11 10 s 128 MB

As if there were not already enough sudoku-like puzzles, the July 2009 issue of Games Magazine describes the following variant that combines facets of both sudoku and dominos. The puzzle is a form of a standard sudoku, in which there is a nine-by-nine grid that must be filled in using only digits 1 through 9. In a successful solution:

- Each row must contain each of the digits 1 through 9.
- Each column must contain each of the digits 1 through 9.
- Each of the indicated three-by-three squares must contain each of the digits 1 through 9.

For a su-domino-ku, nine arbitrary cells are initialized with the numbers

To help you out, we will begin each puzzle by identifying the location of some of the dominos. For example, Figure 1 shows a sample puzzle in its initial state. Figure 2 shows the unique way to complete that puzzle.

Each puzzle description begins with a line containing an integer `N`, for 10 ≤ `N` ≤ 35, representing the number of dominos that are initially placed in the starting configuration. Following that are `N` lines, each describing a single domino as `U` `LU` `V` `LV``U` is one of the numbers on the domino, and `LU` is a two-character string representing the location of value `U` on the board based on the grid system diagrammed in Figure 1. The variables `V` and `LV` representing the respective value and location of the other half of the domino. For example, our first sample input beings with a domino described as `6 B2 1 B3``6` is in row `B`, column `2` and value `1` in row `B`, column `3`. The two locations for a given domino will always be neighboring.

After the specification of the `N` dominos will be a final line that describes the initial locations of the isolated numbers, ordered from

The input file ends with a line containing

For each puzzle, output an initial line identifying the puzzle number, as shown below. Following that, output the 9x9 sudoku board that can be formed with the set of dominos. There will be a unique solution for each puzzle.

## Sample Input | ## Sample Output |
---|---|

10 6 B2 1 B3 2 C4 9 C3 6 D3 8 E3 7 E1 4 F1 8 B7 4 B8 3 F5 2 F6 7 F7 6 F8 5 G4 9 G5 7 I8 8 I9 7 C9 2 B9 C5 A3 D9 I4 A9 E5 A2 C6 I1 11 5 I9 2 H9 6 A5 7 A6 4 B8 6 C8 3 B5 8 B4 3 C3 2 D3 9 D2 8 E2 3 G2 5 H2 1 A2 8 A1 1 H8 3 I8 8 I3 7 I4 4 I6 9 I7 I5 E6 D1 F2 B3 G9 H7 C9 E5 0 | Puzzle 1 872643195 361975842 549218637 126754983 738169254 495832761 284597316 657381429 913426578 Puzzle 2 814267593 965831247 273945168 392176854 586492371 741358629 137529486 459683712 628714935 |