# Practice on Toph

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## 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.

#### 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

Input | Output |
---|---|

2 4 3 | 20 |

Input | Output |
---|---|

20 30 16 | 1089 |

Input | Output |
---|---|

50 55 6 | 3080 |

Input | Output |
---|---|

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 = 2**0. This is the maximum possible answer that we can get in optimal strategy.