Universal Solution

2000ms

262144K

Description:

Recently, you found a bot to play "Rock paper scissors" with. Unfortunately, the bot uses quite a simple algorithm to play: he has a string $$$s = s_1 s_2 \dots s_{n}$$$ of length $$$n$$$ where each letter is either R, S or P.

While initializing, the bot is choosing a starting index $$$pos$$$ ($$$1 \le pos \le n$$$), and then it can play any number of rounds. In the first round, he chooses "Rock", "Scissors" or "Paper" based on the value of $$$s_{pos}$$$:

if $$$s_{pos}$$$ is equal to R the bot chooses "Rock";
if $$$s_{pos}$$$ is equal to S the bot chooses "Scissors";
if $$$s_{pos}$$$ is equal to P the bot chooses "Paper";

In the second round, the bot's choice is based on the value of $$$s_{pos + 1}$$$. In the third round — on $$$s_{pos + 2}$$$ and so on. After $$$s_n$$$ the bot returns to $$$s_1$$$ and continues his game.

You plan to play $$$n$$$ rounds and you've already figured out the string $$$s$$$ but still don't know what is the starting index $$$pos$$$. But since the bot's tactic is so boring, you've decided to find $$$n$$$ choices to each round to maximize the average number of wins.

In other words, let's suggest your choices are $$$c_1 c_2 \dots c_n$$$ and if the bot starts from index $$$pos$$$ then you'll win in $$$win(pos)$$$ rounds. Find $$$c_1 c_2 \dots c_n$$$ such that $$$\frac{win(1) + win(2) + \dots + win(n)}{n}$$$ is maximum possible.

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

Next $$$t$$$ lines contain test cases — one per line. The first and only line of each test case contains string $$$s = s_1 s_2 \dots s_{n}$$$ ($$$1 \le n \le 2 \cdot 10^5$$$; $$$s_i \in \{\text{R}, \text{S}, \text{P}\}$$$) — the string of the bot.

It's guaranteed that the total length of all strings in one test doesn't exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, print $$$n$$$ choices $$$c_1 c_2 \dots c_n$$$ to maximize the average number of wins. Print them in the same manner as the string $$$s$$$.

If there are multiple optimal answers, print any of them.

Sample Input:

3
RRRR
RSP
S

Sample Output:

PPPP
RSP
R

Note:

In the first test case, the bot (wherever it starts) will always choose "Rock", so we can always choose "Paper". So, in any case, we will win all $$$n = 4$$$ rounds, so the average is also equal to $$$4$$$.

In the second test case:

if bot will start from $$$pos = 1$$$, then $$$(s_1, c_1)$$$ is draw, $$$(s_2, c_2)$$$ is draw and $$$(s_3, c_3)$$$ is draw, so $$$win(1) = 0$$$;
if bot will start from $$$pos = 2$$$, then $$$(s_2, c_1)$$$ is win, $$$(s_3, c_2)$$$ is win and $$$(s_1, c_3)$$$ is win, so $$$win(2) = 3$$$;
if bot will start from $$$pos = 3$$$, then $$$(s_3, c_1)$$$ is lose, $$$(s_1, c_2)$$$ is lose and $$$(s_2, c_3)$$$ is lose, so $$$win(3) = 0$$$;

The average is equal to $$$\frac{0 + 3 + 0}{3} = 1$$$ and it can be proven that it's the maximum possible average.

A picture from Wikipedia explaining "Rock paper scissors" game:

$\text{[math]}$

Informação

Provedor Codeforces

Código CF1380B