#include<iostream>
using namespace std;
int N;
int A[1<<17];
int cnt;
int main()
{
	cin>>N;
	for(int i=0;i<N;i++)cin>>A[i];
	for(int i=0;i<N;)
	{
		cnt++;
		int j=i;
		while(j<N&&A[i]==A[j])j++;
		if(j==N)break;
		if(A[i]<A[j])
		{
			while(j+1<N&&A[j]<=A[j+1])j++;
		}
		else
		{
			while(j+1<N&&A[j]>=A[j+1])j++;
		}
		i=j+1;
	}
	cout<<cnt<<endl;
}

### Prompt

In CPP, your task is to solve the following problem:

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.

Examples

Input

6
1 2 3 2 2 1


Output

2


Input

9
1 2 1 2 1 2 1 2 1


Output

5


Input

7
1 2 3 2 1 999999999 1000000000


Output

3

### Response

```cpp
#include<iostream>
using namespace std;
int N;
int A[1<<17];
int cnt;
int main()
{
	cin>>N;
	for(int i=0;i<N;i++)cin>>A[i];
	for(int i=0;i<N;)
	{
		cnt++;
		int j=i;
		while(j<N&&A[i]==A[j])j++;
		if(j==N)break;
		if(A[i]<A[j])
		{
			while(j+1<N&&A[j]<=A[j+1])j++;
		}
		else
		{
			while(j+1<N&&A[j]>=A[j+1])j++;
		}
		i=j+1;
	}
	cout<<cnt<<endl;
}

```