#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 1e5 + 7;

int a[N];

int main()
{
	int n;
	cin >> n;
	for (int i=0; i<n; i++)
		cin >> a[i];
	n = unique(a, a+n) - a;
	int cnt = 0;
	for (int i=1; i+1<n; i++)
	{
		if (a[i] > a[i-1] && a[i] > a[i+1])
			cnt++, i++;
		else
		if (a[i] < a[i-1] && a[i] < a[i+1])
			cnt++, i++;	
	}
	if (cnt != 0)
		cout << cnt + 1 << "\n";
	else
		cout << 1 << "\n";
	return 0;
}
### Prompt

Your challenge is to write a cpp solution to 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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 1e5 + 7;

int a[N];

int main()
{
	int n;
	cin >> n;
	for (int i=0; i<n; i++)
		cin >> a[i];
	n = unique(a, a+n) - a;
	int cnt = 0;
	for (int i=1; i+1<n; i++)
	{
		if (a[i] > a[i-1] && a[i] > a[i+1])
			cnt++, i++;
		else
		if (a[i] < a[i-1] && a[i] < a[i+1])
			cnt++, i++;	
	}
	if (cnt != 0)
		cout << cnt + 1 << "\n";
	else
		cout << 1 << "\n";
	return 0;
}
```