Four Quarters

Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

Description

Four Quarters is a game of chance played with, well, four quarters. Two people, called A and B, each flip two quarters each round. They each gain or lose points each round based on the following tables:

Player B
Player A HH HT TT
HH 1 1 2
HT 0 0 1
TT -1 0 0


Player A's payoff

Player B
Player A HH HT TT
HH 0 -1 -1
HT 1 0 0
TT 2 0 -1

Player B's payoff

There is no difference between Heads/Tails and Tails/Heads. As you can see, the odds are stacked in Player A's favor. At the beginning of the game, each player has 0 points, and points accumulate as the game progresses. At the end of the game, whichever player has the most points wins.

You must write a program that determines the probability that Player A will win, Player B will win, or they will tie, after a certain number of rounds. Assume that the coins are fair, i.e. that heads and tails are equally likely.


Input

There is no input file for this problem.


Output

Output a table that lists the probability that Player A will win, B will win, or they will tie, after each round for 1 to 20 rounds. The output for rounds 1 through 3 is given below.

Probabilities must be expressed as a percent, with 4 places after the decimal.


Sample Input

Round   A wins    B wins    Tie
    1   43.7500%  18.7500%  37.5000%
    2   56.6406%  22.2656%  21.0938%
    3   62.3535%  22.7051%  14.9414%

Sample Output

None

Hint

None

Source

Greater New York 2002

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