Rock-Paper-Scissors-Lizard-Spock
Daniel enjoys watching TV series. One of his favorite is "The Big Bang Theory". The main
characters of this series are: Sheldon – genius theoretical physicist, his friend Leonard – talented
experimental physicist, their attractive, blonde neighbor Penny, and also their friends an
aerospace engineer Howard and a particle astrophysicist Rajesh.
One time Rajesh tells Sheldon:
“I'll tell you what. How about we go rock-paper-scissors?”
“Ooh”, – Sheldon replies – “I don't think so. Anecdotal evidence suggests that in the game of
rock-paper-scissors, players familiar with each other will tie 75 to 80% of the time due to the
limited number of outcomes. I suggest rock-paper-scissors-lizard-Spock”.
“What?”
“It's very simple. Scissors cuts paper. Paper covers rock. Rock crushes lizard. Lizard poisons
Spock. Spock smashes scissors. Scissors decapitates lizard. Lizard eats paper. Paper disproves
Spock. Spock vaporizes rock. And as it always has, rock crushes scissors”.
“Okay, I think I got it”.
And the friends decided to play rock-paper-scissors-lizard-Spock. And we would determine what
the probability that Rajesh beats Sheldon in this game. We know the probabilities that any of the
friends choose any object in the game. Also we know that they play till two wins, so the winner of
the game is the person who first wins two rounds.
Input
The first line of input contains the number t - the number of tests. Next comes the description of t
tests. Each test case consists of two lines. The first line contains five integers RR, RSc, RP, RL,
RSp – the probabilities that Rajesh chooses rock, scissors, paper, lizard or Spock respectively.
The second line contains five integers SR, SSc, SP, SL, SSp – the probabilities that Sheldon
chooses rock, scissors, paper, lizard or Spock respectively. (Note: the order of the objects in the
input is rock, scissors, paper, lizard, Spock. The original problem is in Russian and we have
scissors before paper in Russian variant of the game. Otherwise the rules are the same.)
Constraints
1 <= t <= 500
0 <= RR, RSc, RP, RL, RSp <= 100, RR + RSc + RP + RL + RSp = 100
0 <= SR, SSc, SP, SL, SSp <= 100, SR + SSc + SP + SL + SSp = 100
Output
For each test case print the probability that Rajesh beats Sheldon in percent rounded to the
nearest integer.
Example
Input:
2
10 20 30 40 0
10 10 10 10 60
