[DevTools] Move Input domain implementation to browser.
[DevTools] Move Input domain implementation to browser.

BUG=472077

Review URL: https://codereview.chromium.org/1055373003

git-svn-id: bf5cd6ccde378db821296732a091cfbcf5285fbd@193141 bbb929c8-8fbe-4397-9dbb-9b2b20218538

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