#include <bits/stdc++.h>
using namespace std;
int N;
vector<int> A;
int main() {
	cin >> N;
	A.resize(N);
	for (auto& x : A) cin >> x;
	vector<vector<int>> dp(N+1, vector<int>(2));
	dp[0][0] = dp[0][1] = 1;
	for (int i = 1; i < N; ++ i) {
		dp[i][0] = min(dp[i-1][0] + (A[i-1] < A[i]), dp[i-1][1] + 1);
		dp[i][1] = min(dp[i-1][0] + 1, dp[i-1][1] + (A[i-1] > A[i]));
	}
	cout << min(dp[N-1][0], dp[N-1][1]) << endl;
}

### Prompt

Please formulate 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 <bits/stdc++.h>
using namespace std;
int N;
vector<int> A;
int main() {
	cin >> N;
	A.resize(N);
	for (auto& x : A) cin >> x;
	vector<vector<int>> dp(N+1, vector<int>(2));
	dp[0][0] = dp[0][1] = 1;
	for (int i = 1; i < N; ++ i) {
		dp[i][0] = min(dp[i-1][0] + (A[i-1] < A[i]), dp[i-1][1] + 1);
		dp[i][1] = min(dp[i-1][0] + 1, dp[i-1][1] + (A[i-1] > A[i]));
	}
	cout << min(dp[N-1][0], dp[N-1][1]) << endl;
}

```