Time Limit : sec, Memory Limit : KB

# 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