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 Rust (1.15.1) (judge verdict: Runtime Error)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*);
    }
}

#[allow(unused_imports)]
use std::cmp::{min, max};

#[allow(unused_imports)]
use std::io::Write;

pub mod ds {
    use std::ops::{AddAssign, Sub};
    #[derive(Debug)]
    pub struct BIT<T> {
        data: Vec<T>,
    }
    impl<T> BIT<T>
    where
        T: Copy + AddAssign + Sub<Output = T> + Default,
    {
        pub fn new(size: usize) -> Self {
            let buf_size = size.next_power_of_two();
            BIT {
                data: vec![T::default(); buf_size + 1],
            }
        }
        #[doc = " [l, r) l,r: 1-indexed"]
        pub fn range_sum(&self, l: usize, r: usize) -> T {
            self.sum(r - 1) - self.sum(l - 1)
        }
        #[doc = " i: 1-indexed but returns 0 if i=0 is given."]
        pub fn sum(&self, i: usize) -> T {
            let mut i = i as i64;
            let mut ret = T::default();
            while i > 0 {
                ret += self.data[i as usize];
                i -= i & -i;
            }
            ret
        }
        #[doc = " i: 1-indexed"]
        pub fn add(&mut self, i: usize, value: T) {
            assert!(i > 0);
            let n = self.data.len() as i64;
            let mut i = i as i64;
            while i <= n {
                self.data[i as usize] += value;
                i += i & -i;
            }
        }
    }
}

fn count_inversion_number(a: &Vec<usize>) -> usize {
    let mut vals: Vec<usize> = a.iter().map(|&v| v).collect();
    vals.sort();
    vals.dedup();

    let mut bit = ds::BIT::new(vals.len());
    let mut ans = 0;
    for i in 0..a.len() {
        let idx = vals.binary_search(&a[i]).unwrap() + 1;
        let v = bit.sum(idx);
        ans += (i - v);
        bit.add(idx, 1);
    }
    ans
}

fn main() {
    input!{
      n: usize,
      aa: [usize; n],
    }
    let mut a1 = vec![];
    let mut a2 = vec![];
    for i in 0..n {
        if i%2 == 0 {
            a1.push(aa[i]);
        } else {
            a2.push(aa[i]);
        }
    }
    a1.sort();
    a2.sort();
    let mut aa = vec![];
    for i in 0..n {
        if i%2 == 0 {
            aa.push(a1[i/2])
        } else {
            aa.push(a2[i/2])
        }
    }
    println!("{}", count_inversion_number(&aa));
}