Time Limit: 1000 mSec Memory Limit : 32768 KB

The linear board in this problem is simply a row of n squares numbered from 1 (left
most) to n (right most). Each square contains either a treasure or nothing. The player
will always starts in the first square. In each turn, he will roll two dices and than move
forward m steps where m is he sum of the face numbers of the two rolled dices. If he
stops on a square which contains a treasure, he will get one treasure point. The game
is finished if he moves out of the board. (If he stops on the nth square, he should
continue to play although he is guaranteed to be out in next turn.)

Given the complete information of the linear board, you need to compute the expected value of the treasure point the player will get when the game is finished. To avoid confusion, the first square is always empty.

Given the complete information of the linear board, you need to compute the expected value of the treasure point the player will get when the game is finished. To avoid confusion, the first square is always empty.

The input starts with an integer N (N < 150) which indicates the number of test cases
followed. Each of the following N case consists of one input line. The line contains
only one string which is the linear board. "." means empty square and "T" means a
square with treasure. The length of the string (i.e. the size of the linear board) is
guaranteed to be at least 2 and at most 100.

For each input, output the expected treasure point in a single line with 6 digits after
the decimal point.

9
..
.T
....
.T.T
.TTT
...................T
....TT..T..TTTT..T.T
..T.T..TT..T.TT.T.T.T.T..T.T.TTT.TTTT...TT..T..T...TTT.TT..T
.TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT

0.000000
0.000000
0.000000
0.055556
0.083333
0.142886
1.194170
4.156287
8.059523