Problem:
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The Number of Inversions

For a given sequence $A = \{a_0, a_1, ... a_{n-1}\}$, the number of pairs $(i, j)$ where $a_i > a_j$ and $i < j$, is called the number of inversions. The number of inversions is equal to the number of swaps of Bubble Sort defined in the following program:

bubbleSort(A)
cnt = 0 // the number of inversions
for i = 0 to A.length-1
for j = A.length-1 downto i+1
if A[j] < A[j-1]
swap(A[j], A[j-1])
cnt++

return cnt

For the given sequence $A$, print the number of inversions of $A$. Note that you should not use the above program, which brings Time Limit Exceeded.

Input

In the first line, an integer $n$, the number of elements in $A$, is given. In the second line, the elements $a_i$ ($i = 0, 1, .. n-1$) are given separated by space characters.

output

Print the number of inversions in a line.

Constraints

$ 1 \leq n \leq 200,000$

$ 0 \leq a_i \leq 10^9$

$a_i$ are all different

Sample Input 1

5
3 5 2 1 4

Sample Output 1

6

Sample Input 2

3
3 1 2

Sample Output 2

2

Solution in Rust (judge verdict: Accepted)

use std::io;
use std::io::Read;
use std::iter;

fn merge_sort(xs: &mut [usize], left: usize, right: usize) -> usize {
    if left + 1 < right {
        let mid = (left + right) / 2;
        let ninvleft = merge_sort(xs, left, mid);
        let ninvright = merge_sort(xs, mid, right);
        let ninvthis = merge(xs, left, mid, right);
        ninvleft + ninvright + ninvthis
    } else {
        0
    }
}

fn merge(xs: &mut [usize], left: usize, mid: usize, right: usize) -> usize {
    let nl = mid - left;
    let l: Vec<usize> = xs[left..mid]
        .iter()
        .cloned()
        .chain(iter::once(std::usize::MAX))
        .collect();
    let r: Vec<usize> = xs[mid..right]
        .iter()
        .cloned()
        .chain(iter::once(std::usize::MAX))
        .collect();
    let mut i = 0;
    let mut j = 0;
    let mut ninv = 0;

    for k in left..right {
        if l[i] <= r[j] {
            xs[k] = l[i].clone();
            i += 1;
        } else {
            xs[k] = r[j].clone();
            j += 1;
            ninv += nl - i;
        }
    }

    ninv
}

fn main() {
    let mut stdin = io::stdin();
    let mut buf = String::new();

    stdin.read_to_string(&mut buf);

    let mut iter = buf.split_whitespace();
    let n = iter.next().unwrap().parse().unwrap();
    let mut s: Vec<usize> = iter.map(|s| s.parse().unwrap()).collect();
    let cnt = merge_sort(&mut s, 0, n);
    println!("{}", cnt);
}