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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <sstream>
#include <string>
#include <vector>
#include <functional>
#include <tuple>
#include <climits>
#include <algorithm>
#include <queue>
#include <unordered_map>
#include <unordered_set>
#include <set>
#include <numeric>
#include <map>
#include <cmath>
#include <cstdlib>
#include <iomanip>
#include <array>

using namespace std;

int main()
{
    int N;
    cin >> N;
    vector<int> A(N);
    vector<int> B(N);
    for(int i=0; i<N; i++) {
        int n;
        cin >> n;
        A[i] = n;
        B[i] = n;
    }
    sort(B.begin(), B.end());
    uint64_t count = 0;
    auto start_a = A.begin();
    for(auto v : B) {
        auto it = find(start_a, A.end(), v);
        const int diff = it - start_a;
        if(diff == 0) {
            start_a++;
            continue;
        }
        if(diff % 2 == 0) {
            iter_swap(start_a, it);
        } else {
            iter_swap(next(start_a), it);
            it = next(start_a);
            iter_swap(it, prev(it));
            count++;
        }
        start_a++;
    }
    cout << count << endl;
}