Merging Intervals

You are given $N$ closed intervals $[l_i,r_i]$.

Choose two distinct intervals. Find the maximum possible length of their union.

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

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

For each test case, print the maximum possible length of the union of two intervals on one line.

• $1 \leq T \leq 100$.
• $2 \leq N \leq 200\,000$.
• $0\le l_i\le r_i\le$ ().