Given m, n, and k, print a checkerboard with m block rows and n block columns. Each block has size k x k characters.

Input

• One line containing three positive integers m, n, and k.

Output

• A block whose block-row index plus block-column index is even is filled with *; otherwise it is filled with ..

Constraints

• 1 <= m, n <= 30
• 1 <= k <= 10

Example

Input

3 4 2

Output

**..**..
**..**..
..**..**
..**..**
**..**..
**..**..