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D. Discrete Centrifugal Jumps

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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.

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.

Examples

Input

5 1 3 1 4 5

Output

3

Input

4 4 2 2 4

Output

1

Input

2 1 1

Output

1

Input

5 100 1 100 1 100

Output

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: $$$1 \rightarrow 3 \rightarrow 5$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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