Back in my day, we were allowed to have
snowball fights during recess. Me and my two friends would
split up, build a fort, and stock it with snowballs. When the
fighting started, we threw snowballs at each other’s forts
until there was one left standing. Those were the days.
There are three forts labelled A,
B, and C
that appear in a circle: with B to
the left of A, C to the left of B,
and A to the left of C.
The strengths of the forts are represented as nonnegative
integers. If the strength of a fort is $0$, then it is just rubble and the
person in that fort no longer throws snowballs.
The fight proceeds in rounds. Each round, each person in a
non-rubble fort picks a target. Their target is the fort with
highest strength, apart from their own. If both possible
targets have the same strength, the person chooses the fort on
their left as the target. The people then simultaneously throw
a single snowball at their chosen target. Each snowball reduces
the strength of the target fort by $1$. This repeats until there is at
most one fort that is not reduced to rubble.
Given the initial strengths of the three forts, you are to
determine if there is a fort that is not reduced to rubble and,
if so, the remaining strength of that fort.
Input
Input contains a single line containing three integers
$N_ A$ ($1 \leq N_ A \leq 10^{18}$), which is
the initial strength of fort A,
$N_ B$ ($1 \leq N_ B \leq 10^{18}$), which is
the initial strength of fort B, and
$N_ C$ ($1 \leq N_ C \leq 10^{18}$), which is
the initial strength of fort C.
Output
If all forts are reduced to rubble, display Rubble!. Otherwise, display A, B, or C indicating which fort was left standing
followed by the remaining strength of that fort.
| Sample Input 1 |
Sample Output 1 |
10 3 1
|
A 3
|
| Sample Input 2 |
Sample Output 2 |
3 2 1
|
Rubble!
|
| Sample Input 3 |
Sample Output 3 |
2 3 2
|
C 1
|
| Sample Input 4 |
Sample Output 4 |
100 101 100
|
A 1
|
| Sample Input 5 |
Sample Output 5 |
100 99 100
|
Rubble!
|
| Sample Input 6 |
Sample Output 6 |
1000 5000 1000
|
B 1001
|
| Sample Input 7 |
Sample Output 7 |
2000 1000 1000
|
C 1
|
| Sample Input 8 |
Sample Output 8 |
1000000000000000 2000000000000000 4000000000000000
|
B 1
|
| Sample Input 9 |
Sample Output 9 |
1000000000000000 2000000000000000 4000000000000001
|
Rubble!
|
