frog has a piece of paper divided into $n$ rows and $m$ columns. Today, she would like to draw a rectangle whose perimeter is not greater than $k$.

Find the number of ways of drawing.

Input

The input consists of multiple tests. For each test:

The first line contains $3$ integer $n, m, k$ ($1 \leq n, m \leq 5 \cdot 10^4, 0 \leq k \leq 10^9$).

Output

For each test, write $1$ integer which denotes the number of ways of drawing.

Sample Input

2 2 6
1 1 0
50000 50000 1000000000

Sample Output

8
0
1562562500625000000