#include <iostream>
using namespace std;
int main() {
    int n; cin >> n;
    int a[n]; for (int i = 0; i < n; i++) cin >> a[i];
    int ans = 0, i = 0;
    while (i < n) {
        ans++;
        i++;
        while (i < n && a[i-1] == a[i]) i++;
        if (i == n) break;
        bool inc = a[i-1] < a[i];
        i++;
        while (i < n && (inc && a[i-1] <= a[i] || !inc && a[i-1] >= a[i])) i++;
    }
    cout << ans << endl;
}

### Prompt

Please create a solution in cpp to 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 main() {
    int n; cin >> n;
    int a[n]; for (int i = 0; i < n; i++) cin >> a[i];
    int ans = 0, i = 0;
    while (i < n) {
        ans++;
        i++;
        while (i < n && a[i-1] == a[i]) i++;
        if (i == n) break;
        bool inc = a[i-1] < a[i];
        i++;
        while (i < n && (inc && a[i-1] <= a[i] || !inc && a[i-1] >= a[i])) i++;
    }
    cout << ans << endl;
}

```