#include <bits/stdc++.h>
using namespace std;
int n,i,j,r,a[100100];
bool w;
int main() {
  scanf("%d",&n);
  for (i=0; i<n; i++) scanf("%d",&a[i]);
  for (i=0; i<n; i=j) {
    for (j=i; j<n && a[j]==a[i]; j++);
    i=j-1; r++;
    if (i+1==n) break;
    w=(a[i+1]>=a[i]);
    for (j=i+2; j<n && ((w && a[j]>=a[j-1]) || (!w && a[j]<=a[j-1])); j++);
  }
  printf("%d\n",r);
  return 0;
}


### Prompt

In Cpp, your task is to solve 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,i,j,r,a[100100];
bool w;
int main() {
  scanf("%d",&n);
  for (i=0; i<n; i++) scanf("%d",&a[i]);
  for (i=0; i<n; i=j) {
    for (j=i; j<n && a[j]==a[i]; j++);
    i=j-1; r++;
    if (i+1==n) break;
    w=(a[i+1]>=a[i]);
    for (j=i+2; j<n && ((w && a[j]>=a[j-1]) || (!w && a[j]<=a[j-1])); j++);
  }
  printf("%d\n",r);
  return 0;
}


```