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Maximum Multiplication

Limits: 1s, 512 MB

You will be given three integers a, b and k. You can perform one of the following two operations maximum k times.

  • Increase the value of a by one.
  • Increase the value of b by one.

You have to maximize the value of a*b after performing all the operations.

Input

The first line of the input contains three integers a, b and k.

Constraints

${1 \leq a, b, k \leq 1000}$

Output

Print the maximum value of a*b after performing the above operations maximum k times.

Samples

InputOutput
2 4 3
20
20 30 16
1089
50 55 6
3080
5 9 3
72

In the first sample test case, we can perform the increase operations on the value a by k times. So after all the operations are done a will become 5 and b will become 4. So our final result is 4*5 = 20. This is the maximum possible answer that we can get in optimal strategy.

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