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 Ruby (judge verdict: Accepted)

n=gets.to_i
s=gets.split.map &:to_i
c=0
M=->l,m,r{o=m-l
p=r-m
w=s[l,o]
e=s[m,p]
w<<1e10
e<<1e10
i=j=0
(l...r).map{|k|if w[i]<=e[j]
s[k]=w[i]
i+=1
else
s[k]=e[j]
j+=1
c+=o-i
end}}
S=->f,l,r{if l+1<r
m=(l+r)/2
f[f,l,m]
f[f,m,r]
M[l,m,r]
end}
S[S,0,n]
p c