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: Wrong Answer)

#include <ctime>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cassert>
#include <algorithm>
#include <iostream>
#include <vector>
#include <queue>
#include <stack>
#include <deque>
#include <set>
#include <map>
using namespace std;

typedef long long ll;
typedef double lf;
typedef long double Lf;
typedef pair <int,int> pii;
typedef pair <ll, ll> pll;

#define TRACE(x) cerr << #x << "  " << x << endl
#define FOR(i, a, b) for (int i = (a); i < int(b); i++)
#define REP(i, n) FOR(i, 0, n)
#define all(x) (x).begin(), (x).end()
#define _ << " " <<

#define fi first
#define sec second
#define mp make_pair

const int MAXN = 100100;

int n, p[MAXN];

int start(int x) {
	int ret = 1;
	if (x == n - 1) return ret;

	while (x + 1< n && p[x] == p[x + 1]) {
		ret++;
		x++;
	}

	if (x == n - 1) return ret;

	bool kamo = (p[x] < p[x + 1]);

	while (x + 1 < n && (p[x] < p[x + 1]) == kamo) {
		ret++;
		x++;
	}

	return ret;
}

int main() {
	scanf("%d",&n);
	REP(i, n) scanf("%d",&p[i]);
	
	int sol = 0;
	REP(i, n) {
		sol++;
		i += start(i) - 1;
	}

	printf("%d\n",sol);
	return 0;
}