#include <bits/stdc++.h>
using namespace std;

int n, a[114514];
vector<int> b;
int main(void){
  cin >> n;
  for(int i=0;i<n;i++){
    cin >> a[i];
    if (i==0 || a[i-1] != a[i]) b.push_back(a[i]);
  }
  int ans = 1;
  for(int i=1;i+1<b.size();i++){
    if (b[i-1] > b[i] && b[i] < b[i+1]) {ans++; i++;}
    else if (b[i-1] < b[i] && b[i] > b[i+1]) {ans++; i++;}
  }
  cout << ans << endl;
  return 0;
  
}

### Prompt

Your task is to create 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 n, a[114514];
vector<int> b;
int main(void){
  cin >> n;
  for(int i=0;i<n;i++){
    cin >> a[i];
    if (i==0 || a[i-1] != a[i]) b.push_back(a[i]);
  }
  int ans = 1;
  for(int i=1;i+1<b.size();i++){
    if (b[i-1] > b[i] && b[i] < b[i+1]) {ans++; i++;}
    else if (b[i-1] < b[i] && b[i] > b[i+1]) {ans++; i++;}
  }
  cout << ans << endl;
  return 0;
  
}

```