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 (2.7.1) (judge verdict: Wrong Answer)

#input of int(split by space)
def get_i()
  return gets.chomp.split(" ").map(&:to_i)
end
#input of float(split by space)
def get_f()
  return gets.chomp.split(" ").map(&:to_f)
end
#input of string(split by space)
def get()
  return gets.chomp.split(" ")
end
#input of string(split per one character)
def get_nsp()
  return gets.chomp.split("")
end
#yes or no decision
def yn_judge(bool,y="Yes",n="No")
  return bool ? y : n 
end
#create of array
def array(size1,init=nil,size2=-1)
  if size2==-1
      return Array.new(size1){init}
  else
      return Array.new(size2){Array.new(size1){init}}
  end
end

def max(a,b)
    return a>b ? a : b
end

def min(a,b)
    return a>b ? b : a
end

INF=Float::INFINITY

class UnionFindTree
    attr_accessor:par,:rank
    def initialize(n)
        @par=Array.new(n){|i| i}
        @rank=array(n,0)
    end

    def find(x)
        return x if @par[x]==x
        @par[x]=find(@par[x])
        return @par[x]
    end

    def union(x,y)
        x=find(x)
        y=find(y)
        return if x==y
        if @rank[x]<@rank[y]
            @par[x]=y
        else
            @par[y]=x
            @rank[x]+=1 if @rank[x]==@rank[y]
        end
    end

    def same?(x,y)
        return find(x)==find(y)
    end
end
N=gets.to_i
a=array(N)
kind_a=Hash.new(0)
uft=UnionFindTree.new(N)
N.times do|i|
    a[i]=gets.to_i
    kind_a[a[i]]=1
end
if N==1
    puts 0
    exit
elsif N==2
    puts (a[0]<a[1] ? 0 : 1)
    exit
end
ch_a=Hash.new(-1)
kind_a.sort.each_with_index do|arr,i|
    ch_a[arr[0]]=i
end
N.times do|i|
    a[i]=ch_a[a[i]]
    if i>=2
        uft.union(a[i-2],a[i])
    end
end
b=a.sort
#p a
#p b
ans=0
cnt=0
N.times do|i|
    unless uft.same?(b[i],a[i])
      cnt+=1
    else
      ans+=cnt/2
      cnt=0
    end
end
ans+=cnt
puts ans