Sort input methods names in the language selector by language names.

chrome/browser/chromeos/options/language_config_view.h

Index: chrome/browser/chromeos/options/language_config_view.h
diff --git a/chrome/browser/chromeos/options/language_config_view.h b/chrome/browser/chromeos/options/language_config_view.h
index 0a67fc67bdfee7f5f6813e6e9a13c900077d3866..72f636ad90ec88a3f0bd54546d1cfc5a0b97f649 100644
--- a/chrome/browser/chromeos/options/language_config_view.h
+++ b/chrome/browser/chromeos/options/language_config_view.h
@@ -136,10 +136,16 @@ class LanguageConfigView : public TableModel,
       const std::string& language_code);
 
   // Sorts the given language codes by their corresponding language names,
-  // using the unicode string comparator.
+  // using the unicode string comparator. Uses unstable sorting.
   static void SortLanguageCodesByNames(
       std::vector<std::string>* language_codes);
 
+  // Sorts the given input method ids by their corresponding language names,
+  // using the unicode string comparator. Uses stable sorting.
+  static void SortInputMethodIdsByNames(
+      const std::map<std::string, std::string>& id_to_language_code_map,
+      std::vector<std::string>* input_method_ids);
+
   // Reorders the given input method ids for the language code. For
   // example, if |language_codes| is "fr" and |input_method_ids| contains
   // ["xkb:be::fra", and "xkb:fr::fra"], the list is reordered to