AtCoder Grand Contest 013

A - Sorted Arrays

Time limit時間制限 : 2sec / Memory limitメモリ制限 : 256MB

制約

• 1 \leq N \leq 10^5
• 1 \leq A_i \leq 10^9
• A_i は全て整数である

入力

N
A_1 A_2 ... A_N


入力例 1

6
1 2 3 2 2 1


出力例 1

2


[1,2,3][2,2,1] に分ければよいです。

入力例 2

9
1 2 1 2 1 2 1 2 1


出力例 2

5


入力例 3

7
1 2 3 2 1 999999999 1000000000


出力例 3

3


Score : 300 points

Problem Statement

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.

Sample Input 1

6
1 2 3 2 2 1


Sample Output 1

2


One optimal solution is to divide the array into [1,2,3] and [2,2,1].

Sample Input 2

9
1 2 1 2 1 2 1 2 1


Sample Output 2

5


Sample Input 3

7
1 2 3 2 1 999999999 1000000000


Sample Output 3

3