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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func readf(sc *bufio.Scanner) float64 {
	f, err := strconv.ParseFloat(sc.Text(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

func Abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

func subL(list []int) []int {
	sl := make([]int, len(list)-1)
	for i := range list {
		if i == len(list)-1 {
			continue
		}
		sub := list[i+1] - list[i]
		sl[i] = sub
	}
	return sl
}

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	sc.Scan()
	n, _ := strconv.Atoi(sc.Text())
	a := make([]int, n)
	for i := range a {
		sc.Scan()
		a[i], _ = strconv.Atoi(sc.Text())
	}

	{
		idx := 0
		memo := make([]int, n)
		for {
			isNext := operate3(a, idx)
			if !isNext {
				if Equal(memo, a) {
					break
				}
				copy(memo, a)
				idx = 0
				continue
			}
			idx = idx + 1
		}
	}

	{
		c := 0
		idx := 0
		memo := make([]int, n)
		for {
			isNext := operate2(a, idx, &c)
			if !isNext {
				if Equal(memo, a) {
					break
				}
				copy(memo, a)
				idx = 0
				continue
			}
			idx = idx + 1
		}

		fmt.Println(c)
	}
}

func operate2(x []int, i int, c *int) bool {
	if len(x)-1 < i+1 {
		return false
	}
	if x[i] > x[i+1] {
		*c = *c + 1
		x[i], x[i+1] = x[i+1], x[i]
	}
	return true
}

func operate3(x []int, i int) bool {
	if len(x)-1 < i+2 {
		return false
	}
	if x[i] > x[i+2] {
		x[i], x[i+2] = x[i+2], x[i]
	}
	return true
}

func Equal(a, b []int) bool {
	if len(a) != len(b) {
		return false
	}
	for i, v := range a {
		if v != b[i] {
			return false
		}
	}
	return true
}