p03745 AtCoder Grand Contest 013 - Sorted Arrays
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
```python
N = int(input())
A = list(map(int, input().split()))

sgn = 0
answer = 1
for i in range(N-1):
    cur = A[i+1] - A[i]
    if cur * sgn < 0:
        answer += 1
        sgn = 0
        continue
    if cur != 0:
        sgn = cur
print(answer)
```