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)

use std::io::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let mut a: Vec<usize> = iterator.map(|s| s.parse().unwrap()).collect();

    // let cnt = bubble_sort(&mut a);
    // return cnt.to_string();

    let ans = merge_sort(&mut a, 0, n);

    return ans.to_string();
}

fn merge_sort(a: &mut Vec<usize>, left: usize, right: usize) -> usize {
    if left + 1 < right {
        let mid = (left + right) / 2;
        let mut count = 0;
        count += merge_sort(a, left, mid);
        count += merge_sort(a, mid, right);
        count += merge(a, left, mid, right);
        count
    } else {
        0
    }
}

fn merge(a: &mut Vec<usize>, left: usize, mid: usize, right: usize) -> usize {
    let n1 = mid - left;
    let n2 = right - mid;
    let mut l: Vec<usize> = Vec::new();
    let mut r: Vec<usize> = Vec::new();
    for i in 0..n1 {
        l.push(a[left + i]);
    }
    l.push(std::usize::MAX);
    for i in 0..n2 {
        r.push(a[mid + i]);
    }
    r.push(std::usize::MAX);

    let mut count = 0;

    let mut i = 0;
    let mut j = 0;
    for k in left..right {
        if l[i] <= r[j] {
            a[k] = l[i];
            i += 1;
        } else {
            a[k] = r[j];
            j += 1;
            count += n1 - i;
        }
    }

    count
}

// fn bubble_sort(a: &mut Vec<usize>) -> usize {
//     let mut cnt = 0;
//     for i in 0..a.len() {
//         for j in ((i + 1)..a.len()).rev() {
//             if a[j] < a[j - 1] {
//                 a.swap(j, j - 1);
//                 cnt += 1;
//             }
//         }
//     }
//     cnt
// }