Chaos Game Representation (CGR) is a graphical way of representing a DNA sequence, in such a way that certain patterns in the nucleotide sequence become immediate clear at a glance. The representation is done within the unit square, in which the four corner points are labeled with the four nucleotides: the point (0, 0) corresponds to the letter a, the point (0, 1) to the letter c, the point (1, 1) to the letter g and the point (1, 0) to the letter t. The starting point for each CGR is always the point (0.5, 0.5). Thereafter, for each letter of the nucleotide sequence the next point is computed as the point that is half-way on the line that connects the last point to the corner point that is labeled with the nucleotide. The figure below shows an example of the CGR that is built from the DNA sequence atgcgagtgt.

Input

A number of DNA sequences (strings that only contain the letters a, c, g and t) that are each on their own line. The list of DNA sequences is terminated with a line containing the word stop.

Output

For each DNA sequence from the input, the $$x$$ and the $$y$$ co-ordinate of the last point of the corresponding CGR should be printed on a separate line.

Example

Input:

atgcgagtgt
tcttacaggtaagggggatta
tctcagcgggagaagctcagttaggacgcgaaacccg
gactgcgccaatcgaacatacaaagtttggtct
tagtaaggtgaaagggaggccagaggtcggctcct
stop

Output:

0.95947265625
0.34033203125
0.435980558395
0.0607464313507
0.505093238589
0.945012472414
0.74807859509
0.345834313601
0.589490680417
0.435239574072