URI Online Judge | 2195

Chips Challenge

By ICPC 2011 World Finals US United States

Timelimit: 15

A prominent microprocessor company has enlisted your help to lay out some interchangeable components (widgets) on some of their computer chips. Each chip’s design is an N ×N square of slots. One slot can hold a single component, and you are to try to fit in as many widgets as possible.

Modern processor designs are complex, of course. You unfortunately have several restrictions:

A specification for a chip is N lines of N characters, where ‘.’ indicates an open slot, ‘/’ indicates a disabled slot, and ‘C’ indicates a slot already occupied by a component. For example:

CC/..

././/

..C.C

/.C..

/./C/

If no more than 3/10 of the components may be in any one row or column, the maximum number of widgets that can be added to this 5 × 5 chip is 7. A possible arrangement is below, where ‘W’ indicates a widget added in an open slot.

CC/W.

W/W//

W.C.C

/.CWW

/W/C/

Input

The input consists of several test cases. Each case starts with a line containing three integers: The size of the chip N (1 ≤ N ≤ 40), and A and B (1 ≤ B ≤ 1000, 0 ≤ AB) as described above. Each of the following N lines contains N characters describing the slots, one of ‘.’, ‘/’ or ‘C’, as described above.

The last test case is followed by a line containing three zeros.

Output

For each test case, display a single line beginning with the case number. If there is a solution, display the maximum number of widgets that can be added to the chip. Display “impossible” if there is no solution.

Follow the format of the sample output.

Input Sample Output Sample

2 1 1

/.

//

2 50 100

/.

C/

2 100 100

./

C.

5 3 10

CC/..

././/

..C.C

/.C..

/./C/

5 2 10

CC/..

././/

..C.C

/.C..

/./C/

0 0 0

Case 1: 0

Case 2: 1

Case 3: impossible

Case 4: 7

Case 5: impossible