Problem Statement

Takahashi wants to paint an infinitely extending grid so that the following conditions are satisfied.

• The grid is painted by repeating a pattern of an $H\times W$ grid

• Exactly $K$ colors are used

How many such ways of painting are there? Rotations and reflections are distinguished, but a pattern and the result of translating it to the right or downward any natural number of times are counted as $1$ way. Colors are distinguishable.

緑緑青　と　緑青緑　と　青緑緑

are the same pattern. (They are moved to the right a natural number of times.)

A cell that leaves the range at the top, bottom, left, or right due to the movement moves to the opposite edge.

赤青緑　　　赤緑赤
緑青青　と　青緑赤
赤赤緑　　　青青緑

are the same pattern. (It is translated 2 times to the right and 1 time downward.)

Input

$H\ W\ K$

• $1 \le H \times W \le 10$
• $1 \le K \le 3$

Output

Output the answer on $1$ line. Print a newline at the end.

Sample

2 3 2

12

■□□　■■□　■□□　■□□
□□□　□□□　■□□　□■□

■■□　■□■　■■■　■□■
■□□　■□□　□□□　□■□

□□■　□■■　□■■　□■■
■■■　□■■　■□■　■■■

1 1 1

1

3 3 3

2022