Time Limit: 1 s
Memory Limit: 128 MB

Submission：3
AC：0
Score：99.96

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.

Please Input Input Here

Please Input Output Here

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

0.333
0.667
0.000
1.000