Larger than neighbors

An array of n integers is given. Find how many its elements are bigger than its two neighbours, and output the number of such elements. The leftmost (first) and rightmost (last) elements do not take into account, because they have one neighbour only.

Input

First line contains number n. Next line contains n integers. All numbers do not exceed 100 by absolute value.

Output

Print the number of elements that are larger than their two neighbours.

Examples