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。

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.

Sample Input

Sample Output

Hint

Source