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: Accepted)

#include<stdio.h>
#define MAX 200000
#define SENTINEL 2000000000

int L[MAX/2+2],R[MAX/2+2];

long merge(int A[],int n,int left,int mid,int right){
   int i,j,k=0;
   long cnt=0;
  int n1;
  int n2;
  n1=mid-left;
  n2=right-mid;
  for(i=0;i<n1;i++){
    L[i]=A[left+i];
  }
  for(i=0;i<n2;i++){
    R[i]=A[mid+i];
  }
  L[n1]=SENTINEL;
  R[n2]=SENTINEL;
  i=0,j=0;
  for(k=left;k<right;k++){
      if(L[i]<=R[j]){
	A[k]=L[i];
	i++;
      }
      else{
	A[k]=R[j];
	j++;
	cnt+=n1-i;
      }
    }
  return cnt;
  }



long mergesort(int A[],int n,int left,int right){
  int mid;
  long v1,v2,v3;
  if(left+1<right){
   mid=(left+right)/2;
   v1=mergesort(A,n,left,mid);
   v2=mergesort(A,n,mid,right);
   v3=merge(A,n,left,mid,right);
   return v1+v2+v3;
  }
  else return 0;
}
int main(){
  int A[MAX],n,i;
  long ans=0;
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%d",&A[i]);
  }
  ans=mergesort(A,n,0,n);
  printf("%ld\n",ans);
  return 0;
}