5
100 1 100 1 100
Output
2NoteIn 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.
5
1 3 1 4 5

3
['data structures', 'dp', 'graphs', '*2200']