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 C# (judge verdict: Wrong Answer)

using System;

namespace ALDS1_5_D
{
    public static class Algorithm
    {
        public static int Count;

        public static void MergeSort<T>(this T[] a) where T : IComparable<T>
        {
            Count = 0;
            MergeSort(a, 0, a.Length);
        }

        private static void Merge<T>(this T[] a, int l, int m, int r) where T : IComparable<T>
        {
            int n1 = m - l, n2 = r - m;
            T[] a1 = new T[n1], a2 = new T[n2];
            for (int i = 0; i < n1; i++) a1[i] = a[l + i];
            for (int i = 0; i < n2; i++) a2[i] = a[m + i];
            int i1 = 0, i2 = 0, k = l;
            while (i1 < n1 && i2 < n2)
            {
                if (a1[i1].CompareTo(a2[i2]) <= 0) a[k++] = a1[i1++];
                else
                {
                    a[k++] = a2[i2++];
                    Count+=n1-i1;
                }
            }
            while (i1 < n1) a[k++] = a1[i1++];
            while (i2 < n2) a[k++] = a2[i2++];
        }
        private static void MergeSort<T>(this T[] a, int s, int t) where T : IComparable<T>
        {
            if (s + 1 < t)
            {
                var mid = (s + t) >> 1;
                MergeSort(a, s, mid);
                MergeSort(a, mid, t);
                Merge(a, s, mid, t);
            }
        }
    }

    class Program
    {
        static void Main(string[] args)
        {
            Console.ReadLine();
            var a = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            a.MergeSort();
            Console.WriteLine(Algorithm.Count);
        }
    }
}