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.
Rules of rock-scissors-paper
The result of a rock-scissors-paper match is determined as follows, based on the hands played by the two players.

• If one player plays rock (G) and the other plays scissors (C), the player playing rock (G) wins.
• If one player plays scissors (C) and the other plays paper (P), the player playing scissors (C) wins.
• If one player plays paper (P) and the other plays rock (G), the player playing paper (P) wins.
• If the players play the same hand, the match is drawn.

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.

Constraints

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

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.

见题面 Input 部分

见题面 Output 部分