Problem Statement

There are $2N$ pairwise distinct points, numbered from $1$ to $2N$, on a circle. Starting from point $1$ and going clockwise, the points are arranged as point $2$, point $3$, ..., point $2N$.

You are given $N$ chords on this circle. The endpoints of the $i$-th chord are points $A_i$ and $B_i$, and the $2N$ values $A_1,\ldots,A_N,B_1,\ldots,B_N$ are all distinct.

Perform the following operations on this circle once each in order:

1. Among the $N$ chords on the circle, choose any number of chords such that no two chosen chords intersect, and delete the remaining chords.
2. Add one chord freely to the circle.

Find the maximum possible number of intersection points between chords after the operations are completed.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $1 \leq A_i,B_i \leq 2N$
• The $2N$ values $A_1, \ldots, A_N,B_1,\ldots,B_N$ are pairwise distinct.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 B_1
A_2 B_2
\vdots
A_N B_N

Output

Output the answer.