Maximum Multiplication

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 (1 ≤ a, b, k ≤ 1000).

Output

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

Samples

Input	Output
2 4 3	20
In this 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 be 4. Our final result is 4×5 = 20. This is the maximum possible answer that we can get in optimal strategy.

Input	Output
20 30 16	1089

Input	Output
50 55 6	3080

Input	Output
5 9 3	72