Problem Statement

$N$ mice found $N$ boxes lined up that looked like they could serve as homes.
However, it was a trap: mousetraps had been set in some of the boxes.
The mice noticed this, but since they could not find any other home, they reluctantly decided to enter.
Initially, the mice know only how many of the $N$ boxes are safe and how many are traps.
Then, the $i(1 \le i \le N)$-th mouse enters the $i$-th box.
The $i+1$-th and later mice can learn whether the $i$-th mouse is safe or not.
Your mission is to tell the mice the probability (based only on the information the mice can know) that they will survive without being caught by a mousetrap.

You are given a string $S$ of length $N$.
If the $i$-th character of the string $S$ is 'o', the $i$-th box is safe, and if it is 'x', a mousetrap is set in that box.

For example, if $S$ is "ooxxoxx",
for mouse 1, 3 o's and 4 x's remain, so its probability of surviving is 42.85714%.
Mouse 1 survives, leaving 2 o's and 4 x's, so the probability that mouse 2 survives is 33.33333%.
Mouse 2 survives, leaving 1 o and 4 x's, so the probability that mouse 3 survives is 20.00000%.
Mouse 3 is caught, leaving 1 o and 3 x's, so the probability that mouse 4 survives is 25.00000%.
Mouse 4 is caught, leaving 1 o and 2 x's, so the probability that mouse 5 survives is 33.33333%.
Mouse 5 survives, leaving only 2 x's, so the probability that mouse 6 survives is 0.00000%.
Mouse 6 survives, leaving only 1 x, so the probability that mouse 7 survives is 0.00000%.
Illustration

Input

$S$

The string $S$ is given on one line.
・Constraints
The string $S$ consists only of 'o' and 'x'
$1 \le S$'s length $= N \le 10^5$

Output

$P_1$
$P_2$
$\dots$
$P_N$

Let $P_i$ be the probability (%) that the $i$-th mouse survives, and output $N$ lines.
An error of at most $0.000001=10^{-6}$ is allowed.
A newline is required at the end of the output.

Sample

ooxxoxx

42.8571428571429
33.3333333333333
20.0000000000000
25.0000000000000
33.3333333333333
0.0000000000000
0.0000000000000

xxxxxxxxxx

0.0000000000000
0.0000000000000
0.0000000000000
0.0000000000000
0.0000000000000
0.0000000000000
0.0000000000000
0.0000000000000
0.0000000000000
0.0000000000000

xxooxoxxxxoxoxxoooxo

45.0000000000000
47.3684210526316
50.0000000000000
47.0588235294118
43.7500000000000
46.6666666666667
42.8571428571429
46.1538461538462
50.0000000000000
54.5454545454545
60.0000000000000
55.5555555555556
62.5000000000000
57.1428571428571
66.6666666666667
80.0000000000000
75.0000000000000
66.6666666666667
50.0000000000000
100.0000000000000