Integrity: Find the Tampered File with sha256sum -c

A directory of config files ships with a SHA256SUMS manifest, but one file was modified after the manifest was made. Using /root/case/dist, report in three plain-text files (not directories), one answer each:

• /root/case/tampered.txt — the name of the file that fails verification, e.g. name.conf (the name.conf: FAILED line sha256sum -c prints is accepted too)
• /root/case/okcount.txt — how many files verify OK, as a number
• /root/case/total.txt — how many files were checked in total, as a number

The file set and which one is tampered vary per session. See /root/case/brief.txt.