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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

require('readline').createInterface({
  input: process.stdin,
  output: process.stdout
}).on('line', onReadLine);

var flag = false;

function onReadLine(line) {
  if ((flag = !flag)) return;

  const nums = line.split(' ').map(i => parseInt(i));
  const grads = check(...nums);
  const result = count(1, ...grads);
  console.log(result);
}

function check(a, b, ...next) {
  const sign = Math.sign(b - a);
  return isNaN(sign) ? [] : [sign, ...check(b, ...next)];
}

function count(n, a, b, ...next) {
  // console.log('---', Object.values(arguments));
  if (typeof b == 'undefined') return n;
  return (a != b) ? count(++n, ...next) : count(n, a, ...next);
}