#include <iostream>
using namespace std;

int n, a[100000], b[100000];
int main()
{
    int n;
    scanf("%d",&n);
    for(int i = 0;i < n; i++) 
        cin>>a[i];
    int x, y;
    for(int i = 0;i < n; i++) {
        b[i+1] = 0x3f3f3f3f;
        if(i>=1 && a[i-1]>a[i]) x = i;
        else b[i+1] = b[x]+1;
        if(i>=1 && a[i-1]<a[i]) y = i;
        else b[i+1] = min(b[i+1],b[y]+1); 
    }
    cout<<b[n]<<endl;  
return 0;
}
### 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 <iostream>
using namespace std;

int n, a[100000], b[100000];
int main()
{
    int n;
    scanf("%d",&n);
    for(int i = 0;i < n; i++) 
        cin>>a[i];
    int x, y;
    for(int i = 0;i < n; i++) {
        b[i+1] = 0x3f3f3f3f;
        if(i>=1 && a[i-1]>a[i]) x = i;
        else b[i+1] = b[x]+1;
        if(i>=1 && a[i-1]<a[i]) y = i;
        else b[i+1] = min(b[i+1],b[y]+1); 
    }
    cout<<b[n]<<endl;  
return 0;
}
```