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This is a reland of 9594a943

Original change's description:
> [FileSystem] Add support for selecting multiple files or directories.
>
> Bug: 878581
> Change-Id: I65fc0029da2e3951495a6cd96704085e5c1b942c
> Reviewed-on: https://chromium-review.googlesource.com/1227366
> Reviewed-by: Daniel Cheng <dcheng@chromium.org>
> Reviewed-by: Daniel Murphy <dmurph@chromium.org>
> Commit-Queue: Marijn Kruisselbrink <mek@chromium.org>
> Cr-Commit-Position: refs/heads/master@{#594132}

Tbr: dmurph@chromium.org, dcheng@chromium.org
Bug: 878581
Change-Id: Ic145a6b48279f29368fbbc802751eb3d43b4ef4c
Reviewed-on: https://chromium-review.googlesource.com/c/1265058Reviewed-by: Marijn Kruisselbrink <mek@chromium.org>
Commit-Queue: Marijn Kruisselbrink <mek@chromium.org>
Cr-Commit-Position: refs/heads/master@{#597233}