A891 | Why Did the Cow Cross the Road III--Gold

The layout of Farmer John's farm is quite peculiar, with a large circular road
running around the perimeter of the main field on which his cows graze during
the day. Every morning, the cows cross this road on their way towards the
field, and every evening they all cross again as they leave the field and
return to the barn.
As we know, cows are creatures of habit, and they each cross the road the same
way every day. Each cow crosses into the field at a different point from where
she crosses out of the field, and all of these crossing points are distinct
from each-other. Farmer John owns $N$ cows, conveniently identified with the
integer IDs $1 \ldots N$, so there are precisely $2N$ crossing points around
the road. Farmer John records these crossing points concisely by scanning
around the circle clockwise, writing down the ID of the cow for each crossing
point, ultimately forming a sequence with $2N$ numbers in which each number
appears exactly twice. He does not record which crossing points are entry
points and which are exit points.
Looking at his map of crossing points, Farmer John is curious how many times
various pairs of cows might cross paths during the day. He calls a pair of
cows $(a,b)$ a "crossing" pair if cow $a$'s path from entry to exit must cross
cow $b$'s path from entry to exit. Please help Farmer John count the total
number of crossing pairs.

The first line of input contains $N$ ($1 \leq N \leq 50,000$), and the next
$2N$ lines describe the cow IDs for the sequence of entry and exit points
around the field.

Please print the total number of crossing pairs.