Score : $300$ points

Problem Statement

You are given an array $A$ of length $N$. Your task is to divide it into several contiguous subarrays. Here, all subarrays obtained must be sorted in either non-decreasing or non-increasing order. At least how many subarrays do you need to divide $A$ into?

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq A_i \leq 10^9$
• Each $A_i$ is an integer.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $...$ $A_N$

Output

Print the minimum possible number of subarrays after division of $A$.

6
1 2 3 2 2 1

2

One optimal solution is to divide the array into $[1,2,3]$ and $[2,2,1]$.

9
1 2 1 2 1 2 1 2 1

5

7
1 2 3 2 1 999999999 1000000000

3