!! Challenging
You are given an n x n x n cube.
Each small cell of the cube contains a unique integer from 1 to n3
A sequence of n3 numbers will then be drawn one by one.
Whenever a number is drawn, it is marked in the cube.
If, at any point, all cells along a straight line are marked, we say “bingo.”
A straight line may be:
A row along the x-axis,
A column along the y-axis,
A line along the z-axis,
A diagonal on one of the cube’s faces,
Or one of the four main space diagonals connecting two opposite corners of the cube.
Your task is to determine which drawn number first causes a “bingo.”
The first line contains an integer n (0 < n ≤ 10)
The following n3 integers describe the cube’s contents in row-major order.
That is, the numbers are listed layer by layer, row by row, and column by column.
The next n3 integers represent the sequence of numbers being drawn, in order.
For readability, the numbers may be given with n numbers per line.
Example Walkthrough (Sample Input 1)
3
2 18 4
3 1 20
14 6 12
7 21 15
6 9 17
19 5 22
8 23 12
1 3 5
7 9 11
13 15 17
19 21 23
25 27 2
4 6 8
10 12 14
16 18 20
22 24 26
First Line:
The integer 3 tells us the cube size is 3×3×3.
That means the cube contains 33=27 cells, each filled with a unique number from 1 to 27.
Next 27 Numbers (Cube Contents):
The following numbers describe how the cube is filled.
They are given in row-major order: layer by layer, row by row, left to right.
For n=3, these 27 numbers form a 3×3×3 cube:
| 1 | 18 | 4 |
| 13 | 2 | 20 |
| 24 | 10 | 26 |
| 27 | 14 | 7 |
| 3 | 25 | 16 |
| 21 | 15 | 11 |
| 6 | 9 | 17 |
| 19 | 5 | 22 |
| 8 | 23 | 12 |
After the cube contents, the next block of numbers lists the draw order.
These are the numbers being drawn one by one, and whenever a number is drawn, the corresponding cell in the cube is marked.
The sequence here is:
1 3 5 7 9 11 13 15 17 19 21 23 25 27 2 4 6 8 10 12 14 16 18 20 22 24 26
Print a single integer: the first drawn number that causes a bingo.
Cube contents (layer by layer, row-major):
For example,
| 1 | 18 | 4 |
| 13 | 2 | 20 |
| 24 | 10 | 26 |
| 27 | 14 | 7 |
| 3 | 25 | 16 |
| 21 | 15 | 11 |
| 6 | 9 | 17 |
| 19 | 5 | 22 |
| 8 | 23 | 12 |
The sequence here is:
1 3 5 7 9 11 13 15 17 19 21 23 25 27 2 4 6 8 10 12 14 16 18 20 22 24 26
As we mark numbers in this order, the cube first achieves bingo when 19 is drawn.