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You are given a rectangular cake of integral dimensions *w* × *h*. Your goal is to divide this cake into *m* rectangular pieces of integral dimensions such that the area of the largest piece is minimal. Each cut must be a straight line parallel to one of the sides of the original cake and must divide a piece of cake into two new pieces of positive area. Note that since a cut divides only a single piece, exactly *m* − 1 cuts are needed.

If *w* = 4, *h* = 4, and *m* = 4, then the following cuts minimize the area of the largest piece:

However, if *w* = 4, *h* = 4, and *m* = 3, then the following cuts are optimal:

The input test file will contain multiple test cases, each of which consists of three integers *w*, *h*, *m* separated by a single space, with 1 ≤ *w*, *h*, *m* ≤ 20 and *m* ≤ *wh*. The end-of-file is marked by a test case with *w* = *h* = *m* = 0 and should not be processed.

For each test case, write a single line with a positive integer indicating the area of the largest piece.

```
4 4 4
4 4 3
0 0 0
```

```
4
6
```