Problem:
Score : 300 points

Problem Statement

You are given an array A of length N.
Your task is to divide it into several contiguous subarrays.
Here, all subarrays obtained must be sorted in either non-decreasing or non-increasing order.
At least how many subarrays do you need to divide A into?

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Each A_i is an integer.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible number of subarrays after division of A.

Sample Input 1

6
1 2 3 2 2 1

Sample Output 1

2

One optimal solution is to divide the array into [1,2,3] and [2,2,1].

Sample Input 2

9
1 2 1 2 1 2 1 2 1

Sample Output 2

5

Sample Input 3

7
1 2 3 2 1 999999999 1000000000

Sample Output 3

3

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define REP(i,n) for(ll i=0;i<(ll)(n);i++)
#define REPD(i,n) for(ll i=n-1;i>=0;i--)
#define FOR(i,a,b) for(ll i=a;i<=(ll)(b);i++)
#define FORD(i,a,b) for(ll i=a;i>=(ll)(b);i--)
#define ALL(x) (x).begin(),(x).end() 
#define SIZE(x) ((ll)(x).size())
#define MAX(x) *max_element(ALL(x))
#define MIN(x) *min_element(ALL(x))
#define INF 1000000000
using namespace std;
typedef long long ll;

int main() {
    int N;
    cin >> N;

    int a[N], b[N-1];
    REP(i, N){
        cin >> a[i];
    }

    FOR(i, 1, N){
        b[i-1] = a[i] - a[i-1];
    }

    int res = 1;
    int temp1 = 0;
    int temp2 = 0;

    REP(i, N-1){
        if (b[i] > 0){
            temp2 += 1;
        }
        else if (b[i] < 0){
            temp2 += -1;
        }

        if (abs(temp1) > abs(temp2)){
            res += 1;
            temp1 = 0;
            temp2 = 0;
        }
        else{
            temp1 = temp2;
        }
        
    }

    cout << res << endl;
}