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Language: Dice Puzzle
Description Let's try a dice puzzle. The rules of this puzzle are as follows.
1. Dice with six faces as shown in Figure 6 are used in the puzzle. Your job is to write a program that solves this puzzle. Input The input consists of multiple datasets in the following format.
N N is the number of the datasets. The format of each dataset is as follows. T11 T12 T13 Tij and Fij (1 <= i <= 3, 1 <= j <= 3) are the faces of dice appearing on the top and front views, as shown in Figure 7, or a zero. A zero means that the face at the corresponding position is unknown. Output For each plausible arrangement of dice, compute the sum of the numbers marked on the nine faces appearing on the right side of the cube, that is, with the notation given in Figure 7,Σ _{1<=i<=3}Σ_{1<=j<=3}Rij.
For each dataset, you should output the right view sums for all the plausible arrangements, in ascending order and without duplicates. Numbers should be separated by a single space. When there are no plausible arrangements for a dataset, output a zero. For example, suppose that the top and the front views are given as Figure 10. There are four plausible right views as shown in Figure 11. The right view sums are 33, 36, 32, and 33, respectively. After rearranging them into ascending order and eliminating duplicates, the answer should be "32 33 36". The output should be one line for each dataset. Sample Input 4 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 4 3 3 5 2 2 4 3 3 6 1 1 6 1 1 6 1 0 1 0 0 0 2 0 0 0 0 5 1 2 5 1 2 0 0 0 2 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3 0 1 Sample Output 27 24 32 33 36 0 Source |

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