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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;

namespace ConsoleApplication1
{    

    class Program
    {
        static int[] L;
        static int[] R;
        const int inf = int.MaxValue;

        static void MergeSort(int[] data, int left, int right)
        {
            int mid = 0;

            if(right - left > 1)
            {
                mid = (right + left) / 2;
                MergeSort(data, left, mid);
                MergeSort(data, mid, right);
                Merge(data, left, mid, right);
            }

        }

        static void Merge(int[] data, int left, int mid, int right)
        {
            int n1 = mid - left;
            int n2 = right - mid;
            for (int i = 0; i < n1; i++)
            {
                L[i] = data[left + i];
            }
            for(int i = 0; i < n2; i++)
            {
                R[i] = data[mid + i];
            }

            L[n1] = inf;
            R[n2] = inf;

            int s = 0;
            int t = 0;

            for(int i = left; i < right; i++)
            {
                if(L[s] < R[t])
                {
                    data[i] = L[s++];
                }
                else
                {
                    cnt += n1 - s;
                    data[i] = R[t++];
                }
            }

        }
    
        static long cnt;

        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            string[] input = Console.ReadLine().Split(' ');

            int[] data = new int[n];
            L = new int[n];
            R = new int[n];
            cnt = 0;

            for(int i = 0; i < n; i++)
            {
                data[i] = int.Parse(input[i]);
            }

            MergeSort(data, 0, n);            

            Console.WriteLine(cnt);
        }
    }
}