Problem:
Score : 600 points

Problem Statement

Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct.
He is sorting this sequence in increasing order.
With supernatural power, he can perform the following two operations on the sequence in any order:

Operation 1: choose 2 consecutive elements, then reverse the order of those elements.

Operation 2: choose 3 consecutive elements, then reverse the order of those elements.

Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.

Constraints

1 ≦ N ≦ 10^5

0 ≦ A_i ≦ 10^9

If i ≠ j, then A_i ≠ A_j.

All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of times Operation 1 that Snuke has to perform.

Sample Input 1

4
2
4
3
1

Sample Output 1

1

The given sequence can be sorted as follows:

First, reverse the order of the last three elements. The sequence is now: 2,1,3,4.

Then, reverse the order of the first two elements. The sequence is now: 1,2,3,4.

In this sequence of operations, Operation 1 is performed once. It is not possible to sort the sequence with less number of Operation 1, thus the answer is 1.

Sample Input 2

5
10
8
5
3
2

Sample Output 2

0

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

N = gets.to_i
A = N.times.map { gets.to_i }

evens = []
odds = []

A.each_with_index do |a, i|
  if i.even?
    evens << a
  else
    odds << a
  end
end

evens.sort!
odds.sort!

ans = 0

N.times do |i|
  e = evens[0]
  o = odds[0]

  if i.even?
    if e && o && e > o
      idx = odds.bsearch_index { |x| x >= e } || odds.size
      odds.insert(idx, e)
      ans += 1
      odds.shift
    end

    evens.shift
  else
    if e && o && o > e
      idx = evens.bsearch_index { |x| x >= o } || evens.size
      evens.insert(idx, o)
      ans += 1
      evens.shift
    end

    odds.shift
  end
end

puts ans