Dice Poker is a version of Poker that is played using Dice. Two or more people can play this
game. The detailed rules of the 2 player version of the game are mentioned in the section: Rules
of the Game.

Two players A and B are playing the game of Dice Poker. Being experts in this game, both
always play optimally. A always plays to maximize his chance of winning, and B tries to
minimize the chance of A winning (draw is fine for B). In the first round, Player A rolls the Dice,
followed by player B. You as an onlooker, look closely at the rolls and wonder what will A and
B do next, and what is the probability of A winning. Haven't played this game much before, you
decide to write a program to predict with what probability will A win this Game after the 2nd
(final) round.

Rules of the Game:-

In the first round, two players start of by rolling 5 dice each, one after the other. For this problem
we shall assume that all Dice are 6 sided and fair containing digits 1 to 6. Then a round of betting
happens, which is irrelevant to this problem statement. In the second round the first player picks
between 0 to 5 of his currently rolled dice and rolls them again. All the 5 dice are then merged
(merge here simply means that all the 5 dice are taken together to form a set, including the ones
rolled in the first round and are not re-rolled in the second) to form the final roll (or hand). Then
the second player looks at the final hand of the first player and then similarly re-rolls between 0
to 5 dice to get her final hand. The hands are then compared and one with the higher weight
wins.

In the real game, in case of a tie both the players share the pot, but since this problem specifically
asks for the probability of A winning, we shall assume that a tie is considered as A not winning
(hence B wins).

To determine which of the hands has higher weight, following arrangements are considered and
are in descending order of weight. The first arrangement beats the second and so on.

Arrangements:

• 
  5 of a kind: All the 5 dice show the same number. Example: 3, 3, 3, 3, 3


• 4 of a kind: 4 of the dice show the same number. Example: 2, 2, 2, 2, 5


• Full house (3 of a kind + 2 of a kind): 3 of the 5 show the same number and the rest 2
  show a different number. Example: 4, 4, 4, 6, 6


• Straight: All the 5 dice are in a sequence. Example: 1, 2, 3, 4, 5 (or the other possibility is
  2, 3, 4, 5, 6)


• 3 of a kind: 3 of the dice show the same number. Example: 6, 6, 6, 2, 4


• 2 Pair: There are 2 pairs. Example: 4, 4, 1, 1, 3


• Pair: 2 of the dice show the same number. Example: 3, 3, 1, 2, 4


• Rest: Example: 1, 2, 3, 4, 6

The highest weight arrangement that suits the hand is considered. For example a 5 of a kind is
also a 4 of a kind, but the player would naturally call it 5 of a kind. Also in a particular
arrangement, the higher weight arrangement is the one with the highest value of the most
significant part of the arrangement. If a the tie still remains then it is broken by the next
significant part and so on. For Example, In 4 of a kind the most significant part are the 4 dice
with the same number. So the arrangement 4, 4, 4, 4, 1 is better than 3, 3, 3, 3, 6. In 3 of a kind
the 3 with the same number is the most significant part. However in a 2 pair, there are 2 equally
significant parts, and the one with the highest number will be considered first for breaking the
tie. In the 'Rest' arrangement, first compare the highest numbers of the 2 hands, then the 2nd
highest and so on.