SPOJ in Gyumri

   The class fullness is the minimum of row fullness and column fullness. The column fullness is the maximum number of students in a single column and therow fullness is the maximum number of students in a single row.

   For example there are 16 students shown on the left picture (occupied desks are darkened). The row fullness of this arrangement is 5 (the 4-th row) and thecolumn fullness is 3 (the 1-st, the 3-rd, the 5-th or the 6-th columns). So, the class fullness is 3. But if the students rearrange as shown on the right picture then the column fullness will become 4 (the 5-th column), and so the class fullness will also become 4.

   The students of Dr. Strange need to know the arrangement that maximizes class fullness so they ask you to write a program that calculates it for them.

   The first line of the input file contains three integer numbers: n, r and c (1 ≤ r, c ≤ 100, 1 ≤ n ≤ r × c.) — number of students, rows and columns in the class.

   The first line of the output file must contain a single integer number — the maximum possible class fullness.

   The following r lines must contain the optimal student arrangement. Each line must contain a description of a single row. Row description is a line of ccharacters either "." or "#", where "." denotes an empty desk, and "#" denotes an occupied one. If there are multiple optimal arrangements, output any one.