#include <iostream>
using namespace std;

const int MAXN=1e5+10;
int a[MAXN];

int main(void){
    int n;
    cin >> n;
    for(int i=0; i<n; i++){
        cin >> a[i];
    }
    int ans=0, i=0;
    while(i<n){
        int k=i;
        while(i<n-1&&a[i+1]>=a[i]){
            i++;
        }
        while(k<n-1&&a[k+1]<=a[k]){
            k++;
        }
        i=max(k, i);
        ans++;
        i++;
    }
    cout << ans << 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;

const int MAXN=1e5+10;
int a[MAXN];

int main(void){
    int n;
    cin >> n;
    for(int i=0; i<n; i++){
        cin >> a[i];
    }
    int ans=0, i=0;
    while(i<n){
        int k=i;
        while(i<n-1&&a[i+1]>=a[i]){
            i++;
        }
        while(k<n-1&&a[k+1]<=a[k]){
            k++;
        }
        i=max(k, i);
        ans++;
        i++;
    }
    cout << ans << endl;
    return 0;
}
```