Universal Solution

题意翻译

- 有一个剪刀石头布的AI，以指定的顺序出手势。但是你并不知道他从这个顺序的哪里开始，所以请给出一个另一个顺序，使得你的期望胜利次数最大。 - R: 石头 S: 剪刀 P:布 - 石头赢剪刀，剪刀赢布，布赢石头

题目描述

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.

输入输出格式

输入格式

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 $ .

输出格式

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.

输入输出样例

输入样例 #1

3
RRRR
RSP
S

输出样例 #1

PPPP
RSP
R

说明

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: