#include <bits/stdc++.h>

using namespace std;

const int Nmax = 1e5+5;
int i, n, a[Nmax], j, k, dp[Nmax];

int solve(int id)
{
    if(id==n+1) return 0;

    int i, j;

    for(i=id; i<n && a[i] <= a[i+1]; ++i);
    for(j=id; j<n && a[j] >= a[j+1]; ++j);

    return 1 + solve(max(i,j) + 1);
}

int main()
{
   
    cin.sync_with_stdio(false);

    cin >> n;
    for(i=1; i<=n; ++i) cin >> a[i];

    cout << solve(1) << '\n';

    return 0;
}

### 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
#include <bits/stdc++.h>

using namespace std;

const int Nmax = 1e5+5;
int i, n, a[Nmax], j, k, dp[Nmax];

int solve(int id)
{
    if(id==n+1) return 0;

    int i, j;

    for(i=id; i<n && a[i] <= a[i+1]; ++i);
    for(j=id; j<n && a[j] >= a[j+1]; ++j);

    return 1 + solve(max(i,j) + 1);
}

int main()
{
   
    cin.sync_with_stdio(false);

    cin >> n;
    for(i=1; i<=n; ++i) cin >> a[i];

    cout << solve(1) << '\n';

    return 0;
}

```