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

int main(){
   int n;cin>>n;
   int m[n+3];
   for(int i=1;i<=n;i++) cin>>m[i];
   int cnt=0;
   int i=1;
   while(i<n){
       int j,k;
       for(j=i;j<n && m[j]<=m[j+1];j++);
       for(k=i;k<n && m[k]>=m[k+1];k++);
       //printf("%d %d\n",j,k);
       i=max(j,k)+1;
       //cout << i<<endl;
       if(i!=n+1)cnt++;//i=n+1の時，大小の入れ替わりではなく，端にきたから止まったのでバーは入れない
   }
   cout << cnt+1 << endl;
}

### Prompt

Create a solution in CPP for 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;cin>>n;
   int m[n+3];
   for(int i=1;i<=n;i++) cin>>m[i];
   int cnt=0;
   int i=1;
   while(i<n){
       int j,k;
       for(j=i;j<n && m[j]<=m[j+1];j++);
       for(k=i;k<n && m[k]>=m[k+1];k++);
       //printf("%d %d\n",j,k);
       i=max(j,k)+1;
       //cout << i<<endl;
       if(i!=n+1)cnt++;//i=n+1の時，大小の入れ替わりではなく，端にきたから止まったのでバーは入れない
   }
   cout << cnt+1 << endl;
}

```