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)

fn read_lines() -> Vec<String> {
    use std::io::Read;

    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    return buf.lines().map(|e| e.to_string()).collect::<Vec<_>>();
}

fn main() {
    let input = read_lines();
    let n: usize = input[0].parse().unwrap();
    let mut series = input[1].split_whitespace().map(|s| s.parse().unwrap()).collect::<Vec<u32>>();
    let cnt = merge_sort(&mut series, 0, n);

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

fn merge<T: Ord + Clone>(series: &mut Vec<T>, left: usize, mid: usize, right: usize) -> u64 {
    let ls = series[left..mid].to_vec();
    let rs = series[mid..right].to_vec();

    let mut inv_cnt = 0;
    let mut li = 0;
    let mut ri = 0;
    for i in left..right {
        if ls.len() <= li {
            series[i] = rs[ri].clone();
            ri += 1;            
        } else if rs.len() <= ri {
            series[i] = ls[li].clone();
            li += 1;
        } else if ls[li] > rs[ri] {
            series[i] = rs[ri].clone();
            ri += 1;
            inv_cnt += ls.len() - li;
        } else {
            series[i] = ls[li].clone();
            li += 1;
        }
    }
    return inv_cnt as u64;
}

fn merge_sort<T: Ord + Clone>(series: &mut Vec<T>, left: usize, right: usize) -> u64 {
    if left + 1 < right {
        let mid = (left + right) / 2;
        let c1 = merge_sort(series, left, mid);
        let c2 = merge_sort(series, mid, right);
        let c3 = merge(series, left, mid, right);
        return c1 + c2 + c3;
    } else {
        return 0;
    }
}