C - Swiss-System Tournament

Score : $300$ points

Problem Statement

$2N$ players, with ID numbers $1$ through $2N$, will participate in a rock-scissors-paper contest.

The contest has $M$ rounds. Each round has $N$ one-on-one matches, where each player plays in one of them.

For each $i=0, 1, \ldots, M$, the players' ranks at the end of the $i$-th round are determined as follows.

• A player with more wins in the first $i$ rounds ranks higher.
• Ties are broken by ID numbers: a player with a smaller ID number ranks higher.

Additionally, for each $i=1, \ldots, M$, the matches in the $i$-th round are arranged as follows.

• For each $k=1, 2, \ldots, N$, a match is played between the players who rank $(2k-1)$-th and $2k$-th at the end of the $(i-1)$-th round.

In each match, the two players play a hand just once, resulting in one player's win and the other's loss, or a draw.

Takahashi, who can foresee the future, knows that Player $i$ will play $A_{i, j}$ in their match in the $j$-th round, where $A_{i,j}$ is G, C, or P.
Here, G stands for rock, C stands for scissors, and P stands for paper. (These derive from Japanese.)

Find the players' ranks at the end of the $M$-th round.

Constraints

• $1 \leq N \leq 50$
• $1 \leq M \leq 100$
• $A_{i,j}$ is G, C, or P.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$A_{1,1}A_{1,2}\ldots A_{1,M}$

$A_{2,1}A_{2,2}\ldots A_{2,M}$

$\vdots$

$A_{2N,1}A_{2N,2}\ldots A_{2N,M}$

Output

Print $2N$ lines.

The $i$-th line should contain the ID number of the player who ranks $i$-th at the end of the $M$-th round.

2 3
GCP
PPP
CCC
PPC

3
1
2
4

In the first round, matches are played between Players $1$ and $2$, and between Players $3$ and $4$. Player $2$ wins the former, and Player $3$ wins the latter.
In the second round, matches are played between Players $2$ and $3$, and between Players $1$ and $4$. Player $3$ wins the former, and Player $1$ wins the latter.
In the third round, matches are played between Players $3$ and $1$, and between Players $2$ and $4$. Player $3$ wins the former, and Player $4$ wins the latter.
Therefore, in the end, the players are ranked in the following order: $3,1,2,4$, from highest to lowest.

2 2
GC
PG
CG
PP

1
2
3
4

In the first round, matches are played between Players $1$ and $2$, and between Players $3$ and $4$. Player $2$ wins the former, and Player $3$ wins the latter.
In the second round, matches are played between Players $2$ and $3$, and between Players $1$ and $4$. The former is drawn, and Player $1$ wins the latter.
Therefore, in the end, the players are ranked in the following order: $1,2,3,4$, from highest to lowest.