Problem:
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

Solution in LuaJIT (2.0.4) (judge verdict: Accepted)

local mce, mfl, msq, mmi, mma = math.ceil, math.floor, math.sqrt, math.min, math.max

local up = {}
local down = {}
local a = {}
local n = io.read("*n")
for i = 1, n do a[i] = io.read("*n") end
up[1], down[1] = 1, 1
for i = 1, n - 1 do
  if(a[i] < a[i + 1]) then
    down[i + 1] = mmi(down[i] + 1, up[i] + 1)
    up[i + 1] = mmi(down[i] + 1, up[i])
  elseif(a[i + 1] < a[i]) then
    down[i + 1] = mmi(down[i], up[i] + 1)
    up[i + 1] = mmi(down[i] + 1, up[i] + 1)
  else
    down[i + 1] = mmi(down[i], up[i] + 1)
    up[i + 1] = mmi(up[i], down[i] + 1)
  end
end
print(mmi(up[n], down[n]))