The Peak Detector

Fenwick Mill logs a vibration reading from the main press once a minute. A reading that sits strictly above both of its neighbours is a knock — the press catching on something — and maintenance counts knocks per shift. A reading merely level with a neighbour is not a knock; that is the press running rough, which is a different report altogether.

Task: Print how many knocks the log contains.

Input

The first line holds an integer n, always at least 3. Each of the next n lines holds one reading.

Output

One line: a whole number. The first and last readings can never be knocks, since each has only one neighbour to be compared against. Print 0 when the log holds none.

Example:

Input:
5
1
3
2
4
1

Output:
2