Painting a line

$n$ segments of a number line were painted; segment $i$ is $[L_i, R_i]$. Segments may overlap or lie inside each other. Find the total length of the painted part of the line.

The first line contains $n$ ($1 \le n \le 10^5$). The next $n$ lines contain $L_i$ and $R_i$ ($-2 \cdot 10^9 \le L_i \le R_i \le 2 \cdot 10^9$).

A single number — the length of the painted part.

Sort the segments by their left end and walk through them, keeping the current union $[l, r]$. If the next segment has $L_i \le r$, it joins the union: $r = \max(r, R_i)$. Otherwise the length $r - l$ is added to the answer and a new union starts.

The point segment $[10, 10]$ has length $0$. The answer reaches $4 \cdot 10^9$, which does not fit into a 32-bit int.

Source: acmp.ru, problem 377.