#include<iostream>
#include<vector>
#include<algorithm>

using namespace std;

int main(){
  int N;
  cin>>N;
  vector<int> data(N);
  for(int i=0;i<N;i++)
    cin>>data[i];

  int ans =0;
  for (int s=0;s<N;){
    int ie,de;
    
    for(ie=s+1;ie<N&&data[ie]>=data[ie-1];ie++);
    for(de=s+1;de<N&&data[de]<=data[de-1];de++);

    ans ++;
    s=max(ie,de);
  }

  cout << ans << endl;
  
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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>
#include<vector>
#include<algorithm>

using namespace std;

int main(){
  int N;
  cin>>N;
  vector<int> data(N);
  for(int i=0;i<N;i++)
    cin>>data[i];

  int ans =0;
  for (int s=0;s<N;){
    int ie,de;
    
    for(ie=s+1;ie<N&&data[ie]>=data[ie-1];ie++);
    for(de=s+1;de<N&&data[de]<=data[de-1];de++);

    ans ++;
    s=max(ie,de);
  }

  cout << ans << endl;
  
  return 0;
}

```