Description

有一个芯片，芯片上有N*N（1≤N≤40）个插槽，可以在里面装零件。

有些插槽不能装零件，有些插槽必须装零件，剩下的插槽随意。

要求装好之后满足如下两条要求：

1、第 i 行和第 i 列的零件数目必须一样多（1≤i≤N）。

2、第 i 行的零件数目不能超过总的零件数目的 A/B（1≤i≤N，0≤A≤B≤1000，B≠0）。

求最多可以另外放多少个零件（就是除掉必须放的）。如果无解输出impossible。

Format

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<=A<=1000, 0<=A<=B) 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.

Samples

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