Solve the following sql problem:
List all the load shapes of all head cars of each train and identify which load shape has the highest number. Calculate the percentage of the trains with the said head car that are running eas

Schema:
SCHEMA:
- Table: cars
  - Column: id
    - Samples: [1, 2, 3, 4, 5]
  - Column: train_id
    - Samples: [1, 1, 1, 1, 2]
  - Column: position
    - Samples: [1, 2, 3, 4, 1]
  - Column: shape
    - Samples: [rectangle, rectangle, rectangle, rectangle, rectangle]
  - Column: len
    - Samples: [short, long, short, long, short]
  - Column: sides
    - Samples: [not_double, not_double, not_double, not_double, not_double]
  - Column: roof
    - Samples: [none, none, peaked, none, flat]
  - Column: wheels
    - Samples: [2, 3, 2, 2, 2]
  - Column: load_shape
    - Samples: [circle, hexagon, triangle, rectangle, circle]
  - Column: load_num
    - Samples: [1, 1, 1, 3, 2]
- Table: trains
  - Column: id
    - Samples: [1, 2, 3, 4, 5]
  - Column: direction
    - Samples: [east, east, east, east, east]

SELECT DISTINCT T3.load_shape FROM ( SELECT load_shape, train_id FROM cars WHERE position = 1 ORDER BY train_id DESC ) AS T3 UNION ALL SELECT T4.load_shape FROM ( SELECT load_shape, train_id FROM cars WHERE position = 1 ORDER BY train_id DESC LIMIT 1 ) AS T4 UNION ALL SELECT (CAST(COUNT(DISTINCT CASE WHEN T2.direction = 'east' THEN T2.id ELSE NULL END) AS REAL) * 100 / COUNT(DISTINCT T2.id)) FROM cars AS T1 INNER JOIN trains AS T2 ON T1.train_id = T2.id WHERE T1.position = 1 AND T1.load_shape = ( SELECT T4.load_shape FROM ( SELECT load_shape, train_id FROM cars AS T WHERE position = 1 ORDER BY train_id DESC LIMIT 1 ) AS T4 )