## Problem D: Rock-Paper-Scissors Tournament

Rock-Paper-Scissors is game for two players, A and B,
who each choose, independently of the other, one of
*rock, paper,* or *scissors*. A player
chosing *paper* wins over a player chosing *rock*;
a player chosing *scissors* wins over a player chosing
*paper*; a player chosing *rock* wins over a player
chosing *scissors*. A player chosing the same thing
as the other player neither wins nor loses.
A tournament has been organized in which each of *n*
players plays *k* rock-scissors-paper games with each
of the other players - *k*n*(n-1)/2* games in total.
Your job is to compute the *win average* for each player,
defined as *w / (w + l)* where *w* is the number
of games won, and *l* is the number of games lost, by
the player.

Input consists of several test cases.
The first line of input for each case contains *1 ≤ n ≤ 100*
*1 ≤ k ≤ 100* as defined above. For each game, a line follows
containing p_{1}, m_{1}, p_{2}, m_{2}.
1 ≤ p_{1} ≤ *n* and 1 ≤ p_{2} ≤ *n*
are distinct integers identifying two players;
m_{1} and m_{2} are their respective moves
("rock", "scissors", or "paper"). A line containing 0 follows the
last test case.

Output one line each for player 1, player 2, and so on, through player *n*,
giving the player's win average rounded to three decimal places. If the
win average is undefined, output "-". Output an empty line between cases.

### Sample Input

2 4
1 rock 2 paper
1 scissors 2 paper
1 rock 2 rock
2 rock 1 scissors
2 1
1 rock 2 paper
0

### Output for Sample Input

0.333
0.667
0.000
1.000

Gordon V. Cormack