#include<bits/stdc++.h>
using namespace std;

#define rep(i,l,r) for(int i=l;i<=r;++i)
const int N=1e5+5;
int a[N],n,up[N],down[N],dp[N];

int main()
{
	//freopen("1.in","r",stdin);
	int n;cin>>n;
	rep(i,1,n)scanf("%d",a+i);
	dp[1]=up[1]=down[1]=1;
	rep(i,2,n)
	{
		up[i]=a[i]>=a[i-1]?up[i-1]:i;
		down[i]=a[i]<=a[i-1]?down[i-1]:i;
		dp[i]=dp[min(up[i],down[i])-1]+1;
	}
	cout<<dp[n];
}
### 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<bits/stdc++.h>
using namespace std;

#define rep(i,l,r) for(int i=l;i<=r;++i)
const int N=1e5+5;
int a[N],n,up[N],down[N],dp[N];

int main()
{
	//freopen("1.in","r",stdin);
	int n;cin>>n;
	rep(i,1,n)scanf("%d",a+i);
	dp[1]=up[1]=down[1]=1;
	rep(i,2,n)
	{
		up[i]=a[i]>=a[i-1]?up[i-1]:i;
		down[i]=a[i]<=a[i-1]?down[i-1]:i;
		dp[i]=dp[min(up[i],down[i])-1]+1;
	}
	cout<<dp[n];
}
```