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;
					
public class my
{
		public static void Main()
	{
		var n = my.GetInt();
		var A = my.GetIntArray(n);
		
		var cnt = my.MergeSort(A, 0, n);
		
		Console.WriteLine(cnt);
	}
	
	private static long MergeSort(int[] A, int left, int right)
	{
		long cnt = 0;
		
		if(left +1 < right) {
			int mid = (left + right) / 2;
			
			cnt += my.MergeSort(A, left, mid);
			cnt += my.MergeSort(A, mid, right);
			cnt += my.Merge(A, left, mid, right);
		}
		
		return cnt;
	}
	
	private static long Merge(int[] A, int left, int mid, int right)
	{
		var n1 = mid - left;
		var n2 = right - mid;
		
		var L = new int[n1 + 1];
		Array.Copy(A, left, L, 0, n1);
		var R = new int[n2 + 1];	// for sentinel
		Array.Copy(A, mid, R, 0, n2);
		L[n1] = int.MaxValue;	// Sentinel
		R[n2] = int.MaxValue;
		
		int i = 0, j=0;
		
		long cnt = 0;
		for(int k = left; k < right; k++) {
			if(L[i] <= R[j]) {
				A[k] = L[i++];
			} else {
				A[k] = R[j++];
				cnt += n1 - i;
			}
		}
		
		return cnt;
	}
	
	private static int GetInt()
	{
		return int.Parse(Console.ReadLine());
	}
	
	private static int[] GetIntArray()
	{
		return Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
	}

	private static int[] GetIntArray(int n)
	{
		var A = new int[n];
		var s = Console.ReadLine().Split(' ');

		for(int i = 0; i < n; i++) {
			A[i] = int.Parse(s[i]);
		}
		return A;
	}
	
	private static int[] GetIntArray(int n, string t)
	{
		var A = new int[n];
		var s = t.Split(' ');

		for(int i = 0; i < n; i++) {
			A[i] = int.Parse(s[i]);
		}
		return A;
	}

	private static int[] GetIntArray(char c)
	{
		return Array.ConvertAll(Console.ReadLine().Split(c), int.Parse);
	}
	
	private static int[] GetIntArray(char c, string s)
	{
		return Array.ConvertAll(s.Split(c), int.Parse);
	}
	
	private static int[] GetIntArray(string s)
	{
		return Array.ConvertAll(s.Split(' '), int.Parse);
	}
	
	private static double[] GetDoubleArray()
	{
		return Array.ConvertAll(Console.ReadLine().Split(' '), double.Parse);
	}
	
	public static string Reverse(string s)
	{
		var c = s.ToCharArray();
		Array.Reverse(c);
		
		return new String(c);
	}
	
	private static void WriteArray(int[] a)
	{
		Console.WriteLine(string.Join(" ", Array.ConvertAll( a, x=>x.ToString() ) ) );
	}

	private static void WriteArray(long[] a)
	{
		Console.WriteLine(string.Join(" ", Array.ConvertAll( a, x=>x.ToString() ) ) );
	}
	
	private static void WriteVector(Vector v)
	{
		Console.WriteLine("{0:f8} {1:f8}", v.X, v.Y);
	}
}

public struct Vector
{
	public double X,Y;
}