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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
	implicit none
    integer::N,i,ans
    integer, allocatable :: a(:)
    read(*,*) N
    allocate(a(N))
    read(*, *)(a(i), i = 1,N)
    ans=0
    do i=2,N-1
    	if(a(i-1)<a(i) .and. a(i)<a(i+1)) then
        	ans=ans+1
        else if(a(i-1)>a(i) .and. a(i)>a(i+1)) then
            ans=ans+1
        else 
        	ans=ans
        end if
    end do
    print*,ans
end program