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: Accepted)

'use strict'

const INF = 900719925474099;
function mapint(temp){
    return temp.split(' ').map((v)=>parseInt(v));
}

function lower_bound(d,a,b,e){
    for(var c;1<b-a;)
        d[c=0|(a+b)/2]<e ? a=c : b=c;
    return d[a]<e?b:a
};

const MOD = 1000000007;

function Main(input){
    let temp = input.trim().split('\n');
    let n = parseInt(temp[0]);
    let p = mapint(temp[1]);

    let count = 0;
    for(let i=1;i<n-1;i++){
      let s = [p[i-1],p[i],p[i+1]]
      s.sort((a,b)=>b-a);
      if(s[1] == p[i]) count++;
    }

    console.log(count);

}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));