#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int a[100010];
int main()
{
	int n;
	while(~scanf("%d", &n))
	{
		for(int i=1;i<=n;i++)
		scanf("%d", &a[i]);
		
		int ans = 0;
		for(int i=1;i<=n;i++)
		{
			if(i == n)
			ans++;
			
			else 
			{
				int j=i+1,k=i+1;
				while(j<=n&&a[j]>=a[j-1])j++;
				while(k<=n&&a[k]<=a[k-1])k++;
				ans++;
				i = max(j, k) - 1;
			}
		}
		printf("%d\n", ans);
	}
	return 0;
}
### Prompt

Your task is to create 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<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int a[100010];
int main()
{
	int n;
	while(~scanf("%d", &n))
	{
		for(int i=1;i<=n;i++)
		scanf("%d", &a[i]);
		
		int ans = 0;
		for(int i=1;i<=n;i++)
		{
			if(i == n)
			ans++;
			
			else 
			{
				int j=i+1,k=i+1;
				while(j<=n&&a[j]>=a[j-1])j++;
				while(k<=n&&a[k]<=a[k-1])k++;
				ans++;
				i = max(j, k) - 1;
			}
		}
		printf("%d\n", ans);
	}
	return 0;
}
```