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 N_MAX 500000
#define S_MAX 1000000000
#define INFTY S_MAX+1

int L[N_MAX/2+2];
int R[N_MAX/2+2];

long count;  // 反転数

void merge(int *A, int left, int mid, int right)
{
  int i, j, k;
  int n1 = mid - left;
  int n2 = right - mid;

  // L[0...n1], R[0...n2] を生成
  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; // 番兵を入れる
  R[n2] = INFTY; // 番兵を入れる
  i = 0;
  j = 0;
  for (k = left; k < right; k++) {
    if (L[i] <= R[j]) { // 小さいほうを A にコピー
      A[k] = L[i];
      i = i + 1;
    } else {
      A[k] = R[j];
      j = j + 1;
      count += n1 - i;
    }
  }
}
                
void mergeSort(int *A, int left, int right)
{
  int mid;
  
  if (left+1 < right) {
    mid = (left + right)/2;

    mergeSort(A, left, mid);
    mergeSort(A, mid, right);

    merge(A, left, mid, right);
  }
}

int main(void)
{
  int n;
  int A[N_MAX];
  int i;
  
  scanf("%d", &n);
  for (i = 0; i < n; i++)
    scanf("%d", &A[i]);

  mergeSort(A, 0, n);

  printf("%ld\n", count);
  
  return 0;
}