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This patch removes use of filesystem's FileWriterCallback.  The
motivation is the same as https://crrev.com/844307 .

Bug: 778580
Change-Id: I69866c23290627a84ddedbaceaeae80b584b46e7
Reviewed-on: https://chromium-review.googlesource.com/886762Reviewed-by: Kentaro Hara <haraken@chromium.org>
Reviewed-by: Hitoshi Yoshida <peria@chromium.org>
Commit-Queue: Yuki Shiino <yukishiino@chromium.org>
Cr-Commit-Position: refs/heads/master@{#532362}