#include<iostream>
#include<algorithm>
#include<vector>
using lint=int64_t;
using namespace std;

int main()
{
	int N;
	vector<int> A;
	
	cin >> N;
	for(int i=0;i<N;i++)
	{
		int tmp;
		cin >> tmp;
		A.push_back(tmp);
	}
	
	A.erase(unique(A.begin(),A.end()),A.end());
	
	int cnt=0;
	for(int i=1;i<A.size()-1;i++)
	{
		if((A[i]>A[i-1] && A[i]>A[i+1]) || (A[i]<A[i-1] && A[i]<A[i+1]))
		{
			cnt++;
			i++;
		}
	}
	
	cout << cnt+1 << endl;
	return 0;
}

### Prompt

Create a solution in CPP for 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>
#include<algorithm>
#include<vector>
using lint=int64_t;
using namespace std;

int main()
{
	int N;
	vector<int> A;
	
	cin >> N;
	for(int i=0;i<N;i++)
	{
		int tmp;
		cin >> tmp;
		A.push_back(tmp);
	}
	
	A.erase(unique(A.begin(),A.end()),A.end());
	
	int cnt=0;
	for(int i=1;i<A.size()-1;i++)
	{
		if((A[i]>A[i-1] && A[i]>A[i+1]) || (A[i]<A[i-1] && A[i]<A[i+1]))
		{
			cnt++;
			i++;
		}
	}
	
	cout << cnt+1 << endl;
	return 0;
}

```