102222: [AtCoder]ABC222 C - Swiss-System Tournament

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.

Sample Input 1

2 3
GCP
PPP
CCC
PPC

Sample Output 1

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.

Sample Input 2

2 2
GC
PG
CG
PP

Sample Output 2

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.

问题描述

编号为$1$到$2N$的$2N$名选手将参加一场石头-剪刀-布比赛。

比赛共有$M$轮。每轮有$N$场一对一的比赛，每名选手参加其中一场。

对于每个$i=0, 1, \ldots, M$，在第$i$轮结束时，玩家的排名如下确定。

• 在前$i$轮中获胜次数较多的玩家排名更高。
• 平局由ID号码决定：ID号码较小的玩家排名更高。

此外，对于每个$i=1, \ldots, M$，第$i$轮的比赛如下安排。

• 对于每个$k=1, 2, \ldots, N$，在第$(i-1)$轮结束时排名分别为第$(2k-1)$和$2k$的玩家之间进行一场比赛。

在每场比赛中，两名玩家只玩一次手，导致一名玩家获胜，另一名玩家失利，或者平局。

能够预见未来的高桥知道，第$i$名玩家将在第$j$轮的比赛中玩$A_{i, j}$，其中$A_{i,j}$是G，C或P。

找到在第$M$轮结束时玩家的排名。

约束条件

• $1 \leq N \leq 50$
• $1 \leq M \leq 100$
• $A_{i,j}$是G，C或P。

输入

输入格式如下，从标准输入给出：

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

输出

打印$2N$行。

第$i$行应包含在第$M$轮结束时排名第$i$的玩家的ID号。

样例输入1

2 3
GCP
PPP
CCC
PPC

样例输出1

3
1
2
4

在第一轮中，玩家$1$和$2$，以及玩家$3$和$4$之间进行比赛。玩家$2$赢得了前者，玩家$3$赢得了后者。

在第二轮中，玩家$2$和$3$，以及玩家$1$和$4$之间进行比赛。玩家$3$赢得了前者，玩家$1$赢得了后者。

在第三轮中，玩家$3$和$1$，以及玩家$2$和$4$之间进行比赛。玩家$3$赢得了前者，玩家$4$赢得了后者。

因此，最终玩家的排名顺序如下：$3,1,2,4$，从高到低。

样例输入2

2 2
GC
PG
CG
PP

样例输出2

1
2
3
4

在第一轮中，玩家$1$和$2$，以及玩家$3$和$4$之间进行比赛。玩家$2$赢得了前者，玩家$3$赢得了后者。

在第二轮中，玩家$2$和$3$，以及玩家$1$和$4$之间进行比赛。前者是平局，玩家$1$赢得了后者。

因此，最终玩家的排名顺序如下：$1,2,3,4$，从高到低。