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 <string.h>
#include <stdlib.h>

#define INFTY 1000000009
#define N 2000005
int count = 0;
int A[N];

int merge(int A[],int left,int mid, int right){
  int i,j,k,n1,n2,*L,*R;
  int mcount=0;
  n1 = mid - left;
  n2 = right - mid;
  L = (int *)malloc((n1+1) * sizeof(int));
  R = (int *)malloc((n2+1) * sizeof(int));
  for(i=0; i<n1; i++) L[i] = A[left + i];
  for(i=0; i<n2; i++) R[i] = A[mid + i];
  L[n1] = INFTY;
  R[n2] = INFTY;
  i = 0;
  j = 0;
  for(k=left; k<right; k++){
    count++;
    if(L[i] <= R[j]){
      A[k] = L[i];
      i = i + 1;
    }
    else{
      A[k] = R[j];
      j = j + 1;
      mcount += n1 - i;
    }
  }
  free(L);
  free(R);
  return mcount;
}


int mergeSort(int A[],int left,int right){
  int mid,a,b,c;
  if(left+1 < right){
    mid = (left + right) / 2;
    a = mergeSort(A,left,mid);
    b = mergeSort(A,mid,right);
    c = merge(A,left,mid,right);
    return a+b+c;
  }
  else return 0;
}

int main(){
  int i,n;
  int answer;

  scanf("%d",&n);
  for(i=0; i<n; i++) scanf("%d",&A[i]);
  answer = mergeSort(A,0,n);

  printf("%d\n",answer);

  return 0;

}