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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

process.stdin.resume();
process.stdin.setEncoding('utf8');
 
var lines = [];
var reader = require('readline').createInterface({
  input: process.stdin,
  output: process.stdout
});
reader.on('line', (line) => {
  lines.push(line)
});
 
reader.on('close', () => {
 
  var n = lines[1].split(' ')
  for (var k in n) n[k] = parseInt(n[k])
 
  var r = 0
 
  for (var k in n) {
    k = parseInt(k)
    if (k === 0 || k === n.length - 1) { 
      continue;
    }
    var ary = [
      n[k - 1],
      n[k],
      n[k + 1]
    ]
    ary = ary.sort()
    if (ary[1] === n[k]) r++
  }
 
  console.log(r)
 
});