Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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)

#[allow(unused_imports)]
use std::cmp::{max, min};
use std::io::{stdin, stdout, BufWriter, Write};
use std::collections::BTreeMap;

#[derive(Default)]
struct Scanner {
    buffer: Vec<String>,
}

impl Scanner {
    fn next<T: std::str::FromStr>(&mut self) -> T {
        loop {
            if let Some(token) = self.buffer.pop() {
                return token.parse().ok().expect("Failed parse");
            }
            let mut input = String::new();
            stdin().read_line(&mut input).expect("Failed read");
            self.buffer = input.split_whitespace().rev().map(String::from).collect();
        }
    }
}

struct FenwickTree {
    buf: Vec<i64>,
    size: usize,
}

impl FenwickTree {
    pub fn new(n: usize) -> FenwickTree {
        FenwickTree {
            buf: vec![0; n + 1],
            size: n,
        }
    }

    pub fn add(&mut self, i: usize, v: i64) {
        let mut i = i + 1;
        while i <= self.size {
            self.buf[i] += v;
            i += i & i.wrapping_neg();
        }
    }

    pub fn sum(&self, i: usize) -> i64 {
        let mut i = i + 1;
        let mut sum = 0;
        while i > 0 {
            sum += self.buf[i];
            i -= i & i.wrapping_neg();
        }
        sum
    }
}

fn main() {
    let mut sc = Scanner::default();
    let out = &mut BufWriter::new(stdout());

    let n = sc.next();
    let mut a = vec![0; n];
    let mut map = BTreeMap::<i64, usize>::new();
    for i in 0..n {
        a[i] = sc.next();
        map.insert(a[i], 0);
    }
    for (i, (_, v)) in map.iter_mut().enumerate() {
        *v = i;
    }

    let mut ft = FenwickTree::new(n);
    let mut ans = 0;
    for x in a.iter().rev() {
        let i = map[&x];
        ans += ft.sum(i);
        // writeln!(out, "{} {}: {}", x, i, ans ).ok();
        ft.add(i, 1);
    }
    writeln!(out, "{}", ans).ok();
}