--- Part Two ---
The engineers are surprised by the low number of safe reports until they realize they forgot to tell you about the Problem Dampener.

The Problem Dampener is a reactor-mounted module that lets the reactor safety systems tolerate a single bad level in what would otherwise be a safe report. It's like the bad level never happened!

Now, the same rules apply as before, except if removing a single level from an unsafe report would make it safe, the report instead counts as safe.

More of the above example's reports are now safe:

7 6 4 2 1: Safe without removing any level.
1 2 7 8 9: Unsafe regardless of which level is removed.
9 7 6 2 1: Unsafe regardless of which level is removed.
1 3 2 4 5: Safe by removing the second level, 3.
8 6 4 4 1: Safe by removing the third level, 4.
1 3 6 7 9: Safe without removing any level.
Thanks to the Problem Dampener, 4 reports are actually safe!

Update your analysis by handling situations where the Problem Dampener can remove a single level from unsafe reports. How many reports are now safe?