Air speed of a fully laden swallow

What is the air speed velocity of a fully laden swallow? This fearful question was put to a band of Grail searchers, and their answer, "African or European?", was only partly right. The air speed does depend on the sub-species of swallow. Fearing more questioning in this vein, King Arthur ordered his royal mathematicians to determine the air speed of a fully laden swallow, both African and European.

The mathematicians called on the royal birders to capture a number of swallows of both types, lade them fully, release them from point A, and time their arrival at point B. To keep the two sets of figures apart, the African and European swallows started from different locations, so the two groups flew different distances, while every swallow within one group flew the same distance. The royal map makers then measured both distances in furlongs. Using ten swallows of each type, the mathematicians wanted the average air speed of each group.

The mathematicians cannot agree on how the average should be calculated.

• Method 1: add up the distance covered by all ten swallows of one type, then divide it by the total of their times.
• Method 2: compute the speed of each swallow, add those ten speeds, then divide by ten.

Compute the average both ways, so that no nasty falling out breaks out among the royal mathematicians.

The data is somewhat disorganized. The two breeds are intermixed and the capitalization is inconsistent. Each entry sits on a separate line and begins with a single letter, A or a for African and E or e for European, followed by a single space. The final datum on the line is the elapsed time that swallow flew, in hours. Time keeping of the era was not very accurate, so this value is a real number greater than 0 with a single digit after the decimal point. 1.5 means one and a half hours, and 0.4 means four tenths of an hour.

The first line has two integers greater than 0, separated by a single space. The first integer is the distance the African swallows flew, and the second is the distance the European swallows flew.

Next come the times for the swallows, one per line, 20 lines in total: 10 for African swallows and 10 for European swallows, intermixed in no particular order. The input is 21 lines in total.

Group the output by method and print Method 1 first. Each method produces 3 lines.

• Line 1: the name of the method with the digit that identifies it, so Method 1 or Method 2.
• Line 2: the speed of a fully laden African swallow in furlongs per hour, in the form African: 3.00 furlongs per hour.
• Line 3: the speed of a fully laden European swallow in furlongs per hour, in the form European: 3.00 furlongs per hour.

A speed line is built in this order:

• the full name of the breed of swallow, capitalized, beginning with African
• a colon
• a single space
• the speed to two decimal places, rounded at the third decimal place, with an exact half rounded up, and a leading 0 for values below 1.0
• a single space
• the phrase furlongs per hour