#include<stdio.h>
using namespace std;
 
int N;
int A[100010];
int ans = 1;
 
int main()
{
    scanf("%d",&N);
    for(int i = 0; i < N; i++){scanf("%d",&A[i]);if(i != 0 && A[i] == A[i - 1]){N--;i--;}}
    for(int i = 0; i < N - 2; i++)
    {
        if((A[i] <= A[i + 1] && A[i + 1] <= A[i + 2]) || (A[i] >= A[i + 1] && A[i + 1] >= A[i + 2]));
        else {ans++;i++;}
    }
    printf("%d\n",ans);
    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<stdio.h>
using namespace std;
 
int N;
int A[100010];
int ans = 1;
 
int main()
{
    scanf("%d",&N);
    for(int i = 0; i < N; i++){scanf("%d",&A[i]);if(i != 0 && A[i] == A[i - 1]){N--;i--;}}
    for(int i = 0; i < N - 2; i++)
    {
        if((A[i] <= A[i + 1] && A[i + 1] <= A[i + 2]) || (A[i] >= A[i + 1] && A[i + 1] >= A[i + 2]));
        else {ans++;i++;}
    }
    printf("%d\n",ans);
    return 0;
}

```