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)

// ALDS1_5_D: The Number of Inversions

fn scan<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().parse().ok().unwrap()
}

fn scan_vec<T: std::str::FromStr>() -> Vec<T> {
    let s: String = scan();
    s.split_whitespace().map(|a| T::from_str(a).ok().unwrap()).collect()
}

fn merge(a: &mut Vec<i64>, left: usize, mid: usize, right: usize) -> usize {
    let mut l: Vec<i64> = Vec::new();
    let mut r: Vec<i64> = Vec::new();
    for i in left..mid {
        l.push(a[i]);
    }
    for i in mid..right {
        r.push(a[i]);
    }
    l.push(std::i64::MAX);
    r.push(std::i64::MAX);
    let mut i: usize = 0;
    let mut j: usize = 0;
    let mut cnt: usize = 0;
    for k in left..right {
        if l[i] <= r[j] {
            a[k] = l[i];
            i += 1;
        } else {
            a[k] = r[j];
            j += 1;
            cnt += mid - left - i;
        }
    }
    cnt
}

fn merge_sort(a: &mut Vec<i64>, left: usize, right: usize) -> usize {
    let mut cnt: usize = 0;
    if left + 1 < right {
        let mid = (left + right) / 2;
        cnt += merge_sort(a, left, mid);
        cnt += merge_sort(a, mid, right);
        cnt += merge(a, left, mid, right);
    } 
    cnt
}

fn main() {
    let n: usize = scan();
    let mut a: Vec<i64> = scan_vec();
    let ans = merge_sort(&mut a, 0, n);
    println!("{}", ans);
}