Father's Problem#515
In this task, Vasilyok plays the role of a grown child who no longer believes that St. Nicholas brings gifts. But every year, on December 6, he still reaches his hand under the pillow upon waking up.
This year, he decided to ask his parents to give him a brand new laptop. In response to his request, his father said: "If you solve the problem that you have not been able to overcome for several days, happiness will come to you." The problem was as follows:
A rectangle of size N \times M, divided into unit squares, is given. In one operation, you must draw all possible diagonals in all the squares that existed before the operation. You need to repeat this operation times. After that, you need to count the number of triangles inside which no line has been drawn.
Time is running out, so Vasilyok needs your help.
The first line contains two natural numbers and — the dimensions of the rectangle. The second line contains an integer — the number of times the operation is applied.
Print the answer to Vasilyok's problem. It is guaranteed that the result will not exceed 10^{18}.
Example 1