You've been asked to organize a Rock-Paper-Scissors tournament. The tournament
will have a single-elimination format and will run for **N** rounds;
2** ^{N}** players will participate.

Initially, the players will be lined up from left to right in some order that you specify. In each round, the first and second players in the lineup (starting from the left) will play a match against each other, and the third and fourth players in the lineup (if they exist) will play a match against each other, and so on; all of these matches will occur simultaneously. The winners of these matches will remain in the lineup, in the same relative order, and the losers will leave the lineup and go home. Then a new round will begin. This will continue until only one player remains in the lineup; that player will be declared the winner.

In each Rock-Paper-Scissors match, each of the two players secretly chooses
one of *Rock*, *Paper*, or *Scissors*, and then they compare
their choices. Rock beats Scissors, Scissors beats Paper, and Paper beats Rock.
If one player's choice beats the other players's choice, then that
player wins and the match is over. However, if the players make the
same choice, then it is a tie, and they must choose again and keep playing
until there is a winner.

You know that the players this year are stubborn and not very strategic.
Each one has a *preferred move* and will only play that move in every
match, regardless of what the opponent does. Because of this, if two
players with the same move go up against each other, they will keep tying
and their match will go on forever! If this happens, the tournament will never
end and you will be a laughingstock.

This year, there are **R** players who prefer Rock, **P** players
who prefer Paper, and **S** players who prefer Scissors. Knowing this,
you want to create a lineup that guarantees that the tournament will go to
completion and produce a single winner — that is, no match will ever be a
tie. Your boss has asked you to produce a list of all such lineups (written
in left to right order, with `R`

, `P`

, and `S`

standing for players who prefer Rock, Paper, and Scissors, respectively),
and then put that list in alphabetical order.

You know that the boss will lazily pick the first lineup on the list; what will
that be? Or do you have to tell your boss that it is `IMPOSSIBLE`

to
prevent a tie?

The first line of the input gives the number of test cases, **T**. **T**
lines follow; each represents one test case. Each test case consists of four
integers: **N**, **R**, **P**, and **S**, as described in the
statement above.

For each test case, output one line containing `Case #x: y`

, where
`x`

is the test case number (starting from 1) and `y`

is
either `IMPOSSIBLE`

or a string of length 2** ^{N}**
representing the alphabetically earliest starting lineup that solves the
problem. Every character in a lineup must be

`R`

, `P`

, or
`S`

, and there must be `R`

s, `P`

s, and `S`

s.
**R** + **P** + **S** = 2** ^{N}**.

0 ≤

0 ≤

0 ≤

1 ≤ **T** ≤ 25.

1 ≤ **N** ≤ 3.

1 ≤ **T** ≤ 75.

1 ≤ **N** ≤ 12.

Input |
Output |

4 1 1 1 0 1 2 0 0 2 1 1 2 2 2 0 2 |
Case #1: PR Case #2: IMPOSSIBLE Case #3: PSRS Case #4: IMPOSSIBLE |

In sample case #1, there are only two players and the tournament will
consist of one round. It doesn't matter what order the two line up in; the
Paper-using player will defeat the Rock-using player. You will give
your boss the alphabetically ordered list `PR`

, `RP`

, and
the first element is `PR`

.

In sample case #2, the only two players both play Rock, so a tie is
unavoidable.

In sample case #3, there are four players and the tournament will go on for two
rounds. In the first round, the first player (Paper) will lose to the second
player (Scissors), and the third player (Rock) will defeat the fourth player
(Scissors). The second round lineup will be `PR`

, and the first
remaining player (Paper) will defeat the other remaining player (Rock), so the
tournament will end with a winner and no ties.

Here is an illustration of the tournament for sample case #3:

Other lineups such as

`PSSR`

will appear on the list you give to
your boss, but `PSRS`

is alphabetically first.
In sample case #4, the only way to organize the first round such that there are no ties is to create two matches with one Rock player and one Scissors player. But both of those matches will have a Rock winner, and when these two winners go on to face each other, there will be a tie.

Points | Correct | Attempted |
---|---|---|

4pt | 2295 | 2407 |

14pt | 1866 | 2139 |