A13630 | Universal Solution

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.

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 $2 \cdot 10^5$ .

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.