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<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#define MAXN 100000+100
#define MAXM 1000000+10
using namespace std;
int a[MAXN]; 
int dp[MAXN];
int main()
{
	int n;
	scanf("%d",&n);
	if(n==1) 
	{
		int b;
		scanf("%d",&b);
		printf("1\n");
	}
	else if(n==2)
	{
		int c,d;
		scanf("%d%d",&c,&d);
		printf("1"); 
	}
	else 
	{
		int k=2;
		scanf("%d",&a[1]);
	for(int i=2;i<=n;i++)
	{
		int d;
		scanf("%d",&d);
		if(d==a[k-1]) continue;
		else a[k++]=d;
	}
//	printf("k==%d\n",k);
		if(k<=3) printf("1\n");
		else  
		{
		dp[0]=dp[1]=dp[2]=1;
		for(int i=3;i<k;i++)
		{
			if(dp[i-1]!=dp[i-2]) 
			dp[i]=dp[i-1];
			else 
			{
				if((a[i-1]-a[i-2])*(a[i]-a[i-1]) >0) 
				dp[i]=dp[i-1];
				else dp[i]=dp[i-1]+1;
			}
		}
		printf("%d\n",dp[k-1]);
		}
		
	}
	return 0;
}