AT_past202209_c 偏ったサイコロ

We have three six-sided dice. When the $ i $ -th die is thrown, it shows the number $ j $ with the probability $ \frac{P_{i,j}} {100} $ . If we throw these three dice, what is the probability that the sum of the numbers shown is $ K $ , for each $ K=1,2,\ldots,18 $ ?

Input is given from Standard Input in the following format: > $ P_{1,1} $ $ P_{1,2} $ $ P_{1,3} $ $ P_{1,4} $ $ P_{1,5} $ $ P_{1,6} $ $ P_{2,1} $ $ P_{2,2} $ $ P_{2,3} $ $ P_{2,4} $ $ P_{2,5} $ $ P_{2,6} $ $ P_{3,1} $ $ P_{3,2} $ $ P_{3,3} $ $ P_{3,4} $ $ P_{3,5} $ $ P_{3,6} $

Let $ R_K $ be the probability that the sum of the numbers shown is $ K $ when throwing the three dice. Print $ 18 $ lines, the $ i $ -th of which $ (1 \leq i \leq 18) $ contains $ R_{i} $ . Your output will be considered correct if its absolute or relative errors from the judge's answer are at most $ 10^{-4} $ .

### Constraints - $ 0\leq P_{i,j}\leq 100 $ - $ P_{i,1}+P_{i,2}+P_{i,3}+P_{i,4}+P_{i,5}+P_{i,6} = 100 $ - All values in input are integers.