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)

#include <stdio.h>
#include <stdlib.h>
#define MAX 1000000001
int n,Left[100001],Right[100001],i,j,k,count=0,*A;
void Merge(int left,int mid,int right){
  int n1=mid-left,n2=right-mid;
  for(i=0;i<n1;i++)
    Left[i]=A[left+i];
  for(i=0;i<n2;i++)
    Right[i]=A[mid+i];
  Left[n1]=MAX;
  Right[n2]=MAX;

  for(i=0,j=0,k=left;k<right;k++){
    if(Left[i]<=Right[j])
      A[k]=Left[i++];
    else{
      A[k]=Right[j++];
      count+=n1-i;
    }
  }
}
void MergeSort(int left,int right){
  int mid;
  if(right-left>1){
    mid=(left+right)/2;
    MergeSort(left,mid);
    MergeSort(mid,right);
    Merge(left,mid,right);
  }
}
int main(void){
  scanf("%d",&n);
  A=(int *)malloc(sizeof(int)*n);
  for(i=0;i<n;i++)
    scanf("%d",&A[i]);
  MergeSort(0,n);
  printf("%d\n",count);
  return 0;
}