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 JAVA (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
	public static int merge(int left, int mid, int rigth, int[] arr) {
		int n1 = mid - left;
		int n2 = rigth - mid;
		int[] l = new int[n1 + 1];
		int[] r = new int[n2 + 1];
		for(int i = 0; i < l.length - 1; i++) {
			l[i] = arr[left + 1];
		}
		l[n1] = Integer.MAX_VALUE;
		for (int i = 0; i < r.length - 1; i++) {
			r[i] = arr[mid + i];
		}
		r[n2] = Integer.MAX_VALUE;
		int i = 0;
		int j = 0;
		int count = 0;
		for(int k = left; k < rigth; k++) {
			if (l[i] < r[j]) {
				arr[k] = l[i++];
			} else {
				arr[k] = r[j++];
				count += (n1 - i);
			}
		}
		return count;
	}
	public static int mergeSort(int left, int rigth, int[] arr) {
		int count = 0;
		if (left + 1 < rigth) {
			int mid = (left + rigth) / 2;
			count += mergeSort(left, mid, arr);
			count += mergeSort(mid, rigth, arr);
			count += merge(left, mid, rigth, arr);
		}
		return count;
	}

	public static void main(String[] args) {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		try {
			int n = Integer.parseInt(br.readLine());
			int[] arr = new int[n];
			String[] strings = br.readLine().split(" ");
			for(int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(strings[i]);
			}
			int count = mergeSort(0, n, arr);
			System.out.println(count);

		} catch (IOException e) {
			e.printStackTrace();
		}

	}
}