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JR Shikoku expected to resume service on all the affected lines by Mid September. Recovery cost is expected to.hit 2 Billion Yen in addition to 1 Billion Yen lost of revenue.
For JR Kyushu, among affected lines, only a segment in the Haruda line section of Chikuho Main Line remain closed. However, as part of the segment suffer from many damages, it will "take times" for the recovery work to be completed.
(Looking at the news, it seems like there was a JR Kyushu train derailed due to landslide during the rain last month [which have no passenger], however they didn't notify the prefectural government about the incident?)
For JR Central, Takayama Main Line is affected. A segment of the line, as well as operation of the special express train Hida, will partially resume service on 11th August, however a few more month will be needed before the entire line can be recovered.
And then for non-JR companies, Ibara Railway, Kyoto Tango Railways, Heisei Chikuho Railways, and Nishikigawa Railways are still affected.