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Up until now headers were removed from |sources| and then
reinserted. Cleaner/easier is to never remove them from the start.

Change-Id: I8f7560ef96f409880647e2924c2f71317f519468
Reviewed-on: https://chromium-review.googlesource.com/c/1290969Reviewed-by: Dirk Pranke <dpranke@chromium.org>
Commit-Queue: Daniel Bratell <bratell@opera.com>
Cr-Commit-Position: refs/heads/master@{#602363}