'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
Humpty Dumpty is an unpredictable creature. As soon as he helped Alice
understand the poem about the Jabberwock, he ran away to chase borogoves. Alice
met him at the d6 square, and since that time she has come to the eighth rank
and become a queen, but Humpty Dumpty still hasn't been seen by anyone. As many
as 100^{100100} days passed since their talk (or, maybe, 100^{100100}
years—time flies very fast in the LookingGlass world). Determine the
probabilities of Humpty Dumpty being on the squares of the LookingGlass world.
It is known that every second Humpty Dumpty moved from the square he was on to
one of the adjacent squares (squares are adjacent if they share at least one
vertex). The probability of Humpty Dumpty moving to a square is proportional to
the number of borogoves on it.
Input
The input data are eight lines containing eight integers each. The integers are
the numbers of borogoves on the squares of the LookingGlass world. The first
line describes the first rank (squares from a1 to h1) and the last line
describes the last rank (squares from a8 to h8). There are at least one and at
most 1000 borogoves on each square of the LookingGlass world.
Output
Output eight lines containing eight numbers each. The numbers should be the
probabilities of finding Humpty Dumpty on the squares of the LookingGlass
world. The squares must be described in the order in which they are given in
the input. The numbers must be accurate to at least 10^{−12}.
Sample
input  output 

1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
 0.007 0.012 0.012 0.012 0.012 0.012 0.012 0.007
0.012 0.019 0.019 0.019 0.019 0.019 0.019 0.012
0.012 0.019 0.019 0.019 0.019 0.019 0.019 0.012
0.012 0.019 0.019 0.019 0.019 0.019 0.019 0.012
0.012 0.019 0.019 0.019 0.019 0.019 0.019 0.012
0.012 0.019 0.019 0.019 0.019 0.019 0.019 0.012
0.012 0.019 0.019 0.019 0.019 0.019 0.019 0.012
0.007 0.012 0.012 0.012 0.012 0.012 0.012 0.007

Notes
The answer in the sample is incorrect, because the numbers in it are
given with insufficient accuracy.
Problem Author: Sergey Pupyrev (prepared by Eugene Krokhalev)
Problem Source: The 14th Urals Collegiate Programing Championship, April 10, 2010