CubeOfDice | Topcoder Archive

Problem Statement

    +---+
    | D |
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| E | A | B | F |
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    | C |
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The ASCII art above shows the net of a general 6-sided die. There is a number written on each of the six sides. In the picture, these numbers are denoted A to F. (The net is folded so that the numbers are on the outside, but this information is not necessary to solve the following problem.)

The numbers A to F will be given to you as a int[] values, where A will be values[0], B will be values[1], and so on.

You have N^3 identical dice, each one matching the net shown above. You want to take all the dice, rotate some of them, and assemble a N×N×N cube. The cube will be standing on a table, hence only 5 of its sides will be visible.

You are given the int N, and the int[] values. Write a method that will return the smallest possible sum of the 5N^2 visible faces of the dice.

Definition

Class:: CubeOfDice
Method:: minimumSum
Parameters:: int, int[]
Returns:: long
Method signature:: long minimumSum(int N, int[] values)
(be sure your method is public)

Constraints

N will be between 1 and 1,000,000, inclusive.
values will contain exactly 6 elements.
Each element of values will be between 1 and 50, inclusive.

Examples

```
2
```
```
{1,2,3,4,5,6}
```
```
Returns: 36
```
This input corresponds to 8 classical dice.
```
3
```
```
{1,2,3,4,5,6}
```
```
Returns: 69
```
Now we have 27 classical dice.
```
1000000
```
```
{50,50,50,50,50,50}
```
```
Returns: 250000000000000
```
The largest possible output. Note that all numbers are equal, hence in this case there is only one possible way to arrange the dice.
```
10
```
```
{1,1,1,1,50,1}
```
```
Returns: 500
```
It is possible to rotate and arrange the dice so that no side with the 50 will be visible.

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