Problem Statement 
 You are running a local tournament with 8 competitors.
The tournament will consist of 3 rounds and will be organized as follows.
In round 1 game i is played between competitors 2*i and 2*i+1 (0<=i<=3). 4 winning competitors advance to round 2.
In round 2 game i is played between the winners of games 2*i and 2*i+1 (0<=i<=1). 2 winning competitors advance to round 3.
Finally, the winners of round 2 games play one game in round 3 to determine the winner of the tournament.
You are given a int[] P describing the percent probabilities of each competitor winning a game against another competitor. The first 7 elements of P are the probabilities of competitor 0 winning a game against competitors 1 through 7, the next 6 elements are the probabilities of competitor 1 winning a game against competitors 2 through 7, etc.
Return a double[] containing exactly 8 elements, where the ith element is the probability of competitor i winning the tournament. 

Definition 
 Class:  TournamentWinner  Method:  winningProbabilities  Parameters:  int[]  Returns:  double[]  Method signature:  double[] winningProbabilities(int[] P)  (be sure your method is public) 




Notes 
  The games played in the tournament will not end in a tie. 
  Each element of your return must have an absolute or relative error less than 1e9. 

Constraints 
  P will contain exactly 28 elements. 
  Each element of P will be between 0 and 100, inclusive. 

Examples 
0)  
 {5, 0, 10, 15, 20, 25, 30,
0, 35, 40, 45, 50, 55,
100, 100, 100, 100, 100,
60, 65, 70, 75,
80, 85, 90,
95, 50,
50} 
 Returns: {0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 }  Competitor 2 wins a game against any other competitor with probability 1.0, so he will win the tournament, leaving no chances to other competitors. 


1)  
 {100, 25, 0, 25, 25, 25, 25,
25, 25, 25, 25, 25, 25,
0, 25, 25, 25, 25,
50, 25, 25, 25,
100, 25, 100,
25, 25,
0} 
 Returns: {0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0 }  In round 1, players 0, 3, 4 and 7 win against players 1, 2, 5 and 6, respectively. In round 2, 3 wins against 0 and 4 wins against 7. Finally, both 3 and 4 have a 50% chance to win against the opponent in round 3 and to win the tourney. 


2)  
 {50, 50, 50, 50, 50, 50, 50,
50, 50, 50, 50, 50, 50,
50, 50, 50, 50, 50,
50, 50, 50, 50,
50, 50, 50,
50, 50,
50} 
 Returns: {0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125 }  All competitors have equal chances. 


3)  
 {100, 50, 50, 50, 50, 50, 50,
0, 50, 50, 50, 50, 50,
100, 50, 50, 50, 50,
0, 50, 50, 50,
100, 50, 50,
0, 50,
100} 
 Returns: {0.25, 0.0, 0.25, 0.0, 0.25, 0.0, 0.25, 0.0 }  Competitors 0, 2, 4 and 6 win their games in round 1 and have equal chances in later rounds. 


4)  
 { 50, 50, 50, 50, 50, 50, 50,
50, 50, 50, 50, 50, 50,
50, 50, 50, 50, 50,
50, 50, 50, 50,
100, 100, 100,
10, 20,
30} 
 Returns: {0.125, 0.125, 0.125, 0.125, 0.5, 0.0, 0.0, 0.0 }  Competitor 4 will get to round 3 for sure, while competitors 0, 1, 2 and 3 have equal chances to get to round 3. 


5)  
 { 1, 2, 4, 7, 11, 16, 22,
3, 5, 8, 12, 17, 23,
6, 9, 13, 18, 24,
10, 14, 19, 25,
15, 20, 26,
21, 27,
28} 
 Returns:
{6.88919608E5, 0.009061234459199999, 0.011498979459599998, 0.1853675541204, 0.0328889066112, 0.18542493028680002, 0.17985791390280004, 0.3958315891991999 }  
