Spotlight Cue Brightness Extremes

A theater's lighting board logs the brightness level set for a spotlight at each cue during a performance, recorded in order as an array of n integers. The operator sometimes holds the same brightness across several consecutive cues, so cues with a brightness equal to their immediate neighbor belong to the same plateau and should never be double counted as separate extremes.

For a given cue, look at the nearest cue before it whose brightness differs (skipping over any run of equal values) and the nearest cue after it whose brightness differs. A cue (or, more precisely, an entire plateau of equal-brightness cues) is a flare if its brightness is strictly greater than both of those differing neighbors, and a dip if its brightness is strictly less than both of those differing neighbors. A plateau touching either end of the array, so that no differing neighbor exists on one side, is neither a flare nor a dip. Each qualifying plateau is counted exactly once, no matter how many cues it spans.

Count the total number of flares plus dips.

Input format

• Line 1: a single integer n, the number of cues.
• Line 2: n space-separated integers b_1 ... b_n, the brightness recorded at each cue in order.

Output format

Print a single integer: the total number of flare cues plus dip cues.

Constraints

• 3 <= n <= 10^5
• 0 <= b_i <= 10^9

9
3 3 5 1 1 6 2 2 4

4

7
1 2 3 3 3 4 5

0