Problem:
Score : 200 points

Problem Statement

We have a permutation p = {p_1,\ p_2,\ ...,\ p_n} of {1,\ 2,\ ...,\ n}.

Print the number of elements p_i (1 < i < n) that satisfy the following condition:

p_i is the second smallest number among the three numbers p_{i - 1}, p_i, and p_{i + 1}.

Constraints

All values in input are integers.

3 \leq n \leq 20

p is a permutation of {1,\ 2,\ ...,\ n}.

Input

Input is given from Standard Input in the following format:

n
p_1 p_2 ... p_n

Output

Print the number of elements p_i (1 < i < n) that satisfy the condition.

Sample Input 1

5
1 3 5 4 2

Sample Output 1

2

p_2 = 3 is the second smallest number among p_1 = 1, p_2 = 3, and p_3 = 5. Also, p_4 = 4 is the second smallest number among p_3 = 5, p_4 = 4, and p_5 = 2. These two elements satisfy the condition.

Sample Input 2

9
9 6 3 2 5 8 7 4 1

Sample Output 2

5

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import           Data.Char
import qualified Data.ByteString.Char8 as B
import qualified Data.Vector.Unboxed   as U

main :: IO ()
main = do
  n <- readLn
  ps <- U.unfoldrN n (B.readInt . B.dropWhile isSpace) <$> B.getLine
  print $ solve ps

solve :: U.Vector Int -> Int
solve = U.length . U.filter id . (U.zipWith3 monotone <$> id <*> U.tail <*> U.drop 2)
  where
    monotone x y z
      | x < y     = y <= z
      | otherwise = y >= z