# Rock Paper Scissors Solution | DEC LONG CHALLENGE | Codechef

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There are NN players standing in a line, indexed 11 to NN from left to right. They all play a game of Rock, Paper, Scissors. Each player has already decided which move they want to play. You are given this information as a string SS of length NN, i.e,

• SiSi is equal to RR if player ii will play Rock.
• SiSi is equal to PP if player ii will play Paper.
• SiSi is equal to SS if player ii will play Scissors.

Let W(i,j)W(i,j) denote the move played by the winner if players i,i+1,…,ji,i+1,…,j compete in order from left to right. That is,

• First, players ii and i+1i+1 play a game
• The winner of this game plays against player i+2i+2
• The winner of the second game plays against player i+3i+3

⋮⋮

• The winner of the first j−i−1j−i−1 games plays against player jj, and the move played by the winner of this game is declared to be W(i,j)W(i,j).

If i=ji=j, then player ii is considered to be the winner and W(i,i)=SiW(i,i)=Si.

Your task is to find the value of W(i,N)W(i,N) for all ii from 11 to NN.

Note : If a person with index ii and index jj (i<ji<j) play against each other, then:

• If Si≠SjSi≠Sj, the winner is decided by classical rules, i.e, rock beats scissors, scissors beats paper, and paper beats rock.
• If Si=SjSi=Sj, the player with lower index (in this case, ii) wins.

### Input Format

• The first line of input contains a single integer TT, denoting the number of test cases. The description of TT test cases follows.
• The first line of each test case contains a single integer NN, the number of players.
• The second line of each test case contains the string SS of length NN, denoting the moves chosen by the players.

### Output Format

For each test case, print a single line containing a string of length NN, whose ii-th character is W(i,N)W(i,N).

### Constraints

• 1≤T≤1051≤T≤105
• 1≤N≤5⋅1051≤N≤5⋅105
• SiSi is either RR, PP or SS
• Sum of NN over all test cases doesn’t exceed 5⋅1055⋅105

• 1≤T≤10001≤T≤1000
• 1≤N≤50001≤N≤5000
• Sum of NN over all test cases doesn’t exceed 50005000

• Original constraints

### Sample Input 1

``````2
1
S
4
SSPR
``````

### Sample Output 1

``````S
RRPR
``````

### Explanation

Test Case 1. W(1,1)=SW(1,1)=S as there is only one player.

Test Case 2.

For W(1,4)W(1,4) the game is played as follows :

• Player 11 and 22 compete, player 11 wins.
• Player 11 and 33 compete, player 11 wins.
• Player 11 and 44 compete, player 44 wins.

Hence, we print W(1,4)=S4=RW(1,4)=S4=R

For W(3,4)W(3,4) the game is played as follows :

• Player 33 and 44 compete, player 33 wins.

Hence, we print W(3,4)=S3=P

## SOLUTION

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