P8591 "JROI-8" Traumatic Brain Injury 2.0.

Given $n$ line segments, where the $i$-th segment is $[l_i,r_i]$. Color each segment either red or black, with the following requirements: 1. Any two red segments do not intersect. 2. Any black segment intersects with **at least** one red segment. Minimize the total length of the red segments, and output this total length. The length of a segment $[l_i,r_i]$ is defined as $r_i-l_i$. Two segments $[l_i,r_i]$ and $[l_j,r_j]$ intersect **if and only if** $l_i\le r_j$ and $l_j\le r_i$.

The first line contains one positive integer $n$. The next $n$ lines each contain two integers $l_i,r_i$, separated by a space.

Output one non-negative integer, representing the minimum possible total length of the red segments.

**Constraints** | Test Point ID | $n\le$ | | :----------: | :----------: | | $1\sim4$ | $10$ | | $5\sim8$ | $400$ | | $9\sim20$ | $3000$ | For all testdata, $-10^9\le l_i