Back up and restore the set of enabled IMEs

The restored set of enabled IMEs/subtypes is merged into the
current state of the system, rather than simply replacing it.
This is because we do not want to accidentally disable or
reconfigure something that the user is currently relying on.

There's a certain amount of repetitive activity here, rebuilding
the enabled-state data structures in a different format, but it's
important for maintainability that the restore code be able to
rely on the core InputMethodUtils implementation of reading/writing
the settings element.

Bug 19822542

Change-Id: If0104151b3526da6ecc669adde3119a239ecafeb
diff --git a/core/java/android/provider/Settings.java b/core/java/android/provider/Settings.java
index e6b39b5..de536bd 100644
--- a/core/java/android/provider/Settings.java
+++ b/core/java/android/provider/Settings.java
@@ -5375,6 +5375,7 @@
             BACKUP_AUTO_RESTORE,
             ENABLED_ACCESSIBILITY_SERVICES,
             ENABLED_NOTIFICATION_LISTENERS,
+            ENABLED_INPUT_METHODS,
             TOUCH_EXPLORATION_GRANTED_ACCESSIBILITY_SERVICES,
             TOUCH_EXPLORATION_ENABLED,
             ACCESSIBILITY_ENABLED,