#include <bits/stdc++.h>
using namespace std;
int main(){
  int N,S=0,i;cin>>N;int A[N];
  for(i=0;i<N;i++)cin>>A[i];
  i=0;
  while(i<N){
    S++;int j=i,x=0;
    while(j<N-1&&(A[j]-A[j+1])*x>=0){
      if(x==0&&A[j]!=A[j+1]){
        if(A[j]>A[j+1])x++;
        else x--;
      }
      j++;
    }
    i=j+1;
  }
  cout<<S<<endl;
}
### Prompt

Please formulate a Cpp solution 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 <bits/stdc++.h>
using namespace std;
int main(){
  int N,S=0,i;cin>>N;int A[N];
  for(i=0;i<N;i++)cin>>A[i];
  i=0;
  while(i<N){
    S++;int j=i,x=0;
    while(j<N-1&&(A[j]-A[j+1])*x>=0){
      if(x==0&&A[j]!=A[j+1]){
        if(A[j]>A[j+1])x++;
        else x--;
      }
      j++;
    }
    i=j+1;
  }
  cout<<S<<endl;
}
```