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

见题面

见题面