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++14 (Clang 3.8.0) (judge verdict: Accepted)

#include<iostream>
#include<algorithm>

using namespace std;

int bit[108000];

int cnt(int x){
  x++;
  int res = 0;
  while(x){
    res += bit[x];
    x -= x & -x;
  }
  return res;
}

void add(int x, int val){
  x++;
  while(x < 108000){
    bit[x] += val;
    x += x & -x;
  }
}

int n, a[108000], b[108000];
int res;
int main(){
  cin >> n;
  for(int i = 0;i < n;i++){
    cin >> a[i];
    b[i] = a[i];
  }
  sort(b, b + n);
  for(int i = 0;i < n;i++){
    a[i] = lower_bound(b, b + n, a[i]) - b;
    if((a[i] - i ) % 2 != 0)res++;
  }
  cout << res/2 << endl;
  return 0;
}