#include<iostream>
using namespace std;
int n, i, nr, u;
int v[100005];
int main(){
    cin>> n;
    for(i = 1; i <= n; i++){
        cin>> v[i];
        if(v[i] != v[u]){
            v[++u] = v[i];
        }
    }
    n = u;
    for(i = 2; i < n; i++){
        if( (v[i - 1] < v[i] && v[i + 1] < v[i]) || (v[i - 1] > v[i] && v[i + 1] > v[i]) ){
            nr++;
            i++;
        }
    }
    cout<< nr + 1;
}

### 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<iostream>
using namespace std;
int n, i, nr, u;
int v[100005];
int main(){
    cin>> n;
    for(i = 1; i <= n; i++){
        cin>> v[i];
        if(v[i] != v[u]){
            v[++u] = v[i];
        }
    }
    n = u;
    for(i = 2; i < n; i++){
        if( (v[i - 1] < v[i] && v[i + 1] < v[i]) || (v[i - 1] > v[i] && v[i + 1] > v[i]) ){
            nr++;
            i++;
        }
    }
    cout<< nr + 1;
}

```