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: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace aizu1
{
    public class Solution
    {
        public static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            int[] s = Array.ConvertAll<string, int>(Console.ReadLine().Split(' '), int.Parse);

            Console.WriteLine(bubbleSort(s,n));
        }

        public static int bubbleSort(int [] s,int n)
        {
            int cnt = 0;

            int swap = 0;
            int p1 = 0, p2 = 0;

            for (int i = 0; i < n; i++)
            {
                p1 = p2;
                for (int j = n - 1; j > p1; j--)
                    if (s[j - 1] > s[j]) { int tmp = s[j]; s[j] = s[j - 1]; s[j - 1] = tmp; swap++; p2 = j; cnt++; }
                if (p1 == p2) break;
            }
            return cnt;
        }
    }
}