//In the name of Allah
#include <bits/stdc++.h>
using namespace std; 

const int maxN = 1000 * 100 + 100;

int a[maxN];

int main() { 
    int n; cin >> n; 
    for( int i = 0 ; i < n ; i++ ) 
        cin >> a[i]; 
    n = unique( a , a + n ) - a; 
    int ans = 1; 
    for( int i = 2 ; i < n ; i++ ) 
        if( ( a[i-2] < a[i-1] ) != ( a[i-1] < a[i] ) ) { 
            i++; 
            ans++;
        }
    cout << ans << endl;
}

### Prompt

Develop a solution in CPP to the problem described below:

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
//In the name of Allah
#include <bits/stdc++.h>
using namespace std; 

const int maxN = 1000 * 100 + 100;

int a[maxN];

int main() { 
    int n; cin >> n; 
    for( int i = 0 ; i < n ; i++ ) 
        cin >> a[i]; 
    n = unique( a , a + n ) - a; 
    int ans = 1; 
    for( int i = 2 ; i < n ; i++ ) 
        if( ( a[i-2] < a[i-1] ) != ( a[i-1] < a[i] ) ) { 
            i++; 
            ans++;
        }
    cout << ans << endl;
}

```