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 Pascal (FPC 2.6.2) (judge verdict: Wrong Answer)

uses math;
var i,n,j,max1,max2,res:longint;
    a,b:array[1..20] of integer;
begin
  readln(n);
  for i:=1 to n do read(a[i]);
  for i:=2 to n - 1 do 
    begin
      max1:=0; max2:=0;
      for j:=i- 1 to i + 1 do 
        max1:=max(max1,a[j]);
      for j:=i - 1 to i + 1 do 
        if (a[j] > max2) and (a[j] <> max1) then max2:=a[j];
      b[max2]:=1;
    end;
  for i:=1 to n do if b[i] = 1 then inc(res);
  write(res)
end.