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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.Diagnostics;
using System.Numerics;
using Enu = System.Linq.Enumerable;

public class Program
{
    public void Solve()
    {
        int N = Reader.Int();
        var A = Reader.IntArray(N);
        var even = A.Where((a, i) => i % 2 == 0).OrderBy(a => a).ToArray();
        var odd = A.Where((a, i) => i % 2 == 1).OrderBy(a=>a).ToArray();
        A = Enu.Range(0, N).Select(i => i % 2 == 0 ? even[i / 2] : odd[i / 2]).ToArray();
        Console.WriteLine(Inversion(A));
    }

    long Inversion(int[] A)
    {
        int N = A.Length;
        var sorted = new int[N];
        Array.Copy(A,sorted, N);
        Array.Sort(sorted);
        A = A.Select(a=> Array.BinarySearch(sorted, a)).ToArray();
        long res = 0;
        var bit = new BinaryIndexedTree(N);
        for (int i = 0; i < N; i++)
        {
            res += i - bit.Sum(A[i]);
            bit.Add(A[i], 1);
        }
        return res;
    }
}

class BinaryIndexedTree
{
    private readonly int N;
    private readonly long[] A;

    public BinaryIndexedTree(int N)
    {
        this.N = N + 1;
        A = new long[N + 2];
    }
    public void Add(int i, long val)
    {
        if (i < 0) return;
        for (++i; i <= N; i += i & -i) A[i] += val;
    }
    public void Update(int i, long val)
    {
        Add(i, val - (Sum(i) - Sum(i - 1)));
    }
    public long Sum(int i) // [0, i]
    {
        if (i < 0) return 0;
        i = Math.Min(i + 1, N);
        long sum = 0;
        for (; i > 0; i &= i - 1) sum += A[i];
        return sum;
    }
    public long Sum(int L, int R) // [L, R)
    {
        return Sum(R - 1) - Sum(L - 1);
    }
    public int UpperBound(long val, int L = 0, int R = int.MaxValue)
    {
        for (L--, R = Math.Min(R, N); R - L > 1; )
        {
            int mid = L + R >> 1;
            if (Sum(mid) > val) R = mid;
            else L = mid;
        }
        return R;
    }
}


class Entry { static void Main() { new Program().Solve(); } }
class Reader
{
    static TextReader reader = Console.In;
    static readonly char[] separator = { ' ' };
    static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries;
    static string[] A = new string[0];
    static int i;
    static void Init() { A = new string[0]; }
    public static void Set(TextReader r) { reader = r; Init(); }
    public static void Set(string file) { reader = new StreamReader(file); Init(); }
    public static bool HasNext() { return CheckNext(); }
    public static string String() { return Next(); }
    public static int Int() { return int.Parse(Next()); }
    public static long Long() { return long.Parse(Next()); }
    public static double Double() { return double.Parse(Next()); }
    public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); }
    public static int[] IntArray(int N) { return Range(N, Int); }
    public static int[][] IntTable(int H) { return Range(H, IntLine); }
    public static string[] StringArray(int N) { return Range(N, Next); }
    public static string[][] StringTable(int N) { return Range(N, () => Split(Line())); }
    public static string Line() { return reader.ReadLine().Trim(); }
    public static T[] Range<T>(int N, Func<T> f) { var r = new T[N]; for (int i = 0; i < N; r[i++] = f()) ; return r; }
    static string[] Split(string s) { return s.Split(separator, op); }
    static string Next() { CheckNext(); return A[i++]; }
    static bool CheckNext()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return CheckNext();
        A = Split(line);
        i = 0;
        return true;
    }
}