#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=(a);i<(n);i++)

int n,a[100010];

int sig(int a,int b) {
	if (a<b) return 1;
	if (a>b) return -1;
	return 0;
}

int main() {
	scanf("%d",&n);
	rep(i,0,n) scanf("%d",&a[i]);
	int l=0,ans=0;
	while (l<n) {
		int st=0;
		int r=l+1;
		while (r<n) {
			int u=sig(a[r-1],a[r]);
			if (st&&u&&st!=u) break;
			if (u) st=u;
			r++;
		}
		l=r;
		ans++;
	}
	printf("%d\n",ans);
}
### 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 <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=(a);i<(n);i++)

int n,a[100010];

int sig(int a,int b) {
	if (a<b) return 1;
	if (a>b) return -1;
	return 0;
}

int main() {
	scanf("%d",&n);
	rep(i,0,n) scanf("%d",&a[i]);
	int l=0,ans=0;
	while (l<n) {
		int st=0;
		int r=l+1;
		while (r<n) {
			int u=sig(a[r-1],a[r]);
			if (st&&u&&st!=u) break;
			if (u) st=u;
			r++;
		}
		l=r;
		ans++;
	}
	printf("%d\n",ans);
}
```