Migrated from Lutece 335 Penney Game

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Description

Penney’s game is a simple game typically played by two players. One version of the game calls for each player to choose a unique three-coin sequence such as HEADS TAILS HEADS (HTH). A fair coin is tossed sequentially some number of times until one of the two sequences appears. The player who chose the first sequence to appear wins the game.

For this problem, you will write a program that implements a variation on the Penney Game. You will read a sequence of $40$ coin tosses and determine how many times each three-coin sequence appears. Obviously there are eight such three-coin sequences: TTT, TTH, THT, THH, HTT, HTH, HHT and HHH. Sequences may overlap. For example, if all $40$ coin tosses are heads, then the sequence HHH appears $38$ times.

Input

The first line of input contains a single integer $P$, ($1\leq P\leq 1000$), which is the number of data sets that follow. Each data set consists of $2$ lines. The first line contains the data set number $N$. The second line contains the sequence of $40$ coin tosses. Each toss is represented as an upper case H or an upper case T, for heads or tails, respectively. There will be no spaces on any input line.

Output

For each data set there is one line of output. It contains the data set number followed by a single space, followed by the number of occurrences of each three-coin sequence, in the order shown above, with a space between each one. There should be a total of $9$ space separated decimal integers on each output line.

Samples

4
1
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
2
TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT
3
HHTTTHHTTTHTHHTHHTTHTTTHHHTHTTHTTHTTTHTH
4
HTHTHHHTHHHTHTHHHHTTTHTTTTTHHTTTTHTHHHHT

1 0 0 0 0 0 0 0 38
2 38 0 0 0 0 0 0 0
3 4 7 6 4 7 4 5 1
4 6 3 4 5 3 6 5 6

Resources

Greater New York 2010