Solve the following sql problem:
What is the average number of dishes per menu in the Souper de Luxe menus? Identify what is the name of the dish that appeared the most in all of its menus.

Schema:
SCHEMA:
- Table: Dish
  - Column: id
    - Samples: [1, 2, 3, 4, 5]
  - Column: name
    - Samples: [Consomme printaniere royal, Chicken gumbo, Tomato aux croutons, Onion au gratin, St. Emilion]
  - Column: description
    - Samples: [None, None, None, None, None]
  - Column: menus_appeared
    - Samples: [8, 111, 14, 41, 66]
  - Column: times_appeared
    - Samples: [8, 117, 14, 41, 68]
  - Column: first_appeared
    - Samples: [1897, 1895, 1893, 1900, 1881]
  - Column: last_appeared
    - Samples: [1927, 1960, 1917, 1971, 1981]
  - Column: lowest_price
    - Samples: [0.2, 0.1, 0.25, 0.25, 0.0]
  - Column: highest_price
    - Samples: [0.4, 0.8, 0.4, 1.0, 18.0]
- Table: Menu
  - Column: id
    - Samples: [12463, 12464, 12465, 12466, 12467]
  - Column: name
    - Samples: [None, , None, , ]
  - Column: sponsor
    - Samples: [HOTEL EASTMAN, REPUBLICAN HOUSE, NORDDEUTSCHER LLOYD BREMEN, NORDDEUTSCHER LLOYD BREMEN, NORDDEUTSCHER LLOYD BREMEN]
  - Column: event
    - Samples: [BREAKFAST, [DINNER], FRUHSTUCK/BREAKFAST;, LUNCH;, DINNER;]
  - Column: venue
    - Samples: [COMMERCIAL, COMMERCIAL, COMMERCIAL, COMMERCIAL, COMMERCIAL]
  - Column: place
    - Samples: [HOT SPRINGS, AR, MILWAUKEE, [WI];, DAMPFER KAISER WILHELM DER GROSSE;, DAMPFER KAISER WILHELM DER GROSSE;, DAMPFER KAISER WILHELM DER GROSSE;]
  - Column: physical_description
    - Samples: [CARD; 4.75X7.5;, CARD; ILLUS; COL; 7.0X9.0;, CARD; ILLU; COL; 5.5X8.0;, CARD; ILLU; COL; 5.5X8.0;, FOLDER; ILLU; COL; 5.5X7.5;]
  - Column: occasion
    - Samples: [EASTER;, EASTER;, , , ]
  - Column: notes
    - Samples: [, WEDGEWOOD BLUE CARD; WHITE EMBOSSED GREEK KEY BORDER; "EASTER SUNDAY" ..., MENU IN GERMAN AND ENGLISH; ILLUS, STEAMSHIP AND SAILING VESSEL;, MENU IN GERMAN AND ENGLISH; ILLUS, HARBOR SCENE WITH SAILING VESSEL;, MENU IN GERMAN AND ENGLISH; ILLUS, HARBOR SCENE WITH ROCKS AND LIGHTHO... (truncated)]
  - Column: call_number
    - Samples: [1900-2822, 1900-2825, 1900-2827, 1900-2828, 1900-2829]
  - Column: keywords
    - Samples: [None, None, None, None, None]
  - Column: language
    - Samples: [None, None, None, None, None]
  - Column: date
    - Samples: [1900-04-15, 1900-04-15, 1900-04-16, 1900-04-16, 1900-04-16]
  - Column: location
    - Samples: [Hotel Eastman, Republican House, Norddeutscher Lloyd Bremen, Norddeutscher Lloyd Bremen, Norddeutscher Lloyd Bremen]
  - Column: location_type
    - Samples: [None, None, None, None, None]
  - Column: currency
    - Samples: [None, None, None, None, None]
  - Column: currency_symbol
    - Samples: [None, None, None, None, None]
  - Column: status
    - Samples: [complete, complete, complete, complete, complete]
  - Column: page_count
    - Samples: [2, 2, 2, 2, 4]
  - Column: dish_count
    - Samples: [67, 34, 84, 63, 33]
- Table: MenuPage
  - Column: id
    - Samples: [119, 120, 121, 122, 123]
  - Column: menu_id
    - Samples: [12460, 12460, 12460, 12460, 12461]
  - Column: page_number
    - Samples: [1, 2, 3, 4, 1]
  - Column: image_id
    - Samples: [1603595.0, 1603596.0, 1603597.0, 1603598.0, 1603591.0]
  - Column: full_height
    - Samples: [7230, 5428, 7230, 7230, 7230]
  - Column: full_width
    - Samples: [5428, 7230, 5428, 5428, 5428]
  - Column: uuid
    - Samples: [510d47e4-2955-a3d9-e040-e00a18064a99, 510d47e4-2956-a3d9-e040-e00a18064a99, 510d47e4-2957-a3d9-e040-e00a18064a99, 510d47e4-2958-a3d9-e040-e00a18064a99, 510d47e4-2959-a3d9-e040-e00a18064a99]
- Table: MenuItem
  - Column: id
    - Samples: [1, 2, 3, 4, 5]
  - Column: menu_page_id
    - Samples: [1389, 1389, 1389, 1389, 3079]
  - Column: price
    - Samples: [0.4, 0.6, 0.4, 0.5, 0.5]
  - Column: high_price
    - Samples: [None, None, None, None, 1.0]
  - Column: dish_id
    - Samples: [1, 2, 3, 4, 5]
  - Column: created_at
    - Samples: [2011-03-28 15:00:44 UTC, 2011-03-28 15:01:13 UTC, 2011-03-28 15:01:40 UTC, 2011-03-28 15:01:51 UTC, 2011-03-28 15:21:26 UTC]
  - Column: updated_at
    - Samples: [2011-04-19 04:33:15 UTC, 2011-04-19 15:00:54 UTC, 2011-04-19 19:10:05 UTC, 2011-04-19 19:07:01 UTC, 2011-04-13 15:25:27 UTC]
  - Column: xpos
    - Samples: [0.111429, 0.438571, 0.14, 0.377143, 0.105714]
  - Column: ypos
    - Samples: [0.254735, 0.254735, 0.261922, 0.26272, 0.313178]

SELECT COUNT(*), T1.dish_id FROM MenuItem AS T1 INNER JOIN MenuPage AS T2 ON T1.menu_page_id = T2.id INNER JOIN Menu AS T3 ON T2.menu_id = T3.id INNER JOIN Dish AS T4 ON T1.dish_id = T4.id WHERE T3.name = 'Souper de Luxe' GROUP BY T3.id ORDER BY COUNT(T1.dish_id) DESC LIMIT 1