Rock-Paper-Scissors is a game for two players. It is played in rounds. During each round, every player chooses one of three moves: Rock, Paper, or Scissors. Depending on the chosen moves, the following happens:

- if one player chooses Rock and the other player chooses Paper, the player who chooses Paper wins and gets a point;
- if one player chooses Scissors and the other player chooses Paper, the player who chooses Scissors wins and gets a point;
- if one player chooses Scissors and the other player chooses Rock, the player who chooses Rock wins and gets a point;
- and if both players choose the same move, nobody wins and nobody gets a point.

Monocarp decided to play against a bot. During the game, Monocarp noticed that the bot's behavior is very predictable:

- in the first round, it chooses Rock;
- in every round except the first, it chooses the move that beats the opponent's move in the previous round (for example, if in the previous round its opponent played Scissors, then the bot chooses Rock now).

Monocarp has a favorite string $$$s$$$, consisting of the characters R, P, and/or S. Monocarp decided to play a series of rounds against the bot. However, he wants both of the following conditions to be met:

- the final score is in favor of Monocarp (i. e., the number of rounds he won is strictly greater than the number of rounds the bot won);
- the string $$$s$$$ appears as a contiguous substring in the sequence of the bot's moves (where R denotes Rock, P denotes Paper, and S denotes Scissors).

Help Monocarp and calculate the minimum number of rounds he needs to play against the bot to satisfy both of the aforementioned conditions.

Input format:
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ ($$$1 \le |s| \le 2 \cdot 10^5$$$), consisting of the characters R, P, and/or S.

Additional constraint on the input: the sum of the lengths of the strings $$$s$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
Output format:
For each test case, print a single integer — the minimum number of rounds Monocarp needs to play against the bot to satisfy both of the aforementioned conditions.
Example Input 0:
7
SS
R
RPS
RPPP
SPPRSP
PPP
PR

Example Output 0:
3
1
3
6
7
5
3

Notes:
In the first example, Monocarp can play PPR, then the bot's moves are RSS, and the score is $$$2:1$$$ in favor of Monocarp.

In the second example, Monocarp can play P, then the bot's moves are R, and the score is $$$1:0$$$ in favor of Monocarp.

In the third example, Monocarp can play RPR, then the bot's moves are RPS, and the score is $$$1:0$$$ in favor of Monocarp.

In the fourth example, Monocarp can play RRRSPR, then the bot's moves are RPPPRS, and the score is $$$3:2$$$ in favor of Monocarp.

In the fifth example, Monocarp can play PRRSPRS, then the bot's moves are RSPPRSP, and the score is $$$6:1$$$ in favor of Monocarp.

In the sixth example, Monocarp can play PRRRS, then the bot's moves are RSPPP, and the score is $$$3:2$$$ in favor of Monocarp.

In the seventh example, Monocarp can play RSR, then the bot's moves are RPR, and the score is $$$1:0$$$ in favor of Monocarp.

Example input:
7
SS
R
RPS
RPPP
SPPRSP
PPP
PR


Example output:
3
1
3
6
7
5
3