#include <cstdio>
int N, a[100001], O;
int main()
{
	scanf("%d", &N);
	for (int i = 1; i <= N; i++)
		scanf("%d", a + i);
	for (int i = 1; i <= N; )
	{
		O++;
		int j = i;
		while (j < N && a[j] == a[j + 1])
			j++;
		int k = j;
		while (k < N && (a[j] < a[j + 1] ? a[k] <= a[k + 1] : a[k] >= a[k + 1]))
			k++;
		i = k + 1;
	}
	printf("%d\n", O);
	return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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>
int N, a[100001], O;
int main()
{
	scanf("%d", &N);
	for (int i = 1; i <= N; i++)
		scanf("%d", a + i);
	for (int i = 1; i <= N; )
	{
		O++;
		int j = i;
		while (j < N && a[j] == a[j + 1])
			j++;
		int k = j;
		while (k < N && (a[j] < a[j + 1] ? a[k] <= a[k + 1] : a[k] >= a[k + 1]))
			k++;
		i = k + 1;
	}
	printf("%d\n", O);
	return 0;
}

```