Mia is a dice game for two players. Each roll consist of
two dice. Mia involves bluffing about what a player has rolled,
but in this problem we focus only on its scoring rules. Unlike
most other dice games, the score of a roll is not simply the
sum of the dice.
Instead, a roll is scored as follows:

Mia ($12$ or
$21$) is always
highest.

Next come doubles ($11$, $22$, and so on). Ties are broken
by value, with $66$
being highest.

All remaining rolls are sorted such that the highest
number comes first, which results in a twodigit number.
The value of the roll is the value of that number, e.g.
$3$ and $4$ becomes $43$.
Player $1$ and
$2$ each roll two dice.
You are asked to compute the odds that player 1 will win given
partial knowledge of both rolls.
Input
The input will contain multiple, different test cases. Each
test case contains on a single line four symbols $s_0 \ s_1 \ r_0 \ r_1$ where
$s_0 \ s_1$ represent the
dice rolled by player $1$
and $r_0 \ r_1$ represents
the dice rolled by player $2$. A ‘*’
represents that the value is not known, otherwise a digit
represents the value of the dice. The input will be terminated
by a line containing $4$
zeros.
Output
For each test case output the odds that player $1$ will win. If the odds are
$0$ or $1$, output $0$ or $1$. Otherwise, output the odds in the
form $a/b$ where
$a$ and $b$ represent the nominator and
denominator of a reduced fraction (i.e., in lowest terms).
Sample Output Explanation
For * * 1 2, the best player
$1$ can do is tie, so his
chance of winning is $0$.
For 1 2 * *, player $1$ wins unless player $2$ rolls a Mia, which happens
$1$ out of $18$ times. For 1
2 1 3, 3 1 2 1, and 6 6 6 6 the result is already known. For
* 2 2 2, player $1$ wins only if she rolls a
$1$. For * 2 * 6, player $1$ wins if he rolls a $1$. If he rolls a $2$, he wins with probability
$5/6$. He loses if he
rolls a $3$, $4$, or $5$. If he rolls a $6$ he wins only if player
$2$ rolls a $1$. Thus, his chance of winning is
$1/6 + 5/6 \cdot 1/6 + 1/6 \cdot
1/6 = 12/36 = 1/3$. When no dice are known, Player
$1$ will win in
$615$ of all possible
$1\, 296$ outcomes. Player
$2$ will lose in
$615$ cases, and there are
$66$ possible ties. Thus,
her chance of winning is $615/1296 = 205/432$.
Sample Input 1 
Sample Output 1 
* * 1 2
1 2 * *
1 2 1 3
3 1 2 1
6 6 6 6
* 2 2 2
* 2 * 6
* * * *
0 0 0 0

0
17/18
1
0
0
1/6
1/3
205/432
